
Available Courses
Courses listed are for 2016.
Art and Mathematics (Session 1)
Instructor: Martin Strauss
With just a little historical revisionism, we can say that Art has
provided inspiration for many fields within Mathematics. Conversely,
Mathematics gives techniques for analyzing, appreciating, and even
creating Art, as well as the basis for gallery design, digital
cameras, and processing of images. In this class we will explore the
Mathematics in great works of Art as well as folk art, as a way of
studying and illustrating central mathematical concepts in familiar
and pleasing material. And we'll make our own art, by drawing,
painting, folding origami papers, and more.
Major topics include Projection, Symmetry, Wave Behavior, and
Distortion. Projection includes the depiction of threedimensional
objects in two dimensions. What mathematical properties must be lost,
and what can be preserved? How does an artwork evoke the feeling of
threedimensional space? We'll study perspective, depictions of
globes by maps, and the role of curvature. Turning to symmetry, we'll
study rotational and reflective symmetry that arise in tiling and
other art and math. We'll study more generalized symmetry like
scaling and selfsimilarity that occurs in fractals as well as every
selfportrait, and is central to mathematical concepts of dimension
and unprovability. On the other hand, we'll look at how works of
digital and pointilist art are made up of fine pixels with a character
very different from the work at coarser scalesit is not selfsimilar.
Describing light as waves and color as wavelength at once explains how
mirrors, lenses, and prisms work and explains some uses of light and
color in art. Finally, we ask about distorting fabrics and strings,
and ask about the roles of cutting, gluing, and of stretching without
cutting or gluing. Is a distorted human figure still recognizable, as
long as it has the right number of organs and limbs, connected
properly?
Background in Math and interest in Art suggested. No artistic talent
is necessary, though artistically talented students are encouraged to
bring art supplies if they are inexpensive and easily transportable.
AstroTurf, Diapers, Kevlar and More: Explore the Materials in the World Around you! (Session 1)
Instructor: Anne McNeil
Ever wonder what a raincoat is made out of? Or why Spandex is stretchy? Our course on polymers, the molecules that make up plastics and elastics, holds these answers and more! Make Nylon and participate in laboratory research where you will gain the skills of a materials chemist by making polymers yourself. Learn how polymers have come to make up much of the material you interact with on a daily basis from contact lenses to golf balls. Share your newly gained knowledge with the world by adding content to Wikipedia. Join us on this journey into the world of materials.
Catalysis, Solar Energy and Green Chemical Synthesis (Session 1, Session 2)
Instructor: Corey Stephenson
"The chemist who designs and completes an original and esthetically pleasing multistep synthesis is like the composer, artist or poet who, with great individuality, fashions new forms of beauty from the interplay of mind and spirit."
E.J. Corey, Nobel Laureate
Prior to Friedrich Wöhler’s 1828 synthesis of urea, organic (carboncontaining) matter from living organisms was believed to contain a “vital force” that distinguished it from inorganic material. The discovery that organic molecules can be manipulated at the hands of scientists is considered by many the birth of “organic chemistry”: the study of the structure, properties, and reactions of carboncontaining matter. Organic matter is the foundation of life as we know it, and therefore a fundamental understanding of reactivity at a molecular level is essential to all life sciences. In this class we will survey monumental discoveries in this field over the past two centuries and the technological developments that have enabled them.
“Catalysis, Solar Energy, and Green Chemical Synthesis” will provide a fun and intellectually stimulating handson experience that instills a historical appreciation for the giants whose trials and tribulations have enabled our modern understanding of chemistry and biology. Students will learn modern laboratory techniques including how to set up, monitor, and purify chemical reactions, and most importantly, how to determine what they made! Experiments include the synthesis of biomolecules using some of the most transformative reactions of the 20th century and exposure to modern synthetic techniques, such as the use of metal complexes that absorb visible light to catalyze chemical reactions, an important development in the “Green Science” movement. Finally, industrial applications of chemistry such as polymer synthesis and construction of photovoltaic devices will be performed. Daily experiments will be supplemented with exciting demonstrations by the graduate student instructors.
Climbing the Distance Ladder to the Big Bang: How Astronomers Survey the Universe (Session 2)
Instructor: Dragan Huterer
The furthest objects that astronomers can observe are so distant that their light set out when the Universe was only 800 million years old, and has been traveling to us for about 13 billion years – most of the age of the Universe. Even the Sun's neighborhood – the local part of our Galaxy, where astronomers have successfully searched for planets around other stars – extends to hundreds of light years. How do we measure the distance to such remote objects?
Certainly not in a single step! Astronomers construct the socalled “Distance Ladder,” finding the distance to nearby objects, thus enabling those bodies to be understood and used as probes of yet more distant regions. The first steps in the ladder uses radar ranging to get the distance to the nearby planets and the Sun; and 'triangulation' to get the distances to the nearest stars. Those in turn are used to obtain distances to other stars in our Milky Way Galaxy, stars in other galaxies, and out to the furthest reaches of what is observable.
This class will explore the steps in this ladder, using lectures, discussions, field trips, demonstrations, and computer laboratory exercises. Students will learn basic computer programming for a project to model the effects of gravity, and they will get handson experience of using a small radio telescope to map the the rotation speed of the Milky Way and measure the influence of its dark matter. We will cover concepts involving space, time, and matter that go far beyond the distance ladder, and involve some of the most fascinating mysteries in cosmology and astrophysics: What is it like inside a black hole? What is the Dark Matter? What is the Dark Energy that makes the Universe expand faster and faster? Is there other life in the Universe?
Deep Sea Monsters or Docile Dwellers? The Biology of the Oceans. (Session 3)
Instructor: Janice Pappas
The oceans are vast, majestic bodies of water that harbor a myriad of life forms. The Antarctic, Arctic, Atlantic, Indian, and Pacific Oceans cover 70% of the Earth’s surface and have 80 to 99% of all life on Earth. Only 5% of our oceans have been explored, so the majority of oceanic life has yet to be discovered.
Organisms of all sizes are found throughout the oceans. We will look at examples from diatoms to viper fish to vampire squid to whales. We will examine particular kinds of organisms such as keystone species, bioluminescent animals, and organisms that are able to live in extreme environments.
We will explore marine food webs as a way to understand interdependence among the oceans’ organisms. How do environmental conditions influence what happens to the organisms in the oceans? If an animal goes extinct, what will happen to other organisms in a marine food web? These are just a couple of the many questions that we might address.
Our adventure will begin with a general overview of the physical, chemical and geological aspects of the oceans and sails on to details on the oceans’ biological inhabitants. We will navigate our way to understanding organism interactions through marine food webs. We will dock at an overall assessment of the oceans—where we have come from and where we are going at the present.
Our studies will include microscopy and a field trip to the University of Michigan Exhibits Museum. Students will be required to do research with a focus on a marine food web. Students will work in groups to create a scientific poster of their research findings. Student research will be presented in class.
Prerequisites: having had a science course is helpful, but not necessary. Just bring your interest in learning about our oceans.
Discrete Dynamical Systems (Session 2)
Instructor: Alejandro Uribe
In many areas of Science one is interested in modeling how a particular "something", referred to as a "system", changes with time. Such a model is called a dynamical system. Some examples are: A population of rabbits in a given environment, a billiard ball bouncing around a given billiard table, or the price of a commodity given supply and demand functions. In this course we will concentrate on models where the time is discrete, that is, the values of time are multiples of some unit. In the simplest models the evolution is given by an equation, specifying the state of the system at time n in terms of the state at time n1. Discretetime dynamical systems can be studied graphically, algebraically and numerically, without having to use a lot of calculus.
In this course we will study some of the many fascinating phenomena that dynamical systems can exhibit. We will start by developing a language that includes the concepts of phase space, initial condition, orbit, periodic orbit and fixed point. We will then develop the notions of stability and instability, and attractor. We will see that some systems are "integrable" or very regular, and at the opposite extreme we will try to formulate a precise definition of what a chaotic system is.
The course will include some theory (which will lead us to the idea of limit, and deep questions about the structure of the real numbers), the study of some particular models, and computer experimentation.
Dissecting Life: Human Anatomy and Physiology (Session 1, Session 2, Session 3)
Instructor: Glenn Fox
Dissecting Life will lead students through the complexities and wonder of the human body. Lecture sessions will cover human anatomy and physiology in detail. Students will gain an understanding of biology, biochemistry, histology, and use these as a foundation to study human form and function.
Laboratory sessions will consist of firsthand dissections of a variety of exemplar organisms: lamprey, sharks, cats, etc. Students may also tour the University of Michigan Medical School's Plastination and Gross Anatomy Laboratories where they may observe human dissections.
Explorations of a Field Biologist (Session 2, Session 3)
Instructor: Sheila Schueller
There are so many different kinds of living organisms in this world, and every organism interacts with its physical environment and with other organisms. Understanding this mass of interactions and how humans are affecting them is a mindboggling endeavor! We cannot do this unless we at times set aside our computers and beakers, and instead, get out of the lab and classroom and into the field, which is what we will do in THIS course.
Through our explorations of grasslands, forests, and wetlands of southeastern Michigan, you will learn many natural history facts (from identifying a turkey vulture to learning how mushrooms relate to tree health). You will also practice all the steps of doing science in the field, including making careful observations, testing a hypothesis, sampling and measuring, and analyzing and presenting results.
We will address question such as: How do field mice decide where to eat? Are aquatic insects affected by water chemistry? Does flower shape matter to bees? How do lakes turn into forests? Learning how to observe nature with patience and an inquisitive mind, and then testing your ideas about what you observe will allow you, long after this class, to discover many more things about nature, even your own back yard. Most days will be allday field trips, including handson experience in restoration ecology. Towards the end of the course you will design, carry out, and present your own research project.
Fibonacci Numbers (Session 1, Session 3)
Instructor: Mel Hochster
The Fibonacci numbers are the elements of the sequence 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55… where every term is simply the sum of the two preceding terms. This sequence, which was originally proposed as describing the reproduction of rabbits, occurs in astonishingly many contexts in nature. It will be used as a starting point for the exploration of some very substantial mathematical ideas: recursive methods, modular arithmetic, and other ideas from number theory, and even the notion of a limit: the ratios of successive terms (e.g. 13/8, 21/13. 55/34…) approach the golden mean, already considered by the ancient Greeks, which yields what may be the most aesthetically pleasing dimensions for a rectangle.
As a byproduct of our studies, we will be able to explain how people can test certain, very special but immensely large numbers, for being prime. We'll also consider several games and puzzles whose analysis leads to the same circle of ideas, developing them further and reinforcing the motivations for their study.
Forensic Physics (Session 1, Session 2)
Instructor: Ramon TorresIsea
A fiber is found at a crime scene. Can we identify what type of fiber it is and can we match it to a suspect's fiber sample, for example from a piece of clothing? Likewise, someone claims to have valuable ancient Roman coins, a newlyfound old master painting, or a Viking map of America predating Columbus' voyage. Are they authentic or fakes? How can we determine that using some physicsbased techniques? (These are real examples the Viking map proved to be a forgery.) Also for example, how is a laserbased molecularprobing technique used to stop criminals from trading billions of dollars of counterfeit pharmaceuticals and endangering thousands of lives?
These are a few among many examples of physics techniques applied to several areas of Forensics. In this session, students will be introduced to these methods and have opportunities to make measurements using molecular, atomic and nuclear forensic techniques. Tours of UM facilities used in Forensics or forensicsrelated research will be given. In addition, applications in medical imaging and diagnostics will be introduced. Students will be working at our Intermediate and Advanced Physics Laboratories with the underlying physics for each method presented in detail, followed by demonstrations and laboratory activities, which include the identification of an "unknown" sample. Various crime scenes will challenge students to select and apply one or more of the methods and use their Forensic Physics skills to conduct forensic investigations.
Graph Theory (Session 2, Session 3)
Instructor: Doug Shaw
Ignore your previous knowledge of algebra, geometry, and even arithmetic! Start fresh with a simple concept: Take a collection of points, called vertices, and connect some of them with lines called edges. It doesn't matter where you draw the vertices or how you draw the lines  all that matters is that two vertices are either related, or not. We call that a “graph” and you’ve taken the first step on the Graph Theory road! Graphs turn up in physics, biology, computer science, communications networks, linguistics, chemistry, sociology, mathematics… you name it!
In this course we will discuss properties that graphs may or may not have, hunt for types of graphs that may or may not exist, learn about the silliest theorem in mathematics, and the most depressing theorem in mathematics, learn how to come up with good algorithms, model reality, and construct some mathematical proofs. We will go over fundamental results in the field, and also some results that were only proved in the last year or so! And, of course, we will present plenty of currently unsolved problems for you solve and publish when you get home!
Hex and the 4 Cs (Session 1)
Instructor: Stephen DeBacker
After a very long night of homework, you finally finish your math assignment. While doublechecking your work, you realize that you have done problems from page 221, not page 212 as your teacher requested. In disgust, you rip the paper out of your notebook, wad it up, and toss it back down on your notebook. Too frustrated to begin your assignment anew, your mind begins to wander. You wonder: Is there a point in the wadded up paper that lies exactly above the location from which it started?
After you pour your parent's morning cup of Joe, the coffee comes to rest while you sleepily (because of the whole homework thing) search in the fridge for the cream. After adding and stirring the cream into the cup, you watch the pretty patterns made by the swirling coffee and cream as the contents come to rest. You wonder: Is there a point in the coffee that lies at the same point both before and after the cream was stirred in?
We shall use mathematics to model and answer the above questions. Initially, the above questions will motivate our study of four fundamental concepts in mathematics, all of which begin with the letter C: continuity (what sorts of wadding/stirring are allowed), completeness (what if our paper/coffee has “gaps”), compactness, and connectedness. Interestingly, these are also the concepts one needs in order to rigorously understand why Calculus works. Our modeling will lead us to the Brouwer fixedpoint theorem; a very nice topological result.
To show that the Brouwer fixedpoint theorem is true, we shall also learn about the game of Hex. The game of Hex is an easy to describe board game for two players (Google "Hex game" to find a description). The game has many interesting features. For example: one of the two players must win, the first player to move should (theoretically) win, and nobody knows a strategy to guarantee that the first player wins. We will explore the mathematics required to understand why every game of Hex has a winner.
Finally, we shall stitch all of the above together by showing that the fact that there are no ties in Hex implies that there is a point in your parent’s cup of Joe which lies at the same point both before and after the cream was stirred in.
Hormones and Behavior: The Secret Life of Chemical Messengers (Session 1)
Instructor: Sara Konrath
In this course, we will examine how hormones can produce changes in behavior, but also how behavioral interactions can alter hormones. We will primarily discuss hormonebehavior interactions in mammals with an emphasis on humans and nonhuman primates. Some topics we may explore include hormonal influences on sex determination, sexual behavior, parental behavior, dominance and aggression, responses to stressful stimuli, immune function and homeostasis, biological rhythms, learning and memory, maturation, and several behaviors relevant to humans such as motivation and mood. The course will be taught as a mixture of lecture, discussion, and student presentations. Students will also be trained on how to collect and assay human saliva samples for specific hormones.
Human Identification: Forensic Anthropology Methods (Session 3)
Instructor: Kathleen Alsup
Forensic anthropology methods are used to aid in human identification with skeletal remains. Applications of forensic anthropology lie in the criminal justice system and mass disaster response. In this course, we will address questions such as: What are important differences between male and female skeletons? Utilizing skeletal remains, how would you tell the difference between a 20year old and an 80year old? How do you distinguish between blunt force and sharp force trauma on the skull?
In this handson, laboratorybased course, you will be become familiar with human osteology (the study of bones] and bone biology. Through our exploration of forensic and biological anthropology methods, you will learn how to develop a biological profile [estimates of age at death, sex, ancestry and stature], assess manner of death, estimate postmortem interval, investigate skeletal trauma and pathology, and provide evidence for a positive identification from skeletal remains. Additionally, we will explore various forensic recovery techniques as they apply to an outdoor complex, including various mapping techniques. Towards the end of the course, you will work in small groups in a mock recovery of human remains and analyze the case utilizing the forensic anthropological methods learned throughout the course.
Life, Death and Change: Landscapes and Human Impact (Session 2)
Instructor: David Michener
You’ll never see the same world quite the same way after this course – which is important if you want to make a difference with your life. All environmental studies presume a landscape – yet what seems to be a simple landscape is often far from uniform or stable. A great deal of information critical to anyone entering the “green” sciences can be detected for analysis – including factors that may fundamentally control species diversity, habitat richness, and animal (let alone human) behavior. Resolving human from nonhuman agency is an engaging and important challenge, too – one scientists and “green professionals” grapple with repeatedly. This outdoor class immerses students in realworld landscapes, ranging from the nearlypristine to the highly humanized, to solve problems which may initially appear impossible to address. You can!
Your critical thinking skills are essential rather than prior biological course and field work. Come prepared to look, measure, analyze, discus and learn how the interaction of plants, soils, climate and time (and humans) influences landscape development. Develop basic skills in plant recognition and identification – skills that you can transfer to other terrestrial communities. Address questions about the current vegetation, its stability over time and its future prospects. Gain practical insights into the realities of biological conservation as we address how we can manage species and landscapes for future generations. By the end you’ll have a conceptual skill set that helps you assess how stable and disturbed are the “natural” areas are near your home – and prepares you to put instructors on the spot in college classes to come.
Making it in the "Real World"  Understanding the Physiology Behind Organism Behavior (Session 1)
Instructor: Larissa Sano
An important consideration in studying the biology of life is to understand the ways in which organisms interact with their physical environment. As humans, we are largely able to control many aspects of our physical environment to ensure our comfort and well being  for example, we build insulated homes, use central heating and air conditioning, and shop at a local grocery store. Most other animals, however, have to deal directly with the elements.
In order to do this, animals have developed unusual and sometimes bizarre strategies to help them survive. To understand these survival strategies and to link them with an animal’s physiology, we will combine field observations with laboratory studies and data analysis. Some of the questions we will address include: How does water temperature affect where we find fish in a river? What are the energy requirements of a bird, and how can they forage in a forest to meet their energy needs? and Do insects really fly faster when it is warmer outside? Our ultimate goal will be to understand what it takes for organisms to survive in the “real world.”
Although most of our days will be spent outside, hiking through forests, wading through rivers, and exploring ponds, we will also make time to conduct laboratory experiments, analyze our data, and interpret our results. Towards the end of the course you will design, carry out, and present your own research project.
Mathematical Modeling in Biology (Session 1)
Instructors: Trachette Jackson and Patrick Nelson
Mathematical biology is a relatively new area of applied mathematics and is growing with phenomenal speed. For the mathematician, biology opens up new and exciting areas of study, while for the biologist, mathematical modeling offers another powerful research tool commensurate with a new instrumental laboratory technique. Mathematical biologists typically investigate problems in diverse and exciting areas such as the topology of DNA, cell physiology, the study of infectious diseases, population ecology, neuroscience, tumor growth and treatment strategies, and organ development and embryology.
This course will be a venture into the field of mathematical modeling in the biomedical sciences. Interactive lectures, group projects, computer demonstrations, and laboratory visits will help introduce some of the fundamentals of mathematical modeling and its usefulness in biology, physiology and medicine.
For example, the cell division cycle is a sequence of regulated events which describes the passage of a single cell from birth to division. There is an elaborate cascade of molecular interactions that function as the mitotic clock and ensures that the sequential changes that take place in a dividing cell take place on schedule. What happens when the mitotic clock speeds up or simply stops ticking? These kinds of malfunctions can lead to cancer and mathematical modeling can help predict under what conditions a small population of cells with a compromised mitotic clock can result in a fully developed tumor. This course will study many interesting problems in cell biology, physiology, and immunology.
Mathematics and Music Theory (Session 3)
Instructor: Lon Mitchell
Mathematicians can create complex and beautiful theorems from relatively basic assumptions, while Music Theorists often try to identify basic patterns and “rules” in complex and beautiful music. In this course, we will explore some of the recent attempts to meet in the middle, connecting mathematical patterns and structures to music from the ancient to the modern.
In Mathematics, we will explore topics such as group theory, graph theory, geometry, and metric spaces, encountering some of the most important structures in the modern discipline. Fundamental results of these areas will be discussed, and students will construct and explore examples and related patterns.
In Music Theory, we will take existing music by composers such as Bach and Beethoven and use mathematical structures to provide a possible explanation of what they were thinking as they composed. In addition, we will investigate the techniques of modern composers such as Arnold Schoenberg who advocated composition based on prescribed axioms. Students will be given the chance to write music using these different techniques.
Although we will use the modern (Western) twelvetone scale as a reference, our explorations will take us into discussions of tuning, temperament, and the physics of sound. We will investigate mathematical theories of what makes the best scale, how some of those scales occur in the music of other cultures, and how modern composers have engineered exotic scales to suit their aesthetics.
Software allowing students to experiment with creating their own musical systems will be provided.
Prospective students should have a good command of (highschool) algebra and experience with reading music in some form.
Mathematics and the Internet (Session 3)
Instructor: Mark Conger
How can gigabytes of information move over unreliable airwaves using unreliable signaling, and arrive perfectly intact? How can I have secure communication with a website run by a person I've never met? How can a large image or sound file be transferred quickly? Why is Google so good at finding what I'm looking for? How do computers work, anyway?
The answers to all these questions involve applications of abstract mathematics. In Mathematics and the Internet, we'll develop the math on its own, but also show how it is essential to making the Internet operate as it does. Our journey will take us through logic, probability, group theory, finite fields, calculus, number theory, and any other areas of math that might come up. We'll apply our results to coding theory, cryptography, search engines, and compression. We'll also spend several days building primitive computers out of transistors, logic gates, and lots of wire. If all goes well, we'll connect them to the Internet!
Mathematics of Cryptography (Session 3)
Instructor: Anton Lukyanenko
Ever since humans first developed the ability to write there has been an ongoing battle between codemakers and codebreakers. The armies of ancient Sparta and Rome both used ciphers to relay secret battle plans, and the ancient Mesopotamians developed encryption techniques in order to protect commercially valuable techniques for glazing pottery. From a modern perspective, the codes used by the ancients are laughably insecure. Indeed, much of what made them secure was that they were being used during a period when most people were illiterate.
Because of the advent of computers, codemakers today need to use far more sophisticated techniques in order to create secure codes. Many of these techniques are mathematical in nature. One of the cryptography systems that we will discuss in this class is called RSA and is used to ensure the security of your credit card information when you make a purchase on the internet. We'll see that at its heart, what makes the RSA system secure is that it is very hard to factor a big number. The numbers used in the RSA system are actually so big that factoring them would take you millions of years. Even if you were using a supercomputer!
This class will give an historical introduction to the mathematics of cryptography, beginning with codes used by the Roman legions and building up to the RSA cryptography system discussed above. What will really make the class unique is that there won't be any lecturing. You will discover the mathematics of cryptography by working on problems and sharing your solutions with your classmates.
Mathematics of Decisions, Elections and Games (Session 2)
Instructor: Michael A. Jones
You make decisions every day, including whether or not to sign up for this course. The decision you make under uncertainty says a lot about who you are and how you value risk. To analyze such decisions and provide a mathematical framework, utility theory will be introduced and applied to determine, among other things, the offer the banker makes to a contestant in the television show Deal or No Deal.
Elections are instances in which more than one person’s decision is combined to arrive at a collective choice. But how are votes tallied? Naturally, the best election procedure should be used. But Kenneth Arrow was awarded the Nobel Prize in Economics in 1972, in part, because he proved that there is no best election procedure. Because there is no one best election procedure, once the electorate casts its ballots, it is useful to know what election outcomes are possible under different election procedures. This suggests mathematical and geometric treatments to be taught in the course. Oddly, the outcome of an election often says more about which election procedure was used, rather than the preferences of the voters! Besides politics, this phenomenon is present in other settings that we’ll consider which include: the Professional Golfers’ Association tour which determines the winner of tournaments under different scoring rules (e.g. stroke play and the modified Stableford system), the method used to determine rankings of teams in the NCAA College Football Coaches poll, and Major League Baseball MVP balloting.
Anytime one person’s decisions can affect what happens to another person, that situation can be modeled by game theory. That there is still a best decision to make that takes into account that others are trying to make their best decisions is, in part, why John F. Nash was awarded the Nobel Prize in Economics in 1994 (see A Beautiful Mind, 2002). Besides understanding and applying Nash’s results in settings as diverse as the baseball mind games between a pitcher and batter and bidding in auctions, we’ll examine how optimal play in a particular game is related to a proof that there are the same number of counting numbers {1, 2, 3, …} as there are positive fractions. We will also examine the GaleShapley algorithm, which is used, for example, to match physicians to residency programs and to match students to colleges (the college admissions problem). Lloyd S. Shapley and Alvin E. Roth were awarded the Nobel Prize in Economics in 2012 for their work on matching.
Organic Chemistry 101: Orgo Boot Camp (Session 3)
Instructor: Kathleen Nolta
This course will introduce students to the techniques and concepts taught in the first term of organic chemistry at the University of Michigan. The emphasis will be on exploring concepts through problem solving (there will be lots of practice problems to do!), and the students will even have an opportunity to take examinations given to college students. This minicourse will introduce students to principles of nomenclature, as well as the structural organization of molecules including connectivity, stereochemistry, and conformational chemistry. We will also explore the complexity of curved arrow mechanisms for proton chemistry, substitution reactions, and electrophilic additions. Students will be able to explore the chemistry in various laboratory applications. By focusing on the concepts and trying some of the techniques, students will gain a better understanding of what organic chemistry is and how to enjoy it.
Predicting & Forecasting Natural Hazards (Session 3)
Instructor: Eric Hetland
Natural disasters have resulted in almost $4 trillion in losses and over a billion fatalities in the past 35 years. Naturally occurring events, such as earthquakes, volcanic eruptions, tsunamis, landslides, floods, hurricanes, tornadoes, and extreme temperatures, occur every year and affect nearly every part of the Earth. Most of these natural hazards involve a relatively sudden release of a large amount of energy over a small spatial area – when this concentration of energy and society intersect, disaster results. Considerable effort has gone into our ability to estimate our risk from natural hazards, as well as forecast hazards. Forecasting of hazards is done both over long time periods, and time periods over the life of the hazard. For example, forecasts for hurricane activity are made as early as a year before a hurricane season, while once a hurricane forms the path of that hurricane is forecast and adjusted throughout the life of the hurricane. A complicating factor when discussing natural hazards is that the number and cost of natural disasters has been increasing over the last few decades. This may be due to natural hazards increasing in number, size, or extent, or may be due to an increase in vulnerability of modern society.
In this course, we will explore estimating risk of, predicting, and forecasting natural hazards, including earthquakes, hurricanes, tornadoes, and extreme temperatures. Our focus will be on how the dynamic complexities of natural hazards makes forecasting hazard possible, but also hinder our ability to predict those hazards. We will discuss the scientific assessment of precursors, as well as the evidence/arguments that the frequency or severity of hazards are increasing over just the past few decades. We will cover fundamental mathematics related to estimation and forecasting, including probabilistic inference, chaos, complexity, random walks (e.g., Markov chains), and predictive filtering. The majority of the handson exercises will be computerbased. Earth science knowledge is not required.
Roller Coaster Physics (Session 2)
Instructor: David Winn
What are the underlying principles that make roller coasters run? By studying the dynamics of roller coasters and other amusement park rides in the context of Newtonian physics and human physiology, we will begin to understand these complex structures. Students first review Newtonian mechanics, a = f/m in particular, with some handson experiments using airtables. This will then be followed by digitalvideo analysis of motion of some reallife objects (humans, cars, and toy rockets) and studentdevised roller coaster models.
Then, a field trip to Cedar Point Amusement Park (outside of the regularly scheduled weekend trip) where students, riding roller coasters and other rides, will provide real data for analysis back at UM. Students will carry portable data loggers and 3axis accelerometers to provide onsite, and later offsite, analysis of the motion and especially, the "gforces" experienced. The information collected will then be analyzed in terms of human evolution and physiology; we shall see why these limit the designs of rides.
In addition to exploring the physics of roller coasters, cuttingedge topics in physics will be introduced: high energy physics, nuclear astrophysics, condensedmatter theory, biophysics and medical physics. Students will then have a chance to see the physics in action by touring some of UM's research facilities. Students will have the opportunity to see scientists doing research at the Solid State Electronics Laboratory, the Michigan Ion Beam Laboratory, and the Center for Ultrafast Optical Science.
By the end of the twoweek session, students will gain insight and understanding in physics and take home the knowledge that physics is an exciting, reallife science that involves the objects and motions surrounding us on a daily basis.
Sampling, Monte Carlo and Problem Solving: How Analyzing Statistics Helps us Improve (Session 1)
Instructor: Edward Rothman
Political candidates drop out of elections for the U.S. Senate and New York Governorship because their poll numbers are low, while Congress fights over whether and how much statistics can be used to establish the meaning of the U.S. Census for a host of apportionment purposes influencing all our lives.
Suppose we need to learn reliably how many people have a certain disease? How safe is a new drug? How much air pollution is given off by industry in a certain area? Or even how many works someone knows?
For any of these problems we need to develop ways of figuring out how many or how much of something will be found without actually tallying results from a large portion of the population, which means we have to understand how to count this by sampling.
And Monte Carlo? Sorry, no field trips to the famous casino! But, Monte Carlo refers to a way of setting up random experiments to which one can compare real data: does the data tell us anything significant, or it is just random noise? Did you know you can even calculate the number ? This way?!?!The survey and sampling techniques that allow us to draw meaningful conclusions about the whole, but based on the analysis of a small part, will be the main subject of this course.
Surface Chemistry (Session 2)
Instructor: Zhan Chen
This course will be divided into three units: applications, properties, and techniques. The first unit will introduce students to surface science that exists within the human body, surfaces in modern science and technology, and surfaces found in everyday life. Our bodies contain many different surfaces that are vital to our wellbeing. Surface reactions are responsible for protein interaction with cell surfaces, hormone receptor interactions, and ling function. Modern science has explored and designed surfaces for many applications: antibiofouling surfaces are being researched for marine vessels; high temperature resistant surfaces are important for space shuttles; and heterogeneous catalysis, studies by surface reactions, is important in industry and environmental preservation. The usefulness of many common items is determined by surface properties; contact lenses must remain wetted; while raincoats are deigned to be nonwetting; and coatings are applied to cookware for easy cleanup.
The second unit will examine the basic properties of surfaces. Lectures will focus on the concepts of hydrophobicity, friction, lubrication, adhesion, wearability, and biocompatibility. The instrumental methods used to study surfaces will be covered in the last unit. Traditional methods, such as contact angle measurements will be covered first. Then vacuum techniques will be examined. Finally, molecular level in situ techniques such as AFM and SFG will be covered, and students will be able to observe these techniques in the lab.
Multimedia PowerPoint presentations will be used for all lectures. By doing this, it's hoped to promote high school students' interest in surface science, chemistry, and science in general. A website introducing modern analytical chemistry in surface and interfacial sciences will be created.
Surviving in an Uncertain World: Human Adaptive Response to Climate Change (Session 3)
Instructors: John Kingston and Laura MacLatchy
Climate change is not a distant problem. It’s happening now and is having real consequences for human populations worldwide, affecting foodproducing economies, shifting disease demographics, and resulting in loss of biodiversity. Despite these realizations, it is important to appreciate that climate and environmental change have always been part of the human landscape and much of the adaptability and flexibility that characterize humans may have been shaped by these fluctuations. In this course we’ll unpack the concept of climate change and explore how our evolutionary trajectory has been a response to ecological volatility and uncertainty as well as contemplate future outcomes.
The Physics of Magic and the Magic of Physics (Session 2)
Instructors: Fred Becchetti and Georg Raithel
Rabbits that vanish; objects that float in air defying gravity; a tiger that disappears and then reappears elsewhere; mind reading, telepathy and xray vision; objects that penetrate solid glass; steel rings that pass through each other: these are some of the amazing tricks of magic and magicians. Yet even more amazing phenomena are found in nature and the world of physics and physicists: matter than can vanish and reappear as energy and viceversa; subatomic particles that can penetrate steel; realistic 3D holographic illusions; objects that change their dimensions and clocks that speed up or slow down as they move (relativity); collapsed stars that trap their own light (black holes); xrays and lasers; fluids that flow uphill (liquid helium); materials without electrical resistance (superconductors.)
In this class students will first study the underlying physics of some classical magic tricks and learn to perform several of these (and create new ones.) The "magic" of corresponding (and real) physical phenomena will then be introduced and studied with handson, mindson experiments. Finally, we will visit a number of research laboratories where students can meet some of the "magicians" of physics  physics students and faculty  and observe experiments at the forefront of physics research.
To be or not to be? Biodiversity and Mass Extinctions through Deep Time (Session 2)
Instructor: Janice Pappas
Life on the 4.6 billion year old Earth began around 3.5 billion years ago. How did life on Earth come about? What kinds of life forms emerged? When did these forms come into existence? We will explore the fossil record and the events that shaped the biological world as we know it today. We will study life on Earth from the perspective of biodiversity and phylogenetic trees of life. We will focus on the Ediacaran period, the Cambrian explosion, and the Mesozoic Marine Revolution as times of great biodiversity. We will explore the five major mass extinction events that occurred at the OrdovicianSilurian, the Late Devonian, the PermianTriassic, the TriassicJurassic, and the CretaceousPaleogene. Why did life on Earth vanish in such large quantities at these events? How did this happen? What happened to biodiversity in the aftermath? These are just some of the many questions we might address for each extinction event.
Our journey begins with an overview of what Earth looked like at the time life first appeared from a geological and climatological perspective. We will advance toward studying various organisms and biodiversity over time. We will be haltingly taken aback at the catastrophic consequences of mass extinction. We will emerge from such events and take stock of biodiversity to the present. We may even have time to consider fossils and their importance in astrobiology.
Our studies will include field trips to the University of Michigan Exhibits Museum. Students will be required to do research covering biodiversity with respect to an extinction event. Students will work in groups to create a scientific poster of their research findings. Student research will be presented in class.
Prerequisites: Having had a science course is helpful, but not necessary. Just bring your enthusiasm to learn about the history of life on Earth.
Art and Mathematics
Instructor: Martin Strauss
With just a little historical revisionism, we can say that Art has
provided inspiration for many fields within Mathematics. Conversely,
Mathematics gives techniques for analyzing, appreciating, and even
creating Art, as well as the basis for gallery design, digital
cameras, and processing of images. In this class we will explore the
Mathematics in great works of Art as well as folk art, as a way of
studying and illustrating central mathematical concepts in familiar
and pleasing material. And we'll make our own art, by drawing,
painting, folding origami papers, and more.
Major topics include Projection, Symmetry, Wave Behavior, and
Distortion. Projection includes the depiction of threedimensional
objects in two dimensions. What mathematical properties must be lost,
and what can be preserved? How does an artwork evoke the feeling of
threedimensional space? We'll study perspective, depictions of
globes by maps, and the role of curvature. Turning to symmetry, we'll
study rotational and reflective symmetry that arise in tiling and
other art and math. We'll study more generalized symmetry like
scaling and selfsimilarity that occurs in fractals as well as every
selfportrait, and is central to mathematical concepts of dimension
and unprovability. On the other hand, we'll look at how works of
digital and pointilist art are made up of fine pixels with a character
very different from the work at coarser scalesit is not selfsimilar.
Describing light as waves and color as wavelength at once explains how
mirrors, lenses, and prisms work and explains some uses of light and
color in art. Finally, we ask about distorting fabrics and strings,
and ask about the roles of cutting, gluing, and of stretching without
cutting or gluing. Is a distorted human figure still recognizable, as
long as it has the right number of organs and limbs, connected
properly?
Background in Math and interest in Art suggested. No artistic talent
is necessary, though artistically talented students are encouraged to
bring art supplies if they are inexpensive and easily transportable.
AstroTurf, Diapers, Kevlar and More: Explore the Materials in the World Around you!
Instructor: Anne McNeil
Ever wonder what a raincoat is made out of? Or why Spandex is stretchy? Our course on polymers, the molecules that make up plastics and elastics, holds these answers and more! Make Nylon and participate in laboratory research where you will gain the skills of a materials chemist by making polymers yourself. Learn how polymers have come to make up much of the material you interact with on a daily basis from contact lenses to golf balls. Share your newly gained knowledge with the world by adding content to Wikipedia. Join us on this journey into the world of materials.
Catalysis, Solar Energy and Green Chemical Synthesis
Instructor: Corey Stephenson
"The chemist who designs and completes an original and esthetically pleasing multistep synthesis is like the composer, artist or poet who, with great individuality, fashions new forms of beauty from the interplay of mind and spirit."
E.J. Corey, Nobel Laureate
Prior to Friedrich Wöhler’s 1828 synthesis of urea, organic (carboncontaining) matter from living organisms was believed to contain a “vital force” that distinguished it from inorganic material. The discovery that organic molecules can be manipulated at the hands of scientists is considered by many the birth of “organic chemistry”: the study of the structure, properties, and reactions of carboncontaining matter. Organic matter is the foundation of life as we know it, and therefore a fundamental understanding of reactivity at a molecular level is essential to all life sciences. In this class we will survey monumental discoveries in this field over the past two centuries and the technological developments that have enabled them.
“Catalysis, Solar Energy, and Green Chemical Synthesis” will provide a fun and intellectually stimulating handson experience that instills a historical appreciation for the giants whose trials and tribulations have enabled our modern understanding of chemistry and biology. Students will learn modern laboratory techniques including how to set up, monitor, and purify chemical reactions, and most importantly, how to determine what they made! Experiments include the synthesis of biomolecules using some of the most transformative reactions of the 20th century and exposure to modern synthetic techniques, such as the use of metal complexes that absorb visible light to catalyze chemical reactions, an important development in the “Green Science” movement. Finally, industrial applications of chemistry such as polymer synthesis and construction of photovoltaic devices will be performed. Daily experiments will be supplemented with exciting demonstrations by the graduate student instructors.
Dissecting Life: Human Anatomy and Physiology
Instructor: Glenn Fox
Dissecting Life will lead students through the complexities and wonder of the human body. Lecture sessions will cover human anatomy and physiology in detail. Students will gain an understanding of biology, biochemistry, histology, and use these as a foundation to study human form and function.
Laboratory sessions will consist of firsthand dissections of a variety of exemplar organisms: lamprey, sharks, cats, etc. Students may also tour the University of Michigan Medical School's Plastination and Gross Anatomy Laboratories where they may observe human dissections.
Fibonacci Numbers
Instructor: Mel Hochster
The Fibonacci numbers are the elements of the sequence 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55… where every term is simply the sum of the two preceding terms. This sequence, which was originally proposed as describing the reproduction of rabbits, occurs in astonishingly many contexts in nature. It will be used as a starting point for the exploration of some very substantial mathematical ideas: recursive methods, modular arithmetic, and other ideas from number theory, and even the notion of a limit: the ratios of successive terms (e.g. 13/8, 21/13. 55/34…) approach the golden mean, already considered by the ancient Greeks, which yields what may be the most aesthetically pleasing dimensions for a rectangle.
As a byproduct of our studies, we will be able to explain how people can test certain, very special but immensely large numbers, for being prime. We'll also consider several games and puzzles whose analysis leads to the same circle of ideas, developing them further and reinforcing the motivations for their study.
Forensic Physics
Instructor: Ramon TorresIsea
A fiber is found at a crime scene. Can we identify what type of fiber it is and can we match it to a suspect's fiber sample, for example from a piece of clothing? Likewise, someone claims to have valuable ancient Roman coins, a newlyfound old master painting, or a Viking map of America predating Columbus' voyage. Are they authentic or fakes? How can we determine that using some physicsbased techniques? (These are real examples the Viking map proved to be a forgery.) Also for example, how is a laserbased molecularprobing technique used to stop criminals from trading billions of dollars of counterfeit pharmaceuticals and endangering thousands of lives?
These are a few among many examples of physics techniques applied to several areas of Forensics. In this session, students will be introduced to these methods and have opportunities to make measurements using molecular, atomic and nuclear forensic techniques. Tours of UM facilities used in Forensics or forensicsrelated research will be given. In addition, applications in medical imaging and diagnostics will be introduced. Students will be working at our Intermediate and Advanced Physics Laboratories with the underlying physics for each method presented in detail, followed by demonstrations and laboratory activities, which include the identification of an "unknown" sample. Various crime scenes will challenge students to select and apply one or more of the methods and use their Forensic Physics skills to conduct forensic investigations.
Hex and the 4 Cs
Instructor: Stephen DeBacker
After a very long night of homework, you finally finish your math assignment. While doublechecking your work, you realize that you have done problems from page 221, not page 212 as your teacher requested. In disgust, you rip the paper out of your notebook, wad it up, and toss it back down on your notebook. Too frustrated to begin your assignment anew, your mind begins to wander. You wonder: Is there a point in the wadded up paper that lies exactly above the location from which it started?
After you pour your parent's morning cup of Joe, the coffee comes to rest while you sleepily (because of the whole homework thing) search in the fridge for the cream. After adding and stirring the cream into the cup, you watch the pretty patterns made by the swirling coffee and cream as the contents come to rest. You wonder: Is there a point in the coffee that lies at the same point both before and after the cream was stirred in?
We shall use mathematics to model and answer the above questions. Initially, the above questions will motivate our study of four fundamental concepts in mathematics, all of which begin with the letter C: continuity (what sorts of wadding/stirring are allowed), completeness (what if our paper/coffee has “gaps”), compactness, and connectedness. Interestingly, these are also the concepts one needs in order to rigorously understand why Calculus works. Our modeling will lead us to the Brouwer fixedpoint theorem; a very nice topological result.
To show that the Brouwer fixedpoint theorem is true, we shall also learn about the game of Hex. The game of Hex is an easy to describe board game for two players (Google "Hex game" to find a description). The game has many interesting features. For example: one of the two players must win, the first player to move should (theoretically) win, and nobody knows a strategy to guarantee that the first player wins. We will explore the mathematics required to understand why every game of Hex has a winner.
Finally, we shall stitch all of the above together by showing that the fact that there are no ties in Hex implies that there is a point in your parent’s cup of Joe which lies at the same point both before and after the cream was stirred in.
Hormones and Behavior: The Secret Life of Chemical Messengers
Instructor: Sara Konrath
In this course, we will examine how hormones can produce changes in behavior, but also how behavioral interactions can alter hormones. We will primarily discuss hormonebehavior interactions in mammals with an emphasis on humans and nonhuman primates. Some topics we may explore include hormonal influences on sex determination, sexual behavior, parental behavior, dominance and aggression, responses to stressful stimuli, immune function and homeostasis, biological rhythms, learning and memory, maturation, and several behaviors relevant to humans such as motivation and mood. The course will be taught as a mixture of lecture, discussion, and student presentations. Students will also be trained on how to collect and assay human saliva samples for specific hormones.
Making it in the "Real World"  Understanding the Physiology Behind Organism Behavior
Instructor: Larissa Sano
An important consideration in studying the biology of life is to understand the ways in which organisms interact with their physical environment. As humans, we are largely able to control many aspects of our physical environment to ensure our comfort and well being  for example, we build insulated homes, use central heating and air conditioning, and shop at a local grocery store. Most other animals, however, have to deal directly with the elements.
In order to do this, animals have developed unusual and sometimes bizarre strategies to help them survive. To understand these survival strategies and to link them with an animal’s physiology, we will combine field observations with laboratory studies and data analysis. Some of the questions we will address include: How does water temperature affect where we find fish in a river? What are the energy requirements of a bird, and how can they forage in a forest to meet their energy needs? and Do insects really fly faster when it is warmer outside? Our ultimate goal will be to understand what it takes for organisms to survive in the “real world.”
Although most of our days will be spent outside, hiking through forests, wading through rivers, and exploring ponds, we will also make time to conduct laboratory experiments, analyze our data, and interpret our results. Towards the end of the course you will design, carry out, and present your own research project.
Mathematical Modeling in Biology
Instructors: Trachette Jackson and Patrick Nelson
Mathematical biology is a relatively new area of applied mathematics and is growing with phenomenal speed. For the mathematician, biology opens up new and exciting areas of study, while for the biologist, mathematical modeling offers another powerful research tool commensurate with a new instrumental laboratory technique. Mathematical biologists typically investigate problems in diverse and exciting areas such as the topology of DNA, cell physiology, the study of infectious diseases, population ecology, neuroscience, tumor growth and treatment strategies, and organ development and embryology.
This course will be a venture into the field of mathematical modeling in the biomedical sciences. Interactive lectures, group projects, computer demonstrations, and laboratory visits will help introduce some of the fundamentals of mathematical modeling and its usefulness in biology, physiology and medicine.
For example, the cell division cycle is a sequence of regulated events which describes the passage of a single cell from birth to division. There is an elaborate cascade of molecular interactions that function as the mitotic clock and ensures that the sequential changes that take place in a dividing cell take place on schedule. What happens when the mitotic clock speeds up or simply stops ticking? These kinds of malfunctions can lead to cancer and mathematical modeling can help predict under what conditions a small population of cells with a compromised mitotic clock can result in a fully developed tumor. This course will study many interesting problems in cell biology, physiology, and immunology.
Sampling, Monte Carlo and Problem Solving: How Analyzing Statistics Helps us Improve
Instructor: Edward Rothman
Political candidates drop out of elections for the U.S. Senate and New York Governorship because their poll numbers are low, while Congress fights over whether and how much statistics can be used to establish the meaning of the U.S. Census for a host of apportionment purposes influencing all our lives.
Suppose we need to learn reliably how many people have a certain disease? How safe is a new drug? How much air pollution is given off by industry in a certain area? Or even how many works someone knows?
For any of these problems we need to develop ways of figuring out how many or how much of something will be found without actually tallying results from a large portion of the population, which means we have to understand how to count this by sampling.
And Monte Carlo? Sorry, no field trips to the famous casino! But, Monte Carlo refers to a way of setting up random experiments to which one can compare real data: does the data tell us anything significant, or it is just random noise? Did you know you can even calculate the number ? This way?!?!The survey and sampling techniques that allow us to draw meaningful conclusions about the whole, but based on the analysis of a small part, will be the main subject of this course.
Catalysis, Solar Energy and Green Chemical Synthesis
Instructor: Corinna Schindler
"The chemist who designs and completes an original and esthetically pleasing multistep synthesis is like the composer, artist or poet who, with great individuality, fashions new forms of beauty from the interplay of mind and spirit."
E.J. Corey, Nobel Laureate
Prior to Friedrich Wöhler’s 1828 synthesis of urea, organic (carboncontaining) matter from living organisms was believed to contain a “vital force” that distinguished it from inorganic material. The discovery that organic molecules can be manipulated at the hands of scientists is considered by many the birth of “organic chemistry”: the study of the structure, properties, and reactions of carboncontaining matter. Organic matter is the foundation of life as we know it, and therefore a fundamental understanding of reactivity at a molecular level is essential to all life sciences. In this class we will survey monumental discoveries in this field over the past two centuries and the technological developments that have enabled them.
“Catalysis, Solar Energy, and Green Chemical Synthesis” will provide a fun and intellectually stimulating handson experience that instills a historical appreciation for the giants whose trials and tribulations have enabled our modern understanding of chemistry and biology. Students will learn modern laboratory techniques including how to set up, monitor, and purify chemical reactions, and most importantly, how to determine what they made! Experiments include the synthesis of biomolecules using some of the most transformative reactions of the 20th century and exposure to modern synthetic techniques, such as the use of metal complexes that absorb visible light to catalyze chemical reactions, an important development in the “Green Science” movement. Finally, industrial applications of chemistry such as polymer synthesis and construction of photovoltaic devices will be performed. Daily experiments will be supplemented with exciting demonstrations by the graduate student instructors.
Climbing the Distance Ladder to the Big Bang: How Astronomers Survey the Universe
Instructor: Dragan Huterer
The furthest objects that astronomers can observe are so distant that their light set out when the Universe was only 800 million years old, and has been traveling to us for about 13 billion years – most of the age of the Universe. Even the Sun's neighborhood – the local part of our Galaxy, where astronomers have successfully searched for planets around other stars – extends to hundreds of light years. How do we measure the distance to such remote objects?
Certainly not in a single step! Astronomers construct the socalled “Distance Ladder,” finding the distance to nearby objects, thus enabling those bodies to be understood and used as probes of yet more distant regions. The first steps in the ladder uses radar ranging to get the distance to the nearby planets and the Sun; and 'triangulation' to get the distances to the nearest stars. Those in turn are used to obtain distances to other stars in our Milky Way Galaxy, stars in other galaxies, and out to the furthest reaches of what is observable.
This class will explore the steps in this ladder, using lectures, discussions, field trips, demonstrations, and computer laboratory exercises. Students will learn basic computer programming for a project to model the effects of gravity, and they will get handson experience of using a small radio telescope to map the the rotation speed of the Milky Way and measure the influence of its dark matter. We will cover concepts involving space, time, and matter that go far beyond the distance ladder, and involve some of the most fascinating mysteries in cosmology and astrophysics: What is it like inside a black hole? What is the Dark Matter? What is the Dark Energy that makes the Universe expand faster and faster? Is there other life in the Universe?
Discrete Dynamical Systems
Instructor: Alejandro Uribe
In many areas of Science one is interested in modeling how a particular "something", referred to as a "system", changes with time. Such a model is called a dynamical system. Some examples are: A population of rabbits in a given environment, a billiard ball bouncing around a given billiard table, or the price of a commodity given supply and demand functions. In this course we will concentrate on models where the time is discrete, that is, the values of time are multiples of some unit. In the simplest models the evolution is given by an equation, specifying the state of the system at time n in terms of the state at time n1. Discretetime dynamical systems can be studied graphically, algebraically and numerically, without having to use a lot of calculus.
In this course we will study some of the many fascinating phenomena that dynamical systems can exhibit. We will start by developing a language that includes the concepts of phase space, initial condition, orbit, periodic orbit and fixed point. We will then develop the notions of stability and instability, and attractor. We will see that some systems are "integrable" or very regular, and at the opposite extreme we will try to formulate a precise definition of what a chaotic system is.
The course will include some theory (which will lead us to the idea of limit, and deep questions about the structure of the real numbers), the study of some particular models, and computer experimentation.
Dissecting Life: Human Anatomy and Physiology
Instructor: Glenn Fox
Dissecting Life will lead students through the complexities and wonder of the human body. Lecture sessions will cover human anatomy and physiology in detail. Students will gain an understanding of biology, biochemistry, histology, and use these as a foundation to study human form and function.
Laboratory sessions will consist of firsthand dissections of a variety of exemplar organisms: lamprey, sharks, cats, etc. Students may also tour the University of Michigan Medical School's Plastination and Gross Anatomy Laboratories where they may observe human dissections.
Explorations of a Field Biologist
Instructor: Sheila Schueller
There are so many different kinds of living organisms in this world, and every organism interacts with its physical environment and with other organisms. Understanding this mass of interactions and how humans are affecting them is a mindboggling endeavor! We cannot do this unless we at times set aside our computers and beakers, and instead, get out of the lab and classroom and into the field, which is what we will do in THIS course.
Through our explorations of grasslands, forests, and wetlands of southeastern Michigan, you will learn many natural history facts (from identifying a turkey vulture to learning how mushrooms relate to tree health). You will also practice all the steps of doing science in the field, including making careful observations, testing a hypothesis, sampling and measuring, and analyzing and presenting results.
We will address question such as: How do field mice decide where to eat? Are aquatic insects affected by water chemistry? Does flower shape matter to bees? How do lakes turn into forests? Learning how to observe nature with patience and an inquisitive mind, and then testing your ideas about what you observe will allow you, long after this class, to discover many more things about nature, even your own back yard. Most days will be allday field trips, including handson experience in restoration ecology. Towards the end of the course you will design, carry out, and present your own research project.
Forensic Physics
Instructor: Ramon TorresIsea
A fiber is found at a crime scene. Can we identify what type of fiber it is and can we match it to a suspect's fiber sample, for example from a piece of clothing? Likewise, someone claims to have valuable ancient Roman coins, a newlyfound old master painting, or a Viking map of America predating Columbus' voyage. Are they authentic or fakes? How can we determine that using some physicsbased techniques? (These are real examples the Viking map proved to be a forgery.) Also for example, how is a laserbased molecularprobing technique used to stop criminals from trading billions of dollars of counterfeit pharmaceuticals and endangering thousands of lives?
These are a few among many examples of physics techniques applied to several areas of Forensics. In this session, students will be introduced to these methods and have opportunities to make measurements using molecular, atomic and nuclear forensic techniques. Tours of UM facilities used in Forensics or forensicsrelated research will be given. In addition, applications in medical imaging and diagnostics will be introduced. Students will be working at our Intermediate and Advanced Physics Laboratories with the underlying physics for each method presented in detail, followed by demonstrations and laboratory activities, which include the identification of an "unknown" sample. Various crime scenes will challenge students to select and apply one or more of the methods and use their Forensic Physics skills to conduct forensic investigations.
Graph Theory
Instructor: Doug Shaw
Ignore your previous knowledge of algebra, geometry, and even arithmetic! Start fresh with a simple concept: Take a collection of points, called vertices, and connect some of them with lines called edges. It doesn't matter where you draw the vertices or how you draw the lines  all that matters is that two vertices are either related, or not. We call that a “graph” and you’ve taken the first step on the Graph Theory road! Graphs turn up in physics, biology, computer science, communications networks, linguistics, chemistry, sociology, mathematics… you name it!
In this course we will discuss properties that graphs may or may not have, hunt for types of graphs that may or may not exist, learn about the silliest theorem in mathematics, and the most depressing theorem in mathematics, learn how to come up with good algorithms, model reality, and construct some mathematical proofs. We will go over fundamental results in the field, and also some results that were only proved in the last year or so! And, of course, we will present plenty of currently unsolved problems for you solve and publish when you get home!
Life, Death and Change: Landscapes and Human Impact
Instructor: David Michener
You’ll never see the same world quite the same way after this course – which is important if you want to make a difference with your life. All environmental studies presume a landscape – yet what seems to be a simple landscape is often far from uniform or stable. A great deal of information critical to anyone entering the “green” sciences can be detected for analysis – including factors that may fundamentally control species diversity, habitat richness, and animal (let alone human) behavior. Resolving human from nonhuman agency is an engaging and important challenge, too – one scientists and “green professionals” grapple with repeatedly. This outdoor class immerses students in realworld landscapes, ranging from the nearlypristine to the highly humanized, to solve problems which may initially appear impossible to address. You can!
Your critical thinking skills are essential rather than prior biological course and field work. Come prepared to look, measure, analyze, discus and learn how the interaction of plants, soils, climate and time (and humans) influences landscape development. Develop basic skills in plant recognition and identification – skills that you can transfer to other terrestrial communities. Address questions about the current vegetation, its stability over time and its future prospects. Gain practical insights into the realities of biological conservation as we address how we can manage species and landscapes for future generations. By the end you’ll have a conceptual skill set that helps you assess how stable and disturbed are the “natural” areas are near your home – and prepares you to put instructors on the spot in college classes to come.
Mathematics of Decisions, Elections and Games
Instructor: Michael A. Jones
You make decisions every day, including whether or not to sign up for this course. The decision you make under uncertainty says a lot about who you are and how you value risk. To analyze such decisions and provide a mathematical framework, utility theory will be introduced and applied to determine, among other things, the offer the banker makes to a contestant in the television show Deal or No Deal.
Elections are instances in which more than one person’s decision is combined to arrive at a collective choice. But how are votes tallied? Naturally, the best election procedure should be used. But Kenneth Arrow was awarded the Nobel Prize in Economics in 1972, in part, because he proved that there is no best election procedure. Because there is no one best election procedure, once the electorate casts its ballots, it is useful to know what election outcomes are possible under different election procedures. This suggests mathematical and geometric treatments to be taught in the course. Oddly, the outcome of an election often says more about which election procedure was used, rather than the preferences of the voters! Besides politics, this phenomenon is present in other settings that we’ll consider which include: the Professional Golfers’ Association tour which determines the winner of tournaments under different scoring rules (e.g. stroke play and the modified Stableford system), the method used to determine rankings of teams in the NCAA College Football Coaches poll, and Major League Baseball MVP balloting.
Anytime one person’s decisions can affect what happens to another person, that situation can be modeled by game theory. That there is still a best decision to make that takes into account that others are trying to make their best decisions is, in part, why John F. Nash was awarded the Nobel Prize in Economics in 1994 (see A Beautiful Mind, 2002). Besides understanding and applying Nash’s results in settings as diverse as the baseball mind games between a pitcher and batter and bidding in auctions, we’ll examine how optimal play in a particular game is related to a proof that there are the same number of counting numbers {1, 2, 3, …} as there are positive fractions. We will also examine the GaleShapley algorithm, which is used, for example, to match physicians to residency programs and to match students to colleges (the college admissions problem). Lloyd S. Shapley and Alvin E. Roth were awarded the Nobel Prize in Economics in 2012 for their work on matching.
Roller Coaster Physics
Instructor: David Winn
What are the underlying principles that make roller coasters run? By studying the dynamics of roller coasters and other amusement park rides in the context of Newtonian physics and human physiology, we will begin to understand these complex structures. Students first review Newtonian mechanics, a = f/m in particular, with some handson experiments using airtables. This will then be followed by digitalvideo analysis of motion of some reallife objects (humans, cars, and toy rockets) and studentdevised roller coaster models.
Then, a field trip to Cedar Point Amusement Park (outside of the regularly scheduled weekend trip) where students, riding roller coasters and other rides, will provide real data for analysis back at UM. Students will carry portable data loggers and 3axis accelerometers to provide onsite, and later offsite, analysis of the motion and especially, the "gforces" experienced. The information collected will then be analyzed in terms of human evolution and physiology; we shall see why these limit the designs of rides.
In addition to exploring the physics of roller coasters, cuttingedge topics in physics will be introduced: high energy physics, nuclear astrophysics, condensedmatter theory, biophysics and medical physics. Students will then have a chance to see the physics in action by touring some of UM's research facilities. Students will have the opportunity to see scientists doing research at the Solid State Electronics Laboratory, the Michigan Ion Beam Laboratory, and the Center for Ultrafast Optical Science.
By the end of the twoweek session, students will gain insight and understanding in physics and take home the knowledge that physics is an exciting, reallife science that involves the objects and motions surrounding us on a daily basis.
Surface Chemistry
Instructor: Zhan Chen
This course will be divided into three units: applications, properties, and techniques. The first unit will introduce students to surface science that exists within the human body, surfaces in modern science and technology, and surfaces found in everyday life. Our bodies contain many different surfaces that are vital to our wellbeing. Surface reactions are responsible for protein interaction with cell surfaces, hormone receptor interactions, and ling function. Modern science has explored and designed surfaces for many applications: antibiofouling surfaces are being researched for marine vessels; high temperature resistant surfaces are important for space shuttles; and heterogeneous catalysis, studies by surface reactions, is important in industry and environmental preservation. The usefulness of many common items is determined by surface properties; contact lenses must remain wetted; while raincoats are deigned to be nonwetting; and coatings are applied to cookware for easy cleanup.
The second unit will examine the basic properties of surfaces. Lectures will focus on the concepts of hydrophobicity, friction, lubrication, adhesion, wearability, and biocompatibility. The instrumental methods used to study surfaces will be covered in the last unit. Traditional methods, such as contact angle measurements will be covered first. Then vacuum techniques will be examined. Finally, molecular level in situ techniques such as AFM and SFG will be covered, and students will be able to observe these techniques in the lab.
Multimedia PowerPoint presentations will be used for all lectures. By doing this, it's hoped to promote high school students' interest in surface science, chemistry, and science in general. A website introducing modern analytical chemistry in surface and interfacial sciences will be created.
The Physics of Magic and the Magic of Physics
Instructors: Fred Becchetti and Georg Raithel
Rabbits that vanish; objects that float in air defying gravity; a tiger that disappears and then reappears elsewhere; mind reading, telepathy and xray vision; objects that penetrate solid glass; steel rings that pass through each other: these are some of the amazing tricks of magic and magicians. Yet even more amazing phenomena are found in nature and the world of physics and physicists: matter than can vanish and reappear as energy and viceversa; subatomic particles that can penetrate steel; realistic 3D holographic illusions; objects that change their dimensions and clocks that speed up or slow down as they move (relativity); collapsed stars that trap their own light (black holes); xrays and lasers; fluids that flow uphill (liquid helium); materials without electrical resistance (superconductors.)
In this class students will first study the underlying physics of some classical magic tricks and learn to perform several of these (and create new ones.) The "magic" of corresponding (and real) physical phenomena will then be introduced and studied with handson, mindson experiments. Finally, we will visit a number of research laboratories where students can meet some of the "magicians" of physics  physics students and faculty  and observe experiments at the forefront of physics research.
To be or not to be? Biodiversity and Mass Extinctions through Deep Time
Instructor: Janice Pappas
Life on the 4.6 billion year old Earth began around 3.5 billion years ago. How did life on Earth come about? What kinds of life forms emerged? When did these forms come into existence? We will explore the fossil record and the events that shaped the biological world as we know it today. We will study life on Earth from the perspective of biodiversity and phylogenetic trees of life. We will focus on the Ediacaran period, the Cambrian explosion, and the Mesozoic Marine Revolution as times of great biodiversity. We will explore the five major mass extinction events that occurred at the OrdovicianSilurian, the Late Devonian, the PermianTriassic, the TriassicJurassic, and the CretaceousPaleogene. Why did life on Earth vanish in such large quantities at these events? How did this happen? What happened to biodiversity in the aftermath? These are just some of the many questions we might address for each extinction event.
Our journey begins with an overview of what Earth looked like at the time life first appeared from a geological and climatological perspective. We will advance toward studying various organisms and biodiversity over time. We will be haltingly taken aback at the catastrophic consequences of mass extinction. We will emerge from such events and take stock of biodiversity to the present. We may even have time to consider fossils and their importance in astrobiology.
Our studies will include field trips to the University of Michigan Exhibits Museum. Students will be required to do research covering biodiversity with respect to an extinction event. Students will work in groups to create a scientific poster of their research findings. Student research will be presented in class.
Prerequisites: Having had a science course is helpful, but not necessary. Just bring your enthusiasm to learn about the history of life on Earth.
Deep Sea Monsters or Docile Dwellers? The Biology of the Oceans.
Instructor: Janice Pappas
The oceans are vast, majestic bodies of water that harbor a myriad of life forms. The Antarctic, Arctic, Atlantic, Indian, and Pacific Oceans cover 70% of the Earth’s surface and have 80 to 99% of all life on Earth. Only 5% of our oceans have been explored, so the majority of oceanic life has yet to be discovered.
Organisms of all sizes are found throughout the oceans. We will look at examples from diatoms to viper fish to vampire squid to whales. We will examine particular kinds of organisms such as keystone species, bioluminescent animals, and organisms that are able to live in extreme environments.
We will explore marine food webs as a way to understand interdependence among the oceans’ organisms. How do environmental conditions influence what happens to the organisms in the oceans? If an animal goes extinct, what will happen to other organisms in a marine food web? These are just a couple of the many questions that we might address.
Our adventure will begin with a general overview of the physical, chemical and geological aspects of the oceans and sails on to details on the oceans’ biological inhabitants. We will navigate our way to understanding organism interactions through marine food webs. We will dock at an overall assessment of the oceans—where we have come from and where we are going at the present.
Our studies will include microscopy and a field trip to the University of Michigan Exhibits Museum. Students will be required to do research with a focus on a marine food web. Students will work in groups to create a scientific poster of their research findings. Student research will be presented in class.
Prerequisites: having had a science course is helpful, but not necessary. Just bring your interest in learning about our oceans.
Dissecting Life: Human Anatomy and Physiology
Instructor: Glenn Fox
Dissecting Life will lead students through the complexities and wonder of the human body. Lecture sessions will cover human anatomy and physiology in detail. Students will gain an understanding of biology, biochemistry, histology, and use these as a foundation to study human form and function.
Laboratory sessions will consist of firsthand dissections of a variety of exemplar organisms: lamprey, sharks, cats, etc. Students may also tour the University of Michigan Medical School's Plastination and Gross Anatomy Laboratories where they may observe human dissections.
Explorations of a Field Biologist
Instructor: Sheila Schueller
There are so many different kinds of living organisms in this world, and every organism interacts with its physical environment and with other organisms. Understanding this mass of interactions and how humans are affecting them is a mindboggling endeavor! We cannot do this unless we at times set aside our computers and beakers, and instead, get out of the lab and classroom and into the field, which is what we will do in THIS course.
Through our explorations of grasslands, forests, and wetlands of southeastern Michigan, you will learn many natural history facts (from identifying a turkey vulture to learning how mushrooms relate to tree health). You will also practice all the steps of doing science in the field, including making careful observations, testing a hypothesis, sampling and measuring, and analyzing and presenting results.
We will address question such as: How do field mice decide where to eat? Are aquatic insects affected by water chemistry? Does flower shape matter to bees? How do lakes turn into forests? Learning how to observe nature with patience and an inquisitive mind, and then testing your ideas about what you observe will allow you, long after this class, to discover many more things about nature, even your own back yard. Most days will be allday field trips, including handson experience in restoration ecology. Towards the end of the course you will design, carry out, and present your own research project.
Fibonacci Numbers
Instructor: Mel Hochster
The Fibonacci numbers are the elements of the sequence 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55… where every term is simply the sum of the two preceding terms. This sequence, which was originally proposed as describing the reproduction of rabbits, occurs in astonishingly many contexts in nature. It will be used as a starting point for the exploration of some very substantial mathematical ideas: recursive methods, modular arithmetic, and other ideas from number theory, and even the notion of a limit: the ratios of successive terms (e.g. 13/8, 21/13. 55/34…) approach the golden mean, already considered by the ancient Greeks, which yields what may be the most aesthetically pleasing dimensions for a rectangle.
As a byproduct of our studies, we will be able to explain how people can test certain, very special but immensely large numbers, for being prime. We'll also consider several games and puzzles whose analysis leads to the same circle of ideas, developing them further and reinforcing the motivations for their study.
Graph Theory
Instructor: Doug Shaw
Ignore your previous knowledge of algebra, geometry, and even arithmetic! Start fresh with a simple concept: Take a collection of points, called vertices, and connect some of them with lines called edges. It doesn't matter where you draw the vertices or how you draw the lines  all that matters is that two vertices are either related, or not. We call that a “graph” and you’ve taken the first step on the Graph Theory road! Graphs turn up in physics, biology, computer science, communications networks, linguistics, chemistry, sociology, mathematics… you name it!
In this course we will discuss properties that graphs may or may not have, hunt for types of graphs that may or may not exist, learn about the silliest theorem in mathematics, and the most depressing theorem in mathematics, learn how to come up with good algorithms, model reality, and construct some mathematical proofs. We will go over fundamental results in the field, and also some results that were only proved in the last year or so! And, of course, we will present plenty of currently unsolved problems for you solve and publish when you get home!
Human Identification: Forensic Anthropology Methods
Instructor: Kathleen Alsup
Forensic anthropology methods are used to aid in human identification with skeletal remains. Applications of forensic anthropology lie in the criminal justice system and mass disaster response. In this course, we will address questions such as: What are important differences between male and female skeletons? Utilizing skeletal remains, how would you tell the difference between a 20year old and an 80year old? How do you distinguish between blunt force and sharp force trauma on the skull?
In this handson, laboratorybased course, you will be become familiar with human osteology (the study of bones] and bone biology. Through our exploration of forensic and biological anthropology methods, you will learn how to develop a biological profile [estimates of age at death, sex, ancestry and stature], assess manner of death, estimate postmortem interval, investigate skeletal trauma and pathology, and provide evidence for a positive identification from skeletal remains. Additionally, we will explore various forensic recovery techniques as they apply to an outdoor complex, including various mapping techniques. Towards the end of the course, you will work in small groups in a mock recovery of human remains and analyze the case utilizing the forensic anthropological methods learned throughout the course.
Mathematics and Music Theory
Instructor: Lon Mitchell
Mathematicians can create complex and beautiful theorems from relatively basic assumptions, while Music Theorists often try to identify basic patterns and “rules” in complex and beautiful music. In this course, we will explore some of the recent attempts to meet in the middle, connecting mathematical patterns and structures to music from the ancient to the modern.
In Mathematics, we will explore topics such as group theory, graph theory, geometry, and metric spaces, encountering some of the most important structures in the modern discipline. Fundamental results of these areas will be discussed, and students will construct and explore examples and related patterns.
In Music Theory, we will take existing music by composers such as Bach and Beethoven and use mathematical structures to provide a possible explanation of what they were thinking as they composed. In addition, we will investigate the techniques of modern composers such as Arnold Schoenberg who advocated composition based on prescribed axioms. Students will be given the chance to write music using these different techniques.
Although we will use the modern (Western) twelvetone scale as a reference, our explorations will take us into discussions of tuning, temperament, and the physics of sound. We will investigate mathematical theories of what makes the best scale, how some of those scales occur in the music of other cultures, and how modern composers have engineered exotic scales to suit their aesthetics.
Software allowing students to experiment with creating their own musical systems will be provided.
Prospective students should have a good command of (highschool) algebra and experience with reading music in some form.
Mathematics and the Internet
Instructor: Mark Conger
How can gigabytes of information move over unreliable airwaves using unreliable signaling, and arrive perfectly intact? How can I have secure communication with a website run by a person I've never met? How can a large image or sound file be transferred quickly? Why is Google so good at finding what I'm looking for? How do computers work, anyway?
The answers to all these questions involve applications of abstract mathematics. In Mathematics and the Internet, we'll develop the math on its own, but also show how it is essential to making the Internet operate as it does. Our journey will take us through logic, probability, group theory, finite fields, calculus, number theory, and any other areas of math that might come up. We'll apply our results to coding theory, cryptography, search engines, and compression. We'll also spend several days building primitive computers out of transistors, logic gates, and lots of wire. If all goes well, we'll connect them to the Internet!
Mathematics of Cryptography
Instructor: Anton Lukyanenko
Ever since humans first developed the ability to write there has been an ongoing battle between codemakers and codebreakers. The armies of ancient Sparta and Rome both used ciphers to relay secret battle plans, and the ancient Mesopotamians developed encryption techniques in order to protect commercially valuable techniques for glazing pottery. From a modern perspective, the codes used by the ancients are laughably insecure. Indeed, much of what made them secure was that they were being used during a period when most people were illiterate.
Because of the advent of computers, codemakers today need to use far more sophisticated techniques in order to create secure codes. Many of these techniques are mathematical in nature. One of the cryptography systems that we will discuss in this class is called RSA and is used to ensure the security of your credit card information when you make a purchase on the internet. We'll see that at its heart, what makes the RSA system secure is that it is very hard to factor a big number. The numbers used in the RSA system are actually so big that factoring them would take you millions of years. Even if you were using a supercomputer!
This class will give an historical introduction to the mathematics of cryptography, beginning with codes used by the Roman legions and building up to the RSA cryptography system discussed above. What will really make the class unique is that there won't be any lecturing. You will discover the mathematics of cryptography by working on problems and sharing your solutions with your classmates.
Organic Chemistry 101: Orgo Boot Camp
Instructor: Kathleen Nolta
This course will introduce students to the techniques and concepts taught in the first term of organic chemistry at the University of Michigan. The emphasis will be on exploring concepts through problem solving (there will be lots of practice problems to do!), and the students will even have an opportunity to take examinations given to college students. This minicourse will introduce students to principles of nomenclature, as well as the structural organization of molecules including connectivity, stereochemistry, and conformational chemistry. We will also explore the complexity of curved arrow mechanisms for proton chemistry, substitution reactions, and electrophilic additions. Students will be able to explore the chemistry in various laboratory applications. By focusing on the concepts and trying some of the techniques, students will gain a better understanding of what organic chemistry is and how to enjoy it.
Predicting & Forecasting Natural Hazards
Instructor: Eric Hetland
Natural disasters have resulted in almost $4 trillion in losses and over a billion fatalities in the past 35 years. Naturally occurring events, such as earthquakes, volcanic eruptions, tsunamis, landslides, floods, hurricanes, tornadoes, and extreme temperatures, occur every year and affect nearly every part of the Earth. Most of these natural hazards involve a relatively sudden release of a large amount of energy over a small spatial area – when this concentration of energy and society intersect, disaster results. Considerable effort has gone into our ability to estimate our risk from natural hazards, as well as forecast hazards. Forecasting of hazards is done both over long time periods, and time periods over the life of the hazard. For example, forecasts for hurricane activity are made as early as a year before a hurricane season, while once a hurricane forms the path of that hurricane is forecast and adjusted throughout the life of the hurricane. A complicating factor when discussing natural hazards is that the number and cost of natural disasters has been increasing over the last few decades. This may be due to natural hazards increasing in number, size, or extent, or may be due to an increase in vulnerability of modern society.
In this course, we will explore estimating risk of, predicting, and forecasting natural hazards, including earthquakes, hurricanes, tornadoes, and extreme temperatures. Our focus will be on how the dynamic complexities of natural hazards makes forecasting hazard possible, but also hinder our ability to predict those hazards. We will discuss the scientific assessment of precursors, as well as the evidence/arguments that the frequency or severity of hazards are increasing over just the past few decades. We will cover fundamental mathematics related to estimation and forecasting, including probabilistic inference, chaos, complexity, random walks (e.g., Markov chains), and predictive filtering. The majority of the handson exercises will be computerbased. Earth science knowledge is not required.
Surviving in an Uncertain World: Human Adaptive Response to Climate Change
Instructors: John Kingston and Laura MacLatchy
Climate change is not a distant problem. It’s happening now and is having real consequences for human populations worldwide, affecting foodproducing economies, shifting disease demographics, and resulting in loss of biodiversity. Despite these realizations, it is important to appreciate that climate and environmental change have always been part of the human landscape and much of the adaptability and flexibility that characterize humans may have been shaped by these fluctuations. In this course we’ll unpack the concept of climate change and explore how our evolutionary trajectory has been a response to ecological volatility and uncertainty as well as contemplate future outcomes.
Human Identification: Forensic Anthropology Methods (Session 3)
Instructor: Kathleen Alsup
Forensic anthropology methods are used to aid in human identification with skeletal remains. Applications of forensic anthropology lie in the criminal justice system and mass disaster response. In this course, we will address questions such as: What are important differences between male and female skeletons? Utilizing skeletal remains, how would you tell the difference between a 20year old and an 80year old? How do you distinguish between blunt force and sharp force trauma on the skull?
In this handson, laboratorybased course, you will be become familiar with human osteology (the study of bones] and bone biology. Through our exploration of forensic and biological anthropology methods, you will learn how to develop a biological profile [estimates of age at death, sex, ancestry and stature], assess manner of death, estimate postmortem interval, investigate skeletal trauma and pathology, and provide evidence for a positive identification from skeletal remains. Additionally, we will explore various forensic recovery techniques as they apply to an outdoor complex, including various mapping techniques. Towards the end of the course, you will work in small groups in a mock recovery of human remains and analyze the case utilizing the forensic anthropological methods learned throughout the course.
Surviving in an Uncertain World: Human Adaptive Response to Climate Change (Session 3)
Instructors: John Kingston and Laura MacLatchy
Climate change is not a distant problem. It’s happening now and is having real consequences for human populations worldwide, affecting foodproducing economies, shifting disease demographics, and resulting in loss of biodiversity. Despite these realizations, it is important to appreciate that climate and environmental change have always been part of the human landscape and much of the adaptability and flexibility that characterize humans may have been shaped by these fluctuations. In this course we’ll unpack the concept of climate change and explore how our evolutionary trajectory has been a response to ecological volatility and uncertainty as well as contemplate future outcomes.
Art and Mathematics (Session 1)
Instructor: Martin Strauss
With just a little historical revisionism, we can say that Art has
provided inspiration for many fields within Mathematics. Conversely,
Mathematics gives techniques for analyzing, appreciating, and even
creating Art, as well as the basis for gallery design, digital
cameras, and processing of images. In this class we will explore the
Mathematics in great works of Art as well as folk art, as a way of
studying and illustrating central mathematical concepts in familiar
and pleasing material. And we'll make our own art, by drawing,
painting, folding origami papers, and more.
Major topics include Projection, Symmetry, Wave Behavior, and
Distortion. Projection includes the depiction of threedimensional
objects in two dimensions. What mathematical properties must be lost,
and what can be preserved? How does an artwork evoke the feeling of
threedimensional space? We'll study perspective, depictions of
globes by maps, and the role of curvature. Turning to symmetry, we'll
study rotational and reflective symmetry that arise in tiling and
other art and math. We'll study more generalized symmetry like
scaling and selfsimilarity that occurs in fractals as well as every
selfportrait, and is central to mathematical concepts of dimension
and unprovability. On the other hand, we'll look at how works of
digital and pointilist art are made up of fine pixels with a character
very different from the work at coarser scalesit is not selfsimilar.
Describing light as waves and color as wavelength at once explains how
mirrors, lenses, and prisms work and explains some uses of light and
color in art. Finally, we ask about distorting fabrics and strings,
and ask about the roles of cutting, gluing, and of stretching without
cutting or gluing. Is a distorted human figure still recognizable, as
long as it has the right number of organs and limbs, connected
properly?
Background in Math and interest in Art suggested. No artistic talent
is necessary, though artistically talented students are encouraged to
bring art supplies if they are inexpensive and easily transportable.
Mathematics and Music Theory (Session 3)
Instructor: Lon Mitchell
Mathematicians can create complex and beautiful theorems from relatively basic assumptions, while Music Theorists often try to identify basic patterns and “rules” in complex and beautiful music. In this course, we will explore some of the recent attempts to meet in the middle, connecting mathematical patterns and structures to music from the ancient to the modern.
In Mathematics, we will explore topics such as group theory, graph theory, geometry, and metric spaces, encountering some of the most important structures in the modern discipline. Fundamental results of these areas will be discussed, and students will construct and explore examples and related patterns.
In Music Theory, we will take existing music by composers such as Bach and Beethoven and use mathematical structures to provide a possible explanation of what they were thinking as they composed. In addition, we will investigate the techniques of modern composers such as Arnold Schoenberg who advocated composition based on prescribed axioms. Students will be given the chance to write music using these different techniques.
Although we will use the modern (Western) twelvetone scale as a reference, our explorations will take us into discussions of tuning, temperament, and the physics of sound. We will investigate mathematical theories of what makes the best scale, how some of those scales occur in the music of other cultures, and how modern composers have engineered exotic scales to suit their aesthetics.
Software allowing students to experiment with creating their own musical systems will be provided.
Prospective students should have a good command of (highschool) algebra and experience with reading music in some form.
Climbing the Distance Ladder to the Big Bang: How Astronomers Survey the Universe (Session 2)
Instructor: Dragan Huterer
The furthest objects that astronomers can observe are so distant that their light set out when the Universe was only 800 million years old, and has been traveling to us for about 13 billion years – most of the age of the Universe. Even the Sun's neighborhood – the local part of our Galaxy, where astronomers have successfully searched for planets around other stars – extends to hundreds of light years. How do we measure the distance to such remote objects?
Certainly not in a single step! Astronomers construct the socalled “Distance Ladder,” finding the distance to nearby objects, thus enabling those bodies to be understood and used as probes of yet more distant regions. The first steps in the ladder uses radar ranging to get the distance to the nearby planets and the Sun; and 'triangulation' to get the distances to the nearest stars. Those in turn are used to obtain distances to other stars in our Milky Way Galaxy, stars in other galaxies, and out to the furthest reaches of what is observable.
This class will explore the steps in this ladder, using lectures, discussions, field trips, demonstrations, and computer laboratory exercises. Students will learn basic computer programming for a project to model the effects of gravity, and they will get handson experience of using a small radio telescope to map the the rotation speed of the Milky Way and measure the influence of its dark matter. We will cover concepts involving space, time, and matter that go far beyond the distance ladder, and involve some of the most fascinating mysteries in cosmology and astrophysics: What is it like inside a black hole? What is the Dark Matter? What is the Dark Energy that makes the Universe expand faster and faster? Is there other life in the Universe?
Deep Sea Monsters or Docile Dwellers? The Biology of the Oceans. (Session 3)
Instructor: Janice Pappas
The oceans are vast, majestic bodies of water that harbor a myriad of life forms. The Antarctic, Arctic, Atlantic, Indian, and Pacific Oceans cover 70% of the Earth’s surface and have 80 to 99% of all life on Earth. Only 5% of our oceans have been explored, so the majority of oceanic life has yet to be discovered.
Organisms of all sizes are found throughout the oceans. We will look at examples from diatoms to viper fish to vampire squid to whales. We will examine particular kinds of organisms such as keystone species, bioluminescent animals, and organisms that are able to live in extreme environments.
We will explore marine food webs as a way to understand interdependence among the oceans’ organisms. How do environmental conditions influence what happens to the organisms in the oceans? If an animal goes extinct, what will happen to other organisms in a marine food web? These are just a couple of the many questions that we might address.
Our adventure will begin with a general overview of the physical, chemical and geological aspects of the oceans and sails on to details on the oceans’ biological inhabitants. We will navigate our way to understanding organism interactions through marine food webs. We will dock at an overall assessment of the oceans—where we have come from and where we are going at the present.
Our studies will include microscopy and a field trip to the University of Michigan Exhibits Museum. Students will be required to do research with a focus on a marine food web. Students will work in groups to create a scientific poster of their research findings. Student research will be presented in class.
Prerequisites: having had a science course is helpful, but not necessary. Just bring your interest in learning about our oceans.
Dissecting Life: Human Anatomy and Physiology (Session 1, Session 2, Session 3)
Instructor: Glenn Fox
Dissecting Life will lead students through the complexities and wonder of the human body. Lecture sessions will cover human anatomy and physiology in detail. Students will gain an understanding of biology, biochemistry, histology, and use these as a foundation to study human form and function.
Laboratory sessions will consist of firsthand dissections of a variety of exemplar organisms: lamprey, sharks, cats, etc. Students may also tour the University of Michigan Medical School's Plastination and Gross Anatomy Laboratories where they may observe human dissections.
Explorations of a Field Biologist (Session 2, Session 3)
Instructor: Sheila Schueller
There are so many different kinds of living organisms in this world, and every organism interacts with its physical environment and with other organisms. Understanding this mass of interactions and how humans are affecting them is a mindboggling endeavor! We cannot do this unless we at times set aside our computers and beakers, and instead, get out of the lab and classroom and into the field, which is what we will do in THIS course.
Through our explorations of grasslands, forests, and wetlands of southeastern Michigan, you will learn many natural history facts (from identifying a turkey vulture to learning how mushrooms relate to tree health). You will also practice all the steps of doing science in the field, including making careful observations, testing a hypothesis, sampling and measuring, and analyzing and presenting results.
We will address question such as: How do field mice decide where to eat? Are aquatic insects affected by water chemistry? Does flower shape matter to bees? How do lakes turn into forests? Learning how to observe nature with patience and an inquisitive mind, and then testing your ideas about what you observe will allow you, long after this class, to discover many more things about nature, even your own back yard. Most days will be allday field trips, including handson experience in restoration ecology. Towards the end of the course you will design, carry out, and present your own research project.
Life, Death and Change: Landscapes and Human Impact (Session 2)
Instructor: David Michener
You’ll never see the same world quite the same way after this course – which is important if you want to make a difference with your life. All environmental studies presume a landscape – yet what seems to be a simple landscape is often far from uniform or stable. A great deal of information critical to anyone entering the “green” sciences can be detected for analysis – including factors that may fundamentally control species diversity, habitat richness, and animal (let alone human) behavior. Resolving human from nonhuman agency is an engaging and important challenge, too – one scientists and “green professionals” grapple with repeatedly. This outdoor class immerses students in realworld landscapes, ranging from the nearlypristine to the highly humanized, to solve problems which may initially appear impossible to address. You can!
Your critical thinking skills are essential rather than prior biological course and field work. Come prepared to look, measure, analyze, discus and learn how the interaction of plants, soils, climate and time (and humans) influences landscape development. Develop basic skills in plant recognition and identification – skills that you can transfer to other terrestrial communities. Address questions about the current vegetation, its stability over time and its future prospects. Gain practical insights into the realities of biological conservation as we address how we can manage species and landscapes for future generations. By the end you’ll have a conceptual skill set that helps you assess how stable and disturbed are the “natural” areas are near your home – and prepares you to put instructors on the spot in college classes to come.
Making it in the "Real World"  Understanding the Physiology Behind Organism Behavior (Session 1)
Instructor: Larissa Sano
An important consideration in studying the biology of life is to understand the ways in which organisms interact with their physical environment. As humans, we are largely able to control many aspects of our physical environment to ensure our comfort and well being  for example, we build insulated homes, use central heating and air conditioning, and shop at a local grocery store. Most other animals, however, have to deal directly with the elements.
In order to do this, animals have developed unusual and sometimes bizarre strategies to help them survive. To understand these survival strategies and to link them with an animal’s physiology, we will combine field observations with laboratory studies and data analysis. Some of the questions we will address include: How does water temperature affect where we find fish in a river? What are the energy requirements of a bird, and how can they forage in a forest to meet their energy needs? and Do insects really fly faster when it is warmer outside? Our ultimate goal will be to understand what it takes for organisms to survive in the “real world.”
Although most of our days will be spent outside, hiking through forests, wading through rivers, and exploring ponds, we will also make time to conduct laboratory experiments, analyze our data, and interpret our results. Towards the end of the course you will design, carry out, and present your own research project.
Mathematical Modeling in Biology (Session 1)
Instructors: Trachette Jackson and Patrick Nelson
Mathematical biology is a relatively new area of applied mathematics and is growing with phenomenal speed. For the mathematician, biology opens up new and exciting areas of study, while for the biologist, mathematical modeling offers another powerful research tool commensurate with a new instrumental laboratory technique. Mathematical biologists typically investigate problems in diverse and exciting areas such as the topology of DNA, cell physiology, the study of infectious diseases, population ecology, neuroscience, tumor growth and treatment strategies, and organ development and embryology.
This course will be a venture into the field of mathematical modeling in the biomedical sciences. Interactive lectures, group projects, computer demonstrations, and laboratory visits will help introduce some of the fundamentals of mathematical modeling and its usefulness in biology, physiology and medicine.
For example, the cell division cycle is a sequence of regulated events which describes the passage of a single cell from birth to division. There is an elaborate cascade of molecular interactions that function as the mitotic clock and ensures that the sequential changes that take place in a dividing cell take place on schedule. What happens when the mitotic clock speeds up or simply stops ticking? These kinds of malfunctions can lead to cancer and mathematical modeling can help predict under what conditions a small population of cells with a compromised mitotic clock can result in a fully developed tumor. This course will study many interesting problems in cell biology, physiology, and immunology.
AstroTurf, Diapers, Kevlar and More: Explore the Materials in the World Around you! (Session 1)
Instructor: Anne McNeil
Ever wonder what a raincoat is made out of? Or why Spandex is stretchy? Our course on polymers, the molecules that make up plastics and elastics, holds these answers and more! Make Nylon and participate in laboratory research where you will gain the skills of a materials chemist by making polymers yourself. Learn how polymers have come to make up much of the material you interact with on a daily basis from contact lenses to golf balls. Share your newly gained knowledge with the world by adding content to Wikipedia. Join us on this journey into the world of materials.
Catalysis, Solar Energy and Green Chemical Synthesis (Session 1, Session 2)
Instructor: Corey Stephenson
"The chemist who designs and completes an original and esthetically pleasing multistep synthesis is like the composer, artist or poet who, with great individuality, fashions new forms of beauty from the interplay of mind and spirit."
E.J. Corey, Nobel Laureate
Prior to Friedrich Wöhler’s 1828 synthesis of urea, organic (carboncontaining) matter from living organisms was believed to contain a “vital force” that distinguished it from inorganic material. The discovery that organic molecules can be manipulated at the hands of scientists is considered by many the birth of “organic chemistry”: the study of the structure, properties, and reactions of carboncontaining matter. Organic matter is the foundation of life as we know it, and therefore a fundamental understanding of reactivity at a molecular level is essential to all life sciences. In this class we will survey monumental discoveries in this field over the past two centuries and the technological developments that have enabled them.
“Catalysis, Solar Energy, and Green Chemical Synthesis” will provide a fun and intellectually stimulating handson experience that instills a historical appreciation for the giants whose trials and tribulations have enabled our modern understanding of chemistry and biology. Students will learn modern laboratory techniques including how to set up, monitor, and purify chemical reactions, and most importantly, how to determine what they made! Experiments include the synthesis of biomolecules using some of the most transformative reactions of the 20th century and exposure to modern synthetic techniques, such as the use of metal complexes that absorb visible light to catalyze chemical reactions, an important development in the “Green Science” movement. Finally, industrial applications of chemistry such as polymer synthesis and construction of photovoltaic devices will be performed. Daily experiments will be supplemented with exciting demonstrations by the graduate student instructors.
Organic Chemistry 101: Orgo Boot Camp (Session 3)
Instructor: Kathleen Nolta
This course will introduce students to the techniques and concepts taught in the first term of organic chemistry at the University of Michigan. The emphasis will be on exploring concepts through problem solving (there will be lots of practice problems to do!), and the students will even have an opportunity to take examinations given to college students. This minicourse will introduce students to principles of nomenclature, as well as the structural organization of molecules including connectivity, stereochemistry, and conformational chemistry. We will also explore the complexity of curved arrow mechanisms for proton chemistry, substitution reactions, and electrophilic additions. Students will be able to explore the chemistry in various laboratory applications. By focusing on the concepts and trying some of the techniques, students will gain a better understanding of what organic chemistry is and how to enjoy it.
Surface Chemistry (Session 2)
Instructor: Zhan Chen
This course will be divided into three units: applications, properties, and techniques. The first unit will introduce students to surface science that exists within the human body, surfaces in modern science and technology, and surfaces found in everyday life. Our bodies contain many different surfaces that are vital to our wellbeing. Surface reactions are responsible for protein interaction with cell surfaces, hormone receptor interactions, and ling function. Modern science has explored and designed surfaces for many applications: antibiofouling surfaces are being researched for marine vessels; high temperature resistant surfaces are important for space shuttles; and heterogeneous catalysis, studies by surface reactions, is important in industry and environmental preservation. The usefulness of many common items is determined by surface properties; contact lenses must remain wetted; while raincoats are deigned to be nonwetting; and coatings are applied to cookware for easy cleanup.
The second unit will examine the basic properties of surfaces. Lectures will focus on the concepts of hydrophobicity, friction, lubrication, adhesion, wearability, and biocompatibility. The instrumental methods used to study surfaces will be covered in the last unit. Traditional methods, such as contact angle measurements will be covered first. Then vacuum techniques will be examined. Finally, molecular level in situ techniques such as AFM and SFG will be covered, and students will be able to observe these techniques in the lab.
Multimedia PowerPoint presentations will be used for all lectures. By doing this, it's hoped to promote high school students' interest in surface science, chemistry, and science in general. A website introducing modern analytical chemistry in surface and interfacial sciences will be created.
Discrete Dynamical Systems (Session 2)
Instructor: Alejandro Uribe
In many areas of Science one is interested in modeling how a particular "something", referred to as a "system", changes with time. Such a model is called a dynamical system. Some examples are: A population of rabbits in a given environment, a billiard ball bouncing around a given billiard table, or the price of a commodity given supply and demand functions. In this course we will concentrate on models where the time is discrete, that is, the values of time are multiples of some unit. In the simplest models the evolution is given by an equation, specifying the state of the system at time n in terms of the state at time n1. Discretetime dynamical systems can be studied graphically, algebraically and numerically, without having to use a lot of calculus.
In this course we will study some of the many fascinating phenomena that dynamical systems can exhibit. We will start by developing a language that includes the concepts of phase space, initial condition, orbit, periodic orbit and fixed point. We will then develop the notions of stability and instability, and attractor. We will see that some systems are "integrable" or very regular, and at the opposite extreme we will try to formulate a precise definition of what a chaotic system is.
The course will include some theory (which will lead us to the idea of limit, and deep questions about the structure of the real numbers), the study of some particular models, and computer experimentation.
Mathematics and the Internet (Session 3)
Instructor: Mark Conger
How can gigabytes of information move over unreliable airwaves using unreliable signaling, and arrive perfectly intact? How can I have secure communication with a website run by a person I've never met? How can a large image or sound file be transferred quickly? Why is Google so good at finding what I'm looking for? How do computers work, anyway?
The answers to all these questions involve applications of abstract mathematics. In Mathematics and the Internet, we'll develop the math on its own, but also show how it is essential to making the Internet operate as it does. Our journey will take us through logic, probability, group theory, finite fields, calculus, number theory, and any other areas of math that might come up. We'll apply our results to coding theory, cryptography, search engines, and compression. We'll also spend several days building primitive computers out of transistors, logic gates, and lots of wire. If all goes well, we'll connect them to the Internet!
Art and Mathematics (Session 1)
Instructor: Martin Strauss
With just a little historical revisionism, we can say that Art has
provided inspiration for many fields within Mathematics. Conversely,
Mathematics gives techniques for analyzing, appreciating, and even
creating Art, as well as the basis for gallery design, digital
cameras, and processing of images. In this class we will explore the
Mathematics in great works of Art as well as folk art, as a way of
studying and illustrating central mathematical concepts in familiar
and pleasing material. And we'll make our own art, by drawing,
painting, folding origami papers, and more.
Major topics include Projection, Symmetry, Wave Behavior, and
Distortion. Projection includes the depiction of threedimensional
objects in two dimensions. What mathematical properties must be lost,
and what can be preserved? How does an artwork evoke the feeling of
threedimensional space? We'll study perspective, depictions of
globes by maps, and the role of curvature. Turning to symmetry, we'll
study rotational and reflective symmetry that arise in tiling and
other art and math. We'll study more generalized symmetry like
scaling and selfsimilarity that occurs in fractals as well as every
selfportrait, and is central to mathematical concepts of dimension
and unprovability. On the other hand, we'll look at how works of
digital and pointilist art are made up of fine pixels with a character
very different from the work at coarser scalesit is not selfsimilar.
Describing light as waves and color as wavelength at once explains how
mirrors, lenses, and prisms work and explains some uses of light and
color in art. Finally, we ask about distorting fabrics and strings,
and ask about the roles of cutting, gluing, and of stretching without
cutting or gluing. Is a distorted human figure still recognizable, as
long as it has the right number of organs and limbs, connected
properly?
Background in Math and interest in Art suggested. No artistic talent
is necessary, though artistically talented students are encouraged to
bring art supplies if they are inexpensive and easily transportable.
Discrete Dynamical Systems (Session 2)
Instructor: Alejandro Uribe
In many areas of Science one is interested in modeling how a particular "something", referred to as a "system", changes with time. Such a model is called a dynamical system. Some examples are: A population of rabbits in a given environment, a billiard ball bouncing around a given billiard table, or the price of a commodity given supply and demand functions. In this course we will concentrate on models where the time is discrete, that is, the values of time are multiples of some unit. In the simplest models the evolution is given by an equation, specifying the state of the system at time n in terms of the state at time n1. Discretetime dynamical systems can be studied graphically, algebraically and numerically, without having to use a lot of calculus.
In this course we will study some of the many fascinating phenomena that dynamical systems can exhibit. We will start by developing a language that includes the concepts of phase space, initial condition, orbit, periodic orbit and fixed point. We will then develop the notions of stability and instability, and attractor. We will see that some systems are "integrable" or very regular, and at the opposite extreme we will try to formulate a precise definition of what a chaotic system is.
The course will include some theory (which will lead us to the idea of limit, and deep questions about the structure of the real numbers), the study of some particular models, and computer experimentation.
Fibonacci Numbers (Session 1, Session 3)
Instructor: Mel Hochster
The Fibonacci numbers are the elements of the sequence 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55… where every term is simply the sum of the two preceding terms. This sequence, which was originally proposed as describing the reproduction of rabbits, occurs in astonishingly many contexts in nature. It will be used as a starting point for the exploration of some very substantial mathematical ideas: recursive methods, modular arithmetic, and other ideas from number theory, and even the notion of a limit: the ratios of successive terms (e.g. 13/8, 21/13. 55/34…) approach the golden mean, already considered by the ancient Greeks, which yields what may be the most aesthetically pleasing dimensions for a rectangle.
As a byproduct of our studies, we will be able to explain how people can test certain, very special but immensely large numbers, for being prime. We'll also consider several games and puzzles whose analysis leads to the same circle of ideas, developing them further and reinforcing the motivations for their study.
Graph Theory (Session 2, Session 3)
Instructor: Doug Shaw
Ignore your previous knowledge of algebra, geometry, and even arithmetic! Start fresh with a simple concept: Take a collection of points, called vertices, and connect some of them with lines called edges. It doesn't matter where you draw the vertices or how you draw the lines  all that matters is that two vertices are either related, or not. We call that a “graph” and you’ve taken the first step on the Graph Theory road! Graphs turn up in physics, biology, computer science, communications networks, linguistics, chemistry, sociology, mathematics… you name it!
In this course we will discuss properties that graphs may or may not have, hunt for types of graphs that may or may not exist, learn about the silliest theorem in mathematics, and the most depressing theorem in mathematics, learn how to come up with good algorithms, model reality, and construct some mathematical proofs. We will go over fundamental results in the field, and also some results that were only proved in the last year or so! And, of course, we will present plenty of currently unsolved problems for you solve and publish when you get home!
Hex and the 4 Cs (Session 1)
Instructor: Stephen DeBacker
After a very long night of homework, you finally finish your math assignment. While doublechecking your work, you realize that you have done problems from page 221, not page 212 as your teacher requested. In disgust, you rip the paper out of your notebook, wad it up, and toss it back down on your notebook. Too frustrated to begin your assignment anew, your mind begins to wander. You wonder: Is there a point in the wadded up paper that lies exactly above the location from which it started?
After you pour your parent's morning cup of Joe, the coffee comes to rest while you sleepily (because of the whole homework thing) search in the fridge for the cream. After adding and stirring the cream into the cup, you watch the pretty patterns made by the swirling coffee and cream as the contents come to rest. You wonder: Is there a point in the coffee that lies at the same point both before and after the cream was stirred in?
We shall use mathematics to model and answer the above questions. Initially, the above questions will motivate our study of four fundamental concepts in mathematics, all of which begin with the letter C: continuity (what sorts of wadding/stirring are allowed), completeness (what if our paper/coffee has “gaps”), compactness, and connectedness. Interestingly, these are also the concepts one needs in order to rigorously understand why Calculus works. Our modeling will lead us to the Brouwer fixedpoint theorem; a very nice topological result.
To show that the Brouwer fixedpoint theorem is true, we shall also learn about the game of Hex. The game of Hex is an easy to describe board game for two players (Google "Hex game" to find a description). The game has many interesting features. For example: one of the two players must win, the first player to move should (theoretically) win, and nobody knows a strategy to guarantee that the first player wins. We will explore the mathematics required to understand why every game of Hex has a winner.
Finally, we shall stitch all of the above together by showing that the fact that there are no ties in Hex implies that there is a point in your parent’s cup of Joe which lies at the same point both before and after the cream was stirred in.
Mathematical Modeling in Biology (Session 1)
Instructors: Trachette Jackson and Patrick Nelson
Mathematical biology is a relatively new area of applied mathematics and is growing with phenomenal speed. For the mathematician, biology opens up new and exciting areas of study, while for the biologist, mathematical modeling offers another powerful research tool commensurate with a new instrumental laboratory technique. Mathematical biologists typically investigate problems in diverse and exciting areas such as the topology of DNA, cell physiology, the study of infectious diseases, population ecology, neuroscience, tumor growth and treatment strategies, and organ development and embryology.
This course will be a venture into the field of mathematical modeling in the biomedical sciences. Interactive lectures, group projects, computer demonstrations, and laboratory visits will help introduce some of the fundamentals of mathematical modeling and its usefulness in biology, physiology and medicine.
For example, the cell division cycle is a sequence of regulated events which describes the passage of a single cell from birth to division. There is an elaborate cascade of molecular interactions that function as the mitotic clock and ensures that the sequential changes that take place in a dividing cell take place on schedule. What happens when the mitotic clock speeds up or simply stops ticking? These kinds of malfunctions can lead to cancer and mathematical modeling can help predict under what conditions a small population of cells with a compromised mitotic clock can result in a fully developed tumor. This course will study many interesting problems in cell biology, physiology, and immunology.
Mathematics and Music Theory (Session 3)
Instructor: Lon Mitchell
Mathematicians can create complex and beautiful theorems from relatively basic assumptions, while Music Theorists often try to identify basic patterns and “rules” in complex and beautiful music. In this course, we will explore some of the recent attempts to meet in the middle, connecting mathematical patterns and structures to music from the ancient to the modern.
In Mathematics, we will explore topics such as group theory, graph theory, geometry, and metric spaces, encountering some of the most important structures in the modern discipline. Fundamental results of these areas will be discussed, and students will construct and explore examples and related patterns.
In Music Theory, we will take existing music by composers such as Bach and Beethoven and use mathematical structures to provide a possible explanation of what they were thinking as they composed. In addition, we will investigate the techniques of modern composers such as Arnold Schoenberg who advocated composition based on prescribed axioms. Students will be given the chance to write music using these different techniques.
Although we will use the modern (Western) twelvetone scale as a reference, our explorations will take us into discussions of tuning, temperament, and the physics of sound. We will investigate mathematical theories of what makes the best scale, how some of those scales occur in the music of other cultures, and how modern composers have engineered exotic scales to suit their aesthetics.
Software allowing students to experiment with creating their own musical systems will be provided.
Prospective students should have a good command of (highschool) algebra and experience with reading music in some form.
Mathematics and the Internet (Session 3)
Instructor: Mark Conger
How can gigabytes of information move over unreliable airwaves using unreliable signaling, and arrive perfectly intact? How can I have secure communication with a website run by a person I've never met? How can a large image or sound file be transferred quickly? Why is Google so good at finding what I'm looking for? How do computers work, anyway?
The answers to all these questions involve applications of abstract mathematics. In Mathematics and the Internet, we'll develop the math on its own, but also show how it is essential to making the Internet operate as it does. Our journey will take us through logic, probability, group theory, finite fields, calculus, number theory, and any other areas of math that might come up. We'll apply our results to coding theory, cryptography, search engines, and compression. We'll also spend several days building primitive computers out of transistors, logic gates, and lots of wire. If all goes well, we'll connect them to the Internet!
Mathematics of Cryptography (Session 3)
Instructor: Anton Lukyanenko
Ever since humans first developed the ability to write there has been an ongoing battle between codemakers and codebreakers. The armies of ancient Sparta and Rome both used ciphers to relay secret battle plans, and the ancient Mesopotamians developed encryption techniques in order to protect commercially valuable techniques for glazing pottery. From a modern perspective, the codes used by the ancients are laughably insecure. Indeed, much of what made them secure was that they were being used during a period when most people were illiterate.
Because of the advent of computers, codemakers today need to use far more sophisticated techniques in order to create secure codes. Many of these techniques are mathematical in nature. One of the cryptography systems that we will discuss in this class is called RSA and is used to ensure the security of your credit card information when you make a purchase on the internet. We'll see that at its heart, what makes the RSA system secure is that it is very hard to factor a big number. The numbers used in the RSA system are actually so big that factoring them would take you millions of years. Even if you were using a supercomputer!
This class will give an historical introduction to the mathematics of cryptography, beginning with codes used by the Roman legions and building up to the RSA cryptography system discussed above. What will really make the class unique is that there won't be any lecturing. You will discover the mathematics of cryptography by working on problems and sharing your solutions with your classmates.
Mathematics of Decisions, Elections and Games (Session 2)
Instructor: Michael A. Jones
You make decisions every day, including whether or not to sign up for this course. The decision you make under uncertainty says a lot about who you are and how you value risk. To analyze such decisions and provide a mathematical framework, utility theory will be introduced and applied to determine, among other things, the offer the banker makes to a contestant in the television show Deal or No Deal.
Elections are instances in which more than one person’s decision is combined to arrive at a collective choice. But how are votes tallied? Naturally, the best election procedure should be used. But Kenneth Arrow was awarded the Nobel Prize in Economics in 1972, in part, because he proved that there is no best election procedure. Because there is no one best election procedure, once the electorate casts its ballots, it is useful to know what election outcomes are possible under different election procedures. This suggests mathematical and geometric treatments to be taught in the course. Oddly, the outcome of an election often says more about which election procedure was used, rather than the preferences of the voters! Besides politics, this phenomenon is present in other settings that we’ll consider which include: the Professional Golfers’ Association tour which determines the winner of tournaments under different scoring rules (e.g. stroke play and the modified Stableford system), the method used to determine rankings of teams in the NCAA College Football Coaches poll, and Major League Baseball MVP balloting.
Anytime one person’s decisions can affect what happens to another person, that situation can be modeled by game theory. That there is still a best decision to make that takes into account that others are trying to make their best decisions is, in part, why John F. Nash was awarded the Nobel Prize in Economics in 1994 (see A Beautiful Mind, 2002). Besides understanding and applying Nash’s results in settings as diverse as the baseball mind games between a pitcher and batter and bidding in auctions, we’ll examine how optimal play in a particular game is related to a proof that there are the same number of counting numbers {1, 2, 3, …} as there are positive fractions. We will also examine the GaleShapley algorithm, which is used, for example, to match physicians to residency programs and to match students to colleges (the college admissions problem). Lloyd S. Shapley and Alvin E. Roth were awarded the Nobel Prize in Economics in 2012 for their work on matching.
To be or not to be? Biodiversity and Mass Extinctions through Deep Time (Session 2)
Instructor: Janice Pappas
Life on the 4.6 billion year old Earth began around 3.5 billion years ago. How did life on Earth come about? What kinds of life forms emerged? When did these forms come into existence? We will explore the fossil record and the events that shaped the biological world as we know it today. We will study life on Earth from the perspective of biodiversity and phylogenetic trees of life. We will focus on the Ediacaran period, the Cambrian explosion, and the Mesozoic Marine Revolution as times of great biodiversity. We will explore the five major mass extinction events that occurred at the OrdovicianSilurian, the Late Devonian, the PermianTriassic, the TriassicJurassic, and the CretaceousPaleogene. Why did life on Earth vanish in such large quantities at these events? How did this happen? What happened to biodiversity in the aftermath? These are just some of the many questions we might address for each extinction event.
Our journey begins with an overview of what Earth looked like at the time life first appeared from a geological and climatological perspective. We will advance toward studying various organisms and biodiversity over time. We will be haltingly taken aback at the catastrophic consequences of mass extinction. We will emerge from such events and take stock of biodiversity to the present. We may even have time to consider fossils and their importance in astrobiology.
Our studies will include field trips to the University of Michigan Exhibits Museum. Students will be required to do research covering biodiversity with respect to an extinction event. Students will work in groups to create a scientific poster of their research findings. Student research will be presented in class.
Prerequisites: Having had a science course is helpful, but not necessary. Just bring your enthusiasm to learn about the history of life on Earth.
Climbing the Distance Ladder to the Big Bang: How Astronomers Survey the Universe (Session 2)
Instructor: Dragan Huterer
The furthest objects that astronomers can observe are so distant that their light set out when the Universe was only 800 million years old, and has been traveling to us for about 13 billion years – most of the age of the Universe. Even the Sun's neighborhood – the local part of our Galaxy, where astronomers have successfully searched for planets around other stars – extends to hundreds of light years. How do we measure the distance to such remote objects?
Certainly not in a single step! Astronomers construct the socalled “Distance Ladder,” finding the distance to nearby objects, thus enabling those bodies to be understood and used as probes of yet more distant regions. The first steps in the ladder uses radar ranging to get the distance to the nearby planets and the Sun; and 'triangulation' to get the distances to the nearest stars. Those in turn are used to obtain distances to other stars in our Milky Way Galaxy, stars in other galaxies, and out to the furthest reaches of what is observable.
This class will explore the steps in this ladder, using lectures, discussions, field trips, demonstrations, and computer laboratory exercises. Students will learn basic computer programming for a project to model the effects of gravity, and they will get handson experience of using a small radio telescope to map the the rotation speed of the Milky Way and measure the influence of its dark matter. We will cover concepts involving space, time, and matter that go far beyond the distance ladder, and involve some of the most fascinating mysteries in cosmology and astrophysics: What is it like inside a black hole? What is the Dark Matter? What is the Dark Energy that makes the Universe expand faster and faster? Is there other life in the Universe?
Forensic Physics (Session 1, Session 2)
Instructor: Ramon TorresIsea
A fiber is found at a crime scene. Can we identify what type of fiber it is and can we match it to a suspect's fiber sample, for example from a piece of clothing? Likewise, someone claims to have valuable ancient Roman coins, a newlyfound old master painting, or a Viking map of America predating Columbus' voyage. Are they authentic or fakes? How can we determine that using some physicsbased techniques? (These are real examples the Viking map proved to be a forgery.) Also for example, how is a laserbased molecularprobing technique used to stop criminals from trading billions of dollars of counterfeit pharmaceuticals and endangering thousands of lives?
These are a few among many examples of physics techniques applied to several areas of Forensics. In this session, students will be introduced to these methods and have opportunities to make measurements using molecular, atomic and nuclear forensic techniques. Tours of UM facilities used in Forensics or forensicsrelated research will be given. In addition, applications in medical imaging and diagnostics will be introduced. Students will be working at our Intermediate and Advanced Physics Laboratories with the underlying physics for each method presented in detail, followed by demonstrations and laboratory activities, which include the identification of an "unknown" sample. Various crime scenes will challenge students to select and apply one or more of the methods and use their Forensic Physics skills to conduct forensic investigations.
Roller Coaster Physics (Session 2)
Instructor: David Winn
What are the underlying principles that make roller coasters run? By studying the dynamics of roller coasters and other amusement park rides in the context of Newtonian physics and human physiology, we will begin to understand these complex structures. Students first review Newtonian mechanics, a = f/m in particular, with some handson experiments using airtables. This will then be followed by digitalvideo analysis of motion of some reallife objects (humans, cars, and toy rockets) and studentdevised roller coaster models.
Then, a field trip to Cedar Point Amusement Park (outside of the regularly scheduled weekend trip) where students, riding roller coasters and other rides, will provide real data for analysis back at UM. Students will carry portable data loggers and 3axis accelerometers to provide onsite, and later offsite, analysis of the motion and especially, the "gforces" experienced. The information collected will then be analyzed in terms of human evolution and physiology; we shall see why these limit the designs of rides.
In addition to exploring the physics of roller coasters, cuttingedge topics in physics will be introduced: high energy physics, nuclear astrophysics, condensedmatter theory, biophysics and medical physics. Students will then have a chance to see the physics in action by touring some of UM's research facilities. Students will have the opportunity to see scientists doing research at the Solid State Electronics Laboratory, the Michigan Ion Beam Laboratory, and the Center for Ultrafast Optical Science.
By the end of the twoweek session, students will gain insight and understanding in physics and take home the knowledge that physics is an exciting, reallife science that involves the objects and motions surrounding us on a daily basis.
The Physics of Magic and the Magic of Physics (Session 2)
Instructors: Fred Becchetti and Georg Raithel
Rabbits that vanish; objects that float in air defying gravity; a tiger that disappears and then reappears elsewhere; mind reading, telepathy and xray vision; objects that penetrate solid glass; steel rings that pass through each other: these are some of the amazing tricks of magic and magicians. Yet even more amazing phenomena are found in nature and the world of physics and physicists: matter than can vanish and reappear as energy and viceversa; subatomic particles that can penetrate steel; realistic 3D holographic illusions; objects that change their dimensions and clocks that speed up or slow down as they move (relativity); collapsed stars that trap their own light (black holes); xrays and lasers; fluids that flow uphill (liquid helium); materials without electrical resistance (superconductors.)
In this class students will first study the underlying physics of some classical magic tricks and learn to perform several of these (and create new ones.) The "magic" of corresponding (and real) physical phenomena will then be introduced and studied with handson, mindson experiments. Finally, we will visit a number of research laboratories where students can meet some of the "magicians" of physics  physics students and faculty  and observe experiments at the forefront of physics research.
Life, Death and Change: Landscapes and Human Impact (Session 2)
Instructor: David Michener
You’ll never see the same world quite the same way after this course – which is important if you want to make a difference with your life. All environmental studies presume a landscape – yet what seems to be a simple landscape is often far from uniform or stable. A great deal of information critical to anyone entering the “green” sciences can be detected for analysis – including factors that may fundamentally control species diversity, habitat richness, and animal (let alone human) behavior. Resolving human from nonhuman agency is an engaging and important challenge, too – one scientists and “green professionals” grapple with repeatedly. This outdoor class immerses students in realworld landscapes, ranging from the nearlypristine to the highly humanized, to solve problems which may initially appear impossible to address. You can!
Your critical thinking skills are essential rather than prior biological course and field work. Come prepared to look, measure, analyze, discus and learn how the interaction of plants, soils, climate and time (and humans) influences landscape development. Develop basic skills in plant recognition and identification – skills that you can transfer to other terrestrial communities. Address questions about the current vegetation, its stability over time and its future prospects. Gain practical insights into the realities of biological conservation as we address how we can manage species and landscapes for future generations. By the end you’ll have a conceptual skill set that helps you assess how stable and disturbed are the “natural” areas are near your home – and prepares you to put instructors on the spot in college classes to come.
Predicting & Forecasting Natural Hazards (Session 3)
Instructor: Eric Hetland
Natural disasters have resulted in almost $4 trillion in losses and over a billion fatalities in the past 35 years. Naturally occurring events, such as earthquakes, volcanic eruptions, tsunamis, landslides, floods, hurricanes, tornadoes, and extreme temperatures, occur every year and affect nearly every part of the Earth. Most of these natural hazards involve a relatively sudden release of a large amount of energy over a small spatial area – when this concentration of energy and society intersect, disaster results. Considerable effort has gone into our ability to estimate our risk from natural hazards, as well as forecast hazards. Forecasting of hazards is done both over long time periods, and time periods over the life of the hazard. For example, forecasts for hurricane activity are made as early as a year before a hurricane season, while once a hurricane forms the path of that hurricane is forecast and adjusted throughout the life of the hurricane. A complicating factor when discussing natural hazards is that the number and cost of natural disasters has been increasing over the last few decades. This may be due to natural hazards increasing in number, size, or extent, or may be due to an increase in vulnerability of modern society.
In this course, we will explore estimating risk of, predicting, and forecasting natural hazards, including earthquakes, hurricanes, tornadoes, and extreme temperatures. Our focus will be on how the dynamic complexities of natural hazards makes forecasting hazard possible, but also hinder our ability to predict those hazards. We will discuss the scientific assessment of precursors, as well as the evidence/arguments that the frequency or severity of hazards are increasing over just the past few decades. We will cover fundamental mathematics related to estimation and forecasting, including probabilistic inference, chaos, complexity, random walks (e.g., Markov chains), and predictive filtering. The majority of the handson exercises will be computerbased. Earth science knowledge is not required.
Hormones and Behavior: The Secret Life of Chemical Messengers (Session 1)
Instructor: Sara Konrath
In this course, we will examine how hormones can produce changes in behavior, but also how behavioral interactions can alter hormones. We will primarily discuss hormonebehavior interactions in mammals with an emphasis on humans and nonhuman primates. Some topics we may explore include hormonal influences on sex determination, sexual behavior, parental behavior, dominance and aggression, responses to stressful stimuli, immune function and homeostasis, biological rhythms, learning and memory, maturation, and several behaviors relevant to humans such as motivation and mood. The course will be taught as a mixture of lecture, discussion, and student presentations. Students will also be trained on how to collect and assay human saliva samples for specific hormones.
Sampling, Monte Carlo and Problem Solving: How Analyzing Statistics Helps us Improve (Session 1)
Instructor: Edward Rothman
Political candidates drop out of elections for the U.S. Senate and New York Governorship because their poll numbers are low, while Congress fights over whether and how much statistics can be used to establish the meaning of the U.S. Census for a host of apportionment purposes influencing all our lives.
Suppose we need to learn reliably how many people have a certain disease? How safe is a new drug? How much air pollution is given off by industry in a certain area? Or even how many works someone knows?
For any of these problems we need to develop ways of figuring out how many or how much of something will be found without actually tallying results from a large portion of the population, which means we have to understand how to count this by sampling.
And Monte Carlo? Sorry, no field trips to the famous casino! But, Monte Carlo refers to a way of setting up random experiments to which one can compare real data: does the data tell us anything significant, or it is just random noise? Did you know you can even calculate the number ? This way?!?!The survey and sampling techniques that allow us to draw meaningful conclusions about the whole, but based on the analysis of a small part, will be the main subject of this course.
