Current Course Status -ALL COURSES ARE FULL 4-19-2013

SESSION 1 – June 23 - July 5, 2013

Climbing the Distance Ladder: How Astronomers Survey the Universe Instructors: Miller and Huterer. Dept of Astronomy. Course Full - 4-8-13

Dissecting Life: Human Anatomy and Physiology Instructor: Fox. Dept. of Ecology and Evolutionary Biology. (Available both sessions and content material is identical in both offerings.) - COURSE FULL- 3/01/13

Explorations of a Field Biologist Instructor: Schueller. Dept. of Ecology and Evolutionary Biology. (Available both sessions and content material is identical in both offerings.) Course Full 4-8-13

Fibonacci Numbers Instructor: Hochster. Dept. of Mathematics.

Forensic Physics Instructor: Torres-Isea. Dept. of Physics. (Available both sessions and content material is identical in both offerings.) Course Full 4-8-13

Fortunes Made and Lost: Financial Mathematics Instructor: Moore. Dept. of Mathematics. Course Full 4-8-13

Genes to Genomics Instructor: Jeyabalan. Dept. of Molecular, Cellular and Developmental Biology. (Available both sessions and content material is identical in both offerings.) Course Full 4-8-13

Graph Theory Instructor: Shaw. Dept. of Mathematics.

Hex and the 4 Cs Instructor: DeBacker. Dept. of Mathematics.

Mathematical Modeling in Biology Instructors: Jackson and Nelson. Dept. of Mathematics. Course Full 4-8-13

Roller Coaster Physics Instructor: Winn. Dept. of Physics. Course full 4-11-13

Sampling, Surveys, Monte Carlo and Inference Instructor: Rothman. Dept of Statistics.

SESSION 2 – July 7 - July 19, 2013

Combinatorial Combat Instructor: Shaw. Dept. of Mathematics. Course Full 4-8-13

Dissecting Life: Human Anatomy and Physiology Instructor: Fox. Dept. of Ecology and Evolutionary Biology. (Available both sessions and content material is identical in both offerings.) - COURSE FULL- 3/14/13

Explorations of a Field Biologist Instructor: Schueller. Dept. of Ecology and Evolutionary Biology. (Available both sessions and content material is identical in both offerings.) Course full 4-11-13

Exploring Landscape Diversity Instructor: Michener. Program in the Environment.

Forensic Physics Instructor: Torres-Isea. Dept. of Physics. (Available both sessions and content material is identical in both offerings.) Course Full 4-8-13

Genes to Genomics Instructor: Jeyabalan. Dept. of Molecular, Cellular and Developmental Biology. (Available both sessions and content material is identical in both offerings.) - COURSE FULL- 3/14/13

Mathematics and the Internet Instructor: Conger. Dept. of Mathematics. Course Full 4-11-13

Mathematics of Decisions, Elections, and Games Instructor: Jones. Dept. of Mathematics. Course Full 4-8-13

The Physics of Magic and the Magic of Physics Instructors: Becchetti and Raithel. Dept. of Physics. Course Full 4-12-13

Stupid Interpolation Tricks: Beyond "Connect the Dots." Instructor: Strauss. Dept. of Mathematics.

Surface Chemistry Instructor: Chen. Dept. of Chemistry. Course Full 4-12-13

The Michigan Math and Science Scholars program is proud to feature courses from various departments in the College of Literature, Science and the Arts. These courses are unique in that enrollments are limited to approximately 15 students per class, thus making the ratio of students to faculty very low and allowing for an intense, fun and memorable learning experience.

DEPARTMENT OF ASTRONOMY

Climbing the Distance Ladder: How Astronomers Survey the Universe (Session 1)
Instructors: Brendan Miller and Dragan Huterer
Click here for syllabus

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 so-called “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 step on this ladder is to measure the distance to the planet Venus, by timing the round-trip for radar waves bounced from its surface. Knowing the laws of planetary motion, we can use information to get the distance to the Sun. Knowing the distance to the Sun, we can use the tiny shift in the apparent position of nearby stars as the Earth orbits during a year, to "triangulate" the distance to those stars. And so on out: through the Galaxy, the local group of galaxies, the local supercluster, to the furthest reaches of what is observable.

DEPARTMENT OF CHEMISTRY

Surface Chemistry (Session 2)
Instructor: Zhan Chen
Click here for syllabus

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 well-being. 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: anti-biofouling 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 non-wetting; 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.

DEPARTMENT OF ECOLOGY AND EVOLUTIONARY BIOLOGY

Dissecting Life: Human Anatomy and Physiology (Session 1 AND Session 2)
Instructor: Glenn Fox
Click here for a daily schedule
(Available both sessions and content material is identical in both offerings.)

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 first-hand 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 1 AND Session 2)
Instructor: Sheila K. Schueller
Click here for syllabus
(Available both sessions and content material is identical in both offerings.)

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 mind-boggling 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 all-day field trips, including hands-on experience in restoration ecology. Towards the end of the course you will design, carry out, and present your own research project.

DEPARTMENT OF MATHEMATICS

Combinatorial Combat (Session 2)
Instructor: Doug Shaw
Click here for a syllabus

We will play and analyze a variety of two person competitive strategic games. All of these games will have simple rules, perfect information (i.e. you know everything that has happened at each point in the game, no luck involved,) win/lose/or draw, and be interesting and challenging. We will study such notions as "formal strategy," "game tree," and "natural outcome," and investigate methods of solving some of the games. We’ll study Hex and a related game Y and an unrelated game “Poison Cookie,” and examine John Nash's (of the Beautiful Mind) proof that the first player has a winning strategy in each of these games even though nobody knows what the winning strategy actually in! Games such as Num and Fibonacci Nim will allow us to see how some good math can be used to solve many games. Other games such as "Dwarfs and Giants," "Fox and Geese," and Dodgem will be analyzed without any mathematics, but with good logic skills. We will also come across many games that are "isomorphic" (i.e. the same) even though they do not seem to be at first. If you ever played games such as Tic-Tac-Toe, Connect Four, Othello, Gomoku (Pente), Chess and Checkers, then this course is right for you.

No previous knowledge of any specific game is required.

Fibonacci Numbers (Session 1)
Instructor: Mel Hochster
Click here for syllabus

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 by-product 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.

Fortunes Made and Lost: Financial Mathematics (Session 1)
Instructor: Kristen Moore
Click here for syllabus

Is it possible to predict tomorrow's stock prices? Can you use mathematics to earn money through investments in a sure way? Is the financial world truly random? We will explore these and other questions by discussing the applications of probability theory to financial markets. We will discuss both the financial lingo you might encounter in the Wall Street Journal - for example, options, futures, and hedge funds - and the mathematics behind it. The course will end with the Black-Scholes formula that revolutionized trading stock options and earned its authors the Nobel Prize. In the meantime, we will build optimal portfolios, analyze risk, discuss arbitrage and understand the benefit of insurance. We will even talk about how you can make money from hot summer weather.

The morning sessions will involve two major components. The finance part will focus on the terminology and setup of financial markets and associated products. The math part will explore tools of probability used in modeling randomness and obtaining quantitative results. A significant portion of time will be used for thinking about computational methods and using technology to get answers. To tie the two components together, students will create a virtual portfolio of $100,000. The students will trade securities each day using the virtual account and will use ideas from the mornings in their investment strategies. At the end of the session, we will award prizes to the most successful traders.

Graph Theory (Session 1)
Instructor: Doug Shaw
Click here for syllabus

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
Click here for syllabus

After a very long night of homework, you finally finish your math assignment. While double-checking 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 fixed-point theorem; a very nice topological result.

To show that the Brouwer fixed-point 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
Click here for syllabus

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 simple 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 the Internet (Session 2)
Instructor: Mark Conger
Click here for syllabus

How can gigabytes of information move over unreliable airwaves using unreliable signaling, and arrive perfectly intact? How can I have a 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?

In Mathematics and the Internet, we'll answer these questions. We will also learn how to use abstract mathematical tools for studying such system, including graph theory, probability, logic theory, and coding theory. All of these fields, heavily studied before the internet, find new practical uses every day. In addition, we will finally build primitive computers out of transistors, logic gates, and LOTS of wire.

Mathematics of Decisions, Elections, and Games (Session 2)
Instructor: Michael A. Jones
Click here for syllabus

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 momentary offer the banker makes to 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 procedures 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, and this suggests mathematical and geometric treatments to be taught in the course. Oddly, the outcome of an election often stays 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 another person, that situation can be modified 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 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.

Stupid Interpolation Tricks: Beyond “Connect the Dots” (Session 2)
Instructor: Martin Strauss
Click here for syllabus

Two points determine a line; three points determine a plane or a quadratic polynomial.  Starting from these facts, we explore techniques and applications of interpolation, including: How to multiply polynomials and long number much faster than is normally taught in school, how to share a secret, e.g., the location of a treasure, so that no two pirates can locate the treasure but any three can, and even how to compute on the secret, e.g., how to compute the new location of the treasure after an earthquake, while preserving the "no-two-but-any-three" property, how to find the frequency content (bass or treble?) of music from samples of the air pressure, how mobile phones can communicate reliably, and how disks can store data reliably, even if there is noise present, how to find all occurrences of a given pattern in a given text, much faster than looking everywhere.

DEPARTMENT OF MOLECULAR, CELLULAR AND DEVELOPMENT BIOLOGY

Genes to Genomics (Session 1 AND Session 2)
Instructor: Santhadevi Jeyabalan
Click here for syllabus
(Available both sessions and content material is identical in both offerings.)

This course will cover basic aspects of Mendelian and molecular genetics, and then focus on a few human disorders in detail. We will introduce human genome sequence as an aid to cloning the genes responsible for these disorders, and will demonstrate how comparative genomics allows genetic diseases to be studied using model organisms like yeast, drosophila, nematodes, and mice.

In addition to lectures, we will work with fruit flies, yeast, and will do human DNA fingerprinting in a genetics laboratory. We will use computers to carry out molecular and phylogenetic analysis of DNA sequences. This class should provide an understanding Human Genome Projects and recent advances in medicine.

DEPARTMENT OF PHYSICS

Forensic Physics (Session 1 AND Session 2)
Instructor: Ramon Torres-Isea
Click here for syllabus
(Available both sessions and content material is identical in both offerings.)

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 newly-found old master painting, or a Viking map of America predating Columbus' voyage. Are they authentic or fakes? How can we determine that using some physics-based techniques? (These are real examples (the Viking map proved to be a forgery.) Also for example, how do we chart the time-scale of human evolution and accurately date other ancient artifacts, including the oldest rocks here on Earth? 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 atomic and nuclear forensic techniques. Tours of UM facilities used in forensics 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. At the conclusion of the session, students will be challenged to select and apply one or more of the methods and use their Forensic Physics skills to identify a complex sample (such as might be present in a crime scene of other forensic investigation.)

Roller Coaster Physics (Session 1)
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 hands-on experiments using air-tables. This will then be followed by digital-video analysis of motion of some real-life objects (humans, cars, and toy rockets) and student-devised 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 3-axis accelerometers to provide on-site, and later off-site, analysis of the motion and especially, the "g-forces" 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, cutting-edge topics in physics will be introduced: high energy physics, nuclear astrophysics, condensed-matter 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 two-week session, students will gain insight and understanding in physics and take home the knowledge that physics is an exciting, real-life 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: Frederick Becchetti and Georg Raithel
Click here for syllabus

Rabbits that vanish; objects that float in air defying gravity; a tiger that disappears and then reappears elsewhere; mind reading, telepathy and x-ray 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 vice-versa; subatomic particles that can penetrate steel; realistic 3-D 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); x-rays 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 hands-on, minds-on 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.

PROGRAM IN THE ENVIRONMENT

Exploring Landscape Diversity (Session 2)
Instructor: David C. Michener
Click here for syllabus

You'll never look out the window the same way after this course. Landscapes can be "read" for a great deal of information not evident to the untrained observer. We'll be conducting class outdoors and compare different but nearby landscapes to generate compelling questions that require field observations of various types to understand and resolve. In this field-intensive class, we'll explore several University-managed natural and research areas in the Ann Arbor area to learn how to orient oneself to a landscape and begin to analyze important components. From our field work, we'll address questions about the current vegetation and its stability in time; its past site history (post-settlement, pre-settlement) and future prospects. Current issues in biological conservation will raise themselves since some of the sites have native stands of rare plant species which we'll see and try to understand "why here?" We will work with plant identification and survey skills on-site, as well as comparing photographic documentation and then better understand the limitations of our "gut level" reading of the sites. Finally, we'll examine areas commonly understood as "natural," that upon inspection turn out to be designed and modified by humans. This may be a springboard into your future research interests here at UM!

No prior field-work or knowledge of the local climate, flora, fauna, geology, or history is expected.

DEPARTMENT OF STATISTICS

Sampling, Surveys, Monte Carlo and Inference (Session 1)
Instructor: Edward Rothman
Click here for syllabus

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 π 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.