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ONLINE Courses
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COURSES ASTRONOMY The Large Scale Structure of the Universe (Session I) If the Universe came into existence with a 'Big Bang', as a hot, dense soup of matter and radiation, where did the objects that we see today - the stars, galaxies, and galaxy clusters - come from? Observations made over the last decades reveal tiny variations in the intensity of the radiation that permeates space - a relic of that early fireball in which the Universe was born. Those variations are the fingerprints of the equally tiny variations in the density of matter, eventually pulled together by gravity to form the large-scale structures that we see today. And, remarkably, that visible Universe of stars and galaxies explored by modern telescopes is only the tip of the iceberg. Most of the mass in the Universe is a mysterious 'dark matter' whose nature is still unknown! Morning lectures and discussions will explore the history and future of our Universe, from the time that all matter and radiation were contained within a volume the size of an atom, to the dim and distant future predicted by the latest observations of an accelerating space-time. We will emphasize the epochs during which the Universe assumed its current form and learn how astronomers map the Universe, and what they have learned from surveys spanning hundreds of millions of light years. We will see how computer simulations enable us to reproduce the large-scale structure of the Universe, and by comparing the results of different simulations with observations, how we can learn about the quantity and nature of the "dark matter". During the afternoon computer laboratory sessions we will measure the distances to clusters of galaxies, revealing both the expansion of the Universe, and its large-scale structure. We will explore the dynamics of clusters by exploring the history of our own cluster, the "local group", simulating the exchange of satellite galaxies and the future collision of the Milky Way with our massive neighbor, Andromeda. After running a simulation of structure formation, there will be an opportunity to compare the results with observations, to see how such comparisons can shed light on the nature of "dark matter" and the fate of the Universe.
BIOLOGY Explorations
of a Field Biologist (Session II) There
are so many different kinds of living organisms in this world, and every
organism interacts with its physical environment and with individuals
belonging to both its own and to other species. Understanding this mass
of interactions and how humans are affecting them in the short and long-term
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.
You will not only learn a slew of natural history factoids, but also
become well-acquainted with the how's and why's of practicing field
biology, from making observations to hypothesis-testing in the field.
We will address a myriad of questions from what mushrooms can tell you
about trees, to how big a chipmunk territory is, to whether a flower
shape matters to bees, to how lakes turn into forests, to how plants
care for their young...to whatever questions arise in our explorations
of the grasslands, forests, and wetlands of southeastern Michigan or
in our discussions of other parts of the world. Learning this approach
to addressing questions about what you see in nature will allow you,
long after this class, to discover many more things about the natural
world, even in your own back yard. In many ways, the course is inspired by my reading of the autobiography of an examplary field biologist, E.O. Wilson. Whether he is in his own back yard or in a tropical rain forest, Wilson observes nature with patience, dilligence and an inquisitive mind. His career shows the value of making field observations and notes and of asking questions - and that is exactly what we practice in "Explorations of a Field Biologist." Through field activities and discussions, we will practice seven steps of field biology. The first is discovering patterns in nature. Equipped with binoculars, hand lenses, field guides and a notebook, you will develop an eye for the behaviors and abundances of micro- and macro-organisms and for the identifying characteristics of different plants, animals and fungi. The second and third steps are asking questions about what you see and making a guess at the answer. For this we will tap each other's brains and learn how to refer to the physical and electronic library of past field biology research. Fourth, you will design an experiment that not only looks good on paper, but actually works when you are knee-deep in a bog. Fifth, you will use sophisticated and simple equipment (bridal veil?!) to count and measure variables in the field. Finally, you will practice analyzing and then drawing conclusions from your results, which inevitably leads to more questions and more field trips! Genome
Sequences and Human Health (Session I) 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. The
Mysteries of Embryology (Session I) Embryology is the science dealing with the formation, early growth and development of living organisms. This course addresses the mysteries and processes of embryology. Questions that will be investigated include: Why do babies move in the womb? Why does the lens fit the eye? Why do all human hearts have a hole in them at birth and why isn't it lethal? Why would exposure to a particular chemical throughout the majority of pregnancy have no effect, whereas exposure during the first month of pregnancy could cause severe birth defects? This course examines the fundamentals of embryology during lecture and through experiments with chicken embryos (before central nervous system development and the ability to feel pain) in laboratory. We will be working in groups to research how disrupting development mechanisms causes birth defects and then post our findings on the world wide web.
A Journey Through
Modern Molecular Science (Session I) The scope of chemistry is constantly broadening, from applications in computational chemistry to exploration of complex bio-molecules and drug design. The goal of this course is to put into perspective an important aspect of modern chemistry - one that deals with complex biologically active molecules. In order to do this, this course will focus first on core chemical principles including functional groups, acid-base chemistry and analytical spectroscopic techniques. The latter half of the course will explore chemical principles in a biological context, including key concepts such as catalysis and further application of chemical knowledge in drug design. Laboratories will feature a wide variety of activities including polymer synthesis, spectroscopic characterization of unknown compounds, genomic DNA extraction and computer modeling of proteins and nucleic acids. The course will also feature many enrichment activities such as lunch lectures with chemistry faculty, demonstrations of state-of-the-art technologies used in chemistry, research laboratory tours and primary literature research techniques.
GEOLOGY
Michigan Rocks! (Session II) The region surrounding Ann Arbor affords a simply excellent opportunity to examine a host of fascinating geologic phenomena outside of a classroom setting, and that's exactly what we will be doing in this course. We will spend equal amounts of time in the classroom learning about the geology of the region and about the geological features we will be examining in the field. Traveling beyond Ann Arbor to collect and examine various minerals, rocks, fossils, and other fascinating features and settings in the area comprises the field research course component. Day trips will include travel to Kirkfield, Ontario to look at rocks and collect fossils from the Devonian Period now exposed along the Au Sable River. If you like the feeling of being part of natural grandeur, then take a walk along the Au Sable's banks where the river has cut its way through an ancient seabed exposing strata of limestone and shale in which fossil remains of an equally ancient life have been entombed. Another trip includes East Lansing, where we will collect plant fossils and examine the rocks exposed along the Grand River. We will spend the day picking up bits of giant ferns and other plant fragments where ancient coal swamps were once found. Through this course, you will gain a geologic perspective about the processes that give rise to the surrounding land and establish an understanding of the regions that have been in a state of rapid change for thousands of years. Check out Michigan Rocks! from the Michigan Math and Science Scholars 2001 offering!
MATHEMATICS Codes,
Ciphers and Secret Messages (Session II) Around 4000 years ago in Egypt, the tomb of Khnumhotep II was nearing completion. In one particular section of the inscription, a master scribe chose to replace the usual hieroglyphic symbols with new, nonsensical ones. This act rendered that important passage of Khnumhotep's funerary inscription unintelligible except to those who knew what replacement the scribe had made. This inscription is the oldest surviving record of the use of secret codes. Nowadays, you can order goods over the Internet with a credit card. When you forward your credit card number over the network, powerful public key encryption schemes put this information in a form that is presumably unreadable to the electronic eavesdropper. Although the sophistication of Internet code is vast compared to the simple substitution made by the Egyptian scribe, the security of both schemes are based on the difficulty of solving certain kinds of mathematical problems. This course is about
the mathematics that underlies secret codes and attacks on secret codes.
We will proceed historically, beginning with substitutional codes, like
the one used by our Egyptian scribe, and ending with modern public key
encryption, like that used by Internet vendors. This study of secret
codes introduces topics in discrete mathematics, statistics, information
theory and number theory. The use of technology will be emphasized throughout.
Each afternoon, students will participate in a computer lab in which
they will use MAPLE, an advanced general-purpose mathematical package,
to run experiments pertinent to the course material. Most importantly,
students will get plenty of practice creating their own codes and trying
to crack those of their instructor and their classmates.
Geometry
and the Imagination (Session I) The study of geometry and topology has a rich history with problems dating back to the ancient Greeks. In this course we will investigate some of these topics, and use them as a basis for experimenting, conjecturing, discussing and theorizing --- that is, doing mathematics! Geometry is the study of the measurement of objects and topology is the study of their shape, but as we will see, these endeavors go hand in hand. Here is a description of some of the topics we will consider. Tying knots is part of learning to be a sailor or a Scout. This seemingly simple activity is one of the most interesting and difficult areas of study in modern topology. We will learn to measure the mathematical complexity of knots, and we will see that some are indeed "knottier" than others Can a sphere be turned inside out? If we imagine it to be made of highly elastic material that can pass through itself, the question becomes subtle. We will see that although a circle cannot (under these circumstances) be turned inside out, so-called "sphere eversions" exist. Try this activity: cut out of cardboard several equilateral triangles of the same size. Tape them together along the edges so that only two triangles meet at every edge and three triangles meet at each vertex. What shape do you get? What happens if we require that four triangles meet at every vertex? Five? This activity is an easy example of tiling, another focus of our course. The central role played by tilings in nature and in throughout the ages is an example of the kind of application we will investigate. Check out this link to Geometry and the Imagination from last years Michigan Math and Science Scholars.
Mathematical
Modeling in Biology (Session II) 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 such as AIDS, the biology of populations, neuroscience and the study of the brain, 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 ensure 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.
Fibonacci
Numbers (Session I) 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 one by-product of our studies we will be able to explain how people 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.
The
Nature of Infinity (Session II) Is 0.99999... equal to 1 or just infinitely close to it? How can you do infinitely many things in a finite amount of time? What role does the infinite play in our daily lives? How can we justify the statement that one kind of infinity is bigger than another? How can a finite region have an infinite boundary? How can we, with our finite minds, even assess the quality of our reasoning on the nature of infinity? Pondering infinity has both fascinated and terrified mathematicians, philosophers and poets (and regular folk!) since time immemorial. As we shall see, "common sense" is a very poor guide when dealing with infinity. However, some of the most brilliant minds of all times have grappled with the question of infinity, and they have found some astonishing answers. Come prepared to stretch your mind to the limit! Check out the online course, "The Nature of Infinity"
PHYSICS Roller
Coaster Physics (Session I) 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 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 and 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 physicists doing both theoretical and applied research at the Spin Physics Center, 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. Check out last years Roller Coaster Physics course from MMSS 2002. The
Physics of Magic and the Magic of Physics (Session II) 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 that 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.
STATISTICS Sampling,
Surveys, Monte Carlo and Inference (Session I) Political candidates drop out of elections for the U.S. Senate and New York Governor 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.
Statistics
and the World Around Us (Session II) Statistics is the art and science of drawing reliable conclusions on large amounts of data based on the analysis of a manageable sample. This exploratory course in introductory statistics will acquaint participants with modern statistical practices utilizing a problem-based approach to the field. Consider, for instance, one of the first examples analyzed in the course -- “What’s in the Bag?” -- which illustrates many aspects of the process of making decisions with statistics: There are two identical bags, Bag A and Bag B. Each contains 20 vouchers, small slips of paper identical in size and appearance except for the positive and negative dollar values printed on them. The contents of the bags, in terms of the face values and frequencies of the dollar amounts, are the following. Bag A: -$1000 (1), $10 (7), $20 (6), $30 (2), $40 (2), $50 (1), $60 (1). Bag B: $10 (1), $20 (1), $30 (2), $40 (2), $50 (6), $60 (7), $1000 (1). You must pick a bag to keep and you agree to receive the sum of the face values of the vouchers it contains: you will pay $560 if you pick Bag A (watch the minus sign!) and win $1890 if you pick Bag B. You will be shown one of the two bags and you will be allowed to sample some datafrom this bag. Based on your analysis of that data, you must decide whether to keep or exchange the bag you were shown. How would you proceed? You’ll only be able to examine this small portion of the data. You’ll be doing another version of this problem later with many, many vouchers, and no strategy based on seeing a large portion of the data will be allowed! Although this problem touches on many sophisticated ideas, there are ways we can calculate which is the better choice in this experiment. The relatively small number of data points simplifies the calculations. Throughout this course we will spend mornings discovering new concepts and implementing them on small examples. Afternoons, we will usually work in the computer laboratories implementing statistical programs which will bring more realistic sized examples into our range.
Michigan
Math & Science Scholars Program University
of Michigan | Office of the Provost
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