**Black Holes: Illuminating the Abyss** – *Monica Valluri*

This course deals with astrophysical black holes, from stellar-mass objects arising from the death of massive stars, to super-massive black holes lurking at the center of galaxies. Far from being hypothetical constructs of theoretical physics, observations of the Universe over the entire electromagnetic spectrum from radio waves, through optical, UV, X-rays and gamma rays have revealed that black holes are fascinating objects, some of which are surrounded by extremely bright disks of matter from which astronomers have learned about their remarkable properties. These “accretion disks” and their associated jets have led to discoveries about the structure and evolution of the Universe and show that black holes have had a remarkable influence on the Universe itself. The course will include an introduction to the basic physics and astronomy necessary to understand the advances that astrophysicists have made in our understanding of these strange and fascinating objects.

**Brain and Behavior** – *Jen Cummings *

Ever wonder how that gelatinous blob in your head controls everything you do and think? What exactly are neurons? How do they talk to each other? And to the rest of your body? Have you ever wondered about things like: how does stress affect your body? Is exercise really that good for your brain? What happens if you miss a few nights of sleep? It makes sense that your brain affects your experiences- but can experiences actually change your brain?? We will answer these questions (and more!) in Brain and Behavior, as we explore the amazing field of behavioral neuroscience. We will begin with a section on the basic functionality of the brain and nervous system, and then will go on to investigate how the system can be affected by things like stress, learning & memory, hormones, and neuropsychiatric disorders. We will leave some time for a session on student-selected topics in behavioral neuroscience, so if there’s something else you’ve been pondering with respect to the brain, don’t worry! We’ve got you covered.

**Dissecting Life: Human Anatomy and Physiology** – *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 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.

**Fibonacci Numbers** – *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 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.

**Forensic Physics** – *Ramon Torres-Isea *

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 is a laser-based molecular-probing 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 experimental physics methods 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. In addition, applications to 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 investigations.

**Graph Theory** – *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!

**Mathematical Modeling in Biology** – *Trachette Jackson and Patrick Nelson*

Mathematical biology is an exciting interdisciplinary field that combines applied mathematics, scientific computing, biology, ecology, physiology and medicine. This branch of mathematics is growing with phenomenal speed! For the mathematician, biology opens up new and exciting areas of study, while for the biologist, mathematical and computational modeling offers another powerful research tool that can provide insight into the complexity of a biological system. Mathematical biologists typically investigate problems in diverse and exciting areas such as the topology of DNA, cell physiology, the study and spread 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 biology and the biomedical sciences using techniques from calculus, dynamical systems and scientific computing. Interactive lectures, group projects, computer demonstrations, and guest speakers 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. Students who can speak the languages of mathematics and computation along with biology and medicine will be able to solve some of the most challenging problems of the 21^{st} century. Wouldn’t it be amazing if mathematics could guide future experiments that lead to a cure AIDS or Cancer?

**Mathematics of Cryptography** – *Anna Weigandt *

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.

**Relativity: A Journey through Warped Space and Time** – *Daniel Mayerson *

Einstein forever altered our understanding of the nature of space and time with his theories of relativity. These theories tell us that the speed of light is a universal constant, declare that the fabric of space and time is warped by matter, and demand that matter moves through spacetime by following its curvature. Introduced 100 years ago, these concepts clash mightily with our everyday physical intuition, but are nevertheless cornerstones of modern-day physics. In this course we will explore the exciting world of relativity (both the special and general theories). After briefly reviewing classical mechanics (Newton’s laws), we will use thought experiments to understand the ideas behind relativity and see how they are actually ultimately simpler and more natural than classical mechanics. Along the way we will encounter strange paradoxes that push the limits of our understanding and learn powerful mathematics that will allow us to quantify our relativistic understanding of the universe. Using our new knowledge, we will delve into black holes, learn how GPS systems work, and debate the possibility of time machines and wormholes. Prerequisites: basic concepts in geometry (e.g. coordinates, distance formulae) and working knowledge of elementary calculus (e.g. what a derivative is and how to take one). We will introduce some multivariable calculus (e.g. partial differentiation) and integration techniques, so prior knowledge of those is a bonus. An open, curious and interested mind is absolutely necessary; you must be willing to think deeply about physics and the nature of our universe!

**Surface Chemistry** – *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 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. 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.

**Sustainable Polymers** – *Anne McNeil*

From grocery bags and food packaging to contact lenses and therapeutics, there is no doubt that polymers have had a positive impact in our lives. Most of these polymers are made from petroleum-based feedstocks, which are dwindling in supply. And although some plastics are recycled, most of them end up contaminating our lands and oceans. Through hands-on lab work and interactive lessons, this class will introduce the future of polymer science – that is: polymers made from sustainable materials that ultimately biodegrade! Students will conduct research experiments to make, analyze, and degrade renewable plastics. We will also examine commercial biodegradable materials and plastics used for energy and environmental remediation, and practice science communication through a creative stop-motion animation project.

**Survey in Modern Physics** – *Jun Nian
*How can we describe curved spacetime? What is the difference between black hole and worm hole? Is a time machine ever possible? What is Schrödinger’s cat? What is quantum entanglement? Are there parallel universes? What are four elementary interactions in nature? What are anti-matter, dark matter and dark energy? What is Big Bang Theory? What is String Theory? We may have seen these words in many movies and science fictions, but what do they really mean? To answer these questions and to understand the concepts mentioned above, we need to first learn two fundamental pillars of modern physics, relativity and quantum mechanics, both of which take years of physics courses. This mini course is aimed at providing a crash course in these subjects. We will begin with elementary physics taught in high school, and then step by step survey in relativity and quantum mechanics, or more generally in modern physics. The key concepts will be demystified with a lot of examples, demonstrations and discussions. To help understand physics problems and methods, some tutorials and labs will be provided, accompanying the lectures everyday. Basic knowledge in calculus will be helpful, but not necessary. Good knowledge in mathematics and physics at high school level should be enough. Some advanced mathematics will be introduced during the course. The only prerequisite is the passion in science and modern physics.