Session 2 (July 7 – July 19)

Art and Mathematics –  Martin Strauss (FULL)
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 three-dimensional objects in two dimensions. What mathematical properties must be lost, and what can be preserved? How does an artwork evoke the feeling of three-dimensional 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 self-similarity that occurs in fractals as well as every self-portrait, and is central to mathematical concepts of dimension and un very different from the work at coarser scales—it is not self-similar. 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.

Brain and Behavior Jen Cummings (FULL)
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.

Forensic Physics Ramon Torres-Isea (FULL)
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 (FULL)
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 to solve and publish!

Human Identification: Forensic Anthropology Methods –  Isabel Hermsmeyer (FULL)
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 20-year old and an 80-year old? How do you distinguish between blunt force and sharp force trauma on the skull? In this hands-on, laboratory-based course, you will 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.

Hunting for the Dark: Black Holes and Dark Matter in the Milky WayMonica Valluri (FULL)
This course deals with how astronomers determine the properties of two of the most mysterious “dark components” of the universe – dark matter and black holes. While dark matter is only known by its gravitational influence on normal matter, black holes make their presence known by swallowing material from their surroundings. Prior to being swallowed, the in-falling matter forms a glowing hot accretion disk whose spectrum tells us much about the black hole such as its mass and spin. This course will discuss stars, how they evolve and lead to formation of exotic objects like white dwarfs, neutron stars and black holes. We will then move on to discussing the components and the structure of our own Milky Way Galaxy and other galaxies in the Universe, including dark matter and supermassive black holes. The course will focus on how astronomers gain information about these dark components of the universe using observations over the entire electromagnetic spectrum from radio waves, visible light, X-rays and gamma rays and from the recently discovered gravitational waves. 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. It will include daily lab activities, Python programming and working with astronomical data. The class is recommended for students with a strong high-school mathematics background, including some exposure to geometry, trigonometry, logarithms and vectors.

Informational Thermodynamics: Turning Knowledge Into PowerSean Fancher (FULL)
As you read these words, your brain is performing an incredible feat. Oxygen and sugar molecules are being broken down to fire neurons in intricate patterns, thus allowing you to decipher the message stored within this paragraph. This is one of the many, many ways in which we consume energy to generate information on a daily basis. However, if it is not only possible but commonplace to convert energy into information, is it also possible to run such a process in reverse and literally turn knowledge into power? In this course we will explore this intriguing possibility by approaching the enigmatic field of thermodynamics through the lens of information theory as laid out in Claude Shannon’s foundational 1948 work. Along the way we will uncover the roots of probability theory found in games of chance, discover the relation between the kind of information stored in computer hard drives and that of living organisms, encode messages in temperature variation, and learn about the limits placed on everyday interactions by the laws of thermodynamics. Through these efforts we will develop a deep understanding of the oft ill defined concept known as “entropy” and see the pivotal role it plays in the operations of the universe. Finally, we will investigate some modern research on these topics and build our own model information engine.

Mathematics and the Internet  –  Mark Conger (FULL)
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!

Science of Happiness –  Dina Gohar (FULL)
This course will introduce you to the exciting field of positive psychology–the scientific study of positive experiences, traits, relationships, and the institutions and practices that facilitate their development. Although psychological science has traditionally concentrated on “fixing what is wrong” (e.g., treating depression, anxiety, and other disorders), positive psychology focuses on “cultivating what is right” (e.g., promoting happiness and flourishing) and what makes life worth living. What truly makes us happy? How can YOU feel happier and more satisfied in your life? As you will learn, core research findings suggest that happiness is inextricably linked to: 1) using your strengths and contributing to something bigger than yourself, 2) staying grateful and optimistic, and 3) cultivating strong social connections. You will not only learn about but also practice some research-based strategies to improve both your learning and your own happiness and life satisfaction this summer. Through lively lectures, seminar-style discussions, activities, and interactive technology (e.g., documentaries, TED talks, etc.), we will examine the major topics of concern in positive psychology–pleasure, engagement, and meaning in life, and a critical source of these experiences: interpersonal relationships–and explore its applications to your everyday life as teenagers. We may also have some time to cover student-selected topics related to happiness in our last week.

Surface Chemistry  –  Zhan Chen (FULL)
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 lung 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 designed 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.

The Biology of Extreme Adaptations –  Sarah Raubenheimer (FULL)
Earth is full of weird and wonderful creatures and plants. The real interesting thing is why they are how they are! This course will investigate the foundations of life and survival in fauna and flora living in extreme and/or hazardous environments. We will use examples of plants and animals that persist in harsh environments (e.g., deserts, deep seas, arctic regions, caves, volcanoes, within humans and other mammals) to delve into the evolutionary adaptations that have enabled them to move into and persist in these environments. We will also relate these adaptations to global change and elaborate on how living things will need to adapt to a changing climate and how those already adapted to things like drought and extreme temperatures may be at an advantage or disadvantage depending on the system. Students taking this course will have the opportunity to research their own favorite weird and wonderful extreme forms of life, presenting this to the class as a showcase of the organisms’ lifestyle and evolutionary history (a great excuse to learn about something new and to get some experience with research and communicating science to an audience). There are so many amazing plants and animals living in extreme places, and with everything rapidly changing with global change, this creates a fascinating topic to explore as a group.

The Physics of Magic and the Magic of Physics  –  Georg Raithel (FULL)
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.