Adventures in Combinatorial Game Theory — Adrienne Stanley FULL
In this course we are going to explore the surprising mathematics in games. This will be unlike any mathematics you have seen. This is not algebra and not calculus. There will be numbers, but they will behave unlike the numbers you have seen before. We will explore logic and strategy transforming play into problem-solving. After we have discovered the theory behind games, we will endeavor to create our own games. We then will analyze these and share them with a final game fair. Let the games begin!
Biology in the Real World – Lynn Carpenter FULL
So many times, we take biology courses and just work to remember the information, without realizing how important this information is and how often we apply it in everyday life. The purpose of this course is to give students an intensive, yet fun, hands-on course where students are introduced to the methods and techniques behind how biologists investigate real-world problems. We will focus on a variety of topics, from molecular biology and genetics to ecology, health and biotechnology. Each day we will blend short lectures, collaborative labs, and authentic research activities that will mirror professional scientific inquiry. Students will be asked to help design and run experiments as well as collect data, analyze their results (with help) and present their findings in a final showcase.
CS Math: Truth, Proofs, and Impossibility – Emily Graetz FULL
This course will take you from the deepest foundations of mathematical truth to the farthest reaches of what is possible for logic. We will start by drilling down to what it means for an argument to be true, and how we can build complex ideas out of base axioms. The proof techniques you will learn are applicable all the way from debunking misleading statistics to solving high-level competitive math problems. We will introduce additional discrete structures as needed, such as sets, functions, and graphs. Later, we will introduce what a computer scientist means by an “algorithm” and how one can “solve a problem”. Finally, we will work our way to showing that there are some problems that cannot be solved by any algorithm. In the mornings, we will work together as a class to come up with definitions and techniques to solve challenging problems. Afternoons will be more open, with time spent working on problems in smaller groups or playing games with logical underpinnings. This course will only expect familiarity with techniques and concepts from Algebra, as it will build up its own branch of math, separate from Calculus. However, it will be fairly rigorous and will expect you to be open to learning this new way of looking at the world. This material is wild and strange; all questions are welcome, and there is no such thing as a stupid question.
Geometry and the Imagination – Caleb Ashley FULL
In this MMSS course we will explore, via good will and example, the rich interplay between topology, geometry, algebra, and dynamics. We will focus particularly on low dimensional structures, curves and surfaces primarily. Our goal will be to emphasize our intuition of what is meant by a mathematical manifold and build sufficient technical apparatus to allow us to make basic computations. For example, we will develop what we mean for a space to be Euclidean, or hyperbolic or elliptic. — A guiding principle in our explorations will be that there is a kind of duality between spaces and mappings between spaces. That is, we can organize the study of more complicated spaces around the principle that mappings are a means to decompose spaces into smaller spaces or reconfigure smaller spaces into larger spaces.
We will explore the Euler characteristic, the topological classification of surfaces, and Gauss-Bonnet theorem. We will have the opportunity to build visualizations by hand and with computer programs. We will be exposed to more sophisticated 3-dimensional phenomena such as knots, Whitney’s embedding theorem, and scissors congruence.
[* note well that the name of this course is not original; it has been borrowed from several famous historical sources.]
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 – Emily Orlikoff 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 context, 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 Way – Monica 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.
Introduction to Quantum Computing – Vanessa Sih FULL
The development of quantum physics at the beginning of the 20th century made possible current technology, including computer chips, solar cells, and flat screen displays. We are now at an exciting time when quantum computers are being developed that could more efficiently solve some problems than existing “classical” computers. However, quantum physics is mysterious and predicts behavior that is not intuitive. What does it mean for a particle to tunnel through a barrier? How can objects exist in a superposition like the Schrodinger’s cat, which is both dead and alive? How is a quantum computer different from a “classical” computer? This course will introduce students to quantum theory and its applications in modern technology and quantum computing and incorporate a mix of group problem solving and hands-on activities, including demonstrations, laboratory activities, and simulations.
Modeling the Physical World – Ben Torralva FULL
Whether we are interested in designing and building the latest computer chips or Formula 1 racecars, or we wish to push the forefront of scientific understanding, computer modeling plays an essential role. In nearly all cases today, a computer model of the system is created. Sometimes the models are used to discover fundamental physics of the system. In other cases, they are used in the design and development process. Oftentimes, they are used to interpret and understand the results of tests and experiments. In this course, we will delve into the microscopic world. Our goal is to simulate the heating and melting of a solid copper crystal. We will first build the crystal one atom at a time. We will then use our computer model to simulate its heating and melting. The mathematical approximations and algorithms needed to simulate the dynamics of the interacting atoms will be developed as we progress. Surprisingly, the only math we will need is algebra. You will use the Python programming language to write your program; however, prior knowledge of Python is not necessary – we will learn the language as we go. It is only required that you have a basic understanding of how to use a computer and how to program at a rudimentary level in any programming language.
Neuroimaging: Seeing the Brain in Action – Molly Simmonite FULL
Have you ever wondered how thoughts, emotions, and memories are represented in the brain? This course explores how scientists use cutting-edge neuroimaging technology to unravel the mysteries of the mind. You’ll dive deep into techniques such as MRI, fMRI, and EEG, learning how they reveal the inner workings of the brain. Through hands-on activities, interactive demonstrations, and real-world case studies, you’ll discover how neuroimaging is used to study everything from learning and memory to emotions and decision-making. Get ready to explore the challenges of brain research, analyze real brain scans, and even design your own neuroimaging experiments. You’ll also explore the ethical considerations of neuroimaging and its impact on society and create a scientific poster that you’ll present at a mini neuroimaging conference. Embark on an exciting journey into the human brain!
Sustainable Polymers – Anne McNeil FULL
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.
Your Journey Into Data Science with Python – Xian Zhang FULL
Unlock the power of data and discover how programming can transform raw numbers into meaningful stories. This immersive course introduces students to the exciting world of data science through hands-on Python programming. The course begins with an accelerated introduction to general programming in Python. Then we will focus on Python’s scientific computing stack: NumPy and SciPy. Lastly, we will create our own data-driven projects where we can learn to clean, analyze and visualize data. From understanding basic coding concepts (data structure and algorithm) to analyzing real-world datasets, you will develop the skills that are shaping the future of technology, research and decision-making.
