This course focuses on theoretical mathematics that is not typically part of a traditional high school curriculum. The course covers a variety of topics including: logic, set theory, number theory and combinatorics. An emphasis is placed on proof throughout the course and different techniques of proof, including mathematical induction, direct proof and proof by contradiction will be discussed. While some applications will be considered, this course will primarily focus on theoretical concepts.

This course is titled A Bridge to Higher Mathematics because it will help to teach you the reasoning and proof - writing skills that you will need for higher - level university mathematics, and more generally, STEM courses. It will give you a path for learning the skills that you need to succeed in higher - level mathematics.

Is the universe infinite or finite? What is the curvature and overall shape of the space we live in, and how might we detect this? In this course, participants learn how models for topological spaces relate to theories on the shape of the physical universe. Philosophical discussions are informed by pencil and paper computations, experiments with common household materials, and interactive online games and modules.Participants gain, in addition to early exposure to modern content at the intersection of topology and physical cosmology, an appreciation for rigorous mathematical thinking that is motivated not so much by numbers and quantity as by profound questions about the nature of our world.

Designed for aspiring physicists and mathematicians, students will delve into the powerful mathematical tools essential for understanding and solving complex physical problems.

Students will develop an understanding of these methods by learning to model, analyze, conduct theoretical investigations and interpret physical phenomena. Through engaging lectures, hands-on problem-solving, and interactive projects, participants will gain proficiency in applying concepts to real-world scenarios. Emphasis will be placed on developing critical thinking skills and intuition to tackle challenges encountered in theoretical and experimental physics.

This course provides a valuable head start for those planning to pursue studies in physics, engineering, mathematics, or related fields at the collegiate level. 

In this course, you'll explore how statistics plays a crucial role in the world of finance. From understanding how financial markets work to learning how to manage risk and make predictions, this course introduces you to the tools that finance professionals use every day. Whether you're interested in stocks, investment strategies, or risk management, you'll gain a solid foundation in how to analyze financial data and make informed decisions using statistical methods.

Throughout the course, you'll work with real-world financial data, apply statistical techniques like probability and regression, and explore the basics of portfolio management and/or market trends. You’ll also participate in group projects, stock market simulations, and case studies that help bring the theory to life. By the end of the course, you'll not only understand how statistics and finance are connected, but you’ll also have the skills to analyze financial information and even predict future trends. Whether you're considering a career in finance, economics, or data science, this course will give you a head start and a deeper understanding of the power of numbers in the business world.

In this course intended for students who enjoy mathematics and logical reasoning, participants explore innovative ways in which math is used in the real world, in fields such as economics, computer science, media, and the physical sciences. By engaging with challenging practical problems, students hone their independent thinking and problem-solving skills.

Areas covered include the following:

• Graph theory, a topic heavily developed by both mathematicians and computer scientists. We explore algorithmic ways to compute, for example, the optimal path between two points on a map (minimizing cost, time, or another parameter). Another application is minimizing the cost of an electrical network which has to provide power to all residents in a new neighborhood.
• Probability and its numerous applications. We look at how probabilities are applied in economics and in popular media, and examine how they can sometimes be counter-intuitive or even deceptive.
• Various counting methods, combinatorics, and examples of Nash equilibria. We study applications of these techniques in economics (the prisoner's dilemma), computer science (assessing the complexity of an algorithm), finance (loans and investments), and biology (population growth).

Students work individually and in groups to find creative solutions to given problems. Each student also works on a project of his or her own choosing, on a topic about which he or she is passionate.