# Courses

There are two mini-courses that all SWiM participants take, and they are related to the SWiM group projects.  For each course, two SWiM counselors will be assigned to assist the instructor and to help participants with their group projects.

This year’s program, SWiM2020, offers two courses. The titles, descriptions, and instructors are listed below.

### Randomness in Numbers

Instructor: Jiuya Wang

TA: TBD

Number theory studies the first object we learn in mathematics, the integers. It is the oldest subject in not only mathematics, but also among almost all science. However it still remains mysterious nowadays. The atoms of all integers are called prime numbers. These are the numbers that cannot be written as a product of smaller integers. Many questions are asked about these fundamental numbers. For example, how many are there? How do we locate them? How many of them can be written as 4n+1? How many of them can be written as x^2+y^2, x^2+2y^2,…, x^2+dy^2, and how do we effectively locate these prime numbers with special properties? We will explore these problems with both numerical tests and theoretical deductions. We will also relate some questions about integers to probability and graph theory. No calculus experience is required.

### Strike a pose! Intro to Math Modeling

Instructor: Inmaculada C. Sorribes Rodriguez

TA: TBD

When we think about mathematical problems, we usually imagine equations and proofs; however, when we think about solving real-world problems, subjects such as biology, chemistry, or engineering more frequently come to mind. Mathematical modeling is the bridge that allows a mathematician to be a biologist, chemist, or an ecologist, depending on the problem that he/she is tackling. Applying mathematical tools, real-world problems, such as the spread of infectious diseases, can be translated to equations that mimic their behavior. When a solution to the mathematical problem is obtained, the results can be interpreted back into the language of biology, chemistry, or ecology to make predictions and find new solutions, such as new treatments. With such models, a mathematician can perform “experiments” in the mathematical representations of a real-world problem, instead of undertaking experiments in a lab, which is not always possible with these issues. In this course, we will learn how to navigate through this modeling process and become versed in the modeling of various biological problems using analytical and basic programming techniques. In particular, we will focus on population dynamics, chemical reactions, cancer, epidemics, and vaccination. No calculus or programming experience is required, just curiosity and open-mindedness!