MATH 100 - The Art of Mathematical Thinking: An Introduction to the Beauty and Power of Mathematical Ideas

FDR: FM
Credits: 3 in fall and winter; 3 or 4 in spring.

Topics vary from term to term. Mathematics is a creative process whose artistic outcome is often a powerful tool for the sciences. This course gives you a new perspective into the world of mathematics while also developing your analytical reasoning skills. May be repeated for degree credit if the topics are different.

Spring 2022, MATH 100-01: The Art of Mathematical Thinking: The Mathematics of Puzzles and Games (3). Any high school mathematics class is sufficient preparation for this material. Students gain a new perspective into the world of mathematics while also developing their analytical and creative reasoning skills. In so doing, they gain an understanding of how theoretical results and concepts can be developed, used for problem-solving or for further investigation, and then how to clearly and coherently communicate their ideas and discoveries to others. In this course, we focus on mathematical reasoning to analyze various puzzles and games, which then leads to figuring out how to increase our chances of winning. The springboard for our discussion comes from the answers to the following questions: 1) Is there a good way to predict the winner of a game before the game ends? 2) Is there a strategy that will improve a player’s chance of winning a game? 3) Is the game fair? The answers depend on what we mean by good and fair. We start by carefully and precisely formulating environments in which we can discuss approaches to solving puzzles and playing games. Then, we contemplate criteria that capture the notions of goodness and fairness within these environments. Along the way, students learn the importance of precise definitions and consistent rules of logic in mathematical reasoning. (FM) Finch-Smith.

Spring 2022, MATH 100A-01: The Art of Mathematical Thinking: Mathematical Foundations of Data Science (3). This course is intended to introduce mathematical foundations of data science. We will focus on linear algebra, numerical computation, data science and the programming language. After successfully completing this course, students will develop the necessary mathematical background for data science and will be able to solve a variety of real-world data-based problems. Furthermore, via numerous examples in real life, we learn how to access information logically, understand connection analytically, and model questions mathematically. (FM) Wang.

Winter 2022, MATH 100-02: The Art of Mathematical Thinking: Mathematics of Tilings and Patterns (3). In this course we study tiling and counting proofs for many famous formulas involving the Fibonacci numbers, the Lucas numbers, continued fractions, and binomial coefficients. No prior knowledge is needed. (FM) Dresden.