MATH 113
The Beauty of Numbers Spring 2025
Division III Quantitative/Formal Reasoning

This course will be an introduction to number theory and mathematical thinking and logic, with emphasis throughout on mathematics as a way of thinking and approaching the world. Have you ever wondered what keeps your credit card information safe every time you buy something online? Number theory! Number Theory is one of the oldest branches of mathematics. In this course, we will discover the beauty and usefulness of numbers, from ancient Greece to modern cryptography. We will look for patterns, make conjectures, and learn how to prove these conjectures. Starting with nothing more than basic high school algebra, we will develop the logic and critical thinking skills required to realize and prove mathematical results. Topics to be covered include the meaning and content of proof, prime numbers, divisibility, rationality, modular arithmetic, Fermat’s Last Theorem, the Golden ratio, Fibonacci numbers, coding theory, and unique factorization. This course is meant to give you an appreciation for numbers and mathematics and to enhance your logical reasoning skills. Although most people will not use calculus or geometry in their jobs or everyday lives, mathematics enhances our abilities to think logically and reason effectively. This skill is useful in all aspects of life. Number theory, in particular, is a great area of mathematics that allows one to jump in right away without a lot of pre-requisite knowledge. We will look at examples, look for patterns, make conjectures, and we will spend a lot of time learning how to rigorously prove those conjectures.