This page hosts material for a course I taught in spring 2018 called *Problems from the History of Mathematics* (MT 550),* *which was made possible through the Deans’ Faculty Fellowship program.

This class chronicles the history of mathematics through a diverse selection of famous historical problems. Students will learn about these problems, their solutions, and the impact each problem had on mathematics and/or metamathematics.

**LECTURE NOTES:**

Lecture 1 (1/24-1/26): The Pythagorean Theorem and Pythagorean Triples

Lecture 2 (1/29): Representation via Egyptian Fractions

Lecture 3 (1/31): The Parallel Postulate

Lecture 4 (2/2-2/5): Impossible Constructions

Lecture 5 (2/7): Classification of Regular Polyhedra

Lecture 6 (2/9): Greek Proto-Calculus

Lecture 7 (2/12-2/14): The Cattle Problem of Archimedes

Lecture 8 (2/16): Classification of Perfect Numbers

Lecture 9 (2/21): Solution to the Cubic Equation

Lecture 10 (2/23-2/26): The Fundamental Theorem of Algebra

Lecture 11 (2/28-3/2): Insolubility of the Quintic

Lecture 12 (3/5): The Congruent Number Problem

Lecture 13 (3/9): Fermat’s Last Theorem

Lecture 14 (3/12): Logarithms

Lecture 15 (3/14): Approximating Pi

Lecture 16 (3/16-3/21): Integration of Elementary Functions

Lecture 17 (3/23): The Basel Problem

Lecture 18 (4/2): The Bridges of Konigsberg

Lecture 19 (4/4-4/6): The Four Color Theorem

Lecture 20 (4/9-4/11): Kepler’s Conjecture

Lecture 21 (4/13-4/16): The Prime Number Theorem and the Riemann Hypothesis

Lecture 22 (4/18-4/25): Hilbert’s 23 Problems

Lecture 23 (4/27): A Brief History of Cryptography

**PROBLEM SETS:**

Problem Set #1 (due 2/2)

Problem Set #2 (due 2/9)

Problem Set #3 (due 2/16)

Problem Set #4 (due 2/23)

Problem Set #5 (due 3/2)

Problem Set #6 (due 3/9)

Problem Set #7 (due 3/16)

Midterm (due 3/23)

Problem Set #8 (due 4/13)

Problem Set #9 (due 4/20)

Problem Set #10 (due 4/27)

Final Exam (due 5/11)