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)