MT 550

This page hosts material for a course I am currently teaching 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)