Duke University, Math 305S (number theory)

Lecture notes

• Lecture 1: Introduction to number theory
• Lecture 1, 2: Pythagorean triples
• Lecture 3, 4, 5, 6: Modular arithmetic
• Lecture 6, 7: Sums of two squares
• Lecture 7, 8: Modular arithmetic II
• Lecture 9, 11, 12, 13: Continued fractions
• Lecture 14, 15, 16, 17: Continued fractions II
• Lecture 17, 18, 19, 21, 22: Quadratic Reciprocity
• Lecture 22, 23: Binary Quadratic Forms
• Lecture 24: Modular Forms

The textbook used for this course was "An introduction to The Theory of Numbers", fifth edition, by Niven, Zuckerman, and Montgomery. Some of the arguments in the above notes are from this text.