Notes from Class
The continued fraction expansion of $\frac{4}{\pi}$ exhibits a beautiful pattern.
Lecture notes from class will appear here each evening after class.
Some students have noticed that the International Edition of the textbook mysteriously does not include the chapter Is -1 a Square Modulo $p$? Is 2?, and so I've scanned that chapter and put it online here.
- Lecture 01 - Introduction
- Lecture 02 - Pythagorean Triples
- Introduction to Sage
- Lecture 03 - The Division Algorithm and Euclid's Algorithm
- Lecture 04 - The Fundamental Theorem of Arithmetic
- Lecture 05 - Congruences
- Lecture 06 - Fermat's Little Theorem
- Lecture 07 - The Chinese Remainder Theorem
- Lecture 08 - Some facts about primes
- Lecture 09 - Squares and roots modulo $m$
- Lecture 10 - Cryptography
- Lecture 11 - Primality Testing
- Lecture 12 - Quadratic Reciprocity
- Lecture 13 - Sums of divisors
- Lecture 14 - Primitive Roots
- Lecture 15 - Indices
- Lecture 16 - Continued Fractions