Class Notes List
These are given in reverse chronological order. I give no guarantees on their correctness! If you find any mistakes, feel free to email me with corrections.
You might be interested in consulting last year's notes. The notes from this year will be based on last year's, but they'll be updated. Besides typo correction, I might add or remove a few examples, and the notes will also be made more friendly for computer reading, as the pdfs will have internal links which will facilitate navigation of the notes.
- Class 28, Nov 28, 30 2011: Calculating the Legendre symbol
- Class 27, Nov 22 2011: Introduction to quadratic residues
- Class 26, Nov 21 2011: Calculations with primitive roots
- Class 25, Nov 18 2011: The general case of \( U_{n} \)
- Class 24, Nov 16 2011: \( U_{p^e} \), when \( p \) is an odd prime
- Class 23, Nov 14 2011: Primitive roots, \( U_{p} \) is cyclic
- Class 21, 22, Nov 9, 11 2011: Introduction to group theory
- Class 20, Nov 4 2011: Hensel's Lemma
- Class 19, Nov 2 2011: The Caesar cipher and RSA cryptosystem
- Class 17, 18, Oct 28, 31 2011: The Fermat-Euler Theorem
- Class 16, Oct 26 2011: Compositeness tests
- Class 15, Oct 24 2011: Fermat's Little Theorem
- Class 13, 14, Oct 19, 21 2011: Polynomial congruences mod a prime p
- Class 12, Oct 17 2011: The Chinese Remainder Theorem, simultaneous linear congruences
- Class 11, Oct 14 2011: Linear congruences
- Class 10, Oct 12 2011: Introduction to congruences
- Class 9, Oct 10 2011: Primality testing, factorization, the sieve of Eratosthenes
- Class 8, Oct 7 2011: Mersenne and Fermat numbers
- Class 7, Oct 5 2011: Counting primes
- Class 6, Oct 3 2011: The Fundamental Theorem of Arithmetic
- Class 5, Sep 30 2011: Euclid's Lemma, least common multiples.
- Class 4, Sep 28 2011: Bezout's identity
- Class 3, Sep 26 2011: Euclidean divisions, greatest common divisors, and the Euclidean algorithm
- Class 2, Sep 23 2011: Sets, logical statements, induction, divisibility
- Class 1, Sep 21 2011: Introduction to number theory
- Introductory Presentation, Sep 21 2011