Calendar

SES # TOPICS KEY DATES
1 Introduction, Diophantine Equations, Divisibility, GCD  
2 Euclidean Algorithm, Primes Pset 1 out
3 Binomial Coefficients, Congruences  
4 Fermat, Euler, Wilson, Linear Congruences Pset 1 due, Pset 2 out
5 Linear Congruences, Chinese Remainder Theorem, Algorithms Pset 2 due, Pset 3 out
6

Primality, Factoring, RSA, Hensel's Lemma

  
7 Congruences mod Primes, Order, Primitive Roots Pset 3 due, Pset 4–1 out
8 Primitive Roots (Prime Powers), Index Calculus  
9 Midterm 1 Pset 4–2 out
10 Quadratic Residues, Quadratic Reciprocity  
11 Jacobi Symbol, Computation, Zolotareff's Definition Pset 4 due
12 Square Roots, Tonelli's Algorithm, Number of Consecutive Pairs of Squares mod p Pset 5 out
13 Cyclotomic Polynomials, Primes Congruent to 1 mod n  
14 Arithmetic Functions  
15 Mobius Inversion Formula, Zeta Functions Pset 5 due, Pset 6 out
16 Linear Recurrences  
17 Generating Functions Pset 6 due, Pset 7 out
18 Midterm 2  
19 More on Generating Functions, Two Squares Theorem  
20 Continued Fractions I Pset 7 due, Pset 8 out
21 Continued Fractions II: Inequalities  
22 Periodic Continued Fractions, Quadratic Irrationalities Pset 8 due, Pset 9 out
23 Brahmagupta-Pell Equation  
24 Four Squares Theorem Pset 9 due
25 Pythagorean Triples, Fermat Descent  
26 Rational Points on Conics