Theory of Numbers

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