Math 40520 Theory of Numbers (Fall 2020)
Undergraduate number theory

 

Due Set Topics
8/26 Homework 1 Gcd, Euclidean algorithm, Bezout, factorizations, base p expansions
9/2 Homework 2 The Euclidean algorithm, diophantine equations using congruences, inversion mod n
9/9 Homework 3 Multiplicative orders, Euler's function, Chinese Remainder Theorem
9/17 Homework 4 Euler's theorem, Chinese Remainder Theorem, multiplicative orders
9/23 Homework 5 The Chinese Remainder Theorem, lifting the exponent, multiplicative orders
9/30 Homework 6 The Chinese Remainder Theorem, roots mod n, Hensel's lemma, binomial coefficients mod p, Euler's function
10/7 Take-home Midterm
10/14 Homework 7 Primes, probabilistic models, Hensel's lemma, primitive roots
10/21 Homework 8 Quadratic residues, quadratic equations, Legendre symbols
10/28 Homework 9 Diophantine equations mod p, Hasse local-global, solving quadratics
11/4 Homework 10 Hasse's theorem, Hensel's lemma, continued fractions
11/11 Homework 11 Continued fractions, rational approximations, Pell's equation

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