Kevin Milans : Teaching : Fall 2019 Math545: Number Theory 1

Kevin Milans (milans@math.wvu.edu)
Office: Armstrong Hall 408H
Office Hours: MW 10:30am-11:30am, and by appointment
Class Meetings: TR 2:30pm-3:45pm in Armstrong Hall 313
Home | Course Syllabus (PDF) | Homework

Course Schedule

No. Date Class Summary Sections(s) Comments
1 Aug 22 Introduction; Induction; the sum 1 + ... + n; basis representation 1.1, 1.2 -
2 Aug 27 Basis representation; Euclid's Division Lemma; GCDs 1.2, 2.1, 2.2 HW1 assigned.
3 Aug 29 Fundamental Theorem of Arithmetic 2.4 -
4 Sep 3 Linear Diophantine Eqns; Permutations and Combinations 2.3, 3.1 -
5 Sep 5 Fermat's Little Theorem; Basic Congruence Properties 3.2, 4.1 -
6 Sep 10 Residue Systems; Riffling 4.2, 4.3 HW1 due. HW2 assigned.
7 Sep 12 Linear congruences; Fermat's and Wilson's Theorems 5.1,5.2 -
8 Sep 17 Chinese Remainder Theorem; Polynomial Congruences 5.3,5.4 -
9 Sep 18 Combinatorial Study of Phi function 6.1 -
10 Sep 24 Phi function and C.R.T.; Multiplicative functions 6.2-6.3 HW2 due. HW3 assigned.
11 Sep 26 Mobius Inversion 6.4 -
12 Oct 1 Properties of Reduced Reside Systems 7.1 -
13 Oct 3 Primitive roots modulo a prime 7.2 -
14 Oct 8 Prime Numbers 8.1 HW3 due. HW4 assigned.
- Oct 10 Fall Break: No Class - -
15 Oct 15 Prime Numbers II, divergence of sum of 1/p 8.1 -
16 Oct 17 Midterm Exam - -
17 Oct 22 Chebychev's Theorem 8.2 HW4 due. HW5 assigned.
18 Oct 24 Bertrand's Postulate; Open problems on primes 8.2 -
19 Oct 29 Euler's Criterion; Legendre Symbol 9.1,9.2 -
20 Oct 31 Gauss's Lemma; Legendre symbols (-1/p) and (2/p) 9.3 -
21 Nov 5 Quadratic Reciprocity Law I 9.3 HW5 due.
22 Nov 7 Quadratic Reciprocity Law II 9.3 HW6 assigned.
23 Nov 12 Quadratic Reciprocity Law II 9.3,9.4 HW5 due; HW6 assigned.
24 Nov 14 Consecutive quadratic residue pairs 10.1 -
25 Nov 19 Consecutive quadratic residue triples I 10.2 -
26 Nov 20 Consecutive quadratic resuide triples II 10.2 Note: Makeup Class; HW6 Due Thurs Nov. 21
27 Dec 3 Numbers representable as the sums of two squares 11.1 HW7 assigned.
28 Dec 5 Sums of four squares 11.2 -
29 Dec 10 Partition Identities 12 -
30 Dec 12 Geometric number theory 15 -
- Dec 20 Final Exam: Fri Dec 20 8am to 10am - -
milans@math.wvu.edu