Kevin Milans : Teaching : Fall 2021 Math545: Number Theory 1

Kevin Milans (milans@math.wvu.edu)
Office: Armstrong Hall 408H
Office Hours: Tu 11:30am-12:30pm, W 2:30pm-3:30pm, and by appointment
Class Meetings: TuTh 4:00pm-5:15pm in Armstrong Hall 313
Home | Course Syllabus (PDF) | Homework

Course Schedule

No. Date Class Summary Sections(s) Comments
1 Aug 19 Introduction; Induction; the sum 1 + ... + n; basis representation 1.1, 1.2 -
2 Aug 24 Basis representation; Euclid's Division Lemma; GCDs 1.2, 2.1, 2.2 HW1 assigned.
3 Aug 26 GCD Properties; Extended Euclidean Algorithm 2.2 -
4 Aug 31 Linear Diophantine Eqns; Fundamental Theorem Of Algebra 2.3, 2.4 -
5 Sep 2 Permutations and Combinations; Fermat's Little Theorem 3.1, 3.2 -
6 Sep 7 Wilson's Theorem; Residue Systems I 3.3, 4.2 HW1 due.
7 Sep 9 Residue Systems II; Riffling 4.2,4.3 HW2 assigned.
8 Sep 14 Linear Congruences 5.1,5.2 -
9 Sep 16 Chinese Remainder Theorem; Polynomial Congruences 5.3,5.4 -
10 Sep 21 Combinatorial Study of Phi function 6.1 -
11 Sep 23 Phi function and C.R.T.; Multiplicative functions 6.2-6.3 HW2 due. HW3 assigned.
12 Sep 28 Mobius Inversion 6.4 -
13 Sep 30 Properties of Reduced Reside Systems 7.1 -
14 Oct 5 Midterm Exam - -
- Oct 7 Fall Break: No Class - -
15 Oct 12 Primitive Root Modulo a Prime; Primes 7.2,8.1 HW3 due. HW4 assigned.
16 Oct 14 Prime Numbers II, divergence of sum of 1/p 8.1 -
17 Oct 19 Prime factorization of the middle binomial coefficient 8.1 -
18 Oct 21 Chebychev's Theorem 8.2 -
19 Oct 26 Bertrand's Postulate; Open problems on primes 8.2 -
20 Oct 28 Quadratic Residues; Euler's Criterion; Gauss's Lemma 9.1,9.2 HW4 due. HW5 assigned.
21 Nov 2 Quadratic Reciprocity Law 9.1,9.2 -
22 Nov 4 Seminar Talk - -
23 Nov 9 Quadratic Reciprocity Law Applications 9.4 -
24 Nov 11 Consecutive quadratic residue pairs 10.1 HW5 due. HW6 assigned.
25 Nov 16 Consecutive quadratic residue triples I 10.2 -
26 Nov 18 Consecutive quadratic resuide triples II 10.2 -
27 Nov 30 Numbers representable as the sums of two squares 11.1 HW6 due.
28 Dec 2 Characters of Groups - -
29 Dec 7 Dirichlet characters; Dirichlet L-series - -
30 Dec 9 Proof outline of Dirichlet's Theorem - -
- Dec 15 Final Exam: Wed Dec 15 8am to 10am - -
milans@math.wvu.edu