Time | Location | Zoom Meeting ID | Zoom Password |
---|---|---|---|
T 9:30-10:00 | ORCH 3009 | N/A | N/A |
Th 9:30-11:00 | ORCH 3009 and on Zoom | 694 6667 3745 | 914585 |
F 11:45-13:00 | at PIMS and on Zoom | 676 1308 4912 | 139267 |
This is an introductory course in number theory, intended for math majors. The book by Jones and Jones is available for free download through the UBC library (you need to be on campus or loggen on to the VPN for that). That said, any book titled "elementary number theory" or the like would be good. You can also look at the notes by Freitas and Gherga.
Week | Date | Material | Reading | Scan | Notes | |
---|---|---|---|---|---|---|
Jones^2 | Rosen | |||||
1 | M 11/1 | The Integers: Induction | §1.1 | §1.3, §1.5 | Scan | Slides |
W 13/1 | Divisibility | §1.1 | §1.3, §1.5 | Scan | ||
F 15/1 | The GCD; Euclid's Algorithm | §1.2 | §3.3, §3.4 | Scan | ||
2 | M 18/1 | (continued) | Scan | |||
W 20/1 | primes | §2.1 | §3.1 | Scan | CP1 due | |
F 22/1 | Unique factorization | §2.2 | §3.2, §3.5 | Scan | ||
3 | M 25/1 | Diophantine equations | §1.5 | §3.7 | Scan | |
W 27/1 | Test 1 | Info | ||||
F 29/1 | (continued) | Scan | ||||
4 | M 1/2 | Congruence | §3.1 | §4.1 | Scan | |
W 3/2 | Divisibility tests | §5.1, §5.5 | Scan | CP2 due | ||
F 5/2 | Linear Congruences | §3.2 | §4.2 | Scan | ||
5 | M 8/2 | The CRT | §3.3 | §4.3 | Scan | |
W 10/2 | Test 2 | |||||
F 12/2 | (continued) | Scan | ||||
6 | M 22/2 | Wilson's Theorem | §4.1 | §6.1 | Scan | |
W 24/2 | Fermat's Little Theorem | §4.2 | §6.2 | Scan | ||
F 26/2 | Euler's Theorem and Pseudoprimes | §§5.1-2 | §6.3 | Scan | ||
7 | M 1/3 | Arithmetic Functions | §8.1 | §7.1, §7.2 | Scan | |
W 3/3 | (continued) | Scan | CP3 due | |||
F 5/3 | Möbius Inversion; Mersenne Primes | §8.3 | §7.4, § 7.3 | Scan | ||
8 | M 8/3 | Character & block ciphers | Wiki: 1, 2, | §8.1 | Scan | |
W 10/3 | Test 3 | |||||
F 12/3 | (continued) | Scan | ||||
9 | M 15/3 | RSA | Wiki | §8.4, §8.6 | Scan | |
W 17/3 | (continued) | Scan | CP4 due | |||
F 19/3 | Primitive Roots | §6.2, §6.3 | §9.1, §9.2 | Scan | ||
10 | M 22/3 | (continued) | Scan | |||
W 24/3 | Test 4 | |||||
F 26/3 | Existence mod p | Scan | ||||
11 | M 29/3 | Quadratic residues | §§7.1-3 | §9.4, §10.2, §11.1 | Scan | |
W 31/3 | (continued) | Scan | ||||
W 7/4 | Quadratic reciprocity | §7.4 | §11.1, §11.2 | Scan | CP5 due | |
F 9/4 | (continued) | Scan | ||||
12 | M 12/4 | The Gaussian Integers | Scan | |||
W 14/4 | Elliptic Curves | Scan | ||||
W 21/4 | Final Exam: 8:30am-11am |
Clarification: the writings on these pages are generally my own creations (to which I own the copyright), and are made available for traditional academic reuse. If you wish to republish substantial portions (including in "derivative works") please ask me for permission. The material is expressly excluded from the terms of UBC Policy 81.