This is an introductory course in number theory, intended for math majors students. 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 | Notes | |
|---|---|---|---|---|---|
| Jones^2 | Rosen | ||||
| 1 | T 15/5 | The Integers: Induction, divisibility | §1.1 | §1.3, §1.5 | Slides Scan |
| W 16/5 | The GCD, Euclid's Algorithm | §1.2 | §3.3, §3.4 | Scan | |
| Th 17/5 | (continued) Primes |
§2.1 |
§3.1 |
Scan | |
| F 18/5 | Unique factorization | §2.2 | §3.2, §3.5 | PS1 due Scan |
|
| 2 | T 22/5 | Diophantine equations | §1.5 | §3.7 | Scan |
| W 23/5 | Congruence | §3.1 | §4.1 | Scan | |
| Th 24/5 | Linear Congruences, divisibility tests, check digits | §3.2 | §4.2, §5.1, §5.5 | PS2 due Scan |
|
| F 25/5 | The CRT | §3.3 | §4.3 | Scan | |
| 3 | T 29/5 | (continued) Wilson's Theorem |
§4.1 |
§6.1 |
Scan |
| W 30/5 | Fermat's Little Theorem | §4.2 | §6.2 | Scan | |
| Th 31/5 | Euler's Theorem and Pseudoprimes Review |
§§5.1-2 |
§6.3 |
PS3 due Scan |
|
| F 1/6 | Midterm | Info | |||
| 4 | T 5/6 | Multiplicative Functions | §8.1 | §7.1, §7.2 | Scan |
| W 6/6 | Möbius Inversion; Mersenne Primes | §8.3 | §7.4, § 7.3 | Scan | |
| Th 7/6 | Character & block cyphers | Wiki: 1, 2, | §8.1 | PS4 due Scan |
|
| F 8/6 | RSA | Wiki | §8.4, §8.6 | Scan | |
| 5 | T 12/6 | Primitive Roots | §6.2, §6.3 | §9.1, §9.2 | Scan |
| W 13/6 | Existence mod p | Scan | |||
| Th 14/6 | Quadratic residues | §§7.1-3 | §9.4, §10.2, §11.1 | PS5 due Scan |
|
| F 15/6 | Quadratic reciprocity | §7.4 | §11.1, §11.2 | Scan | |
| 6 | T 19/6 | The Gaussian Integers | Scan | ||
| W 20/6 | Elliptic curves | Scan | |||
| Th 21/6 | Review | PS6 due Scan |
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| T 26/6 | Final Exam: 15:30-18:00 at LSK 201 | ||||
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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.