# Math 312: Introduction to Number Theory

Summer Term 1, 2018
Lior Silberman

## General Information

• Office: MATX 1112, 604-827-3031
• Email: "lior" (at) Math.UBC.CA (please include the course number in the subject line, if applicable)
• Office hours: by appointment

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.

## References

1. Jones and Jones, Elementary Number Theory, Springer.
2. Rosen, Elementary Number Theory and its applications, Addison Wesley (5th or 6th edition recommended).
3. Freitas and Gherga, Math 312 notes.
4. Rivest, Shamir and Adelman, A method for obtaining digital signatures and public-key cryptosystems, Comm. ACM 21 no. 2 (1978), 120–126.)

## Lecture-by-Lecture information

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 MÃ¶bius 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
T 26/6 Final Exam: 15:30-18:00 at LSK 201

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