MATH 342: Elementary Number Theory

Summer 2019


Instructor: Dr. Imin Chen, SC-K 10528, ichen@sfu.ca. Generally speaking, it is preferable to see me in person than to correspond by email. Please note that in cases when the response will be of benefit to others in the class, instead of replying to your email, I will respond by making an announcement or clarification in the next lecture.

Office Hours: During semester:

Lectures: M 2:30-4:20 pm C 9001, W 2:30-3:20 pm C9001

Tutorials:

Course Outline Additional course policies

Textbook: Elementary Number Theory and its Applications (6th edition) by Kenneth Rosen, publisher - Pearson Addison Wesley. ISBN #: 0-321-50031-8.

Exams:

Assignments are to be handed in using the Crowdmark system (you will receive an individualized email link for each assignment submission). Selected solutions will be posted on canvas.sfu.ca or explained in the tutorials.

The lowest assignment grade (percentage terms) will be dropped from the grading scheme.

Summary Slides: [Download latest version: July 26, 2019] Please note that I will be updating these summary slides as needed throughout the semeser and they are subject to changes.

 

Reminder: Press the refresh button on your browser to get the latest version of this page.

 

Course Table

  Coverage, due dates, holidays. Additonal materials and comments.
Week 1

Mathematical Reasoning and Proofs

§1.1 Example of proofs

§1.5, §3.1, §3.3 Divisibility, Prime Numbers, Greatest Common Divisors

 

Rudiments of logic and some math prizes

Week 2

§3.4 The Euclidean Algorithm

§12.2 Continued Fraction Expansions

§3.7 Linear Diophantine Equations

[Simultaneous Linear Diophantine Equations]

05.15 -> Tutorials start

05.17 -> Assignment 1

 
Week 3

§3.5 The Fundamental Theorem of Arithmetic

05.19 -> Drop Date without WD

05.20 -> Victoria Day (no classes)

 
Week 4

§4.1-§4.2 Introduction to Conguences, Linear Congruences

05.29 -> Quiz [Solutions]

05.31 -> Assignment 2

 

Week 5

§4.3-§4.5 Systems of Linear Congruences, Chinese Remainder Theorem, Polynomial Congruences

§6.1-§6.3 Wilson's Theorem, Fermat's Little Theorem, Pseudoprimes, Euler's Theorem

 

06.07-> Assignment 3

Screencast 1: Chinese Remainder Theorem

 

Week 6

§8.4 Public Key Cryptography

[Primality tests]

[Primitive Factorization Methods]

§7.1 The Euler Phi Function

§7.2-§7.3 Multiplicative Functions

06.09-> Drop Date with WD

06.14 -> Assignment 4

Screencast 2: Primitive Factorization Methods

1. Alford, W. and Granville, A. and Pomerance, C. There are infinitely many Carmichael Numbers. Ann. of Math. (2) 139 (1994), no.3, 703--722.

2. Agrawal, M. and Kayal, N. and Saxena, N. PRIMES is in P. Ann. of Math. (2) 160 (2004), no. 2, 781--793.

Week 7

§7.4 Möbius Inversion

[Greatest Integer Function]

06.21 -> Assignment 5

Practice Midterm [Solutions]

Week 8

§9.1-§9.3 Primitive Roots and Power Residues

06.26 -> Midterm [Solutions]

 
Week 9

§9.1-§9.4 Primitive Roots and Power Residues, Discrete Logarithms

07.01 -> Canada Day (no classes)

07.05 -> Assignment 6

 
Week 10

Elementary Prime Number Estimates [§3.2 The Distribution of Primes]

Probability of two natural numbers being coprime

07.12 -> Assignment 7

Screencast 3: Chebychev Theorem
Week 11

§11.1.-§11.3 Quadratic Residues, Quadratic Reciprocity, Jacobi Symbol

§13.3 Sums of Squares

07.19 -> Assignment 8

 
Week 12

§13.1 Pythagorean Triples

[Survey of Some Diophantine Equations]

§13.4 Pell's Equation

07.26 -> Assignment 9

 
Week 13

Additional Topics

Review

Practice Final [Solutions]

Short List of Topics