# Summer 2023 - MATH 342 D100

## Overview

• #### Course Times + Location:

May 8 – Aug 4, 2023: Mon, 2:30–4:20 p.m.
Burnaby

May 8 – Aug 4, 2023: Wed, 2:30–3:20 p.m.
Burnaby

• #### Exam Times + Location:

Aug 14, 2023
Mon, 8:30–11:30 a.m.
Burnaby

• #### Instructor:

Imin Chen
ichen@sfu.ca
1 778 782-3339
• #### Instructor:

Jonathan Jedwab
jed@sfu.ca
1 778 782-3337
• #### Prerequisites:

MATH 240 or 232, with a minimum grade of C-, and one additional 200-level MATH or MACM course.

## Description

#### CALENDAR DESCRIPTION:

The prime numbers, unique factorization, congruences and quadratic reciprocity. Topics include the RSA public key cryptosystem and the prime number theorem. Quantitative.

#### COURSE DETAILS:

Topics Include:

• Numbers and Sequences, Divisibility, Prime Numbers, Dirichlet's Theorem.
• Greatest Common Divisors, The Euclidean Algorithm, Continued Fraction Expansions, Linear Diophantine Equations.
• The Fundamental Theorem of Arithmetic.
• Introduction to Congruences, Linear Congruences, The Chinese Remainder Theorem, Solving Polynomial Congruences.
• Systems of Linear Congruences, The Distribution of Primes.
• Wilson's Theorem and Fermat's Little Theorem, Euler's Theorem, Pseudoprimes.
• The Euler Phi-Function, The Sum and Number of Divisors, Moebius Inversion, Perfect Numbers and Mersenne Primes.
• Integer factorization methods, primality testing, RSA public key crypto system.
• The Order of an Integer and Primitive Roots, Primitive Roots for Primes, Index Arithmetic, The Existence of Primitive Roots.
• Quadratic Residues and Nonresidues, The Law of Quadratic Reciprocity, The Jacobi Symbol.
• Sums of Squares, Pythagorean Triples, Infinite Descent, Pell's Equation.

• Assignments 10%
• Quizzes 10%
• Midterm 20%
• Final Exam 60%

#### NOTES:

THE INSTRUCTOR RESERVES THE RIGHT TO CHANGE ANY OF THE ABOVE INFORMATION.
Students should be aware that they have certain rights to confidentiality concerning the return of course papers and the posting of marks.  Please pay careful attention to the options discussed in class at the beginning of the semester.

## Materials

Elementary Number Theory and Its Applications. Kenneth Rosen. 6th Edition; 2011 Pearson.

E-Text available via VitalSource
ISBN: 9780321500311

Your personalized Course Material list, including digital and physical textbooks, are available through the SFU Bookstore website by simply entering your Computing ID at: shop.sfu.ca/course-materials/my-personalized-course-materials.