# Summer 2022 - MATH 342 D100

## Overview

• #### Course Times + Location:

Mo 2:30 PM – 4:20 PM
SWH 10041, Burnaby

We 2:30 PM – 3:20 PM
SWH 10041, Burnaby

• #### Exam Times + Location:

Aug 10, 2022
12:00 PM – 3:00 PM
AQ 3181, Burnaby

• #### Instructor:

Imin Chen
ichen@sfu.ca
1 778 782-3339
• #### 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 30%
• Quizzes 10%
• Midterm 20%
• Final Exam 40%

#### NOTES:

THE INSTRUCTOR RESERVES THE RIGHT TO CHANGE ANY OF THE ABOVE INFORMATION.

## Materials

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

E-Text available via VitalSource
ISBN: 9780321500311