Summer 2022  MATH 342 D100
Elementary Number Theory (3)
Class Number: 3772
Delivery Method: In Person
Overview

Course Times + Location:
Mo 2:30 PM – 4:20 PM
SWH 10041, BurnabyWe 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 7823339

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 PhiFunction, 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.
 Additional topics and applications.
Grading
 Assignments 30%
 Quizzes 10%
 Midterm 20%
 Final Exam 40%
NOTES:
THE INSTRUCTOR RESERVES THE RIGHT TO CHANGE ANY OF THE ABOVE INFORMATION.
Materials
REQUIRED READING:
Elementary Number Theory and Its Applications. Kenneth Rosen. 6th Edition; 2011 Pearson.
EText available via VitalSource
ISBN: 9780321500311
Registrar Notes:
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TEACHING AT SFU IN SUMMER 2022
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Students with hidden or visible disabilities who may need class or exam accommodations, including in the context of remote learning, are advised to register with the SFU Centre for Accessible Learning (caladmin@sfu.ca or 7787823112) as early as possible in order to prepare for the summer 2022 term.