Summer 2022 - MATH 342 D100

Elementary Number Theory (3)

Class Number: 3772

Delivery Method: In Person

Overview

  • Course Times + Location:

    May 10 – Aug 8, 2022: Mon, 2:30–4:20 p.m.
    Burnaby

    May 10 – Aug 8, 2022: Wed, 2:30–3:20 p.m.
    Burnaby

  • Exam Times + Location:

    Aug 10, 2022
    Wed, 12:00–3:00 p.m.
    Burnaby

  • 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.
  • 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.

E-Text available via VitalSource
ISBN: 9780321500311

Registrar Notes:

ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS

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TEACHING AT SFU IN SUMMER 2022

Teaching at SFU in summer 2022 will involve primarily in-person instruction.  Some courses may be offered through alternative methods (remote, online, blended), and if so, this will be clearly identified in the schedule of classes. 

Enrolling in a course acknowledges that you are able to attend in whatever format is required.  You should not enroll in a course that is in-person if you are not able to return to campus, and should be aware that remote, online, or blended courses study may entail different modes of learning, interaction with your instructor, and ways of getting feedback on your work than may be the case for in-person classes.

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 778-782-3112) as early as possible in order to prepare for the summer 2022 term.