Simon Fraser University
Engaging the World

Course Outlines

Summer 2020 - MATH 342 D100

Elementary Number Theory (3)

Class Number: 1234

Delivery Method: In Person

Overview

  • Course Times + Location:

    May 11 – Aug 10, 2020: Mon, 2:30–4:20 p.m.
    Burnaby

    May 11 – Aug 10, 2020: Wed, 2:30–3:20 p.m.
    Burnaby

  • Exam Times + Location:

    Aug 16, 2020
    Sun, 12:00–3:00 p.m.
    Location: TBA

  • Prerequisites:

    MATH 240 or 232, 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 20%
  • Quizzes 20%
  • Midterm 20%
  • Final Exam 40%

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 t he posting of marks.
Please pay careful attention to the options discussed in class at the beginning of the semester.

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

SFU’s Academic Integrity web site http://www.sfu.ca/students/academicintegrity.html is filled with information on what is meant by academic dishonesty, where you can find resources to help with your studies and the consequences of cheating.  Check out the site for more information and videos that help explain the issues in plain English.

Each student is responsible for his or her conduct as it affects the University community.  Academic dishonesty, in whatever form, is ultimately destructive of the values of the University. Furthermore, it is unfair and discouraging to the majority of students who pursue their studies honestly. Scholarly integrity is required of all members of the University. http://www.sfu.ca/policies/gazette/student/s10-01.html

TEACHING AT SFU IN SUMMER 2020

Please note that all teaching at SFU in summer term 2020 will be conducted through remote methods. Enrollment in this course acknowledges that remote 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 believe they may need class or exam accommodations, including in the current context of remote learning, are encouraged to register with the SFU Centre for Accessible Learning (caladmin@sfu.ca or 778-782-3112) as soon as possible to ensure that they are eligible and that approved accommodations and services are implemented in a timely fashion.