Simon Fraser University
Engaging the World

Course Outlines

Summer 2023 - MATH 342 D100

Elementary Number Theory (3)

Class Number: 2193

Delivery Method: In Person

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

  • 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 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

REQUIRED READING:

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

E-Text available via VitalSource
ISBN: 9780321500311

REQUIRED READING NOTES:

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.

Registrar Notes:

ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS

SFU’s Academic Integrity website 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

RELIGIOUS ACCOMMODATION

Students with a faith background who may need accommodations during the semester are encouraged to assess their needs as soon as possible and review the Multifaith religious accommodations website. The page outlines ways they begin working toward an accommodation and ensure solutions can be reached in a timely fashion.