Summer 2021 - MATH 342 D100

Elementary Number Theory (3)

Class Number: 1358

Delivery Method: Remote

Overview

  • Course Times + Location:

    May 12 – Aug 9, 2021: Mon, 2:30–4:20 p.m.
    Burnaby

    May 12 – Aug 9, 2021: Wed, 2:30–3:20 p.m.
    Burnaby

  • Exam Times + Location:

    Aug 17, 2021
    Tue, 3:30–6:30 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.
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.

REQUIREMENTS:

Access to strong and reliable internet.
Ability to scan documents (phone app acceptable)
Access to webcam and microphone (embedded in computer sufficient)

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 2021

Teaching at SFU in summer 2021 will be conducted primarily through remote methods, but we will continue to have in-person experiential activities for a selection of courses.  Such course components will be clearly identified at registration, as will course components that will be “live” (synchronous) vs. at your own pace (asynchronous). Enrollment 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. To ensure you can access all course materials, we recommend you have access to a computer with a microphone and camera, and the internet. In some cases your instructor may use Zoom or other means requiring a camera and microphone to invigilate exams. If proctoring software will be used, this will be confirmed in the first week of class.

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).