Simon Fraser University
Engaging the World

Course Outlines

Fall 2017 - MATH 340 D100

Algebra II: Rings and Fields (3)

Class Number: 1319

Delivery Method: In Person

Overview

  • Course Times + Location:

    Sep 5 – Dec 4, 2017: Mon, 11:30 a.m.–12:20 p.m.
    Burnaby

    Sep 5 – Dec 4, 2017: Wed, Fri, 11:30 a.m.–12:20 p.m.
    Burnaby

  • Exam Times + Location:

    Dec 10, 2017
    Sun, 12:00–3:00 p.m.
    Burnaby

  • Prerequisites:

    MATH 240 (or MATH 232 with a grade of at least B).

Description

CALENDAR DESCRIPTION:

The integers and mathematical proof. Relations and modular arithmetic. Rings and fields, polynomial rings, the Euclidean algorithm. The complex numbers and the fundamental theorem of algebra. Construction of finite fields, primitive elements in finite fields, and their application. Students with credit for MATH 332 may not take this course for further credit. Quantitative.

COURSE DETAILS:

Outline:

Integers and modular arithmetic (11 lectures)

-Proof by induction
-Integer division and the Euclidean Algorithm
-The primes and the fundamental theorem of arithmetic
-Equivalence relations and applications
-Invertible elements in Zn and Euler’s phi function
-The Chinese remainder theorem  

Rings and Fields (11 lectures)
-Ring and field axioms, zero divisors and integral domains
-Subrings, subfields, isomorphism
-Polynomial rings, division
-Roots of polynomials and the Euclidean algorithm
-The complex numbers and the fundamental theorem of algebra
-Irreducible polynomials Polynomial interpolation  

Finite Fields (12 lectures)
-Construction of finite fields
-Extension fields, number fields
-Multiplicative structure of finite fields
-Primitive elements in finite fields
-The Zech logarithm representation for small finite fields
-Minimal polynomials
-Error correcting codes Gourps, subgroups, cyclic groups

Grading

  • Assignments 20%
  • Midterm 20%
  • Final Exam 60%

Materials

REQUIRED READING:

Introduction to Applied Apgebraic Systems
Norman Reilly
Oxford University Press, 2009

*Note: This textbook is available at www.ebooks.com and will not be available at the SFU Bookstore.
ISBN: 9780199709922

Registrar Notes:

SFU’s Academic Integrity web site http://students.sfu.ca/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

ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS