Simon Fraser University
Engaging the World

Course Outlines

Fall 2018 - MATH 340 D100

Algebra II: Rings and Fields (3)

Class Number: 4376

Delivery Method: In Person

Overview

  • Course Times + Location:

    Sep 4 – Dec 3, 2018: Mon, 11:30 a.m.–12:20 p.m.
    Burnaby

    Sep 4 – Dec 3, 2018: Wed, Fri, 11:30 a.m.–12:20 p.m.
    Burnaby

  • Exam Times + Location:

    Dec 15, 2018
    Sat, 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:


Integers and Modular Arithmetic and Polynomials
Induction
Integer division and the Euclidean algorithm
The primes and the fundamental theorem of arithmetic
Modular arithmetic and applications
Polynomial arithmetic and factorization

Rings, Domains, and Fields
Ring and field axioms
Zero divisors, units, integral domains and fields
The complex numbers and the fundamental theorem of algebra  

Ring Isomorphisms, Ideals, and Homomorphisms
Ring Homomorphisms
Functions, equivalence relations
Ideals and Kernels
Rings of Cosets
The Isomorphism Theorem for rings
Direct Product rings
Chinese Remainder Theorem

Field Extensions
Finite and Algebraic Extensions
Minimal polynomials
Classification of Finite fields

Grading

  • Assignments 15%
  • Midterm 15%
  • Final Exam 70%

Materials

REQUIRED READING:

A First Course in Abstract Algebra: Rings, Groups, and Fields
Marlow Anderson and Todd Feil
3E/2014 CRC Press LLC
ISBN: 9781482245523

RECOMMENDED READING:

Abstract Algebra
Dummit and Foote
3E/2003 Wiley
ISBN: 978-0471433347

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