Simon Fraser University
Engaging the World

Course Outlines

Fall 2019 - MATH 340 D100

Algebra II: Rings and Fields (3)

Class Number: 4049

Delivery Method: In Person

Overview

  • Course Times + Location:

    Sep 3 – Dec 2, 2019: Mon, 11:30 a.m.–12:20 p.m.
    Burnaby

    Sep 3 – Dec 2, 2019: Wed, 11:30 a.m.–12:20 p.m.
    Burnaby

    Sep 3 – Dec 2, 2019: Fri, 11:30 a.m.–12:20 p.m.
    Burnaby

  • Exam Times + Location:

    Dec 4, 2019
    Wed, 8:30–11:30 a.m.
    Burnaby

  • Prerequisites:

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

Description

CALENDAR DESCRIPTION:

The integers, fundamental theorem of arithmetic. Equivalence relations, modular arithmetic. Univariate polynomials, unique factorization. Rings and fields. Units, zero divisors, integral domains. Ideals, ring homomorphisms. Quotient rings, the ring isomorphism theorem. Chinese remainder theorem. Euclidean, principal ideal, and unique factorization domains. Field extensions, minimal polynomials. Classification of finite fields. 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 (Weekly assignments, weighted equally) 15%
  • Midterm/In-Class Quiz 25%
  • Final Exam 60%

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://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

ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS