Simon Fraser University
Engaging the World

Course Outlines

Fall 2024 - MATH 340 D100

Algebra II: Rings and Fields (3)

Class Number: 3943

Delivery Method: In Person

Overview

  • Course Times + Location:

    Sep 4 – Dec 3, 2024: Mon, Wed, Fri, 11:30 a.m.–12:20 p.m.
    Burnaby

    Oct 15, 2024: Tue, 11:30 a.m.–12:20 p.m.
    Burnaby

  • Exam Times + Location:

    Dec 17, 2024
    Tue, 12:00–3:00 p.m.
    Burnaby

  • Prerequisites:

    MATH 240 with a minimum grade of C- 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:


Binary Operations
Ring axioms
Zero divisors, units, integral domains and fields
Integers and Modular Arithmetic and Polynomials
 
Functions, equivalence relations
Induction
Ring Isomorphisms and Homomorphisms
 
Prime and irreducible elements
Ideals
Euclidean, principal ideal, and unique factorization domains
Euclidean algorithm for integers and polynomials
Unique factorization for integers and polynomials
 
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
The complex numbers and the fundamental theorem of algebra  
 

Grading

  • Assignments 15%
  • Midterm 25%
  • Final Exam 50%
  • Participation 10%

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:

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

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 term 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.