# Fall 2022 - MATH 340 D100

## Overview

• #### Course Times + Location:

Mo, We, Fr 11:30 AM – 12:20 PM
WMC 3260, Burnaby

• #### Exam Times + Location:

Dec 11, 2022
3:30 PM – 6:30 PM
WMC 3260, Burnaby

• #### Instructor:

Nils Bruin
nbruin@sfu.ca
1 778 782-3794
• #### 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:

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

• Assignments (Weekly assignments, weighted equally) 15%
• Midterm/In-Class Quiz 25%
• Final Exam 60%

#### 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 ofmarks.
Please pay careful attention to the options discussed in class at the beginning of the semester.

#### REQUIREMENTS:

This course is delivered in person, on campus. Should public health guidelines recommend limits on in person gatherings, this course may include virtual meetings. As such, all students are recommended to have access to strong and reliable internet, the ability to scan documents (a phone app is acceptable) and access to a webcam and microphone (embedded in a computer is sufficient).

## Materials

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

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.