# Fall 2020 - MATH 340 D100

## Overview

• #### Course Times + Location:

Mo, We, Fr 11:30 AM – 12:20 PM
REMOTE LEARNING, Burnaby

• #### Exam Times + Location:

Dec 9, 2020
3:30 PM – 6:30 PM
REMOTE LEARNING, 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:

This course will be delivered online. You are expected to have access to a reliable internet connection. You will need a computer from which you can download course materials and activities and watch live and/or recorded lectures and participate in live tutorials or workshops.

You will need a camera to take photographs of your work. A phone is acceptable.

#### Topics

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

#### Course Delivery

•  Lecture: synchronous- lectures will be held at fixed times, on-line
•  Midterm(s): synchronous; date: TBA
•  Final exam: synchronous; date: TBA

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

#### REQUIREMENTS:

• Ability to scan documents (phone app acceptable)

## 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