**MATH 3020.06** **Algebra
I**, 2001/2002

Time: T/R 2:30--4:00pm

Location: Vari Hall 3006

INSTRUCTOR: Yun
Gao,

Office:
Ross S624,

Telephone:
736-2100 ext. 33952

e-mail:
ygao@yorku.ca

Course page:
http://www.math.yorku.ca/Who/Faculty/YGao

OFFICE HOURS: Tuesdays and Thursdays: 4:00--5:00pm or by appointment.

Course assistant: Hernandez Hernandez,
N616 Ross

Telephone: 736-2100 ext. 20196

TEXTBOOK:

John B. Fraleigh, **A First Course in Abstract Algebra,**

6th edition, published by Addison Wesley, 1999

TOPICS TO BE COVERED:

Introduction to the basic concepts of abstract algebra, with applications:

groups (cyclic, symmetric, Lagrange's theorem, quotients,
homomorphism theorems);

rings (congruences, quotients, polynomials, integral
domains, unique factorization);

fields (field extensions, constructions with ruler
and compass).

***********************

Algebra is the study of algebraic systems, that is, sets of elements
endowed with certain operations.

A familiar example is the set of integers with the operations of addition
and multiplication.

Algebra is used in almost every branch of mathematics; indeed, it has simplified the study of mathematics by indicating connections between seemingly unrelated topics. In addition the success of the methods of algebra in unraveling the structure of complicated systems has led to its use in many fields outside of mathematics.

One aim of this course is to help students learn to write clear and concise proofs, read the mathematical literature, and communicate mathematical ideas effectively, both orally and in writing.

*Prerequisite*: AS/SC MATH 2022.03 or AS/SC/AK MATH 2222.03

Problem Session: TBA

SYLLABUS: We will study the
following sections:

Chapter 1: Groups and Subgroups
Sections 1--5

Chapter 2: More Groups and Cosets
Sections 1--4

Chapter 3: Homomorphisms and Factor Groups
Sections 1--3

Chapter 5: Introduction to Rings and Fields
Sections 1--2, 4--6

Chapter 6: Factor Rings and Ideals
Sections 1--2

Chapter 8: Extension Fields
Sections 1--4

HOMEWORK: There will be about 10 assignments. You are expected to do all of the assigned homework. The only way to learn algebra is to do it! The amount you learn in this course and the grade you receive will be proportional to the amount of time you spend doing problems.

EXAMS: There will be two tests and the final exam.

Tests:
2:30 p.m. Thursday, November 15 and February 7.

Marks:
Each of the two tests 20%; Final exam 40%;

Assignments, presentations and class participation 20%.

MISSED EXAMS: There will be no make-up exams for missed tests. Upon presentation of documentation of a valid excuse, the corresponding percentage of the final mark will be added to the final exam. With no presentation of such documentation a grade of zero will be entered for the missed tests.

IMPORTANT DATES:

Drop deadline: February 8, 2002.

HELPFUL LINKS:

York
Undergraduate Math Program