Text: An Introduction to Abstract Algebra with
Notes to the Future Teacher, by Olympia Nicodemi, Melissa Sutherland and Gary
Towsley,
Pearson, 2007.
Prerequisites: Math 222
is listed, but little or no calculus will be assumed, just the
mathematical maturity that develops from taking Calc I, II and III.
Course Summary: You
have all been exposed to oodles of algebra from the time you
were in middle school, Algebra I, II, III, Intermediate Algebra,
College Algebra and so on.
This course will serve as a bridge between what you learned in
all of those courses and what
mathematicians today refer to as modern algebra or abstract
algebra. In modern algebra one
attempts to discover the common threads and patterns inherent in our
familiar objects such
as integers and polynomials and then "abstract" them to a more general
setting.
We begin the course with a brief introduction to Number Theory, the
study of the natural numbers,
including the principal of induction, Euclidean algorithm, divisibility
properties, factorization and
congruences. Next we will look at familiar sets such as complex
numbers, polynomials and matrices.
We'll learn about rings,
fields and domains. Finally we
will study the
concept of groups, including
permutation groups and groups of symmetries.
Content: We will cover
most of the material in the following sections of the book:
Chapter 1: Sections 1,2,3,4,6,7
Chapter 2: Sections 1,2,3,4,5,6
Chapter 3: Sections 1,2,4,5,6,7,9
Chapter 4: Sections 1,2,3,4,5,6,7,9
Chapter 5: Sections 1,2,4,6
Grading:
There will be weekly homework assignments,
the lowest of which will be dropped (the total will be about 200
points),
three hourly exams worth 80 points each and a final exam worth
160 points. Thus you may earn up to 600 points altogether.
Important dates: M-September 3, University Holiday
F-September 21, Test 1
M-October 1, University Holiday
F-October 26, Test 2
WUF-November 21-23, University Holiday
F-November 30, Test 3
M-December 10, 11:50 am - 1:40 pm, Final Exam