MAT 333 Abstract Algebra
This is a sample syllabus only. Ask your instructor for the
official syllabus for your course.
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Course Description
The theory of groups, rings, ideals, integral domains,
fields and related results.
MAT 333 meets for three hours of lecture per week.
Prerequisites
Students must have earned at least a "C" in a course
equivalent to MAT 271Foundations of Higher Mathematics before
enrolling in this course. A semester of linear algebra (MAT
331) is recommended but not required.
Objectives
After completing MAT 333 the student should be able to
 state definitions of basic concepts (e.g., congruence,
groups, rings, integral domains, fields, subrings,
homomorphism, ideal)
 understand and use the Euclidean algorithm
 understand and use modular arithmetic and the Chinese
remainder theorem
 state major theorems (e.g., the division algorithm, the
unique factorization theorem, the remainder theorem, the
factor theorem, the first, second, and third isomorphism
theorems, classification of cyclic groups, Cayley's theorem)
and be able to identify the structures to which each theorem
applies (e.g. the integers, integral domains, polynomial
rings k[x] where k is a field, groups, etc.)
 find examples of objects that satisfy given algebraic
properties (a noncommutative ring, a commutative ring but not
an integral domain, etc)
 determine whether a given conjecture is true or false,
then prove or disprove it, constructing examples where
appropriate
 prove that two rings or groups are, or are not,
isomorphic
 prove that a given set is, or is not, a subring
(subgroup, subfield, ...) of a given ring (group,
field,...)
 prove that congruence classes (or cosets) in a set S do,
or do not, inherit given properties from S
 write proofs of other simple propositions using basic
definitions and theorems
 use the techniques of abstract algebra to solve applied
problems, as appropriate.
Expected outcomes
Students should be able to demonstrate through written
assignments, tests, and/or oral presentations, that they
have achieved the objectives of MAT 333.
Method of Evaluating Outcomes
Evaluations are based on homework, class participation,
short tests and scheduled examinations covering students'
understanding of topics that are covered in MAT 333.
Text
Abstract Algebra, An Introduction (2nd edition), by
Thomas W. Hungerford.
Suggested List of Topics
 Arithmetic in the Integers

 The Division algorithm
 Divisibility
 Primes and Unique Factorization
 Congruence in the Integers and Modular Arithmetic

 Congruence and Congruence Classes
 Modular arithmetic
 Rings

 Definitions, Examples, and Properties of Rings
 Subrings, Integral Domains, and Fields
 Isomorphisms and Homomorphisms
 Arithmetic in Polynomial Rings F[x]

 Division Algorithm and Divisibility in F[x]
 Irreducibles and Unique Factorization
 Polynomial Functions, Roots, and Reducibility
 Irreducibility in Polynomial Rings over the
Rationals, Reals, and Complex Fields
 Congruence in F[x]

 CongruenceClass Arithmetic in F[x]
 The Structure of F[x]/(p(x)) when p(x) is
Irreducible
 Ideals and Quotient Rings

 Ideals and Congruence
 Quotient Rings and Homomorphisms
 The Structure of R/I when I is Prime or Maximal
 Groups

 Definitions, Examples, and Properties of Groups
 Subgroups
 Isomorphisms and Homomorphisms
 Additional Topics as time permits
Grading Policy
Students' grades are based on homework, class participation,
short tests, and scheduled examinations covering students'
understanding of the topics covered in MAT 333. The instructor
determines the relative weights of these factors.
Attendance Requirements
Attendance policy is set by the instructor.
Policy on Due Dates and MakeUp Work
Due dates and policy regarding makeup work are set by
the instructor.
Schedule of Examinations
The instructor sets all test dates except the date of the
final exam. The final exam is given at the date and time
announced in the Schedule of Classes.
Academic Integrity
The mathematics department does not tolerate cheating.
Students who have questions or concerns about academic
integrity should ask their professors or the counselors in the
Student Development Office, or refer to the University Catalog
for more information. (Look in the index under "academic
integrity".)
Accomodations for Students with Disabilities
Cal State Dominguez Hills adheres to all applicable federal, state, and local laws, regulations, and guidelines with respect to providing reasonable accommodations for students with temporary and permanent disabilities. If you have a disability that may adversely affect your work in this class, I encourage you to register with Disabled Student Services (DSS) and to talk with me about how I can best help you. All disclosures of disabilities will be kept strictly confidential. Please note: no accommodation may be made until you register with the DSS in WH B250. For information call (310) 2433660 or to use telecommunications Device for the Deaf, call (310) 2432028.
Revision history:
Prepared by J. Barab 2/04/00. Revised 4/28/01, 7/25/06 (G. Jennings).