MAT 333 Abstract Algebra
This is a sample syllabus only. Ask your instructor for the
official syllabus for your course.
The theory of groups, rings, ideals, integral domains,
fields and related results.
MAT 333 meets for three hours of lecture per week.
Students must have earned at least a "C" in a course
equivalent to MAT 271-Foundations of Higher Mathematics before
enrolling in this course. A semester of linear algebra (MAT
331) is recommended but not required.
After completing MAT 333 the student should be able to
- state definitions of basic concepts (e.g., congruence,
groups, rings, integral domains, fields, subrings,
- understand and use the Euclidean algorithm
- understand and use modular arithmetic and the Chinese
- 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
- prove that two rings or groups are, or are not,
- prove that a given set is, or is not, a subring
(subgroup, subfield, ...) of a given ring (group,
- 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.
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.
Abstract Algebra, An Introduction (2nd edition), by
Thomas W. Hungerford.
Suggested List of Topics
- Arithmetic in the Integers
- The Division algorithm
- Primes and Unique Factorization
- Congruence in the Integers and Modular Arithmetic
- Congruence and Congruence Classes
- Modular arithmetic
- 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]
- Congruence-Class Arithmetic in F[x]
- The Structure of F[x]/(p(x)) when p(x) is
- Ideals and Quotient Rings
- Ideals and Congruence
- Quotient Rings and Homomorphisms
- The Structure of R/I when I is Prime or Maximal
- Definitions, Examples, and Properties of Groups
- Isomorphisms and Homomorphisms
- Additional Topics as time permits
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 policy is set by the instructor.
Policy on Due Dates and Make-Up Work
Due dates and policy regarding make-up work are set by
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.
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
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) 243-3660 or to use telecommunications Device for the Deaf, call (310) 243-2028.
Prepared by J. Barab 2/04/00. Revised 4/28/01, 7/25/06 (G. Jennings).