MATH 3330 - Abstract Algebra - University of Houston
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MATH 3330 - Abstract Algebra

***This is a course guideline.  Students should contact instructor for the updated information on current course syllabus, textbooks, and course content***

Prerequisite: MATH 2318 and MATH 3325

Course Description: An introduction to groups and rings: groups, subgroups, quotients, products, homomorphisms and isomorphisms, ideals, integral domains and division rings

*Note: Formerly MATH 2431.

Textbook: Abstract Algebra: A First Course, 2nd Edition, Dan Saracino, ISBN: 9781577665366, Waveland Press, Inc.

Course Purpose: An introduction to abstract algebraic structures, emphasizing group and ring theory.

Course Objectives: Upon completion of this course, students may take Advanced Abstract Algebra - Math 4333 or Graph Theory with Applications - Math 4315.

Course Content: Sets, Cartesian products and binary operations. Properties of Integers including Principle of Mathematical Induction, congruences, Division and Euclidean Algorithms and the Fundamental Theorem of Arithmetic.

Groups, cyclic and normal subgroups, isomorphisms and homomorphisms. Finite
permutation groups, normal subgroups and quotient groups.

Rings, integral domains and fields. Time permitting - complex numbers and historical outline and significance of Galois theory and algebraic geometry emphasizing its computational character. This part of the course apart from possibly introduction to complex numbers will be excluded from tests.

Grading: Please consult your instructor's syllabus regarding any and all grading guidelines.


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