STATE UNIVERSITY COLLEGE AT BUFFALO

Department of Mathematics

Revised Course Proposal

I. Number and title of course

Mathematics 301 - Fundamentals of Abstract Algebra
II. Reasons for addition to the present curriculum: (presently offered)
A. The course is an introduction to the topics of abstract algebra. Most of these topics are considered essential components for any student working in modern mathematics and their applications
B. The course provides a foundation for further or advanced study in abstract algebra and related areas in which the concepts are used.
III. Major objectives of the course
A. To acquaint the student with the fundamental concepts of abstract algebra such as groups, rings, and fields.
B. To give the student an understanding of the basic structure theorem for each of the algebraic systems, as well as an understanding of their proofs.
C. To show the students some applications of abstract algebra in and outside the field of mathematics.
IV. Topical Outline
A. Sets, mappings, binary operations, induction, equivalence relations, relational structures, and morphisms.
B. Groups
1. Properties and examples of semigroups, monoids, groups
2. Subgroups
3. Cylic groups
4. Permutaion groups
5. Homomorphisms and factor groups
6. Applications from areas such as finite state machines, matrices, binary group codes, block codes, symmetries, Polya enumeration theory, etc.
C. Other algebraic structures
1. Properties and examples of rings and ideals
2. Properties and examples of integral domains and fields
3. Applications from areas such as coding theory, modular arithmetic, matrices, etc.
 V.BIBLIOGRAPHY

Birkhoff, G. and Bartee, T., Modern Applied Algebra, McGraw Hill, 1970

Budden, F.J., The Fascination of Groups, Cambridge University Press, 1972

Bobrow, L.S. and Arbib, M.A., Discrete Mathematics, N.B. Saunders, 1974

Burton, D.M., Intro. to Modern Abstract Algebra, Addison-Wesley, 1967

Dornhoff, L.L.and Hohn,F.E.,Applied Modern Algebra,Macmillan,1978

Fraleigh, J.B., First Course in Abstract Algebra, Addison & Wesley, 1975

Kim, K.H. and Raush, F.W., Applied Abstract Algebra, Hoisted Press, 1983

Stone, L.S., Discrete Mathematical Structures, SEA, 1973

VI. Presentation and Evaluation

Lectures, class discussions, assigned problems, written exams.
VII. Prerequisites
MAT 202
VIII. Credit
Three semester hours.
IX. Statement of Approval
This revised course proposal was examined in accordance with Mathematics Department on recommended procedures and was approved by the faculty of the Mathematics Department
______________________________Department Chair

X. Catalog Description

Math 301-Fundamentals of Abstract Algebra
An introduction to the fundamental concepts of abstract algebra of sets, mappings, binary operations, relations, and to algebraic structures of groups, rings, fields and applications.
XI. Qualifications of faculty who will teach the course
All members of the Department of Mathematics
XII. Support Services required
Present classroom facilities are adequate.