Department of Mathematics
Revised Course Proposal
I. Number and title of course
Mathematics 301 - Fundamentals of Abstract AlgebraII. 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.
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 202VIII. 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 MathematicsXII. Support Services required
Present classroom facilities are adequate.