STATE UNIVERSITY COLLEGE AT BUFFALO
Department of Mathematics
Request for Course
I. Number and title of course
Mathematics 302 - Abstract Algebra IIII. Reasons for addition to the present curricula
A. The course is a continuation of Math 301, providing a completion of the fundamentals of abstract algebra and its applications.III. Major objectives of the courseB. Topics such as ring properties and field theory can be introduced. These topics are ordinarily left out in the first semester course.
A. To introduce fundamental theorems concerning rings, ideals and fields.
B. To enable the student to be exposed gradually to abstract ideas and proofs, by means of illustrations and familiar examples, so that he /she may develop further facility in understanding abstract systems, their properties and applications.IV. Topical Outline
A. Rings
1. Integers and divisibilityB. Fields2. Euclidean domains and factorization
3. Ideals and congruences
4. Applications and examples
1. Finite dimensional extensionsV. Bibliography, texts, and readings2. Applications to polynomials
3. Applications to geometric constructions
4. Finite fields
5. Splitting fields and solvability
6. Applications from areas such as coding theory, cyclic codes, block designs, latin squares, etc.
Birkhoff, G. and Maclane, S. A Survey of Modern Algebra. New York: Macmillan Co., 1953.VI. Presentation and EvaluationFisher, J.L. Application Oriented Algebra, Harper & Row, 1977.
Gilbert, William J. Modern Algebra with Applications, New York: John Wiley & Sons, 1976.
Hillman & Alexanderson, A Trial Undergraduate Course in Abstract Algebra, Wadsworth, 1983.
Jacobson, N. Lectures in Abstract Algebra Vol. III. D. Van Nostrand Co. Inc., 1951.
McCoy, N.H. Rings and Ideals Buffalo, Mathematical Assoc. of America, La Salle, Illinois: The Open Court Pub. Co., 1948.
McCarthy, P. Algebraic Extensions of Fields. Waltham, Mass ., Blaisdell, 1966.
Sandler & Foster, Modern Algebra, Harper & Row, 1978
Van Der Waerden, B.L. Modern Algebra. Volume II, Ungar Publishing Co., New York, 1950.
Lectures, class discussions assigned problems, examinations.VII. Prerequisite:
Math 301VIII. Credit:
Three semester hoursIX. Statement of Approval
This revised course proposal was examined in accordance with recommended procedures and was approved by the faculty of the Mathematics DepartmentX. Catalog Description__________________________________Department Chair
Mathematics 302: Abstract Algebra II. A continuation of Math 301. Quotient fields of integral domains, polynomials rings, Euclidean domains, ideals, and factorization. Finite fields, extension fields, splitting fields, applications to geometric constructions and solvability, applications chosen from contemporary areas of coding theory, block designs, etc.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.