Abstract Algebra Course Syllabus 19x21

Math 367 Abstract Algebra Syllabus: Week 1 Groups, subgroups, cosets, Lagrange's theorem. Week 2 Normal subgroups, Factor groups, homomorphisms. Week 3 Isomorphism, isomorphism theorems, direct products. Week 4 Groups acting on sets, Cauchy's theorem, Class equation. Week 5 Statements of Sylow theorems and the fundamental theorem on finite abelia n groups. Week 6 Rings, ideals, quotient rings, homomorphisms. Week 7 Isomorphisms, isomorphism theorems, prime and maximal ideals. Week 8 Integral domains, field of fractions. Week 9 Euclidean domains, PIDs, UFDs. Week 10 Polynomials, polynomials in several variables. Week 11 Field extensions, algebraic and transcendental elements. Week 12 Finite extensions, algebraically closed fields. Week 13 Impossibility of certain geometric constructions. Week 14 Finite fields. Goals: The goal of the course is to give fundamental concepts of abstract algebr a and thus to exhibit a typical model of mathematics as much as possible. Prerequisite Course: Math 116 Textbook: Abstract Algebra by I. N. Herstein, Third Edition, Prentice Hall, 1996 . Other Books: "Abstract Algebra" by Dummit and Foote, Prentice Hall, 1991. "Algebra: Abstract and Concrete" by F. M. Goodman, Prentice Hall, 1998. "Contemporary Abstract Algebra" by J. A. Gallian, D. C. Heath and Company, 1994 . "A First Course in Abstract Algebra" by J. J. Rotman, Prentice Hall, 2000. "A First Course in Abstract Algebra" by J. B. Fraleigh, Addison-Wesley. "Fundamentals of Abstract Algebra" by D. S. Malik, J. N. Mordeson, M. K. Sen, M cGraw-Hill, 1997.