This course deals with some fundamental topics of algebra. Specific topics included are introduction to groups, rings and fields, ideals of rings, ring homomorphisms and isomorphisms, factor rings, extensions of fields, finite and algebraic extensions, algebraic closures, solvability of groups, Sylow theorems, free abelian groups, free groups, unique factorization and Euclidean domains, Isomorphism extension theorem, separable extensions and introduction to Galois theory.
Upon completion of this course, students will be able to:
Fraleigh, John B. A First Course in Modern Algebra. 7th Edition, 2002. ISBN: 9780201763904
Weekly Discussions: 20%
Group Projects: 15%