In this course we will try to develop a deeper understanding of Algebra than is found in a typical course. In particular, we will closely consider the proofs of the theorems we encounter. Algebra is a wonderful, beautiful and powerful subject; with hard work we may get a glimpse of its nature.CONTENT:
Our goal is to cover at least the following topics: Sets and relations. The integers, congruences and the Fundamental Theorem of Arithmetic. Groups and their factor groups. Commutative rings, ideals and quotient fields. The theory of polynomials: Euclidean algorithm and unique factorizations. The Fundamental Theorem of Algebra. Fields and field extensions.COURSEWORK:
The work done in conjunction for this course will consist of weekly homework assignments, two in-class midterms, and one final exam. The weekly homework assignments will be posted at http://math.berkeley.edu/~dkarp/courses/113/homework/GRADES:
Grades may be determined as follows:
The required text for this course is I. N. Herstein, Topics in Algebra, 2nd Edition.POLICY:
Late homework may have points deducted. Make-up exams are not allowed unless there is notification 24 hours in advance and is authorized by me, or in case of extreme emergency with written verification.