## matthias beck

some of matt's pictures
 MATH 435/735 Modern Algebra II Fall 2016

 Lecture MWF 10:10-11:00 TH 211 Prerequisites: MATH 335 (Modern Algebra) with a grade of C or better or consent of the instructor Instructor Dr. Matthias Beck Office Thornton Hall 933 Office hours Mondays 2-3 p.m., Wednesdays 11-12 p.m., Fridays 9-10 a.m. & by appointment

Course objectives. Algebra studies the structure of sets with operations, such as integers with addition and multiplication, or vector spaces with linear maps. The abstract point of view, based on an axiomatic approach, reveals many deep ideas behind seemingly innocent structures--such as the arithmetic of counting numbers--and serves as an elegant organizing tool for the vast universe of modern algebra. Generations of brilliant minds have crystallized these ideas in the concepts of groups, rings, fields, modules, and their quotient structures and homomorphisms--the topics of MATH 335 & 435/735. Our main goal in MATH 435/735 is the study of group actions, rings, modules, and fields.

Syllabus. Review of basic properties of groups and rings and their quotient structures and homomorphisms, group actions, Sylow's theorems, principal ideal domains, unique factorization, Euclidean domains, polynomial rings, modules, tensor products, field extensions, primitive roots, finite fields.

Textbook. David S. Dummit & Richard M. Foote, Abstract Algebra (3rd edition), Wiley 2004. [errata]

Homework. I will assign homework problems as we go through the material; the problems assigned in any given week are due at 9 a.m. of the following Friday. If you type your solutions, you are welcome to submit your solutions over email as a pdf attachment. We can discuss the homework problems at any time during class. You may hand them in early to be able to correct your mistakes. Although you may (and should) work together with your class mates, the solutions you hand in have to be your own.