MTH 515   Algebra I

Fall 2014

Instructor: Lubos Thoma                  
Office: Lippitt Hall 101F               Tel: 874.4451
Class schedule: TuTh 12:30 - 1:45pm, Lippitt Hall 201

Description:   This is the first semester of our two semester graduate algebra sequence. Algebra is one of fundamental disciplines of mathematics and an algebraic way of thinking is pervasive in much of mathematics. There are numerous applications of algebra; for example coding, computer graphics, mathematical biology (using algebraic geometry). The goal of this course is to introduce the basic concepts and facts of modern algebra. This should prepare the student to be able to manipulate and understand fairly abstract concepts, and provide the necessary background for further graduate courses.

In the first semester, we will concentrate on properties of basic algebraic structures: groups, rings, and modules. The first semester will tentatively cover chapters 1-9 of our textbook.

The second semester will concentrate on modules, fields, galois theory, commutative algebra, and more advanced topics; approximatively chapters 10, 12-19 of our textbook.

Textbook:     D. Dummit, R. Foote, Abstract Algebra, 3rd edition, Wiley 2003, ISBN-10: 0-471-43334-9, ISBN-13: 978-0-471-43334-7

Additional texts:
      J. S. Milne, Group theory, lecture notes
      T. Hungerford, Algebra, Graduate Texts in Mathematics v. 73 (v. 73), Springer 2003, ISBN-10: 0387905189, ISBN-13: 978-0387905181
      S. Lang, Algebra, Springer 2005, 3rd edition, ISBN-10: 038795385X, ISBN-13: 978-0387953854

Prerequisites: Mathematical maturity and a basic knowledge of groups and rings on the level of MTH316.

Accommodations: Any student with a documented disability is welcome to contact me as early in the semester as possible so that we may arrange reasonable accommodations. As part of this process, please be in touch with Disability Services for Students Office at 330 Memorial Union, 401-874-2098.