Math 113 Home page

In the last hundred years or so, ``algebra'' has come to mean the study of abstract structures involving operations on sets, modeled on the operations that arise from a variety of concrete geometric and combinatorial situations. In almost every branch of mathematics this kind of algebra seems to emerge as the main technical toolset which encodes the mechanics, if not the essence, of the material at hand. Math 113 is intended as an introduction to this toolset, its main applications, and the method of mathematical proof and problem solving. After a very brief review of the language of sets, we will study the main objects of "modern algebra'': groups, rings, and fields. I will try to emphasize the connections among these ideas and other branches of mathematics, as well as geometric and dynamic ways of thinking about them. Students will be expected to ask questions in office hours, class, and by email.. As a text, I will use the seventh edition of John Fraleigh's A First Course in Abstract Algebra. This is a very readable text, and students will be expected to learn a good bit of the material directly from it.. My role is to point out what I feel are the most important topics, to explain and elaborate key or unclear points in the text, and to answer questions. I can do this best if I hear from students ahead of time what may be causing them difficulty, and so I encourge them to contact me by email (ogus@math.berkeley.edu) with questions about the text, preferably before the topic is scheduled for a lecture. I have posted a syllabus, which I will update and modify as the course progresses. Be sure to consult this reguarly and to read the material in the text before the corresponding lecture.

The course will be graded in a serious manner, based on weekly homework assignments, at least one midterm, and the final exam. There may also be unannounced quizzes at random times.My grades mean the following:

A thorough understanding of the material, as well as a demonstration of originality in solving problems and writing proofs.
Good understanding of most of the material, demonstrated by familiarity with definitions and proofs and ability to solve problems.
Firm grasp of the main points, including the important definitions and theorems, ability to solve standard problems.
Familiarility with major concepts, terminology, and problem solving technqiues.
None of the above.

Alex Dugas is the graduate student instructor assigned to help answer questions, especially with the homework. His office hours will be: