This text is intended for either an applied algebra course or a modern algebra course that includes more applications than has been traditional. It is at an advanced undergraduate (junior-senior) level and is suitable for a one-semester or two-quarter course. We assume that students have already had a course in linear algebra (although we briefly review concepts from linear algebra when they are needed in the sections on fields and linear codes).
Our treatment is fairly rigorous, with almost every proof supplied. However, we have tried to concentrate on examples and applications. In an applied algebra course, which usually consists of majors in applied mathematics, computer science, and electrical engineering, the instructor will probably skip many of the proofs and concentrate on statements of results, examples, and algorithms. We also note that the last few exercises in most problem sets are usually of a more theoretical nature and can be omitted. There is too much material to cover in a single semester and the instructor will need' to make some choices.
The instructor of a modern algebra course will likely want to include most proofs but will probably omit the material on switching functions and graph theory. The first flve chapters provide ample material for a one-semester course in modern algebra, which would include many applications. We feel that present abstract algebra courses make algebra seem disjoint from the rest of the mathematics courses that a student takes. We have tried to exploit interactions between algebra and discrete mathematics and to include such contemporary applications as public-key cryptosystems and coding theory.
For an applied algebra course, one possible selection of material would be the first two chapters, III.1-IIL9, a brief discussion of rings and fields (including finite fields), V.1-V.5, and Chapter VI. If there are few electrical engineering majors in the class, then the first half of Chapter IV could be covered in place of material on switching functions.
Lax, R. F., "Modern Algebra and Discrete Structures" (1991). E-Textbooks. 3.
This Material was previously published by Pearson Education, Inc.