Abstract Algebra: A Computational Approach

by Charles C. Sims

From Preface: "This book is intended as a text for a one-year introductory course in abstract algebra in which algorithmic questions and computation are stressed. A significant amount of computer... This description may be from another edition of this product.

• Format: Hardcover
• Language: English
• ISBN: 0471098469
• ISBN13: 9780471098461
• Release Date: January 1984
• Publisher: John Wiley & Sons
• Length: 491 Pages
• Weight: 2.00 lbs.

Customer Reviews

a great book for non-math majors

Abstract Algebra, A Computational Approach is an introductory textbook on abstract algebra that emphasises the "hands on" approach of computing and calculating everything imaginable: Sets, groups, rings, fields, and the operations on them. This wonderful book struggles with a major problem in math education: How do you get a class of 40 students to visualise abstract algebra? Ideally, you'd want to give many examples and problems for them to work out. Soviet books have traditionally taken this approach, so with many Soviet math books there was a compendium of "1000 solved problems in... ". There are similar books in English, but only for the most elementary courses. Having a few dosen books with solved problems in Topology, for example, would have been a great thing, but there isn't any economic motivation for such books. Alternately, if it were possible to calculate and compute things, then students could experiment with and explore the subject matter on their own. This is what graphing calculators, for example, did to intro calculus classes -- it made it possible for students to experiment and visualise the subject matter like nothing else.But how do you visualise abstract algebra? You could write computer programs to do such things as compute permutations, intersect sets, solve matrices, etc, but in "mainstream" programming languages this would take a while, be error prone and slow down the class. It wouldn't be practical. The author's solution: Use APL! APL is a programming language designed specifically for concisely manipulating vectors and matrices. APL programs are so concise that in one or two lines of APL code students can accomplish what would otherwise take hundreds of lines of C code. With a few keystrokes, students could be performing complex operations on groups and fields and sets. APL is fun, quick and concise, and students will be focused on what really matters -- abstract algebra, rather than delving into the nuts and bolts o yet-another programming language. APL to abstract algebra is like a graphing calculator to studying functions -- it helps, it's fun, it gives intuition and insight.The book doesn't cover as much material as, say, Herstein's book. On the other hand, it will give the students a quick feel for the subject matter. Perhaps the book would be ideal for computer science majors and other non-math majors that are expected to take two semesters of abstract algebra. Another minor issue is that the dialect of APL used in the book is a bit old -- the code's great, but I think the students would have a better experience with APL2 or J. J has a richer numeric tower and much of the supporting software is made redundant by it.