Algebra: Abstract And Concrete

Author : Frederick M. Goodman, Department of Mathematics MLH, University Of Iowa
Pages : 585
Publication Date : August 2006
Publisher : Semisimple Press, Iowa City

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Book Excerpts:

This text provides a thorough introduction to "modern" or "abstract" algebra at a level suitable for upper-level undergraduates and beginning graduate students.

The book addresses the conventional topics: groups, rings, fields, and linear algebra, with symmetry as a unifying theme. This subject matter is central and ubiquitous in modern mathematics and in applications ranging from quantum physics to digital communications.

The most important goal of this book is to engage students in the active practice of mathematics. Students are given the opportunity to participate and investigate, starting on the first page. Exercises are plentiful, and working exercises should be the heart of the course.

The required background for using this text is a standard first course in linear algebra. Also included is a brief summary of linear algebra in an appendix to help students review. There are also appendices on sets, logic, mathematical induction, and complex numbers. It might also be useful to recommend a short supplementary text on set theory, logic, and proofs to be used as a reference and aid; several such texts are currently available.

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