Algebra Abstract and Concrete (Stressing Symmetry) (2.5 Edition)

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English | 582 pages | SemiSimple Press (2011) | 9780979914201 | PDF | 5.9 Mb

This text provides a thorough introduction to "modern" or "abstract" alge-bra at a level suitable for upper-level undergraduates and beginning grad-uate students.The book addresses the conventional topics: groups, rings, fields, andlinear algebra, with symmetry as a unifying theme. This subject matter iscentral and ubiquitous in modern mathematics and in applications rangingfrom quantum physics to digital communications.The most important goal of this book is to engage students in the ac-tive practice of mathematics. Students are given the opportunity to partici-pate and investigate, starting on the first page. Exercises are plentiful, andworking exercises should be the heart of the course.The required background for using this text is a standard first coursein linear algebra. I have included a brief summary of linear algebra in anappendix to help students review. I have also provided appendices on sets,logic, mathematical induction, and complex numbers. It might also beuseful to recommend a short supplementary text on set theory, logic, andproofs to be used as a reference and aid several such texts are currently available.






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