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
Terms and Conditions:
| Frederick M. Goodman wrote: |
If you use this text in a course, or if you make serious use of the text for private study, I ask you to do two things.
1. In place of an author's royalty, make a donation of $10 or more to some organization devoted to relieving the misery of the world, for example Unicef, Doctors Without Borders, or Oxfam.
2. Contact me and let me know that you are using the text. I will be happy to hear suggestions for improvements.
|
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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