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  • A Concrete Approach to Abstract Algebra (Dover Books on Mathematics)

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W. W. Sawyer
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A Concrete Approach to Abstract Algebra (Dover Books on Mathematics)

by W. W. Sawyer (Author)
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Brief, clear, and well written, this introduction to abstract algebra bridges the gap between the solid ground of traditional algebra and the abstract territory of modern algebra. The only prerequisite is high school–level algebra.
Author W. W. Sawyer begins with a very basic viewpoint of abstract algebra, using simple arithmetic and elementary algebra. He then proceeds to arithmetic and polynomials, slowly progressing to more complex matters: finite arithmetic, an analogy between integers and polynomials, an application of the analogy, extending fields, and linear dependence and vector spaces. Additional topics include algebraic calculations with vectors, vectors over a field, and fields regarded as vector spaces. The final chapter proves that angles cannot be trisected by Euclidean means, using a proof that shows how modern algebraic concepts can be used to solve an ancient problem. Exercises appear throughout the book, with complete solutions at the end.
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  1. ISBN-10
    0486824616
  2. ISBN-13
    978-0486824611
  3. Publisher
    Dover Publications
  4. Publication date
    August 15, 2018
  5. Part of series
    Dover Books on Mathematics
  6. Language
    English
  7. Dimensions
    5.5 x 0.6 x 8.4 inches
  8. Print length
    240 pages
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Editorial Reviews

About the Author

Walter Warwick Sawyer (1911–2008) studied mathematics at St. John's College, Cambridge, and taught all over the world, starting at the universities of Dundee and Manchester and later at the University of Ghana and Canterbury College in New Zealand. He was Professor of Mathematics at Wesleyan University in Connecticut and on the faculty at the University of Toronto. His 11 books include the Dover publications Prelude to Mathematics, Mathematician's Delight, Vision in Elementary Mathematics, and A First Look at Numerical Functional Analysis.

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Customer reviews

4.8 out of 5 stars
23 global ratings

Top reviews from the United States

  • sp
    5.0 out of 5 stars Excellent down to Earth book on abstract algebra
    Reviewed in the United States on April 29, 2010
    Verified Purchase
    W.W. Sawyer was one of the most innovative mathematics teachers of his
    time. The idea of this book was to make abstract mathematics understandable
    to those looking in from the outside - such as engineers. This book has much
    to offer the reader in terms of originality and pedagogy. However, be warned that
    although it is above the level of bedtime reading, this book
    is not suitable for use as a textbook in a university abstract algebra course as
    it does not cover all the requisite material. Readers looking for a glimpse into modern algebra
    who do not want to deal with the turgid theorem/proof style of modern mathematics
    texts will find this book easy and rewarding reading. Those taking a class in abstract algebra
    will find this book more useful as supplementary reading. If you enjoy this book
    I would also recommend the more mainstream (but still excellent and original)
    text "A Book of Abstract Algebra" by Pinter. The combination of these books
    gave me the tools I needed to learn the basics of abstract algebra without
    having to subject myself to the snobbish and elitist undertones found in most advanced
    mathematics texts on this subject matter.

    Good Luck !
    ~
    43 people found this helpful
    Helpful
     Report
  • HappyGoLucky9
    5.0 out of 5 stars Well written book
    Reviewed in the United States on November 9, 2018
    Format: PaperbackVerified Purchase
    Very helpful explaining a very complex subject
    One person found this helpful
    Helpful
     Report
  • Kyle B.
    5.0 out of 5 stars An Excellent Short Introduction to Modern Algebra
    Reviewed in the United States on March 20, 2021
    Format: PaperbackVerified Purchase
    This is another excellent mathematics textbook written by WW Sawyer. If you would like to learn what Modern Algebra (or "Abstract Algebra") is about, this book starts from simple examples and builds up your intuition excellently. You understand why some axioms or properties are chosen for study, and how they can be used to enrich our understanding of number systems. I also thought the exercises were well crafted. The only complaint I have is that the the degree of a field extension was covered too quickly, and so was not clear to me until I consulted a different abstract algebra book. Other than that, I thought Sawyer clearly presented concepts, motivated them, and gave useful examples. He goes through the steps of examples, as well, which I often find as useful as the surrounding explanations.

    The book is really an introduction to the subject, however, so if you want a full treatment of modern algebra, you will need to consult other texts.
    2 people found this helpful
    Helpful
     Report

Top reviews from other countries

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  • Savino Longo
    5.0 out of 5 stars Go from zero to (algebraic) field theory
    Reviewed in Italy on May 2, 2021
    Format: PaperbackVerified Purchase
    This book is wonderful. At first glance it may seem too elementary, especially for those who have already studied some mathematics, but don't be fooled by the central part where the fundamentals of vector spaces are exposed. You can safely skip these two chapters if you have studied engineering or mathematics or physics. The important thing is to understand that in a book of this type the vector spaces are then used as a tool for the theory of the extensions of algebraic fields! In reality, this book wonderfully explains, with a practical approach, the theory of the extensions of algebraic fields, and then crowns the whole treatment arriving at the demonstration of the impossibility of constructing some angles with ruler and compass. That's all it takes to have a first coherent and contained exposure to the way impossibility theorems are proved in abstract algebra! I suggest reading this book and then moving on to a manual that talks about Galois groups and isomorphisms.
    Report
  • jim
    5.0 out of 5 stars very readable
    Reviewed in the United Kingdom on November 27, 2024
    Format: PaperbackVerified Purchase
    a little gem
    Report
  • Eds
    5.0 out of 5 stars Unusual Approach
    Reviewed in the United Kingdom on February 26, 2013
    Verified Purchase
    This is a classic book that takes an unusual approach to abstract algebra. Worth a look. Not recommended as a standard course though.
    Report
  • Giuseppe
    5.0 out of 5 stars Un testo per comprendere l’algebra moderna.
    Reviewed in Italy on February 13, 2020
    Format: PaperbackVerified Purchase
    Un testo di algebra abbastanza semplice e profondo. L’autore di pone dal punto di vista delle difficoltà del lettore cercando di sviscerare i concetti e lo spirito dell’algebra moderna.
    Report
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