Abstract Algebra and Solution by Radicals

Paperback (Print)
Used and New from Other Sellers
Used and New from Other Sellers
from $2.40
Usually ships in 1-2 business days
(Save 81%)
Other sellers (Paperback)
  • All (11) from $2.40   
  • New (8) from $2.40   
  • Used (3) from $2.40   

Overview

This advanced undergraduate-level text was recommended for teacher education by The American Mathematical Monthly and praised as a "most readable book." An ideal introduction to groups and Galois theory, it provides students with an appreciation of abstraction and arbitrary postulational systems, ideas that are central to automation.
The authors take the algebraic equation and the discovery of the insolubility of the quintic as their theme. Starting with treatments of groups, rings, fields, and polynomials, they advance to Galois theory, radicals and roots of unity, and solution by radicals. Thirteen appendixes supplement this volume, along with numerous examples, illustrations, commentaries, and exercises. Students who have completed a first-year college course in algebra or calculus will find it an accessible and well-written treatment. 

Read More Show Less

Editorial Reviews

Booknews
Reprint of the Saunders edition of 1971, now printed on acid-free paper. Annotation c. Book News, Inc., Portland, OR (booknews.com)
Read More Show Less

Product Details

  • ISBN-13: 9780486477237
  • Publisher: Dover Publications
  • Publication date: 4/21/2010
  • Series: Dover Books on Mathematics Series
  • Pages: 224
  • Sales rank: 1,478,189
  • Product dimensions: 6.10 (w) x 9.20 (h) x 0.60 (d)

Table of Contents

How to Use This Book
The Negative Object of This Book
Ch. 1 Groups 1
Discussion of the Group Properties 3
Further Properties of Groups 5
Examples of Groups 9
Ch. 2 Other Abstract Algebras 18
Examples of Various Abstract Algebras 20
Countable Infinity 25
Equivalence and Other Relations 26
Isomorphism 33
Comparisons Among Abstract Algebras 43
Ch. 3 More About Groups 47
Permutations 49
Subgroups 59
Congruence and Cosets 62
Quotient Groups 70
Ch. 4 Mappings that Preserve Relations 78
Ch. 5 Groups of Prime Order; Two Alternating Groups 88
Historical Intermission 96
Some Comments on the Biographies 100
Ch. 6 Polynomials 104
Factoring Polynomials in I[x] 116
Ch. 7 Algebraic Field Extensions 125
Algebraic Numbers and Transcendental Numbers 126
Ch. 8 Galois Theory 142
Ch. 9 Radicals and Roots of Unity 150
Ch. 10 Solution by Radicals 155
Appendices 161
Appendix A - Q Has [actual symbol not reproducible] Members 163
Appendix B - R Has [actual symbol not reproducible] Members 164
Appendix C - C Has [actual symbol not reproducible] Members 166
Appendix D - Graphing Complex Numbers 167
Appendix E - A Lattice of Abstract Algebras 173
Appendix F - Modular Arithmetic 174
Appendix G - Graphical Group Representations 175
Appendix H - History of Mathematics 176
Appendix I - More About Field Extensions 177
Appendix J - More About Galois Theory 184
Appendix K - The Cyclic Group of nth Roots of Unity 189
Appendix L - Proof That a Solvable Equation Has a Solvable Galois Group 190
Appendix M - Impossible Constructions 194
Answers to Selected Exercises 199
Index 205
Read More Show Less

Customer Reviews

Be the first to write a review
( 0 )
Rating Distribution

5 Star

(0)

4 Star

(0)

3 Star

(0)

2 Star

(0)

1 Star

(0)

Your Rating:

Your Name: Create a Pen Name or

Barnes & Noble.com Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & Noble.com that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & Noble.com does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at BN.com or to post customer reviews. Please see our Terms of Use for more details.

What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

Reviews should not contain any of the following:

  • - HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
  • - Time-sensitive information such as tour dates, signings, lectures, etc.
  • - Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
  • - Comments focusing on the author or that may ruin the ending for others
  • - Phone numbers, addresses, URLs
  • - Pricing and availability information or alternative ordering information
  • - Advertisements or commercial solicitation

Reminder:

  • - By submitting a review, you grant to Barnes & Noble.com and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Noble.com Terms of Use.
  • - Barnes & Noble.com reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & Noble.com also reserves the right to remove any review at any time without notice.
  • - See Terms of Use for other conditions and disclaimers.
Search for Products You'd Like to Recommend

Recommend other products that relate to your review. Just search for them below and share!

Create a Pen Name

Your Pen Name is your unique identity on BN.com. It will appear on the reviews you write and other website activities. Your Pen Name cannot be edited, changed or deleted once submitted.

 
Your Pen Name can be any combination of alphanumeric characters (plus - and _), and must be at least two characters long.

Continue Anonymously

    If you find inappropriate content, please report it to Barnes & Noble
    Why is this product inappropriate?
    Comments (optional)