Abstract Algebra and Solution by Radicals [Paperback]

John E. Maxfield (Author), Margaret W. Maxfield (Author)

Book Description

Publication Date: May 12, 1992

This advanced undergraduate-level introductory textbook first addresses groups, rings, fields and polynomials, then provides coverage of Galois theory and the proof of the unsolvability by radicals of the general equations of degree 5. With many examples, illustrations, commentaries and exercises. Includes 13 appendices. Recommended for teacher education by The American Mathematical Monthly. 1971 edition.

Product Details

• Paperback: 220 pages
• Publisher: Dover Publications (May 12, 1992)
• Language: English
• ISBN-10: 0486671216
• ISBN-13: 978-0486671215
• Product Dimensions: 9.1 x 6 x 0.5 inches
• Shipping Weight: 11.4 ounces
• Average Customer Review: 4.4 out of 5 stars  See all reviews (7 customer reviews)
• Amazon Best Sellers Rank: #1,823,117 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

23 of 23 people found the following review helpful:

5.0 out of 5 stars stunningly good -- geared for general readers, May 31, 2001

By 

Ken Braithwaite (inkster, MI USA) - See all my reviews
(REAL NAME)   

This review is from: Abstract Algebra and Solution by Radicals (Paperback)

This book introduces group theory and all the math needed to prove one of the central results of Galois theory, the insolubility of the quintic. This includes prioving many ruler&compass constructions in geometry are impossible.

That sounds heavy but the remarkable thing is anyone who has taken grade 12 math should be able to follow it (with a bit of work) and anyone who has done first year algebra or calculus should be able to follow it all.

Very discursive, with a lot of sentences not just symbols to explain the ideas, and a lot of examples. Nice physical layout too.

A hard core math text written for non-mathematicians, and it succeeds. I also highly recommend it to anyone encountering groups or Galois theory for the first time.

17 of 17 people found the following review helpful:

5.0 out of 5 stars Excellent text for a first course, March 3, 2006

By 

Mike (Maryland) - See all my reviews

This review is from: Abstract Algebra and Solution by Radicals (Paperback)

I taught out of the hardcover version of this book at SUNY College at Oneonta many moons ago. It was a course for first-semester sophomore mathematics majors. The goal of the book is to develop the subject matter that is needed to prove that the fifth degree polynomial is not solvable by radicals, i.e. there is no analogy to the Quadratic Formula for the quintic. (There is for the cubic and the quartic.) We had a good time because the course was focused on this one goal and the class knew exacly where we were headed. We got there, too. It was very easy to teach from this book and students rated it very highly. The students that I taught had Calculus I and II and a Foundations course as freshmen. The prior exposure to logic, sets and methods of proof (development of the integers) was very helpful, as was the maturity gained from the calculus (although the subject matter of Calculus was not necessary). I supplemented by rigorously developing the rational numbers, saving the reals for the Intro to Analysis course that followed this one. I am now a biostatistician outside of academia, but I hope that professors who are now teaching Abstract (Modern) Algebra will consider using this text in paperback form.

17 of 18 people found the following review helpful:

5.0 out of 5 stars Roots (as in square roots), July 29, 2002

By 

John C. Landon "nemonemini" (New York City) - See all my reviews

This review is from: Abstract Algebra and Solution by Radicals (Paperback)

This charming little introit to abstract algebra is keyed on a theme of the algebraic equation, and the discovery of the insolubility of the quintic. This includes the history and final plight of the circle-squarers, and some of the history of Galois and Abel, working heroically and heuristically in the early nineteenth century without the recent easier access to the subject now available.
All math is divided into three parts, analysis, algebra, and topology and abstract algebra is no doubt abstract, but less so than analysis, and shows the beautiful hidden sructure behind number systems, from monkey-see monkey-do to counting on your fingers, to the square root of minus one and beyond. The progression from simple groups, to rings, and fields and the rest is a revelation of the complexity behind simple things and it is a pity the educational system cannot bring more to these vistas, where the elegant Galois theory caps the summits. A good book to amateurize with, and with a good mouse-hole entry for a look-see to the ultra-clever Galois theory. Superb.