Abstract Algebra and Solution by Radicals

Rating:
Summary: great text
Review: There is a lot of good information here and a lot of good exercises. And at a great price, I highly recommend this little book.

Rating:
Summary: great text
Review: There is a lot of good information here and a lot of good exercises. And at a great price, I highly recommend this little book.

Rating:
Summary: stunningly good -- geared for general readers
Review: 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.

Rating:
Summary: stunningly good -- geared for general readers
Review: 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.

Rating:
Summary: Roots (as in square roots)
Review: 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.