In this presentation of the Galois correspondence, modern theories of groups and fields are used to study problems, some of which date back to the ancient Greeks. The techniques used to solve these problems, rather than the solutions themselves, are of primary importance. The ancient Greeks were concerned with constructibility problems. For example, they tried to determine if it was possible, using straightedge and compass alone, to perform any of the following tasks? (1) Double an arbitrary cube; in particular, construct a cube with volume twice that of the unit cube. (2) Trisect an arbitrary angle. (3) Square an arbitrary circle; in particular, construct a square with area 1r. (4) Construct a regular polygon with n sides for n > 2. If we define a real number c to be constructible if, and only if, the point (c, 0) can be constructed starting with the points (0,0) and (1,0), then we may show that the set of constructible numbers is a subfield of the field R of real numbers containing the field Q of rational numbers. Such a subfield is called an intermediate field of Rover Q. We may thus gain insight into the constructibility problems by studying intermediate fields of Rover Q. In chapter 4 we will show that (1) through (3) are not possible and we will determine necessary and sufficient conditions that the integer n must satisfy in order that a regular polygon with n sides be constructible.

Review

"It is the clearest this reviewer has ever seen... Particularly remarkable is the author's avoidance of all temptations to give pretty proofs of neatly arranged theorems at the cost of clarity... Highly recommended".

--Gian-Carlo Rota

"About this title" may belong to another edition of this title.

Store Description

50+ Million Books in stock & ready to ship! Excellent Prices, Service & Selection.

Visit Seller's Storefront

Seller's business information

Sale & Shipping Terms

Terms of Sale

When you see an item on our listing, it means we have it available in one of our warehouses right here right now, ready for same day or next day processing of your order. Over 50+ Million books in stock & ready to ship same day. Customer Service is a top priority for us, we want every customer to be 100% satisfied. We offer the world's largest selection of books, music and video. Maintaining an accurate inventory of more than 50+ Million items, we are able to ship your order the same day it is r...

More Information

Right of cancellation

Shipping Terms

SUPER FAST SHIPPING!

Shipping rates from U.S.A. to United Kingdom

Shipping rates from U.S.A. to United Kingdom
Order quantity	20 to 30 business days	15 to 25 business days
First item	� 21.96	� 73.23

Delivery times are set by sellers and vary by carrier and location. Orders passing through Customs may face delays and buyers are responsible for any associated duties or fees. Sellers may contact you regarding additional charges to cover any increased costs to ship your items.