{"product_id":"fields-and-galois-theory-paperback","title":"Fields and Galois Theory - Paperback","description":"\u003cp\u003eby \u003cb\u003eJohn M. Howie\u003c\/b\u003e (Author)\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThis book provides a gentle introduction to this popular subject. Assuming a background of a first course in abstract algebra, the book covers rings, ideals, quotients and homomorphisms, introduces polynomials, field extensions and splitting fields, gives a description of finite fields, and includes a brief account of the use of such fields in coding theory. It provides a readable, \"student-friendly\" introduction that takes a more \"natural\" approach to its subject (compared to the more formal introductions by Stewart and Garling), and that features clear explanations and plenty of worked examples and exercises - with full solutions - to encourage independent study.\u003c\/p\u003e\u003ch3\u003eBack Jacket\u003c\/h3\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThe pioneering work of Abel and Galois in the early nineteenth century demonstrated that the long-standing quest for a solution of quintic equations by radicals was fruitless: no formula can be found. The techniques they used were, in the end, more important than the resolution of a somewhat esoteric problem, for they were the genesis of modern abstract algebra.\u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003eThis book provides a gentle introduction to Galois theory suitable for third- and fourth-year undergraduates and beginning graduates. The approach is unashamedly unhistorical: it uses the language and techniques of abstract algebra to express complex arguments in contemporary terms. Thus the insolubility of the quintic by radicals is linked to the fact that the alternating group of degree 5 is simple - which is assuredly not the way Galois would have expressed the connection. \u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003eTopics covered include: \u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003erings and fields \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e \u003cp\u003eintegral domains and polynomials \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e \u003cp\u003efield extensions and splitting fields \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e \u003cp\u003eapplications to geometry \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e \u003cp\u003efinite fields \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e \u003cp\u003ethe Galois group \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e \u003cp\u003eequations \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003eGroup theory features in many of the arguments, and is fully explained in the text. Clear and careful explanations are backed up with worked examples and more than 100 exercises, for which full solutions are provided.\u003c\/p\u003e\u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 226\u003c\/div\u003e\u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 0.52 x 9.26 x 7.08 IN\u003c\/div\u003e\u003cdiv\u003e\n\u003cstrong\u003eIllustrated:\u003c\/strong\u003e Yes\u003c\/div\u003e\u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e December 19, 2005\u003c\/div\u003e","brand":"Books by splitShops","offers":[{"title":"Default Title","offer_id":42712982061119,"sku":"9781852339869","price":61.54,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0105\/8226\/1823\/files\/ce35aee725e8dad22616a19f185fac3a.webp?v=1765063040","url":"https:\/\/dhl-adrianne.myshopify.com\/products\/fields-and-galois-theory-paperback","provider":"BBB","version":"1.0","type":"link"}