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- Springer International Publishing 2014; US$ 32.29
This undergraduate textbook provides an approachable and thorough introduction to the topic of algebraic number theory, taking the reader from unique factorisation in the integers through to the modern-day number field sieve. The first few chapters consider the importance of arithmetic in fields larger than the rational numbers. Whilst some results... more...
- Springer Berlin Heidelberg 2011; US$ 93.67
This book develops the method of "algebraic patching" to realize finite groups and, more generally, to solve finite split embedding problems over fields. The method succeeds over rational function fields of one variable over "ample fields". more...
- Birkhäuser Boston 2012; US$ 106.49
One of the great successes of twentieth century mathematics has been the remarkable qualitative understanding of rational and integral points on curves, gleaned in part through the theorems of Mordell, Weil, Siegel, and Faltings. It has become clear that the study of rational and integral points has deep connections to other branches of mathematics:... more...
- Birkhäuser Boston 2009; US$ 48.37
Using a computational algebra approach, this work addresses the center and cyclicity problems as behaviors of dynamical systems and families of polynomial systems. The self-contained text contains exercises as well as historical notes and algorithms. more...
- Springer New York 2008; US$ 43.56
This book provides an accessible introduction to class field theory. It takes a traditional approach, but in a fashion which is cleaner and more streamlined than most other books on this topic. The book has been class-tested, and the author has included exercises. more...
- CRC Press 2009; US$ 231.00
Decomposing an abelian group into a direct sum of its subsets leads to results that can be applied to a variety of areas, such as number theory, geometry of tilings, coding theory, cryptography, graph theory, and Fourier analysis. Focusing mainly on cyclic groups, Factoring Groups into Subsets explores the factorization theory of abelian groups.... more...
- CRC Press 2008; US$ 67.95
The concept of factorization, familiar in the ordinary system of whole numbers that can be written as a unique product of prime numbers, plays a central role in modern mathematics and its applications. This exposition of the classic theory leads the reader to an understanding of the current knowledge of the subject and its connections to other mathematical... more...
- Springer Berlin Heidelberg 2008; US$ 150.74
Field Arithmetic explores Diophantine fields through their absolute Galois groups. The treatment starts with techniques from algebraic geometry, number theory, and profinite groups. Graduate students can effectively learn generalizations of finite field ideas. more...
- Springer New York 2007; US$ 48.37
Intended for graduate courses or for independent study, this book presents the basic theory of fields. The first part begins with a discussion of polynomials over a ring, the division algorithm, irreducibility, field extensions, and embeddings. The second part is devoted to Galois theory. The third part of the book treats the theory of binomials.... more...