I wrote these notes by following closely the above two chapters. The main objects that we study in this book are number elds, rings of integers of. A brief introduction to classical and adelic algebraic. The first draft of this book followed sd01 closely, but the. The primary sources for the course were chapter 1 of swinnertondyers book a brief guide to algebraic number theory sd01 and chapter 2 of casselss article global fields cas67. This volume is the fruit of an instructional conference on algebraic number. Algebraic number theory is a branch of number theory that uses the techniques of abstract. Pdf algebraic number theory and fermat s last theorem. Updated to reflect current research, algebraic number theory and fermats last theorem, fourth edition introduces fundamental ideas of algebraic numbers and explores one of the most intriguing stories in the history of mathematicsthe quest for a proof of fermats last theorem. Swinnertondyer, trinity college, university of cambridge. Read a brief guide to algebraic number theory online, read in mobile or kindle. Algebraic number theory, which i taught at harvard during spring 2004. Download a brief guide to algebraic number theory ebook free in pdf and epub format. Ma3a6 algebraic number theory university of warwick.
Algebraic number theory studies the arithmetic of algebraic number. Introduction to algebraic number theory william stein. He wrote a very influential book on algebraic number theory in. It doesnt cover as much material as many of the books mentioned here, but has the advantages of being only 100 pages or so and being published by dover so that it costs only a few dollars. Algebraic number theory involves using techniques from mostly commutative algebra and nite group theory to gain a deeper understanding of the arithmetic of number elds and related objects e. An important aspect of number theory is the study of socalled diophantine equations. A brief guide to algebraic number theory london mathematical. This book closely builds on swinnertondyers book sd01 and casselss article cas67. The birch and swinnertondyer conjecture has been proved only in special cases. We will see, that even when the original problem involves only ordinary. Recent progress toward birch and swinnertondyer conjecture. The book covers the two basic methods of approaching algebraic number theory, using ideals and valuations, and includes material on the most usual kinds of algebraic number field, the functional equation of the zeta function and a substantial digression on the classical approach to fermats last theorem, as well as a comprehensive account of. For alternative viewpoints, students may also like to consult the books a brief guide to algebraic number theory, by h. Buy a brief guide to algebraic number theory london mathematical society student texts on.