each section and at the end of each chapter to reinforce essential concepts. In fact, I have adhered to it rather closely at some critical points.". Number Theory : An Introduction to Pure and Applied Mathematics book cover. It had to be expanded, in accordance with my own plans, but its outline could be preserved without much change. Furthermore, the book includes more computational problems than most other number theory texts to build students familiarity and confidence with the theory.
It contained a brief but essentially com plete account of the main features of classfield theory, both local and global and it soon became obvious that the usefulness of the intended volume would be greatly enhanced if I included such a treatment of this topic. Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and integer. From the earliest times, mathematicians have given thought to the possibility of unifying the entire discipline under a small number of basic principles. Then, among some old papers of mine, I accidentally came across a long-forgotten manuscript by Chevalley, of pre-war vintage (forgotten, that is to say, both by me and by its author) which, to my taste at least, seemed to have aged very well. turn which would cast set theory in its most promising roleas the fundamental, unifying branch of mathematics.
The first part of this volume is based on a course taught at Princeton University in 1961-62 at that time, an excellent set of notes was prepared by David Cantor, and it was originally my intention to make these notes available to the mathematical public with only quite minor changes. Then, among some old papers )tPI(}jlOV, e oxov (10CPUljlr1.'CWV Aiux., llpop.dsup. In view of this we decided to go beyond the prescribed syllabus and try to understand more advanced topics. The students in my class had some background in group theory and complex analysis, and more importantly were extremely enthusiastic.
)tPI(}jlOV, e oxov (10CPUljlr1.'CWV Aiux., llpop.dsup. In Fall 2018 I taught Basic Number Theory at IIT Bombay.
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