Introduction To Modern Number Theory PDF Download
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| Author | : Yu. I. Manin |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 519 |
| Release | : 2006-03-30 |
| Genre | : Mathematics |
| ISBN | : 3540276920 |
Download Introduction to Modern Number Theory Book in PDF, ePub and Kindle
This edition has been called ‘startlingly up-to-date’, and in this corrected second printing you can be sure that it’s even more contemporaneous. It surveys from a unified point of view both the modern state and the trends of continuing development in various branches of number theory. Illuminated by elementary problems, the central ideas of modern theories are laid bare. Some topics covered include non-Abelian generalizations of class field theory, recursive computability and Diophantine equations, zeta- and L-functions. This substantially revised and expanded new edition contains several new sections, such as Wiles' proof of Fermat's Last Theorem, and relevant techniques coming from a synthesis of various theories.
| Author | : Kenneth Ireland |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 406 |
| Release | : 2013-04-17 |
| Genre | : Mathematics |
| ISBN | : 147572103X |
Download A Classical Introduction to Modern Number Theory Book in PDF, ePub and Kindle
This well-developed, accessible text details the historical development of the subject throughout. It also provides wide-ranging coverage of significant results with comparatively elementary proofs, some of them new. This second edition contains two new chapters that provide a complete proof of the Mordel-Weil theorem for elliptic curves over the rational numbers and an overview of recent progress on the arithmetic of elliptic curves.
| Author | : Steven J. Miller |
| Publisher | : Princeton University Press |
| Total Pages | : |
| Release | : 2020-08-04 |
| Genre | : Mathematics |
| ISBN | : 0691215979 |
Download An Invitation to Modern Number Theory Book in PDF, ePub and Kindle
In a manner accessible to beginning undergraduates, An Invitation to Modern Number Theory introduces many of the central problems, conjectures, results, and techniques of the field, such as the Riemann Hypothesis, Roth's Theorem, the Circle Method, and Random Matrix Theory. Showing how experiments are used to test conjectures and prove theorems, the book allows students to do original work on such problems, often using little more than calculus (though there are numerous remarks for those with deeper backgrounds). It shows students what number theory theorems are used for and what led to them and suggests problems for further research. Steven Miller and Ramin Takloo-Bighash introduce the problems and the computational skills required to numerically investigate them, providing background material (from probability to statistics to Fourier analysis) whenever necessary. They guide students through a variety of problems, ranging from basic number theory, cryptography, and Goldbach's Problem, to the algebraic structures of numbers and continued fractions, showing connections between these subjects and encouraging students to study them further. In addition, this is the first undergraduate book to explore Random Matrix Theory, which has recently become a powerful tool for predicting answers in number theory. Providing exercises, references to the background literature, and Web links to previous student research projects, An Invitation to Modern Number Theory can be used to teach a research seminar or a lecture class.
| Author | : Anthony Vazzana |
| Publisher | : CRC Press |
| Total Pages | : 530 |
| Release | : 2007-10-30 |
| Genre | : Computers |
| ISBN | : 1584889381 |
Download Introduction to Number Theory Book in PDF, ePub and Kindle
One of the oldest branches of mathematics, number theory is a vast field devoted to studying the properties of whole numbers. Offering a flexible format for a one- or two-semester course, Introduction to Number Theory uses worked examples, numerous exercises, and two popular software packages to describe a diverse array of number theory topi
| Author | : Oystein Ore |
| Publisher | : Courier Corporation |
| Total Pages | : 404 |
| Release | : 2012-07-06 |
| Genre | : Mathematics |
| ISBN | : 0486136434 |
Download Number Theory and Its History Book in PDF, ePub and Kindle
Unusually clear, accessible introduction covers counting, properties of numbers, prime numbers, Aliquot parts, Diophantine problems, congruences, much more. Bibliography.
| Author | : Judith Roitman |
| Publisher | : John Wiley & Sons |
| Total Pages | : 188 |
| Release | : 1990-01-16 |
| Genre | : Mathematics |
| ISBN | : 9780471635192 |
Download Introduction to Modern Set Theory Book in PDF, ePub and Kindle
This is modern set theory from the ground up--from partial orderings and well-ordered sets to models, infinite cobinatorics and large cardinals. The approach is unique, providing rigorous treatment of basic set-theoretic methods, while integrating advanced material such as independence results, throughout. The presentation incorporates much interesting historical material and no background in mathematical logic is assumed. Treatment is self-contained, featuring theorem proofs supported by diagrams, examples and exercises. Includes applications of set theory to other branches of mathematics.
| Author | : Tianxin Cai |
| Publisher | : World Scientific |
| Total Pages | : 430 |
| Release | : 2021-07-21 |
| Genre | : Mathematics |
| ISBN | : 9811218315 |
Download A Modern Introduction To Classical Number Theory Book in PDF, ePub and Kindle
Natural numbers are the oldest human invention. This book describes their nature, laws, history and current status. It has seven chapters. The first five chapters contain not only the basics of elementary number theory for the convenience of teaching and continuity of reading, but also many latest research results. The first time in history, the traditional name of the Chinese Remainder Theorem is replaced with the Qin Jiushao Theorem in the book to give him a full credit for his establishment of this famous theorem in number theory. Chapter 6 is about the fascinating congruence modulo an integer power, and Chapter 7 introduces a new problem extracted by the author from the classical problems of number theory, which is out of the combination of additive number theory and multiplicative number theory.One feature of the book is the supplementary material after each section, there by broadening the reader's knowledge and imagination. These contents either discuss the rudiments of some aspects or introduce new problems or conjectures and their extensions, such as perfect number problem, Egyptian fraction problem, Goldbach's conjecture, the twin prime conjecture, the 3x + 1 problem, Hilbert Waring problem, Euler's conjecture, Fermat's Last Theorem, Laudau's problem and etc.This book is written for anyone who loves natural numbers, and it can also be read by mathematics majors, graduate students, and researchers. The book contains many illustrations and tables. Readers can appreciate the author's sensitivity of history, broad range of knowledge, and elegant writing style, while benefiting from the classical works and great achievements of masters in number theory.
| Author | : George E. Andrews |
| Publisher | : Courier Corporation |
| Total Pages | : 292 |
| Release | : 2012-04-30 |
| Genre | : Mathematics |
| ISBN | : 0486135101 |
Download Number Theory Book in PDF, ePub and Kindle
Undergraduate text uses combinatorial approach to accommodate both math majors and liberal arts students. Covers the basics of number theory, offers an outstanding introduction to partitions, plus chapters on multiplicativity-divisibility, quadratic congruences, additivity, and more.
| Author | : Paul Pollack |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 329 |
| Release | : 2017-08-01 |
| Genre | : Mathematics |
| ISBN | : 1470436531 |
Download A Conversational Introduction to Algebraic Number Theory Book in PDF, ePub and Kindle
Gauss famously referred to mathematics as the “queen of the sciences” and to number theory as the “queen of mathematics”. This book is an introduction to algebraic number theory, meaning the study of arithmetic in finite extensions of the rational number field Q . Originating in the work of Gauss, the foundations of modern algebraic number theory are due to Dirichlet, Dedekind, Kronecker, Kummer, and others. This book lays out basic results, including the three “fundamental theorems”: unique factorization of ideals, finiteness of the class number, and Dirichlet's unit theorem. While these theorems are by now quite classical, both the text and the exercises allude frequently to more recent developments. In addition to traversing the main highways, the book reveals some remarkable vistas by exploring scenic side roads. Several topics appear that are not present in the usual introductory texts. One example is the inclusion of an extensive discussion of the theory of elasticity, which provides a precise way of measuring the failure of unique factorization. The book is based on the author's notes from a course delivered at the University of Georgia; pains have been taken to preserve the conversational style of the original lectures.
| Author | : G. Everest |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 296 |
| Release | : 2007-05-21 |
| Genre | : Mathematics |
| ISBN | : 1852339179 |
Download An Introduction to Number Theory Book in PDF, ePub and Kindle
Includes up-to-date material on recent developments and topics of significant interest, such as elliptic functions and the new primality test Selects material from both the algebraic and analytic disciplines, presenting several different proofs of a single result to illustrate the differing viewpoints and give good insight
