Number Theory

This book takes the reader on a journey from familiar high school mathematics to undergraduate algebra and number theory. The journey starts with the basic idea that new number systems arise from solving different equations, leading to (abstract) algebra...

This informative and exhaustive study gives a problem-solving approach to the difficult subject of analytic number theory. It is primarily aimed at graduate students and senior undergraduates. The goal is to provide a rapid introduction to analytic...

How many people do you need in a room before there'll be a birthday in common? Why is 70 weird, and what can we do about it? How can 56 people eat 1 pizza? In 100 bite-size chapters of no more than three pages each, Adam Spencer gives each number, 1 to...

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...

This book presents a broad, user-friendly introduction to the Langlands program, that is, the theory of automorphic forms and its connection with the theory of L-functions and other fields of mathematics. Each of the twelve chapters focuses on a...

This is the first book on the theory of multiple zeta values since its birth around 1994. Readers will find that the shuffle products of multiple zeta values are applied to complicated counting problems in combinatorics, and numerous interesting...

The present book gives an exposition of the classical basic algebraic and analytic number theory and supersedes my Algebraic Numbers, including much more material, e. g. the class field theory on which 1 make further comments at the appropriate place...

An entertaining and enlightening history of irrational numbers, from ancient Greece to the twenty-first centuryThe ancient Greeks discovered them, but it wasn't until the nineteenth century that irrational numbers were properly understood and rigorously...

This book introduces the theory of modular forms, from which all rational elliptic curves arise, with an eye toward the Modularity Theorem. Discussion covers elliptic curves as complex tori and as algebraic curves; modular curves as Riemann surfaces and...

An outrageous graphic novel that investigates key concepts in mathematicsIntegers and permutations-two of the most basic mathematical objects-are born of different fields and analyzed with separate techniques. Yet when the Mathematical Sciences...

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...

. . . both Gauss and lesser mathematicians may be justified in rejoic ing that there is one science [number theory] at any rate, and that their own, whose very remoteness from ordinary human activities should keep it gentle and clean. - G. H. Hardy, A...

The theory of elliptic curves is distinguished by its long history and by the diversity of the methods that have been used in its study. This book treats the arithmetic approach in its modern formulation, through the use of basic algebraic number theory...

Apologies but we at Booksplease don't have a full description for this book.Book InformationISBN 9780486483863Author Nikolai Vorob'EvFormat PaperbackPage Count 80Imprint Dover Publications Inc.Publisher Dover Publications Inc.Weight(grams)...

English translation of standard mathematical work on theory of numbers, first published in Latin in 1801. "Among the greatest mathematical treatises of all fields and periods."--Asger Aaboe.Book InformationISBN 9780300094732Author Carl...

The most ubiquitous, and perhaps the most intriguing, number pattern in mathematics is the Fibonacci sequence. In this simple pattern beginning with two ones, each succeeding number is the sum of the two numbers immediately preceding it (1, 1, 2, 3, 5,...

The p-adic numbers, the earliest of local fields, were introduced by Hensel some 70 years ago as a natural tool in algebra number theory. Today the use of this and other local fields pervades much of mathematics, yet these simple and natural concepts,...

This 2003 undergraduate introduction to analytic number theory develops analytic skills in the course of studying ancient questions on polygonal numbers, perfect numbers and amicable pairs. The question of how the primes are distributed amongst all the...

This new-in-paperback edition provides a general introduction to algebraic and arithmetic geometry, starting with the theory of schemes, followed by applications to arithmetic surfaces and to the theory of reduction of algebraic curves. The first part...

We see numbers on automobile license plates, addresses, weather reports, and, of course, on our smartphones. Yet we look at these numbers for their role as descriptors, not as an entity in and unto themselves. Each number has its own history of meaning,...

Apologies but we at Booksplease don't have a full description for this book.Book InformationISBN 9780486652412Author Richard W. HammingFormat PaperbackPage Count 752Imprint Dover Publications Inc.Publisher Dover Publications Inc.Weight(grams)...

How can you tell whether a number is prime? What if the number has hundreds or thousands of digits? This question may seem abstract or irrelevant, but in fact, primality tests are performed every time we make a secure online transaction. In 2002,...

The central topic of this research monograph is the relation between p-adic modular forms and p-adic Galois representations, and in particular the theory of deformations of Galois representations recently introduced by Mazur. The classical theory of...

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Part history, part philosophy, part love letter to the study of mathematics, Everything and More is an illuminating tour of infinity. With his infectious curiosity and trademark verbal pyrotechnics, David Foster Wallace takes us from Aristotle to Newton,...

A new edition of a classical treatment of elliptic and modular functions with some of their number-theoretic applications, this text offers an updated bibliography and an alternative treatment of the transformation formula for the Dedekind eta function...

Apologies but we at Booksplease don't have a full description for this book.Book InformationISBN 9780486466705Author J W S CasselsFormat PaperbackPage Count 413Imprint Dover Publications Inc.Publisher Dover Publications Inc.Weight(grams)...

Quantum mechanics and quantum field theory are highly successful physical theo ries that have numerous practical applications. Largely mathematical in character, these theories continue to stimulate the imaginations of applied mathematicians and purists...

This book is divided into two parts. The first one is purely algebraic. Its objective is the classification of quadratic forms over the field of rational numbers (Hasse-Minkowski theorem). It is achieved in Chapter IV. The first three chapters contain...

Vectors in 2 or 3 Dimensions provides an introduction to vectors from their very basics. The author has approached the subject from a geometrical standpoint and although applications to mechanics will be pointed out and techniques from linear algebra...

An elegantly dramatized and illustrated dialog on the square root of two and the whole concept of irrational numbers.ReviewsFrom the reviews: "Written by an expert teacher as a conversation between a 'master' and a 'pupil' on the threshold of...

Apologies but we at Booksplease don't have a full description for this book.Book InformationISBN 9780950273426Author J. W. S. CasselsFormat PaperbackPage Count 392Imprint London Mathematical SocietyPublisher London Mathematical SocietyWeight(grams) 524g

Apologies but we at Booksplease don't have a full description for this book.Book InformationISBN 9780486453071Author Robert T SeeleyFormat PaperbackPage Count 112Imprint Dover Publications Inc.Publisher Dover Publications Inc.Weight(grams)...

First published in 1975, this classic book gives a systematic account of transcendental number theory, that is, the theory of those numbers that cannot be expressed as the roots of algebraic equations having rational coefficients. Their study has...

Apologies but we at Booksplease don't have a full description for this book.Book InformationISBN 9780486856421Author Hans RademacherFormat PaperbackPage Count 160Imprint Dover PublicationsPublisher Dover PublicationsWeight(grams) 454g

In this paper we develop a new approach for studying overlapping iterated function systems. This approach is inspired by a famous result due to Khintchine from Diophantine approximation which shows that for a family of limsup sets, their Lebesgue measure...

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Sorry no description is available for this book at this time.

Analytic Number Theory distinguishes itself by the variety of tools it uses to establish results, many of which belong to the mainstream of arithmetic. One of the main attractions of analytic number theory is the vast diversity of concepts and methods it...

This text is an introduction to algebraic number theory for readers with a moderate knowledge of elementary number theory and some familiarity with the terminology of abstract algebra. With its exceptionally clear prose, hundreds of exercises, and...