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 provides an overview of many interesting properties of natural numbers, demonstrating their applications in areas such as cryptography, geometry, astronomy, mechanics, computer science, and recreational mathematics. In particular, it presents...

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...

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...

. . . 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)...

Apologies but we at Booksplease don't have a full description for this book.Book InformationISBN 9780262536356Author Thomas LinFormat PaperbackPage Count 272Imprint MIT PressPublisher MIT Press Ltd

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...

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...

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

"This book is the first volume of a two-volume textbook for undergraduates and is indeed the crystallization of a course offered by the author at the California Institute of Technology to undergraduates without any previous knowledge of number theory...

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...

Number Theory Revealed: A Masterclass acquaints enthusiastic students with the ""Queen of Mathematics''. The text offers a fresh take on congruences, power residues, quadratic residues, primes, and Diophantine equations and presents hot topics like...

In mathematics, technical difficulties can spark groundbreaking ideas. This book explores one such challenge: a problem that arose in the formative years of algebraic number theory and played a major role in the early development of the field. When...

Why are there more poor people with small bank accounts than rich people with big bank accounts? Why are there more small planets and stars than big ones in the cosmos? And why are there more small rivers than big rivers, and more harmless tremors than...

Written for advanced undergraduate and first-year graduate students, this book aims to introduce students to a serious level of p-adic analysis with important implications for number theory. The main object is the study of G-series, that is, power series...

An examination of some of the remarkable connections between group theory and arithmetic algebraic geometry over finite fieldsExponential sums have been of great interest ever since Gauss, and their importance in analytic number theory goes back a...

Apologies but we at Booksplease don't have a full description for this book.About the AuthorMathias Petreolle, University College London, United Kingdom.Alan D. Sokal, University College London, United Kingdom, and New York University, New York.Bao-Xuan...

Convolution and Equidistribution explores an important aspect of number theory--the theory of exponential sums over finite fields and their Mellin transforms--from a new, categorical point of view. The book presents fundamentally important results and a...

The investigation of three problems, perfect numbers, periodic decimals, and Pythagorean numbers, has given rise to much of elementary number theory. In this book, Daniel Shanks, past editor of Mathematics of Computation, shows how each result leads to...

The book is directed toward students with a minimal background who want to learn class field theory for number fields. The only prerequisite for reading it is some elementary Galois theory. The first three chapters lay out the necessary background in...

The Memoirs of the AMS is devoted to the publication of new research in all areas of pure and applied mathematics. The Memoirs is designed particularly to publish long papers of groups of cognate papers in book form, and is under the supervision of the...

The Memoirs of the AMS is devoted to the publication of new research in all areas of pure and applied mathematics. The Memoirs is designed particularly to publish long papers of groups of cognate papers in book form, and is under the supervision of the...

This comprehensive account of the Gross-Zagier formula on Shimura curves over totally real fields relates the heights of Heegner points on abelian varieties to the derivatives of L-series. The formula will have new applications for the Birch and...