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Books > Science & Mathematics > Mathematics > Number theory

Algebra 1 - Groups, Rings, Fields and Arithmetic (Paperback, Softcover reprint of the original 1st ed. 2017): Ramji, Lal Algebra 1 - Groups, Rings, Fields and Arithmetic (Paperback, Softcover reprint of the original 1st ed. 2017)
Ramji, Lal
R1,813 Discovery Miles 18 130 Ships in 10 - 15 working days

This is the first in a series of three volumes dealing with important topics in algebra. It offers an introduction to the foundations of mathematics together with the fundamental algebraic structures, namely groups, rings, fields, and arithmetic. Intended as a text for undergraduate and graduate students of mathematics, it discusses all major topics in algebra with numerous motivating illustrations and exercises to enable readers to acquire a good understanding of the basic algebraic structures, which they can then use to find the exact or the most realistic solutions to their problems.

A Primer for Undergraduate Research - From Groups and Tiles to Frames and Vaccines (Paperback, Softcover reprint of the... A Primer for Undergraduate Research - From Groups and Tiles to Frames and Vaccines (Paperback, Softcover reprint of the original 1st ed. 2017)
Aaron Wootton, Valerie Peterson, Christopher Lee
R1,776 Discovery Miles 17 760 Ships in 10 - 15 working days

This highly readable book aims to ease the many challenges of starting undergraduate research. It accomplishes this by presenting a diverse series of self-contained, accessible articles which include specific open problems and prepare the reader to tackle them with ample background material and references. Each article also contains a carefully selected bibliography for further reading. The content spans the breadth of mathematics, including many topics that are not normally addressed by the undergraduate curriculum (such as matroid theory, mathematical biology, and operations research), yet have few enough prerequisites that the interested student can start exploring them under the guidance of a faculty member. Whether trying to start an undergraduate thesis, embarking on a summer REU, or preparing for graduate school, this book is appropriate for a variety of students and the faculty who guide them.

Selected Papers II - On Algebraic Geometry, Including Correspondence with Grothendieck (Paperback, 1st ed. 2010): David Mumford Selected Papers II - On Algebraic Geometry, Including Correspondence with Grothendieck (Paperback, 1st ed. 2010)
David Mumford; Contributions by Ching-Li Chai, Amnon Neeman, Takahiro Shiota
R2,528 Discovery Miles 25 280 Ships in 10 - 15 working days

Mumford is a well-known mathematician and winner of the Fields Medal, the highest honor available in mathematics Many of these papers are currently unavailable, and the correspondence with Grothendieck has never before been published

Periods and Nori Motives (Paperback, Softcover reprint of the original 1st ed. 2017): Annette Huber Periods and Nori Motives (Paperback, Softcover reprint of the original 1st ed. 2017)
Annette Huber; Contributions by Benjamin Friedrich, Jonas Von Wangenheim; Stefan Muller-Stach
R5,187 Discovery Miles 51 870 Ships in 10 - 15 working days

This book casts the theory of periods of algebraic varieties in the natural setting of Madhav Nori's abelian category of mixed motives. It develops Nori's approach to mixed motives from scratch, thereby filling an important gap in the literature, and then explains the connection of mixed motives to periods, including a detailed account of the theory of period numbers in the sense of Kontsevich-Zagier and their structural properties. Period numbers are central to number theory and algebraic geometry, and also play an important role in other fields such as mathematical physics. There are long-standing conjectures about their transcendence properties, best understood in the language of cohomology of algebraic varieties or, more generally, motives. Readers of this book will discover that Nori's unconditional construction of an abelian category of motives (over fields embeddable into the complex numbers) is particularly well suited for this purpose. Notably, Kontsevich's formal period algebra represents a torsor under the motivic Galois group in Nori's sense, and the period conjecture of Kontsevich and Zagier can be recast in this setting. Periods and Nori Motives is highly informative and will appeal to graduate students interested in algebraic geometry and number theory as well as researchers working in related fields. Containing relevant background material on topics such as singular cohomology, algebraic de Rham cohomology, diagram categories and rigid tensor categories, as well as many interesting examples, the overall presentation of this book is self-contained.

Notes from the International Autumn School on Computational Number Theory (Paperback, 1st ed. 2019): Ilker Inam, Engin Buyukasik Notes from the International Autumn School on Computational Number Theory (Paperback, 1st ed. 2019)
Ilker Inam, Engin Buyukasik
R2,651 Discovery Miles 26 510 Ships in 10 - 15 working days

This volume collects lecture notes and research articles from the International Autumn School on Computational Number Theory, which was held at the Izmir Institute of Technology from October 30th to November 3rd, 2017 in Izmir, Turkey. Written by experts in computational number theory, the chapters cover a variety of the most important aspects of the field. By including timely research and survey articles, the text also helps pave a path to future advancements. Topics include: Modular forms L-functions The modular symbols algorithm Diophantine equations Nullstellensatz Eisenstein series Notes from the International Autumn School on Computational Number Theory will offer graduate students an invaluable introduction to computational number theory. In addition, it provides the state-of-the-art of the field, and will thus be of interest to researchers interested in the field as well.

Selected Papers I - On the Classification of Varieties and Moduli Spaces (Paperback, 1st ed. 2004): David Mumford Selected Papers I - On the Classification of Varieties and Moduli Spaces (Paperback, 1st ed. 2004)
David Mumford
R2,042 Discovery Miles 20 420 Ships in 10 - 15 working days

Mumford is a well-known mathematician and winner of the Fields Medal, the highest honor available in mathematics. Many of these papers are currently unavailable, and the commentaries by Gieseker, Lange, Viehweg and Kempf are being published here for the first time.

Open Problems in Mathematics (Paperback, Softcover reprint of the original 1st ed. 2016): John Forbes Nash Jr, Michael Th... Open Problems in Mathematics (Paperback, Softcover reprint of the original 1st ed. 2016)
John Forbes Nash Jr, Michael Th Rassias
R6,641 Discovery Miles 66 410 Ships in 10 - 15 working days

The goal in putting together this unique compilation was to present the current status of the solutions to some of the most essential open problems in pure and applied mathematics. Emphasis is also given to problems in interdisciplinary research for which mathematics plays a key role. This volume comprises highly selected contributions by some of the most eminent mathematicians in the international mathematical community on longstanding problems in very active domains of mathematical research. A joint preface by the two volume editors is followed by a personal farewell to John F. Nash, Jr. written by Michael Th. Rassias. An introduction by Mikhail Gromov highlights some of Nash's legendary mathematical achievements. The treatment in this book includes open problems in the following fields: algebraic geometry, number theory, analysis, discrete mathematics, PDEs, differential geometry, topology, K-theory, game theory, fluid mechanics, dynamical systems and ergodic theory, cryptography, theoretical computer science, and more. Extensive discussions surrounding the progress made for each problem are designed to reach a wide community of readers, from graduate students and established research mathematicians to physicists, computer scientists, economists, and research scientists who are looking to develop essential and modern new methods and theories to solve a variety of open problems.

Sequences, Groups, and Number Theory (Paperback, Softcover reprint of the original 1st ed. 2018): Valerie Berthe, Michel Rigo Sequences, Groups, and Number Theory (Paperback, Softcover reprint of the original 1st ed. 2018)
Valerie Berthe, Michel Rigo
R5,176 Discovery Miles 51 760 Ships in 10 - 15 working days

This collaborative book presents recent trends on the study of sequences, including combinatorics on words and symbolic dynamics, and new interdisciplinary links to group theory and number theory. Other chapters branch out from those areas into subfields of theoretical computer science, such as complexity theory and theory of automata. The book is built around four general themes: number theory and sequences, word combinatorics, normal numbers, and group theory. Those topics are rounded out by investigations into automatic and regular sequences, tilings and theory of computation, discrete dynamical systems, ergodic theory, numeration systems, automaton semigroups, and amenable groups. This volume is intended for use by graduate students or research mathematicians, as well as computer scientists who are working in automata theory and formal language theory. With its organization around unified themes, it would also be appropriate as a supplemental text for graduate level courses.

Number-Theoretic Methods in Cryptology - First International Conference, NuTMiC 2017, Warsaw, Poland, September 11-13, 2017,... Number-Theoretic Methods in Cryptology - First International Conference, NuTMiC 2017, Warsaw, Poland, September 11-13, 2017, Revised Selected Papers (Paperback, 1st ed. 2018)
Jerzy Kaczorowski, Josef Pieprzyk, Jacek Pomykala
R2,331 Discovery Miles 23 310 Ships in 10 - 15 working days

This book constitutes the refereed post-conference proceedings of the First International Conference on Number-Theoretic Methods in Cryptology, NuTMiC 2017, held in Warsaw, Poland, in September 2017.The 15 revised full papers presented in this book together with 3 invited talks were carefully reviewed and selected from 32 initial submissions. The papers are organized in topical sections on elliptic curves in cryptography; public-key cryptography; lattices in cryptography; number theory; pseudorandomness; and algebraic structures and analysis.

Mathematical Modelling for Next-Generation Cryptography - CREST Crypto-Math Project (Paperback, Softcover reprint of the... Mathematical Modelling for Next-Generation Cryptography - CREST Crypto-Math Project (Paperback, Softcover reprint of the original 1st ed. 2018)
Tsuyoshi Takagi, Masato Wakayama, Keisuke Tanaka, Noboru Kunihiro, Kazufumi Kimoto, …
R3,143 Discovery Miles 31 430 Ships in 10 - 15 working days

This book presents the mathematical background underlying security modeling in the context of next-generation cryptography. By introducing new mathematical results in order to strengthen information security, while simultaneously presenting fresh insights and developing the respective areas of mathematics, it is the first-ever book to focus on areas that have not yet been fully exploited for cryptographic applications such as representation theory and mathematical physics, among others. Recent advances in cryptanalysis, brought about in particular by quantum computation and physical attacks on cryptographic devices, such as side-channel analysis or power analysis, have revealed the growing security risks for state-of-the-art cryptographic schemes. To address these risks, high-performance, next-generation cryptosystems must be studied, which requires the further development of the mathematical background of modern cryptography. More specifically, in order to avoid the security risks posed by adversaries with advanced attack capabilities, cryptosystems must be upgraded, which in turn relies on a wide range of mathematical theories. This book is suitable for use in an advanced graduate course in mathematical cryptography, while also offering a valuable reference guide for experts.

A Course on Basic Model Theory (Paperback, Softcover reprint of the original 1st ed. 2017): Haimanti Sarbadhikari, Shashi Mohan... A Course on Basic Model Theory (Paperback, Softcover reprint of the original 1st ed. 2017)
Haimanti Sarbadhikari, Shashi Mohan Srivastava
R1,650 Discovery Miles 16 500 Ships in 10 - 15 working days

This self-contained book is an exposition of the fundamental ideas of model theory. It presents the necessary background from logic, set theory and other topics of mathematics. Only some degree of mathematical maturity and willingness to assimilate ideas from diverse areas are required. The book can be used for both teaching and self-study, ideally over two semesters. It is primarily aimed at graduate students in mathematical logic who want to specialise in model theory. However, the first two chapters constitute the first introduction to the subject and can be covered in one-semester course to senior undergraduate students in mathematical logic. The book is also suitable for researchers who wish to use model theory in their work.

Algebraic Geometry and Number Theory - Summer School, Galatasaray University, Istanbul, 2014 (Paperback, Softcover reprint of... Algebraic Geometry and Number Theory - Summer School, Galatasaray University, Istanbul, 2014 (Paperback, Softcover reprint of the original 1st ed. 2017)
Hussein Mourtada, Celal Cem Sarioglu, Christophe Soule, Ayberk Zeytin
R3,365 Discovery Miles 33 650 Ships in 10 - 15 working days

This lecture notes volume presents significant contributions from the "Algebraic Geometry and Number Theory" Summer School, held at Galatasaray University, Istanbul, June 2-13, 2014. It addresses subjects ranging from Arakelov geometry and Iwasawa theory to classical projective geometry, birational geometry and equivariant cohomology. Its main aim is to introduce these contemporary research topics to graduate students who plan to specialize in the area of algebraic geometry and/or number theory. All contributions combine main concepts and techniques with motivating examples and illustrative problems for the covered subjects. Naturally, the book will also be of interest to researchers working in algebraic geometry, number theory and related fields.

Fractal Zeta Functions and Fractal Drums - Higher-Dimensional Theory of Complex Dimensions (Paperback, Softcover reprint of the... Fractal Zeta Functions and Fractal Drums - Higher-Dimensional Theory of Complex Dimensions (Paperback, Softcover reprint of the original 1st ed. 2017)
Michel L Lapidus, Goran Radunovic, Darko Zubrinic
R4,467 Discovery Miles 44 670 Ships in 10 - 15 working days

This monograph gives a state-of-the-art and accessible treatment of a new general higher-dimensional theory of complex dimensions, valid for arbitrary bounded subsets of Euclidean spaces, as well as for their natural generalization, relative fractal drums. It provides a significant extension of the existing theory of zeta functions for fractal strings to fractal sets and arbitrary bounded sets in Euclidean spaces of any dimension. Two new classes of fractal zeta functions are introduced, namely, the distance and tube zeta functions of bounded sets, and their key properties are investigated. The theory is developed step-by-step at a slow pace, and every step is well motivated by numerous examples, historical remarks and comments, relating the objects under investigation to other concepts. Special emphasis is placed on the study of complex dimensions of bounded sets and their connections with the notions of Minkowski content and Minkowski measurability, as well as on fractal tube formulas. It is shown for the first time that essential singularities of fractal zeta functions can naturally emerge for various classes of fractal sets and have a significant geometric effect. The theory developed in this book leads naturally to a new definition of fractality, expressed in terms of the existence of underlying geometric oscillations or, equivalently, in terms of the existence of nonreal complex dimensions. The connections to previous extensive work of the first author and his collaborators on geometric zeta functions of fractal strings are clearly explained. Many concepts are discussed for the first time, making the book a rich source of new thoughts and ideas to be developed further. The book contains a large number of open problems and describes many possible directions for further research. The beginning chapters may be used as a part of a course on fractal geometry. The primary readership is aimed at graduate students and researchers working in Fractal Geometry and other related fields, such as Complex Analysis, Dynamical Systems, Geometric Measure Theory, Harmonic Analysis, Mathematical Physics, Analytic Number Theory and the Spectral Theory of Elliptic Differential Operators. The book should be accessible to nonexperts and newcomers to the field.

Eisenstein Series and Automorphic Representations - With Applications in String Theory (Hardcover): Philipp Fleig, Henrik P. A.... Eisenstein Series and Automorphic Representations - With Applications in String Theory (Hardcover)
Philipp Fleig, Henrik P. A. Gustafsson, Axel Kleinschmidt, Daniel Persson
R2,566 Discovery Miles 25 660 Ships in 12 - 19 working days

This introduction to automorphic forms on adelic groups G(A) emphasises the role of representation theory. The exposition is driven by examples, and collects and extends many results scattered throughout the literature, in particular the Langlands constant term formula for Eisenstein series on G(A) as well as the Casselman-Shalika formula for the p-adic spherical Whittaker function. This book also covers more advanced topics such as spherical Hecke algebras and automorphic L-functions. Many of these mathematical results have natural interpretations in string theory, and so some basic concepts of string theory are introduced with an emphasis on connections with automorphic forms. Throughout the book special attention is paid to small automorphic representations, which are of particular importance in string theory but are also of independent mathematical interest. Numerous open questions and conjectures, partially motivated by physics, are included to prompt the reader's own research.

Fractal Geometry, Complex Dimensions and Zeta Functions - Geometry and Spectra of Fractal Strings (Hardcover, 2nd ed. 2013):... Fractal Geometry, Complex Dimensions and Zeta Functions - Geometry and Spectra of Fractal Strings (Hardcover, 2nd ed. 2013)
Michel L Lapidus, Machiel van Frankenhuijsen
R3,532 R3,341 Discovery Miles 33 410 Save R191 (5%) Ships in 9 - 17 working days

Number theory, spectral geometry, and fractal geometry are interlinked in this in-depth study of the vibrations of fractal strings, that is, one-dimensional drums with fractal boundary.

Throughout "Geometry, Complex Dimensions and Zeta Functions, "Second Edition, new results are examined and anew definition of fractality as the presence of nonreal complex dimensions with positive real parts is presented. Thenewfinal chapterdiscusses several new topics and results obtained since the publication of the first edition."

Discrete Harmonic Analysis - Representations, Number Theory, Expanders, and the Fourier Transform (Hardcover): Tullio... Discrete Harmonic Analysis - Representations, Number Theory, Expanders, and the Fourier Transform (Hardcover)
Tullio Ceccherini-Silberstein, Fabio Scarabotti, Filippo Tolli
R2,655 Discovery Miles 26 550 Ships in 12 - 19 working days

This self-contained book introduces readers to discrete harmonic analysis with an emphasis on the Discrete Fourier Transform and the Fast Fourier Transform on finite groups and finite fields, as well as their noncommutative versions. It also features applications to number theory, graph theory, and representation theory of finite groups. Beginning with elementary material on algebra and number theory, the book then delves into advanced topics from the frontiers of current research, including spectral analysis of the DFT, spectral graph theory and expanders, representation theory of finite groups and multiplicity-free triples, Tao's uncertainty principle for cyclic groups, harmonic analysis on GL(2,Fq), and applications of the Heisenberg group to DFT and FFT. With numerous examples, figures, and over 160 exercises to aid understanding, this book will be a valuable reference for graduate students and researchers in mathematics, engineering, and computer science.

Connections in Discrete Mathematics - A Celebration of the Work of Ron Graham (Paperback): Steve Butler, Joshua Cooper, Glenn... Connections in Discrete Mathematics - A Celebration of the Work of Ron Graham (Paperback)
Steve Butler, Joshua Cooper, Glenn Hurlbert
R1,696 Discovery Miles 16 960 Ships in 12 - 19 working days

Discrete mathematics has been rising in prominence in the past fifty years, both as a tool with practical applications and as a source of new and interesting mathematics. The topics in discrete mathematics have become so well developed that it is easy to forget that common threads connect the different areas, and it is through discovering and using these connections that progress is often made. For over fifty years, Ron Graham has been able to illuminate some of these connections and has helped to bring the field of discrete mathematics to where it is today. To celebrate his contribution, this volume brings together many of the best researchers working in discrete mathematics, including Fan Chung, Erik D. Demaine, Persi Diaconis, Peter Frankl, Alfred W. Hales, Jeffrey C. Lagarias, Allen Knutson, Janos Pach, Carl Pomerance, N. J. A. Sloane, and of course, Ron Graham himself.

Ergodic Theory and Dynamical Systems in their Interactions with Arithmetics and Combinatorics - CIRM Jean-Morlet Chair, Fall... Ergodic Theory and Dynamical Systems in their Interactions with Arithmetics and Combinatorics - CIRM Jean-Morlet Chair, Fall 2016 (Paperback, 1st ed. 2018)
Sebastien Ferenczi, Joanna Kulaga-Przymus, Mariusz Lemanczyk
R2,181 Discovery Miles 21 810 Ships in 10 - 15 working days

This book concentrates on the modern theory of dynamical systems and its interactions with number theory and combinatorics. The greater part begins with a course in analytic number theory and focuses on its links with ergodic theory, presenting an exhaustive account of recent research on Sarnak's conjecture on Moebius disjointness. Selected topics involving more traditional connections between number theory and dynamics are also presented, including equidistribution, homogenous dynamics, and Lagrange and Markov spectra. In addition, some dynamical and number theoretical aspects of aperiodic order, some algebraic systems, and a recent development concerning tame systems are described.

The Block Theory of Finite Group Algebras (Paperback): Markus Linckelmann The Block Theory of Finite Group Algebras (Paperback)
Markus Linckelmann
R1,891 Discovery Miles 18 910 Ships in 12 - 19 working days

This is a comprehensive introduction to the modular representation theory of finite groups, with an emphasis on block theory. The two volumes take into account classical results and concepts as well as some of the modern developments in the area. Volume 1 introduces the broader context, starting with general properties of finite group algebras over commutative rings, moving on to some basics in character theory and the structure theory of algebras over complete discrete valuation rings. In Volume 2, blocks of finite group algebras over complete p-local rings take centre stage, and many key results which have not appeared in a book before are treated in detail. In order to illustrate the wide range of techniques in block theory, the book concludes with chapters classifying the source algebras of blocks with cyclic and Klein four defect groups, and relating these classifications to the open conjectures that drive block theory.

The Block Theory of Finite Group Algebras (Paperback): Markus Linckelmann The Block Theory of Finite Group Algebras (Paperback)
Markus Linckelmann
R1,888 Discovery Miles 18 880 Ships in 12 - 19 working days

This is a comprehensive introduction to the modular representation theory of finite groups, with an emphasis on block theory. The two volumes take into account classical results and concepts as well as some of the modern developments in the area. Volume 1 introduces the broader context, starting with general properties of finite group algebras over commutative rings, moving on to some basics in character theory and the structure theory of algebras over complete discrete valuation rings. In Volume 2, blocks of finite group algebras over complete p-local rings take centre stage, and many key results which have not appeared in a book before are treated in detail. In order to illustrate the wide range of techniques in block theory, the book concludes with chapters classifying the source algebras of blocks with cyclic and Klein four defect groups, and relating these classifications to the open conjectures that drive block theory.

Ramanujan Summation of Divergent Series (Paperback, 1st ed. 2017): Bernard Candelpergher Ramanujan Summation of Divergent Series (Paperback, 1st ed. 2017)
Bernard Candelpergher
R2,224 Discovery Miles 22 240 Ships in 10 - 15 working days

The aim of this monograph is to give a detailed exposition of the summation method that Ramanujan uses in Chapter VI of his second Notebook. This method, presented by Ramanujan as an application of the Euler-MacLaurin formula, is here extended using a difference equation in a space of analytic functions. This provides simple proofs of theorems on the summation of some divergent series. Several examples and applications are given. For numerical evaluation, a formula in terms of convergent series is provided by the use of Newton interpolation. The relation with other summation processes such as those of Borel and Euler is also studied. Finally, in the last chapter, a purely algebraic theory is developed that unifies all these summation processes. This monograph is aimed at graduate students and researchers who have a basic knowledge of analytic function theory.

New Directions in Locally Compact Groups (Paperback): Pierre-Emmanuel Caprace, Nicolas Monod New Directions in Locally Compact Groups (Paperback)
Pierre-Emmanuel Caprace, Nicolas Monod
R2,507 Discovery Miles 25 070 Ships in 12 - 19 working days

This collection of expository articles by a range of established experts and newer researchers provides an overview of the recent developments in the theory of locally compact groups. It includes introductory articles on totally disconnected locally compact groups, profinite groups, p-adic Lie groups and the metric geometry of locally compact groups. Concrete examples, including groups acting on trees and Neretin groups, are discussed in detail. An outline of the emerging structure theory of locally compact groups beyond the connected case is presented through three complementary approaches: Willis' theory of the scale function, global decompositions by means of subnormal series, and the local approach relying on the structure lattice. An introduction to lattices, invariant random subgroups and L2-invariants, and a brief account of the Burger-Mozes construction of simple lattices are also included. A final chapter collects various problems suggesting future research directions.

Galois Theory (Paperback, 5th edition): Ian Stewart Galois Theory (Paperback, 5th edition)
Ian Stewart
R1,828 Discovery Miles 18 280 Ships in 12 - 19 working days

New to the Fourth Edition Reorganised and revised chapter seven and thirteen New exercises and examples Expanded, updated references Further historical material on figures besides Galois: Omar Khayyam, Vandermonde, Ruffini, and Abel A new final chapter discussing other directions in which Galois Theory has developed: the inverse Galois problem, differential Galois theory, and a (very) brief introduction to p-adic Galois representations.

Topics in Computational Number Theory Inspired by Peter L. Montgomery (Hardcover): Joppe W. Bos, Arjen K. Lenstra Topics in Computational Number Theory Inspired by Peter L. Montgomery (Hardcover)
Joppe W. Bos, Arjen K. Lenstra
R3,627 Discovery Miles 36 270 Ships in 12 - 19 working days

Peter L. Montgomery has made significant contributions to computational number theory, introducing many basic tools such as Montgomery multiplication, Montgomery simultaneous inversion, Montgomery curves, and the Montgomery ladder. This book features state-of-the-art research in computational number theory related to Montgomery's work and its impact on computational efficiency and cryptography. Topics cover a wide range of topics such as Montgomery multiplication for both hardware and software implementations; Montgomery curves and twisted Edwards curves as proposed in the latest standards for elliptic curve cryptography; and cryptographic pairings. This book provides a comprehensive overview of integer factorization techniques, including dedicated chapters on polynomial selection, the block Lanczos method, and the FFT extension for algebraic-group factorization algorithms. Graduate students and researchers in applied number theory and cryptography will benefit from this survey of Montgomery's work.

Number Theory: A Very Short Introduction (Paperback): Robin Wilson Number Theory: A Very Short Introduction (Paperback)
Robin Wilson
R298 R269 Discovery Miles 2 690 Save R29 (10%) Ships in 9 - 17 working days

Number theory is the branch of mathematics that is primarily concerned with the counting numbers. Of particular importance are the prime numbers, the 'building blocks' of our number system. The subject is an old one, dating back over two millennia to the ancient Greeks, and for many years has been studied for its intrinsic beauty and elegance, not least because several of its challenges are so easy to state that everyone can understand them, and yet no-one has ever been able to resolve them. But number theory has also recently become of great practical importance - in the area of cryptography, where the security of your credit card, and indeed of the nation's defence, depends on a result concerning prime numbers that dates back to the 18th century. Recent years have witnessed other spectacular developments, such as Andrew Wiles's proof of 'Fermat's last theorem' (unproved for over 250 years) and some exciting work on prime numbers. In this Very Short Introduction Robin Wilson introduces the main areas of classical number theory, both ancient and modern. Drawing on the work of many of the greatest mathematicians of the past, such as Euclid, Fermat, Euler, and Gauss, he situates some of the most interesting and creative problems in the area in their historical context. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.

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