{"title":"Number theory Books","description":"","products":[{"product_id":"simply-maths-9780241515686","title":"Simply Maths","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e","brand":"Dorling Kindersley Ltd","offers":[{"title":"Default Title","offer_id":47832841126231,"sku":"9780241515686","price":11.69,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780241515686.jpg?v=1710338823"},{"product_id":"numbers-to-infinity-and-beyond-9781907155314","title":"Numbers: To Infinity and Beyond","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eWhat are numbers? Where do they come from? Are there different kings of number? Why was Pythagoras fascinated by triangular and square numbers? Is there a link between perfect numbers and primes? In this enlightening illustrated pocket book, mathemagician Oliver Linton reveals the wonderful world of numbers, visiting the questions and answers of great number theorists along the way, from Euclid to Euler, Fibonacci to Fermat, and Archimedes to Gauss. No calculator needed!   WOODEN BOOKS are small but packed with information. \"Fascinating\" FINANCIAL TIMES. \"Beautiful\" LONDON REVIEW OF BOOKS. \"Rich and Artful\" THE LANCET. \"Genuinely mind-expanding\" FORTEAN TIMES. \"Excellent\" NEW SCIENTIST. \"Stunning\" NEW YORK TIMES. Small books, big ideas.","brand":"Wooden Books","offers":[{"title":"Default Title","offer_id":47850606133591,"sku":"9781907155314","price":8.18,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781907155314.jpg?v=1710616213"},{"product_id":"number-theory-9780198798095","title":"Number Theory","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eNumber theory is the branch of mathematics primarily concerned with the counting numbers, especially primes. It dates back to the ancient Greeks, but today it has great practical importance in cryptography, from credit card security to national defence. This book introduces the main areas of number theory, and some of its most interesting problems.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eList of illustrations List of tables 1: What is number theory? 2: Divisibility 3: Primes I 4: Congruences I 5: Diophantine equations 6: Congruences II 7: Primes II 8: The Riemann hypothesis Appendix Further reading Index","brand":"Oxford University Press","offers":[{"title":"Default Title","offer_id":48732787507543,"sku":"9780198798095","price":9.49,"currency_code":"GBP","in_stock":true}]},{"product_id":"problems-in-analytic-number-theory-9780387723495","title":"Problems in Analytic Number Theory","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eProblems.- Arithmetic Functions.- Primes in Arithmetic Progressions.- The Prime Number Theorem.- The Method of Contour Integration.- Functional Equations.- Hadamard Products.- Explicit Formulas.- The Selberg Class.- Sieve Methods.- p-adic Methods.- Equidistribution.- Solutions.- Arithmetic Functions.- Primes in Arithmetic Progressions.- The Prime Number Theorem.- The Method of Contour Integration.- Functional Equations.- Hadamard Products.- Explicit Formulas.- The Selberg Class.- Sieve Methods.- p-adic Methods.- Equidistribution.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eM.R. Murty\u003c\/p\u003e\u003cp\u003e\u003ci\u003eProblems in Analytic Number Theory\u003c\/i\u003e\u003c\/p\u003e\u003cp\u003e\u003ci\u003e\"The reviewer strongly approves of the problem-based approach to learning, and recommends this book to any student of analytic number theory.\"\u003c\/i\u003e\u003c\/p\u003e\u003cp\u003e\u003ci\u003e—\u003c\/i\u003eMATHEMATICAL REVIEWS\u003c\/p\u003e\u003cp\u003eFrom the reviews of the second edition:\u003c\/p\u003e\u003cp\u003e“This expanded and corrected second edition of this useful and interesting book has a new chapter on the topic of equidistribution. … this monograph gives important results and techniques for specific topics, together with many exercises. … I do enjoy this book … and I imagine when I take the graduate course in the subject that it will be of a greater benefit, which is why I offered such a high rating.” (Philosophy, Religion and Science Book Reviews, bookinspections.wordpress.com, July, 2013)\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\"The second edition of the book has eleven chapters … . the book can be used both as a problem book (as its title shows) and also as a textbook (as the series in which the book is published shows). … is ideal as a text for a first course in analytic number theory, either at the senior undergraduate or the graduate level. … I believe that this book will be very useful for students, researchers and professors. It is well written … .\" (Mehdi Hassani, MathDL, April, 2008)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eProblems.- Arithmetic Functions.- Primes in Arithmetic Progressions.- The Prime Number Theorem.- The Method of Contour Integration.- Functional Equations.- Hadamard Products.- Explicit Formulas.- The Selberg Class.- Sieve Methods.- p-adic Methods.- Equidistribution.- Solutions.- Arithmetic Functions.- Primes in Arithmetic Progressions.- The Prime Number Theorem.- The Method of Contour Integration.- Functional Equations.- Hadamard Products.- Explicit Formulas.- The Selberg Class.- Sieve Methods.- p-adic Methods.- Equidistribution.","brand":"Springer-Verlag New York Inc.","offers":[{"title":"Default Title","offer_id":48733726179671,"sku":"9780387723495","price":44.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780387723495.jpg?v=1720001397"},{"product_id":"advanced-topics-in-the-arithmetic-of-elliptic-curves-9780387943282","title":"Advanced Topics in the Arithmetic of Elliptic","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eIn the introduction to the first volume of The Arithmetic of Elliptic Curves (Springer-Verlag, 1986), I observed that \"the theory of elliptic curves is rich, varied, and amazingly vast,\" and as a consequence, \"many important topics had to be omitted.\"\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1.- I Elliptic and Modular Functions.- §1. The Modular Group.- §2. The Modular Curve X(1).- §3. Modular Functions.- §4. Uniformization and Fields of Moduli.- §5. Elliptic Functions Revisited.- §6. q-Expansions of Elliptic Functions.- §7. q-Expansions of Modular Functions.- §8. Jacobi’s Product Formula for ?(?).- §9. Hecke Operators.- §10. Hecke Operators Acting on Modular Forms.- §11. L-Series Attached to Modular Forms.- Exercises.- II Complex Multiplication.- §1. Complex Multiplication over C.- §2. Rationality Questions.- §3. Class Field Theory — A Brief Review.- §4. The Hilbert Class Field.- §5. The Maximal Abelian Extension.- §6. Integrality of j.- §7. Cyclotomic Class Field Theory.- §8. The Main Theorem of Complex Multiplication.- §9. The Associated Grössencharacter.- §10. The L-Series Attached to a CM Elliptic Curve.- Exercises.- III Elliptic Surfaces.- §1. Elliptic Curves over Function Fields.- §2. The Weak Mordell-Weil Theorem.- §3. Elliptic Surfaces.- §4. Heights on Elliptic Curves over Function Fields.- §5. Split Elliptic Surfaces and Sets of Bounded Height.- §6. The Mordell-Weil Theorem for Function Fields.- §7. The Geometry of Algebraic Surfaces.- §8. The Geometry of Fibered Surfaces.- §9. The Geometry of Elliptic Surfaces.- §10. Heights and Divisors on Varieties.- §11. Specialization Theorems for Elliptic Surfaces.- §12. Integral Points on Elliptic Curves over Function Fields.- Exercises.- IV The Néron Model.- §1. Group Varieties.- §2. Schemes and S-Schemes.- §3. Group Schemes.- §4. Arithmetic Surfaces.- §5. Néron Models.- §6. Existence of Néron Models.- §7. Intersection Theory, Minimal Models, and Blowing-Up.- §8. The Special Fiber of a Néron Model.- §9. Tate’s Algorithm to Compute the Special Fiber.- §10. The Conductor of an Elliptic Curve.- §11. Ogg’s Formula.- Exercises.- V Elliptic Curves over Complete Fields.- §1. Elliptic Curves over ?.- §2. Elliptic Curves over ?.- §3. The Tate Curve.- §4. The Tate Map Is Surjective.- §5. Elliptic Curves over p-adic Fields.- §6. Some Applications of p-adic Uniformization.- Exercises.- VI Local Height Functions.- §1. Existence of Local Height Functions.- §2. Local Decomposition of the Canonical Height.- §3. Archimedean Absolute Values — Explicit Formulas.- §4. Non-Archimedean Absolute Values — Explicit Formulas.- Exercises.- Appendix A Some Useful Tables.- §3. Elliptic Curves over ? with Complex Multiplication.- Notes on Exercises.- References.- List of Notation.","brand":"Springer-Verlag New York Inc.","offers":[{"title":"Default Title","offer_id":48733726736727,"sku":"9780387943282","price":54.99,"currency_code":"GBP","in_stock":true}]},{"product_id":"padic-numbers-padic-analysis-and-zetafunctions-9780387960173","title":"padic Numbers padic Analysis and ZetaFunctions","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThe first edition of this work has become the standard introduction to the theory of p-adic numbers at both the advanced undergraduate and beginning graduate level.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eFrom the reviews of the second edition:\u003c\/p\u003e\u003cp\u003e“In the second edition of this text, Koblitz presents a wide-ranging introduction to the theory of p-adic numbers and functions. … there are some really nice exercises that allow the reader to explore the material. … And with the exercises, the book would make a good textbook for a graduate course, provided the students have a decent background in analysis and number theory.” (Donald L. Vestal, The Mathematical Association of America, April, 2011)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eI p-adic numbers.- 1. Basic concepts.- 2. Metrics on the rational numbers.- Exercises.- 3. Review of building up the complex numbers.- 4. The field of p-adic numbers.- 5. Arithmetic in ?p.- Exercises.- II p-adic interpolation of the Riemann zeta-function.- 1. A formula for ?(2k).- 2. p-adic interpolation of the function f(s) = as.- Exercises.- 3. p-adic distributions.- Exercises.- 4. Bernoulli distributions.- 5. Measures and integration.- Exercises.- 6. The p-adic ?-function as a Mellin-Mazur transform.- 7. A brief survey (no proofs).- Exercises.- III Building up ?.- 1. Finite fields.- Exercises.- 2. Extension of norms.- Exercises.- 3. The algebraic closure of ?p.- 4. ?.- Exercises.- IV p-adic power series.- 1. Elementary functions.- Exercises.- 2. The logarithm, gamma and Artin-Hasse exponential functions.- Exercises.- 3. Newton polygons for polynomials.- 4. Newton polygons for power series.- Exercises.- V Rationality of the zeta-function of a set of equations over a finite field.- 1. Hypersurfaces and their zeta-functions.- Exercises.- 2. Characters and their lifting.- 3. A linear map on the vector space of power series.- 4. p-adic analytic expression for the zeta-function.- Exercises.- 5. The end of the proof.- Answers and Hints for the Exercises.  ","brand":"Springer-Verlag New York Inc.","offers":[{"title":"Default Title","offer_id":48733727097175,"sku":"9780387960173","price":64.99,"currency_code":"GBP","in_stock":true}]},{"product_id":"numbers-and-the-making-of-us-9780674237810","title":"Numbers and the Making of Us","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003eA fascinating book. -- James Ryerson * New York Times Book Review *\u003cbr\u003eFascinating…This is bold, heady stuff…The breadth of research Everett covers is impressive, and allows him to develop a narrative that is both global and compelling. He is as much at home describing the niceties of experimental work in cognitive science as he is discussing arcane tribal rituals and the technical details of grammar…It is often poignant, and makes a virtue of the author’s experiences with some of the indigenous peoples he describes, based on a childhood following his missionary parents—in particular his famous father, Daniel Everett—into the Amazon jungle…\u003ci\u003eNumbers \u003c\/i\u003eis eye-opening, even eye-popping. And it makes a powerful case for language, as a cultural invention, being central to the making of us. -- Vyvyan Evans * New Scientist *\u003cbr\u003eEverett buttresses his argument with an impressive array of studies from different fields…It all adds up to a powerful and convincing case for Everett’s main thesis: that numbers are neither natural nor innate to humans but ‘a creation of the human mind, a cognitive invention that has altered forever how we see and distinguish quantities.’ His argument that numbers played a crucial role in the development of agriculture and the complex societies it supported is equally persuasive. -- Amir Alexander * Wall Street Journal *\u003cbr\u003eIn this multi-disciplinary investigation, anthropologist Caleb Everett examines the seemingly limitless possibilities and innovations made possible by the evolution of number systems. -- Rachel E. Gross * Smithsonian *\u003cbr\u003eCaleb Everett provides a fascinating account of the development of human numeracy, from innate abilities to the complexities of agricultural and trading societies, all viewed against the general background of human cultural evolution. He successfully draws together insights from linguistics, cognitive psychology, anthropology, and archaeology in a way that is accessible to the general reader as well as to specialists. He does not avoid controversy, making this a key contribution to a developing debate. -- Bernard Comrie, University of California, Santa Barbara\u003cbr\u003eIn his journey through the millennia of human evolution, from the forests of Amazonia to the deserts of Australia, ever in search of a better understanding of human diversity, Caleb Everett presents a breathtaking narrative of how the human species developed one of its most distinct cognitive and linguistic achievements: to count and to use concepts of quantity to expand and enrich a wide range of cultural activities. -- Bernd Heine, University of Cologne","brand":"Harvard University Press","offers":[{"title":"Default Title","offer_id":48735976587607,"sku":"9780674237810","price":18.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780674237810.jpg?v=1723810423"},{"product_id":"the-mordell-conjecture-9781108845953","title":"The Mordell Conjecture","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThe Mordell conjecture (Faltings''s theorem) is one of the most important achievements in Diophantine geometry, stating that an algebraic curve of genus at least two has only finitely many rational points. This book provides a self-contained and detailed proof of the Mordell conjecture following the papers of Bombieri and Vojta. Also acting as a concise introduction to Diophantine geometry, the text starts from basics of algebraic number theory, touches on several important theorems and techniques (including the theory of heights, the MordellWeil theorem, Siegel''s lemma and Roth''s lemma) from Diophantine geometry, and culminates in the proof of the Mordell conjecture. Based on the authors'' own teaching experience, it will be of great value to advanced undergraduate and graduate students in algebraic geometry and number theory, as well as researchers interested in Diophantine geometry as a whole.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e'This lucid compact book provides a short and direct access to Vojta-Bombieri's proof of Faltings's celebrated theorem. The text itself is mostly self-contained, with all needed results on diophantine geometry presented without unnecessary abstraction, in as concrete a manner as possible. Without doubt, this excellent course will become a standard for anyone wishing to be introduced to the topic of rational points on curves over the rational numbers, and to one of the crowning achievements of the mathematics of our time.' Vincent Maillot, Centre National de la Recherche Scientifique (CNRS), Paris\u003cbr\u003e'In less than 200 pages, the authors have given a complete treatment to the two most important results in diophantine geometry in the last 100 years: the Mordell–Weil theorem and Faltings's theorem. This will be a wonderful reference for everybody interested in diophantine geometry with minimal background in number theory and algebraic geometry.' Shou-Wu Zhang, Princeton University\u003cbr\u003e'This book is a comprehensive introduction, with plenty of motivations, to Mordell conjecture - a deep theorem of Faltings that has far-reaching influences in modern diophantine geometry. Knowledge of algebraic number theory and height theory is considerately refreshed, and the proof of the Mordell conjecture is meticulously structured with all details, which are most helpful for beginners. More experienced readers will appreciate the insights of the authors into the problem and into the domain of diophantine geometry.' Huayi Chen, University of Paris, Mathematics Institute of Jussieu–Paris Rive Gauche\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1. What is the Mordell conjecture?; 2. Some basics of algebraic number theory; 3. Theory of heights; 4. Preliminaries; 5. The proof of Falthing's theorem.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":48738349777239,"sku":"9781108845953","price":59.84,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781108845953.jpg?v=1723811959"},{"product_id":"primes-of-the-form-x2ny2-9781118390184","title":"Primes of the Form x2ny2","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cb\u003eAn exciting approach to the history and mathematics of number theory\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e. . . the author's style is totally lucid and very easy to read . . .the result is indeed a wonderful story. \u003ci\u003eMathematical Reviews\u003cbr\u003e \u003cbr\u003e \u003c\/i\u003eWritten in a unique and accessible style for readers of varied mathematical backgrounds, the \u003ci\u003eSecond Edition\u003c\/i\u003e of \u003ci\u003ePrimes of the Form p = x\u003csub\u003e\u003ci\u003e2\u003c\/i\u003e\u003c\/sub\u003e\u003c\/i\u003e\u003ci\u003e+ ny\u003c\/i\u003e\u003csub\u003e\u003ci\u003e2\u003c\/i\u003e\u003c\/sub\u003e details the history behind how Pierre de Fermat's work ultimately gave birth to quadratic reciprocity and the genus theory of quadratic forms. The book also illustrates how results of Euler and Gauss can be fully understood only in the context of class field theory, and in addition, explores a selection of the magnificent formulas of complex multiplication.\u003c\/p\u003e \u003cp\u003e\u003ci\u003ePrimes of the Form p = x\u003c\/i\u003e\u003csub\u003e\u003ci\u003e2\u003c\/i\u003e\u003c\/sub\u003e \u003ci\u003e+ ny\u003c\/i\u003e\u003csub\u003e\u003ci\u003e2\u003c\/i\u003e\u003c\/sub\u003e\u003ci\u003e, Second Edition\u003c\/i\u003e focuses on addressing the question of when a prime \u003ci\u003ep\u003c\/i\u003e is of the form \u003ci\u003ex\u003c\/i\u003e\u003csub\u003e\u003ci\u003e2\u0026lt;\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface to the First Edition ix\u003cbr\u003e\u003cbr\u003ePreface to the Second Edition xi\u003cbr\u003e\u003cbr\u003eNotation xiii\u003cbr\u003e\u003cbr\u003eIntroduction 1\u003cbr\u003e\u003cbr\u003eChapter One: From Fermat to Gauss\u003cbr\u003e\u003cbr\u003eChapter Two: Class Field Theory\u003cbr\u003e\u003cbr\u003eChapter Three: Complex Multiplication\u003cbr\u003e\u003cbr\u003eChapter Four: Additional Topics\u003cbr\u003e\u003cbr\u003eRefrences\u003cbr\u003e\u003cbr\u003eAdditional References\u003cbr\u003e\u003cbr\u003eIndex\u003c\/i\u003e\u003c\/sub\u003e\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":48738353086807,"sku":"9781118390184","price":46.76,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781118390184.jpg?v=1723811963"},{"product_id":"an-introduction-to-mathematical-cryptography-9781493917105","title":"An Introduction to Mathematical Cryptography","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePreface.- Introduction.- 1 An Introduction to Cryptography.- 2 Discrete Logarithms and Diffie-Hellman.- 3 Integer Factorization and RSA.- 4 Digital Signatures.- 5 Combinatorics, Probability, and Information Theory.- 6 Elliptic Curves and Cryptography.- 7 Lattices and Cryptography.- 8 Additional Topics in Cryptography.- List of Notation.- References.- Index.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e“This book explains the mathematical foundations of public key cryptography in a mathematically correct and thorough way without omitting important practicalities. … I would like to emphasize that the book is very well written and quite clear. Topics are well motivated, and there are a good number of examples and nicely chosen exercises. To me, this book is still the first-choice introduction to public-key cryptography.” (Klaus Galensa, Computing Reviews, March, 2015)\u003c\/p\u003e“This is a text for an upper undergraduate\/lower graduate course in mathematical cryptography. … It is very well written and quite clear. Topics are well-motivated, and there are a good number of examples and nicely chosen exercises. … An instructor of a fairly sophisticated undergraduate course in cryptography who wants to emphasize public key cryptography should definitely take a look at this book.” (Mark Hunacek, MAA Reviews, October, 2014)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface.- Introduction.- 1 An Introduction to Cryptography.- 2 Discrete Logarithms and Diffie-Hellman.- 3 Integer Factorization and RSA.- 4 Digital Signatures.- 5 Combinatorics, Probability, and Information Theory.- 6 Elliptic Curves and Cryptography.- 7 Lattices and Cryptography.- 8 Additional Topics in Cryptography.- List of Notation.- References.- Index.","brand":"Springer-Verlag New York Inc.","offers":[{"title":"Default Title","offer_id":48739724296535,"sku":"9781493917105","price":56.69,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781493917105.jpg?v=1720053001"},{"product_id":"explorations-in-complex-functions-9783030545321","title":"Explorations in Complex Functions","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis textbook explores a selection of topics in complex analysis. From core material in the mainstream of complex analysis itself, to tools that are widely used in other areas of mathematics, this versatile compilation offers a selection of many different paths. Readers interested in complex analysis will appreciate the unique combination of topics and connections collected in this book.\u003cbr\u003e \u003cbr\u003e Beginning with a review of the main tools of complex analysis, harmonic analysis, and functional analysis, the authors go on to present multiple different, self-contained avenues to proceed. Chapters on linear fractional transformations, harmonic functions, and elliptic functions offer pathways to hyperbolic geometry, automorphic functions, and an intuitive introduction to the Schwarzian derivative. The gamma, beta, and zeta functions lead into \u003ci\u003eL\u003c\/i\u003e-functions, while a chapter on entire functions opens pathways to the Riemann hypothesis and Nevanlinna theory. Cauchy transforms give rise to Hilbert and Fourier transforms, with an emphasis on the connection to complex analysis. Valuable additional topics include Riemann surfaces, steepest descent, tauberian theorems, and the Wiener–Hopf method.\u003c\/p\u003e  \u003cp\u003eShowcasing an array of accessible excursions, \u003ci\u003eExplorations in Complex Functions\u003c\/i\u003e is an ideal companion for graduate students and researchers in analysis and number theory. Instructors will appreciate the many options for constructing a second course in complex analysis that builds on a first course prerequisite; exercises complement the results throughout.\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e“This is a suitable book with a proper concept at the right time. It is suitable because it shows the beauty, power and profundity of complex analysis, enlightens how many sided it is with all its inspirations and cross-connections to other branches of mathematics.” (Heinrich Begehr, zbMATH 1460.30001, 2021)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eBasics.- Linear Fractional Transformations.- Hyperbolic geometry.- Harmonic Functions.- Conformal maps and the Riemann mapping theorem.- The Schwarzian derivative.- Riemann surfaces and algebraic curves.- Entire functions.- Value distribution theory.- The gamma and beta functions.- The Riemann zeta function.- L-functions and primes.- The Riemann hypothesis.- Elliptic functions and theta functions.- Jacobi elliptic functions.- Weierstrass elliptic functions.- Automorphic functions and Picard's theorem.- Integral transforms.- Theorems of Phragmén–Lindelöf and Paley–Wiener.- Theorems of Wiener and Lévy; the Wiener–Hopf method.- Tauberian theorems.- Asymptotics and the method of steepest descent.- Complex interpolation and the Riesz–Thorin theorem.","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":48743039893847,"sku":"9783030545321","price":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030545321.jpg?v=1720063846"},{"product_id":"quaternion-algebras-9783030574673","title":"Quaternion Algebras","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis open access textbook presents a comprehensive treatment of the arithmetic theory of quaternion algebras and orders, a subject with applications in diverse areas of mathematics. Written to be accessible and approachable to the graduate student reader, this text collects and synthesizes results from across the literature. Numerous pathways offer explorations in many different directions, while the unified treatment makes this book an essential reference for students and researchers alike.\u003c\/p\u003e  Divided into five parts, the book begins with a basic introduction to the noncommutative algebra underlying the theory of quaternion algebras over fields, including the relationship to quadratic forms. An in-depth exploration of the arithmetic of quaternion algebras and orders follows. The third part considers analytic aspects, starting with zeta functions and then passing to an idelic approach, offering a pathway from local to global that includes strong approximation. Applications of unit groups of quaternion orders to hyperbolic geometry and low-dimensional topology follow, relating geometric and topological properties to arithmetic invariants. Arithmetic geometry completes the volume, including quaternionic aspects of modular forms, supersingular elliptic curves, and the moduli of QM abelian surfaces.\u003cbr\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e  \u003cp\u003e\u003ci\u003eQuaternion Algebras\u003c\/i\u003e encompasses a vast wealth of knowledge at the intersection of many fields. Graduate students interested in algebra, geometry, and number theory will appreciate the many avenues and connections to be explored. Instructors will find numerous options for constructing introductory and advanced courses, while researchers will value the all-embracing treatment. Readers are assumed to have some familiarity with algebraic number theory and commutative algebra, as well as the fundamentals of linear algebra, topology, and complex analysis. More advanced topics call upon additional background, as noted, though essential concepts and motivation are recapped throughout.\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e“The book contains a huge amount of interesting and very well-chosen exercises. … This ‘encyclopedic’ character of the text may play an important role both as a guide to some special topics and as a source of information for both students and those whose research in related fields creates a need to familiarize themselves with the knowledge of the case when quaternion algebras are relevant.” (Juliusz Brzeziński, Mathematical Reviews, September, 2022)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1. Introduction.- 2. Beginnings.- 3. Involutions.- 4. Quadratic Forms.- 5. Ternary Quadratic Forms.- 6. Characteristic 2.- 7. Simple Algebras.- 8. Simple Algebras and Involutions.- 9. Lattices and Integral Quadratic Forms.- 10. Orders.- 11. The Hurwitz Order.- 12. Ternary Quadratic Forms Over Local Fields.- 13. Quaternion Algebras Over Local Fields.- 14. Quaternion Algebras Over Global Fields.- 15. Discriminants.- 16. Quaternion Ideals and Invertability.- 17. Classes of Quaternion Ideals.- 18. Picard Group.- 19. Brandt Groupoids.- 20. Integral Representation Theory.- 21. Hereditary and Extremal Orders.- 22. Ternary Quadratic Forms.- 23. Quaternion Orders.- 24. Quaternion Orders: Second Meeting.- 25. The Eichler Mass Formula.- 26. Classical Zeta Functions.- 27. Adelic Framework.- 28. Strong Approximation.- 29. Idelic Zeta Functions.- 30. Optimal Embeddings.- 31. Selectivity.- 32. Unit Groups.- 33. Hyperbolic Plane.- 34. Discrete Group Actions.- 35. Classical Modular Group.- 36. Hyperbolic Space.- 37. Fundamental Domains.- 38. Quaternionic Arithmetic Groups.- 39. Volume Formula.- 40. Classical Modular Forms.- 41. Brandt Matrices.- 42. Supersingular Elliptic Curves.- 43. Abelian Surfaces with QM.","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":48743041204567,"sku":"9783030574673","price":28.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030574673.jpg?v=1720063852"},{"product_id":"the-eigenbook-eigenvarieties-families-of-galois-representations-p-adic-l-functions-9783030772628","title":"The Eigenbook: Eigenvarieties, families of Galois","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e​This book discusses the \u003ci\u003ep\u003c\/i\u003e-adic modular forms, the eigencurve that parameterize them, and the \u003ci\u003ep\u003c\/i\u003e-adic \u003ci\u003eL\u003c\/i\u003e-functions one can associate to them. These theories and their generalizations to automorphic forms for group of higher ranks are of fundamental importance in number theory.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eFor graduate students and newcomers to this field, the book provides a solid introduction to this highly active area of research. For experts, it will offer the convenience of collecting into one place foundational definitions and theorems with complete and self-contained proofs.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eWritten in an engaging and educational style, the book also includes exercises and provides their solution.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e“This book represented hope. If I read it carefully, maybe I would finally get to know what they were all talking about, and gain some real insight into what are obviously very important and influential ideas. While I cannot claim to be an expert by now, my first skim through, skipping all the exercises, has provided me with a satisfying foundation, and I found that revisited passages responded well to a second reading to consolidate what I had learned.” (Neil P. Dummigan, Mathematical Reviews, May, 2023)\u003cbr\u003e“Complete proofs (or detailed references) of all statements are given and many exercises (with their solutions or hints) are included, hence the book may be addressed to graduate students working in this beautiful area of number theory and arithmetic algebraic geometry. This is a welcome addition to the literature in a field.” (Andrzej Dąbrowski, zbMATH 1493.11002, 2022)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e- Introduction.- \u003cb\u003ePart I The ‘Eigen’ Construction\u003c\/b\u003e.- Eigenalgebras.- Eigenvarieties.- \u003cb\u003ePart II Modular Symbols and \u003ci\u003eL\u003c\/i\u003e-Functions\u003c\/b\u003e.- Abstract Modular Symbols.- Classical Modular Symbols, Modular Forms, \u003ci\u003eL\u003c\/i\u003e-functions.- Rigid Analytic Modular Symbols and \u003ci\u003ep\u003c\/i\u003e-Adic \u003ci\u003eL\u003c\/i\u003e-functions.- \u003cb\u003ePart III The Eigencurve and its \u003ci\u003ep\u003c\/i\u003e-Adic \u003ci\u003eL\u003c\/i\u003e-Functions\u003c\/b\u003e.- The Eigencurve of Modular Symbols.- \u003ci\u003ep\u003c\/i\u003e-Adic \u003ci\u003eL\u003c\/i\u003e-Functions on the Eigencurve.- The Adjoint \u003ci\u003ep\u003c\/i\u003e-Adic \u003ci\u003eL\u003c\/i\u003e-Function and the Ramification Locus of the Eigencurve.- Solutions and Hints to Exercises.","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":48743049134423,"sku":"9783030772628","price":54.99,"currency_code":"GBP","in_stock":true}]},{"product_id":"around-the-unit-circle-mahler-measure-integer-matrices-and-roots-of-unity-9783030800307","title":"Around the Unit Circle: Mahler Measure, Integer","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eMahler measure, a height function for polynomials, is the central theme of this book. It has many interesting properties, obtained by algebraic, analytic and combinatorial methods. It is the subject of several longstanding unsolved questions, such as Lehmer’s Problem (1933) and Boyd’s Conjecture (1981). This book contains a wide range of results on Mahler measure. Some of the results are very recent, such as Dimitrov’s proof of the Schinzel–Zassenhaus Conjecture. Other known results are included with new, streamlined proofs. Robinson’s Conjectures (1965) for cyclotomic integers, and their associated Cassels height function, are also discussed, for the first time in a book.\u003cp\u003eOne way to study algebraic integers is to associate them with combinatorial objects, such as integer matrices. In some of these combinatorial settings the analogues of several notorious open problems have been solved, and the book sets out this recent work. Many Mahler measure results are proved for restricted sets of polynomials, such as for totally real polynomials, and reciprocal  polynomials of integer symmetric as well as symmetrizable matrices. For reference, the book includes appendices providing necessary background from algebraic number theory, graph theory, and other prerequisites, along with tables of one- and two-variable integer polynomials with small Mahler measure.  All theorems are well motivated and presented in an accessible way. Numerous exercises at various levels are given, including some for computer programming. A wide range of stimulating open problems is also included. At the end of each chapter there is a glossary of newly introduced concepts and definitions.\u003c\/p\u003e  \u003cp\u003e\u003ci\u003eAround the Unit Circle\u003c\/i\u003e is written in a friendly, lucid, enjoyable style, without sacrificing mathematical rigour. It is intended for lecture courses at the graduate level, and will also be a valuable reference for researchers interested in Mahler measure. Essentially self-contained, this textbook should also be accessible to well-prepared upper-level undergraduates.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e“The reader at the graduate level having enough time and energy can learn a lot from this book about the Mahler measure, conjugate sets of algebraic integers, and related results. Some chapters of the book are quite accessible to undergraduate students as well, and may serve as an introduction to their research in this area.” (Arturas Dubickas, Mathematical Reviews, May, 2023)\u003cbr\u003e“It contains some material that is unavailable elsewhere. Each chapter is concluded by notes and a glossary of newly introduced definitions. … The reader at the graduate level having enough time and energy from this book can learn a lot about the Mahler measure, conjugate sets of algebraic integers and related results.” (Artūras Dubickas, zbMATH 1486.11003, 2022)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1 Mahler Measures of Polynomials in One Variable.- 2 Mahler Measures of Polynomials in Several Variables.- 3 Dobrowolski's Theorem.- 4 The Schinzel–Zassenhaus Conjecture.- 5 Roots of Unity and Cyclotomic Polynomials.- 6 Cyclotomic Integer Symmetric Matrices I: Tools and Statement of the Classification Theorem.- 7 Cyclotomic Integer Symmetric Matrices II: Proof of the Classification Theorem.- 8 The Set of Cassels Heights.- 9 Cyclotomic Integer Symmetric Matrices Embedded in Toroidal and Cylindrical Tesselations.- 10 The Transfinite Diameter and Conjugate Sets of Algebraic Integers.- 11 Restricted Mahler Measure Results.- 12 The Mahler Measure of Nonreciprocal Polynomials.- 13 Minimal Noncyclotomic Integer Symmetric Matrices.- 14 The Method of Explicit Auxiliary Functions.- 15 The Trace Problem For Integer Symmetric Matrices.- 16 Small-Span Integer Symmetric Matrices.- 17 Symmetrizable Matrices I: Introduction.- 18 Symmetrizable Matrices II: Cyclotomic Symmetrizable Integer Matrices.- 19 Symmetrizable Matrices III: The Trace Problem.- 20 Salem Numbers from Graphs and Interlacing Quotients.- 21 Minimal Polynomials of Integer Symmetric Matrices.- 22 Breaking Symmetry.- A Algebraic Background.- B Combinatorial Background.- C Tools from the Theory of Functions.- D Tables.- References.- Index.","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":48743049199959,"sku":"9783030800307","price":54.99,"currency_code":"GBP","in_stock":true}]},{"product_id":"explorations-in-number-theory-commuting-through-the-numberverse-9783030989309","title":"Explorations in Number Theory: Commuting through","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis innovative undergraduate textbook approaches number theory through the lens of abstract algebra.  Written in an engaging and whimsical style, this text will introduce students to rings, groups, fields, and other algebraic structures as they discover the key concepts of elementary number theory.  Inquiry-based learning (IBL) appears throughout the chapters, allowing students to develop insights for upcoming sections while simultaneously strengthening their understanding of previously covered topics.  The text is organized around three core themes: the notion of what a “number” is, and the premise that it takes familiarity with a large variety of number systems to fully explore number theory; the use of Diophantine equations as catalysts for introducing and developing structural ideas; and the role of abstract algebra in number theory, in particular the extent to which it provides the Fundamental Theorem of Arithmetic for various new number systems.  Other aspects of modern number theory – including the study of elliptic curves, the analogs between integer and polynomial arithmetic, \u003ci\u003ep\u003c\/i\u003e-adic arithmetic, and relationships between the spectra of primes in various rings – are included in smaller but persistent threads woven through chapters and exercise sets.\u003cbr\u003eEach chapter concludes with exercises organized in four categories: Calculations and Informal Proofs, Formal Proofs, Computation and Experimentation, and General Number Theory Awareness.  IBL “Exploration” worksheets appear in many sections, some of which involve numerical investigations.  To assist students who may not have experience with programming languages, Python worksheets are available on the book’s website.  The final chapter provides five additional IBL explorations that reinforce and expand what students have learned, and can be used as starting points for independent projects.  The topics covered in these explorations are public key cryptography, Lagrange’s four-square theorem, units and Pell’s Equation, various cases of the solution to Fermat’s Last Theorem, and a peek into other deeper mysteries of algebraic number theory.\u003cbr\u003eStudents should have a basic familiarity with complex numbers, matrix algebra, vector spaces, and proof techniques, as well as a spirit of adventure to explore the “numberverse.”\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface.- What is a Number?- A Quick Survey of the Last Two Millenia.- Number Theory in $\\mathcal{Z}$ Beginning.- Number Theory in the Mod-n Era.- Gaussian Number Theory: $\\mathcal{Z}[i]$ of the Storm.- Number Theory: From Where We $\\mathcal{R}$ to across the $mathcal{C}$.- Cyclotomic Number Theory: Roots and Reciprocity. Number Theory Unleashed: Release $\\mathcal{Z}_p$!- The Adventure Continues.- Appendix: Number Systems.","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":48743061782871,"sku":"9783030989309","price":47.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030989309.jpg?v=1723812628"},{"product_id":"excursions-in-number-theory-algebra-and-analysis-9783031130168","title":"Excursions in Number Theory, Algebra, and","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis textbook originates from a course taught by the late Ken Ireland in 1972. Designed to explore the theoretical underpinnings of undergraduate mathematics, the course focused on interrelationships and hands-on experience. Readers of this textbook will be taken on a modern rendering of Ireland’s path of discovery, consisting of excursions into number theory, algebra, and analysis. Replete with surprising connections, deep insights, and brilliantly curated invitations to try problems at just the right moment, this journey weaves a rich body of knowledge that is ideal for those going on to study or teach mathematics.\u003c\/p\u003e  \u003cp\u003eA pool of 200 ‘Dialing In’ problems opens the book, providing fuel for active enquiry throughout a course. The following chapters develop theory to illuminate the observations and roadblocks encountered in the problems, situating them in the broader mathematical landscape. Topics cover polygons and modular arithmetic; the fundamental theorems of arithmetic and algebra; irrational, algebraic and transcendental numbers; and Fourier series and Gauss sums. A lively accompaniment of examples, exercises, historical anecdotes, and asides adds motivation and context to the theory. Return trips to the Dialing In problems are encouraged, offering opportunities to put theory into practice and make lasting connections along the way.\u003c\/p\u003e  \u003cp\u003e\u003ci\u003eExcursions in Number Theory, Algebra, and Analysis\u003c\/i\u003e invites readers on a journey as important as the destination. Suitable for a senior capstone, professional development for practicing teachers, or independent reading, this textbook offers insights and skills valuable to math majors and high school teachers alike. A background in real analysis and abstract algebra is assumed, though the most important prerequisite is a willingness to put pen to paper and \u003ci\u003edo some mathematics\u003c\/i\u003e.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e“Rather than being a book that one reads from cover to cover, Excursions is a curated collection problems followed by expository material aimed at providing background material useful for solving these problems. I imagine it would be a great experience to have a course taught out of this book. The second author clearly enjoyed the experience of studying this material under the guidance of the first author and wanted to make that experience available to others.” (John D. Cook, MAA Reviews, June 17, 2023)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface.- 1. Dialing In Problems.- 2. Polygons and Modular Arithmetic.- 3. The Fundamental Theorem of Arithmetic.- 4. The Fundamental Theorem of Algebra.- 5. Irrational, Algebraic and Transcendental Numbers.- 6. Fourier Series and Gauss Sums.- Epilogue.- Notation.- Bibliography.- Index.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743071351127,"sku":"9783031130168","price":47.49,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031130168.jpg?v=1720063984"},{"product_id":"drinfeld-modules-9783031197062","title":"Drinfeld Modules","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis textbook offers an introduction to the theory of Drinfeld modules, mathematical objects that are fundamental to modern number theory.\u003cbr\u003eAfter the first two chapters conveniently recalling prerequisites from abstract algebra and non-Archimedean analysis, Chapter 3 introduces Drinfeld modules and the key notions of isogenies and torsion points. Over the next four chapters, Drinfeld modules are studied in settings of various fields of arithmetic importance, culminating in the case of global fields. Throughout, numerous number-theoretic applications are discussed, and the analogies between classical and function field arithmetic are emphasized.\u003cbr\u003e\u003ci\u003eDrinfeld Modules\u003c\/i\u003e guides readers from the basics to research topics in function field arithmetic, assuming only familiarity with graduate-level abstract algebra as prerequisite. With exercises of varying difficulty included in each section, the book is designed to be used as the primary textbook for a graduate course on the topic, and may also provide a supplementary reference for courses in algebraic number theory, elliptic curves, and related fields. Furthermore, researchers in algebra and number theory will appreciate it as a self-contained reference on the topic.\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface.- Acknowledgements.- Notation and Conventions.- Chapter 1. Algebraic Preliminaries.- Chapter 2. Non-Archimedean Fields.- Chapter 3. Basic Properties of Drinfeld Modules.- Chapter 4. Drinfeld Modules over Finite Fields.- Chapter 5. Analytic Theory of Drinfeld Modules.- Chapter 6. Drinfeld Modules over Local Fields.- Chapter 7. Drinfeld Modules over Global Fields.- Appendix A. Drinfeld modules for general function rings.- Appendix B. Notes on exercises.- Bibliography.- Index.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743075086679,"sku":"9783031197062","price":67.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031197062.jpg?v=1720064000"},{"product_id":"more-almost-impossible-integrals-sums-and-series-a-new-collection-of-fiendish-problems-and-surprising-solutions-9783031212611","title":"More (Almost) Impossible Integrals, Sums, and","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis book, the much-anticipated sequel to \u003ci\u003e(Almost) Impossible, Integrals, Sums, and Series\u003c\/i\u003e, presents a whole new collection of challenging problems and solutions that are not commonly found in classical textbooks. As in the author’s previous book, these fascinating mathematical problems are shown in new and engaging ways, and illustrate the connections between integrals, sums, and series, many of which involve zeta functions, harmonic series, polylogarithms, and various other special functions and constants. Throughout the book, the reader will find both classical and new problems, with numerous original problems and solutions coming from the personal research of the author. Classical problems are shown in a fresh light, with new, surprising or unconventional ways of obtaining the desired results devised by the author. This book is accessible to readers with a good knowledge of calculus, from undergraduate students to researchers. It will appeal to all mathematical puzzlers who love a good integral or series and aren’t afraid of a challenge.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eChapter 1. Integrals.- Chapter 2. Hints.- Chapter 3. Solutions.- Chapter 4. Sums and Series.- Chapter 5. Hints.- Chapter 6. Solutions.\u003cp\u003e\u003c\/p\u003e","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743076069719,"sku":"9783031212611","price":999.99,"currency_code":"GBP","in_stock":false}]},{"product_id":"abelian-varieties-over-the-complex-numbers-a-graduate-course-9783031255694","title":"Abelian Varieties over the Complex Numbers: A","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis textbook offers an introduction to abelian varieties, a rich topic of central importance to algebraic geometry. The emphasis is on geometric constructions over the complex numbers, notably the construction of important classes of abelian varieties and their algebraic cycles.\u003cbr\u003eThe book begins with complex tori and their line bundles (theta functions), naturally leading to the definition of abelian varieties. After establishing basic properties, the moduli space of abelian varieties is introduced and studied. The next chapters are devoted to the study of the main examples of abelian varieties: Jacobian varieties, abelian surfaces, Albanese and Picard varieties, Prym varieties, and intermediate Jacobians. Subsequently, the Fourier–Mukai transform is introduced and applied to the study of sheaves, and results on Chow groups and the Hodge conjecture are obtained.\u003cbr\u003eThis book is suitable for use as the main text for a first course on abelian varieties, for instance as a second graduate course in algebraic geometry. The variety of topics and abundant exercises also make it well suited to reading courses. The book provides an accessible reference, not only for students specializing in algebraic geometry but also in related subjects such as number theory, cryptography, mathematical physics, and integrable systems.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e“The reorganization of the topics is fine surgical work. Several portions of the original monograph are sewn in a natural way in the new book, adding examples or additional text when necessary, and re-arranging the focus to make it a more friendly introduction to the subject. Careful attention to details and the required background makes the book under review accessible to an interested reader and could be a used as textbook for a course on abelian varieties.” (Felipe Zaldivar, MAA Reviews, June 18, 2023)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1. Line Bundles on Complex Tori.- 2 Abelian Varieties.- 3 Moduli Spaces.- 4 Jacobian Varieties.- 5 Main Examples of Abelian Varieties.- 6 The Fourier Transform for Sheaves and Cycles.- 7 Introduction to the Hodge Conjecture for Abelian Varieties.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743077052759,"sku":"9783031255694","price":44.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031255694.jpg?v=1720064009"},{"product_id":"introduction-to-applications-of-modular-forms-computational-aspects-9783031326288","title":"Introduction to Applications of Modular Forms:","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis book is a self-contained treatment for those who study or work on the computational aspects of classical modular forms. The author describes the theory of modular forms and its applications in number theoretic problems such as representations by quadratic forms and the determination of asymptotic formulas for Fourier coefficients of different types of special functions. A detailed account of recent applications of modular forms in number theory with a focus on using computer algorithms is provided. Computer algorithms are included for each presented application to help readers put the theory in context and make new conjectures.  \u003cbr\u003e\u003cbr\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eDirichlet Characters.- Modular Forms: Definition and Some Properties.- Application: Quadratic Forms.- Application: Eta Quotients.- Various Applications.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743080788311,"sku":"9783031326288","price":66.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031326288.jpg?v=1723812628"},{"product_id":"number-theory-an-introduction-via-the-density-of-primes-9783319438733","title":"Number Theory: An Introduction via the Density of","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eNow in its second edition, this textbook provides an introduction and overview of number theory based on the density and properties of the prime numbers. This unique approach offers both a firm background in the standard material of number theory, as well as an overview of the entire discipline. All of the essential topics are covered, such as the fundamental theorem of arithmetic, theory of congruences, quadratic reciprocity, arithmetic functions, and the distribution of primes. New in this edition are coverage of \u003ci\u003ep\u003c\/i\u003e-adic numbers, Hensel's lemma, multiple zeta-values, and elliptic curve methods in primality testing.\u003cbr\u003eKey topics and features include:\u003cul\u003e\n\u003cli\u003eA solid introduction to analytic number theory, including full proofs of Dirichlet's Theorem and the Prime Number Theorem\u003cbr\u003e\n\u003c\/li\u003e\n\u003cli\u003eConcise treatment of algebraic number theory, including a complete presentation of primes, prime factorizations in algebraic number fields, and unique factorization of ideals\u003c\/li\u003e\n\u003cli\u003eDiscussion of the AKS algorithm, which shows that primality testing is one of polynomial time, a topic not usually included in such texts\u003cbr\u003e\n\u003c\/li\u003e\n\u003cli\u003eMany interesting ancillary topics, such as primality testing and cryptography, Fermat and Mersenne numbers, and Carmichael numbers\u003c\/li\u003e\n\u003c\/ul\u003eThe user-friendly style, historical context, and wide range of exercises that range from simple to quite difficult (with solutions and hints provided for select exercises) make \u003ci\u003eNumber Theory: An Introduction via the Density of Primes\u003c\/i\u003e ideal for both self-study and classroom use. Intended for upper level undergraduates and beginning graduates, the only prerequisites are a basic knowledge of calculus, multivariable calculus, and some linear algebra. All necessary concepts from abstract algebra and complex analysis are introduced where needed.\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e“In this text, Fine (mathematics, Fairfield Univ.) and Rosenberger (Univ. of Hamburg, Germany) successfully present number theory from the inception of primes to recent developments in algebraic and analytic number theory and cryptography. … Numerous exercises and open problems are provided. The breadth and depth of topics covered are impressive, making this an excellent text for those interested in the field of number theory. Summing Up: Recommended. Upper-division undergraduates and graduate students.” (J. T. Zerger, Choice, Vol. 54 (9), May, 2017)\u003c\/p\u003e“The book is chatty and leisurely, with lots of historical notes and lots of worked examples. The exercises at the end of each chapter are good and there are a reasonable number of them. … a good text for an introductory course … .” (Allen Stenger, MAA Reviews, maa.org, November, 2016)\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eIntroduction and Historical Remarks.- Basic Number Theory.- The Infinitude of Primes.- The Density of Primes.- Primality Testing: An Overview.- Primes and Algebraic Number Theory.- The Fields Q_\u003ci\u003ep\u003c\/i\u003e of \u003ci\u003ep\u003c\/i\u003e-adic Numbers: Hensel's Lemma.- References.- Index.","brand":"Birkhauser Verlag AG","offers":[{"title":"Default Title","offer_id":48743095566679,"sku":"9783319438733","price":44.99,"currency_code":"GBP","in_stock":true}]},{"product_id":"a-primer-for-undergraduate-research-from-groups-and-tiles-to-frames-and-vaccines-9783319660646","title":"A Primer for Undergraduate Research: From Groups","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis 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.\u003c\/p\u003e\u003cp\u003eThe 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. \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e“This book is a superb resource for students and faculty mentors embarking on undergraduate research in mathematics. Its focus is on topics and applications rarely covered in the traditional undergraduate math curriculum, offering novice researchers a sturdy jumping-off point to a broad array of research problems. … A valuable resource for students and faculty mentors interested in undergraduate research.” (V. K. Chellamuthu, Choice, Vol. 56 (2), October, 2018)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eCoxeter Groups and the Davis Complex (T.A. Schroeder).- A Tale of Two Symmetries: Embeddable and Non-Embeddable Group Actions on Surfaces (V. Peterson, A. Wootton).- Tile Invariants for Tackling Tiling Questions (M.P. Hitchman).- Forbidden Minors: Finding the Finite Few (T.W. Mattman).- Introduction to competitive graph coloring (C. Dunn, V. Larsen, J.F. Nordstrom).- Matrioids (E. McNicholas, N.A. Neudauer, C. Starr).- Finite Frame Theory (S. Datta, J. Oldroyd).- Mathematical decision-making with linear and convex programming (J. Kotas).- Computing weight multiplicities (P. E. Harris).- Vaccination strategies for small worlds. (W. Just, H. C. Highlander).- Steady and Stable: Numerical Investigations of Nonlinear Partial Differential Equations (R. C. Harwood).","brand":"Birkhauser Verlag AG","offers":[{"title":"Default Title","offer_id":48743101366615,"sku":"9783319660646","price":999.99,"currency_code":"GBP","in_stock":false}]},{"product_id":"problem-based-journey-from-elementary-number-theory-to-an-introduction-to-matrix-theory-a-the-president-problems-9789811234873","title":"Problem Based Journey From Elementary Number","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThe book is based on lecture notes of a course 'from elementary number theory to an introduction to matrix theory' given at the Technion to gifted high school students. It is problem based, and covers topics in undergraduate mathematics that can be introduced in high school through solving challenging problems. These topics include Number theory, Set Theory, Group Theory, Matrix Theory, and applications to cryptography and search engines.","brand":"World Scientific Publishing Co Pte Ltd","offers":[{"title":"Default Title","offer_id":48743279558999,"sku":"9789811234873","price":33.25,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789811234873.jpg?v=1720064898"},{"product_id":"thinking-better-the-art-of-the-shortcut-9780008393953","title":"Thinking Better The Art of the Shortcut","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eHow do you remember more and forget less?How can you earn more and become more creative just by moving house?And how do you pack a car boot most efficiently?This is your shortcut to the art of the shortcut.Mathematics is full of better ways of thinking, and with over 2,000 years of knowledge to draw on, Oxford mathematician Marcus du Sautoy interrogates his passion for shortcuts in this fresh and fascinating guide. After all, shortcuts have enabled so much of human progress, whether in constructing the first cities around the Euphrates 5,000 years ago, using calculus to determine the scale of the universe or in writing today's algorithms that help us find a new life partner.As well as looking at the most useful shortcuts in history  such as measuring the circumference of the earth in 240 BC to diagrams that illustrate how modern GPS works  Marcus also looks at how you can use shortcuts in investing or how to learn a musical instrument to memory techniques. He talks to, among many, the \u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e‘enjoyably clever …with vividly illustrated chapters about the real-world applications of algebra, geometry, probability theory…It’s Du Sautoy, in the end, who provides the wisest commentary’ Steven Poole, Guardian\u003c\/p\u003e           \u003cp\u003e‘If you thought Maths was all about long stuff, like long division and long multiplication and taking a long, long time to figure things out, Marcus du Sautoy shows that it's just the opposite. Full of humour, stories and the lightest of touches, this is a sight-seeing tour of some of the world's greatest neat dodges, unexpected turns and useful cut-throughs. Prepare to be caught short’ Michael Rosen\u003c\/p\u003e           \u003cp\u003e‘This book will change the way you look at the world. It's chock full of stories, ideas and clever tricks – I loved it. Marcus is a maestro at making big ideas come alive – he deserves his place alongside Richard Dawkins, E. O. Wilson and Carlo Rovelli in the pantheon of great modern science writers’ Rohan Silva, CEO and founder of Second Home\u003c\/p\u003e           \u003cp\u003e‘If mathematics has proved anything, it is that shortcuts can change the world. Marcus du Sautoy has come up with a smart, well written and entertaining guide to the connecting tunnels, underpasses and other tricks to traverse the trials of everyday life’ Roger Highfield, author, broadcaster and Science Director at the Science Museum\u003c\/p\u003e           \u003cp\u003e‘The joy of du Sautoy’s book isn’t really the art of the real-world shortcut at all. It is the romp through mathematical ideas, from place value to non Euclidean geometry to probability theory…There are vivid historical examples of scientists and others using mathematical ideas to solve problems’ Tim Harford, Financial Times\u003c\/p\u003e","brand":"HarperCollins Publishers","offers":[{"title":"Default Title","offer_id":48863966953815,"sku":"9780008393953","price":9.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780008393953.jpg?v=1722269810"},{"product_id":"fermats-last-theorem-9780008553821","title":"Fermats Last Theorem","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eIntroducing the Collins Modern Classics, a series featuring some of the most significant books of recent times, books that shed light on the human experience  classics which will endure for generations to come.Maths is one of the purest forms of thought, and to outsiders mathematicians may seem almost otherworldly'In 1963, schoolboy Andrew Wiles stumbled across the world's greatest mathematical problem: Fermat's Last Theorem. Unsolved for over 300 years, he dreamed of cracking it.Combining thrilling storytelling with a fascinating history of scientific discovery, Simon Singh uncovers how an Englishman, after years of secret toil, finally solved mathematics' most challenging problem.Fermat's Last Theorem is remarkable story of human endeavour, obsession and intellectual brilliance, sealing its reputation as a classic of popular science writing.To read it is to realise that there is a world of beauty and intellectual challenge that is denied to 99.9 per cent of us who are not high-level mathematicians'The Times\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e‘This is probably \u003cstrong\u003ethe best popular account of a scientific topic I have ever read\u003c\/strong\u003e’ \u003cem\u003eIrish Times\u003c\/em\u003e\u003c\/p\u003e           \u003cp\u003e‘Reads like the chronicle of an obsessive love affair. \u003cstrong\u003eIt has the classic ingredients that Hollywood would recognise\u003c\/strong\u003e’ \u003cem\u003eDaily Mail\u003c\/em\u003e\u003c\/p\u003e           \u003cp\u003e‘To read it is to realise that \u003cstrong\u003ethere is a world of beauty and intellectual challenge that is denied to 99.9 per cent of us who are not high-level mathematicians\u003c\/strong\u003e’ \u003cem\u003eThe Times\u003c\/em\u003e\u003c\/p\u003e           \u003cp\u003e‘This tale has all the elements of a \u003cstrong\u003emost exciting\u003c\/strong\u003e story: \u003cstrong\u003ean impenetrable riddle; the ambition and frustration of generations of hopefuls; and the genius who worked for years in secrecy to realise his childhood dream\u003c\/strong\u003e’ \u003cem\u003eExpress\u003c\/em\u003e\u003c\/p\u003e","brand":"HarperCollins Publishers","offers":[{"title":"Default Title","offer_id":48864019448151,"sku":"9780008553821","price":9.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780008553821.jpg?v=1722270013"},{"product_id":"combinatorial-geometry-9780471588900","title":"Combinatorial Geometry","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eA complete, self-contained introduction to a powerful and resurging mathematical discipline. Combinatorial Geometry presents and explains with complete proofs some of the most important results and methods of this relatively young mathematical discipline, started by Minkowski, Fejes Toth, Rogers, and Erd???s.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cb\u003eARRANGEMENTS OF CONVEX SETS.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eGeometry of Numbers.\u003c\/p\u003e \u003cp\u003eApproximation of a Convex Set by Polygons.\u003c\/p\u003e \u003cp\u003ePacking and Covering with Congruent Convex Discs.\u003c\/p\u003e \u003cp\u003eLattice Packing and Lattice Covering.\u003c\/p\u003e \u003cp\u003eThe Method of Cell Decomposition.\u003c\/p\u003e \u003cp\u003eMethods of Blichfeldt and Rogers.\u003c\/p\u003e \u003cp\u003eEfficient Random Arrangements.\u003c\/p\u003e \u003cp\u003eCircle Packings and Planar Graphs.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eARRANGEMENTS OF POINTS AND LINES.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eExtremal Graph Theory.\u003c\/p\u003e \u003cp\u003eRepeated Distances in Space.\u003c\/p\u003e \u003cp\u003eArrangement of Lines.\u003c\/p\u003e \u003cp\u003eApplications of the Bounds on Incidences.\u003c\/p\u003e \u003cp\u003eMore on Repeated Distances.\u003c\/p\u003e \u003cp\u003eGeometric Graphs.\u003c\/p\u003e \u003cp\u003eEpsilon Nets and Transversals of Hypergraphs.\u003c\/p\u003e \u003cp\u003eGeometric Discrepancy.\u003c\/p\u003e \u003cp\u003eHints to Exercises.\u003c\/p\u003e \u003cp\u003eBibliography.\u003c\/p\u003e \u003cp\u003eIndexes.\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":48864650199383,"sku":"9780471588900","price":155.66,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780471588900.jpg?v=1722272896"},{"product_id":"number-theory-9780486682525","title":"Number Theory","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eWritten by a distinguished mathematician and teacher, this undergraduate text uses a combinatorial approach to accommodate both math majors and liberal arts students. In addition to covering the basics of number theory, it offers an outstanding introduction to partitions, plus chapters on multiplicativity-divisibility, quadratic congruences, additivity, and more.","brand":"Dover Publications Inc.","offers":[{"title":"Default Title","offer_id":48864740606295,"sku":"9780486682525","price":13.04,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780486682525.jpg?v=1722273026"},{"product_id":"elliptic-tales-9780691163505","title":"Elliptic Tales","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eElliptic Tales describes the latest developments in number theory by looking at one of the most exciting unsolved problems in contemporary mathematics--the Birch and Swinnerton-Dyer Conjecture. In this book, Avner Ash and Robert Gross guide readers through the mathematics they need to understand this captivating problem. The key to the conjecture\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"The authors present their discussion in an informal, sometimes playful manner and with detail that will appeal to an audience with a basic understanding of calculus. This book will captivate math enthusiasts as well as readers curious about an intriguing and still unanswered question.\"--Margaret Dominy, Library Journal \"Minimal prerequisites and its clear writing make this book (which even has a few exercises) a great choice for a seminar for mathematics majors, who at some point should have such an excursion to one of the frontiers of mathematics.\"--Mathematics Magazine \"The authors of Elliptic Tales do a superb job in demonstrating the approach that mathematicians take when they confront unsolved problems involving elliptic curves.\"--Sungkon Chang, Times Higher Education \"One cannot help being impressed, in reading the book and pursuing a few of the references, by the magnitude of the enterprise it chronicles.\"--James Case, SIAM News \"Ash and Gross thoroughly explain the statement and significance of the linchpin Birch and Swinnerton-Dyer conjection... [A]sh and Gross deliver ample and current intellectual and technical substance.\"--Choice \"I would envision this book as an excellent text for an undergraduate 'capstone' course in mathematics; the book lends itself to independent reading, but topics may be explored in much greater depth and rigor in the classroom. Additionally, the book indeed brings together ideas from calculus, complex variables and algebra, showing how a single mathematical research question may require an integrated understanding of the various branches of mathematics. Thus, it encourages students to reinforce their understanding of these various fields, while simultaneously introducing them to an open question in mathematics and a vibrant field of study.\"--Lisa A. Berger, Mathematical Reviews Clippings \"The book is very pleasantly written, and in my opinion, the authors have done an admirable job in giving an idea to non-experts what the Birch-Swinnerton Dyer conjecture is about.\"--Jan-Hendrik Evertse, Zentralblatt MATH \"The book's most important contributions ... are the sense of discovery, invention, and insight into the habits of mind used by mathematicians on this journey. I would recommend this book to anyone who wants to be challenged mathematically or who wants to experience mathematics as creative and exciting.\"--Jacqueline Coomes, Mathematics Teacher \"[T]his book is a wonderful introduction to what is arguably one of the most important mathematical problems of our time and for that reason alone it deserves to be widely read. Another reason to recommend this book is the opportunity to share in the readily apparent joy the authors have for their subject and the beauty they see in it, not least because ... joy and beauty are the most important reasons for doing mathematics, irrespective of its dollar value.\"--Rob Ashmore, Mathematics Today \"This book has many nice aspects. Ash and Gross give a truly stimulating introduction to elliptic curves and the BSD conjecture for undergraduate students. The main achievement is to make a relative easy exposition of these so technical topics.\"--Jonathan Sanchez-Hernandez, Mathematical Society\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface xiii Acknowledgments xix Prologue 1   PART I. DEGREE   Chapter 1. Degree of a Curve 13 1.Greek Mathematics 13 2.Degree 14 3.Parametric Equations 20 4.Our Two Definitions of Degree Clash 23   Chapter 2. Algebraic Closures 26 1.Square Roots of Minus One 26 2.Complex Arithmetic 28 3.Rings and Fields 30 4.Complex Numbers and Solving Equations 32 5.Congruences 34 6.Arithmetic Modulo a Prime 38 7.Algebraic Closure 38   Chapter 3. The Projective Plane 42 1.Points at Infinity 42 2.Projective Coordinates on a Line 46 3.Projective Coordinates on a Plane 50 4.Algebraic Curves and Points at Infinity 54 5.Homogenization of Projective Curves 56 6.Coordinate Patches 61   Chapter 4. Multiplicities and Degree 67 1.Curves as Varieties 67 2.Multiplicities 69 3.Intersection Multiplicities 72 4.Calculus for Dummies 76   Chapter 5. B'ezout's Theorem 82 1.A Sketch of the Proof 82 2.An Illuminating Example 88   PART II. ELLIPTIC CURVES AND ALGEBRA   Chapter 6. Transition to Elliptic Curves 95   Chapter 7. Abelian Groups 100 1.How Big Is Infinity? 100 2.What Is an Abelian Group? 101 3.Generations 103 4.Torsion 106 5.Pulling Rank 108 Appendix: An Interesting Example of Rank and Torsion 110   Chapter 8. Nonsingular Cubic Equations 116 1.The Group Law 116 2.Transformations 119 3.The Discriminant 121 4.Algebraic Details of the Group Law 122 5.Numerical Examples 125 6.Topology 127 7.Other Important Facts about Elliptic Curves 131 5.Two Numerical Examples 133   Chapter 9. Singular Cubics 135 1.The Singular Point and the Group Law 135 2.The Coordinates of the Singular Point 136 3.Additive Reduction 137 4.Split Multiplicative Reduction 139 5.Nonsplit Multiplicative Reduction 141 6.Counting Points 145 7.Conclusion 146 Appendix A: Changing the Coordinates of the Singular Point 146 Appendix B: Additive Reduction in Detail 147 Appendix C: Split Multiplicative Reduction in Detail 149 Appendix D: Nonsplit Multiplicative Reduction in Detail 150   Chapter 10. Elliptic Curves over Q 152 1.The Basic Structure of the Group 152 2.Torsion Points 153 3.Points of Infinite Order 155 4.Examples 156   PART III. ELLIPTIC CURVES AND ANALYSIS   Chapter 11. Building Functions 161 1.Generating Functions 161 2.Dirichlet Series 167 3.The Riemann Zeta-Function 169 4.Functional Equations 171 5.Euler Products 174 6.Build Your Own Zeta-Function 176   Chapter 12. Analytic Continuation 181 1.A Difference that Makes a Difference 181 2.Taylor Made 185 3.Analytic Functions 187 4.Analytic Continuation 192 5.Zeroes, Poles, and the Leading Coefficient 196   Chapter 13. L-functions 199 1.A Fertile Idea 199 2.The Hasse-Weil Zeta-Function 200 3.The L-Function of a Curve 205 4.The L-Function of an Elliptic Curve 207 5.Other L-Functions 212   Chapter 14. Surprising Properties of L-functions 215 1.Compare and Contrast 215 2.Analytic Continuation 220 3.Functional Equation 221   Chapter 15. The Conjecture of Birch and Swinnerton-Dyer 225 1.How Big Is Big? 225 2.Influences of the Rank on the Np's 228 3.How Small Is Zero? 232 4.The BSD Conjecture 236 5.Computational Evidence for BSD 238 6.The Congruent Number Problem 240 Epilogue 245 Retrospect 245 Where DoWe Go from Here? 247   Bibliography 249 Index 251","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":48865531167063,"sku":"9780691163505","price":13.29,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691163505.jpg?v=1722274417"},{"product_id":"an-imaginary-tale-9780691169248","title":"An Imaginary Tale","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eIn the title, \"[the square root of minus one]\" appears as a radical over \"-1.\"\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003eOne of Choice's Outstanding Academic Titles for 1999 Honorable Mention for the 1998 Award for Best Professional\/Scholarly Book in Mathematics, Association of American Publishers \"A book-length hymn of praise to the square root of minus one.\"--Brian Rotman, Times Literary Supplement \"An Imaginary Tale is marvelous reading and hard to put down. Readers will find that Nahin has cleared up many of the mysteries surrounding the use of complex numbers.\"--Victor J. Katz, Science \"[An Imaginary Tale] can be read for fun and profit by anyone who has taken courses in introductory calculus, plane geometry and trigonometry.\"--William Thompson, American Scientist \"Someone has finally delivered a definitive history of this 'imaginary' number... A must read for anyone interested in mathematics and its history.\"--D. S. Larson, Choice \"Attempting to explain imaginary numbers to a non-mathematician can be a frustrating experience... On such occasions, it would be most useful to have a copy of Paul Nahin's excellent book at hand.\"--A. Rice, Mathematical Gazette \"Imaginary numbers! Threeve! Ninety-fifteen! No, not those kind of imaginary numbers. If you have any interest in where the concept of imaginary numbers comes from, you will be drawn into the wonderful stories of how i was discovered.\"--Rebecca Russ, Math Horizons \"There will be something of reward in this book for everyone.\"--R.G. Keesing, Contemporary Physics \"Nahin has given us a fine addition to the family of books about particular numbers. It is interesting to speculate what the next member of the family will be about. Zero? The Euler constant? The square root of two? While we are waiting, we can enjoy An Imaginary Tale.\"--Ed Sandifer, MAA Online \"Paul Nahin's book is a delightful romp through the development of imaginary numbers.\"--Robin J. Wilson, London Mathematical Society Newsletter \"You will definitely enjoy it. In fact it clearly reflects the the joy and delight that the author experienced when he was confronted with complex analysis during his engineering studies.\"--Adhemar Bultheel, European Mathematical Society\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e*FrontMatter, pg. i*A Note to the Reader, pg. vii*Contents, pg. ix*Illustrations, pg. xi*Preface to the Paperback Edition, pg. xiii*Preface, pg. xxi*Introduction, pg. 1*CHAPTER ONE The Puzzles of Imaginary Numbers, pg. 8*CHAPTER TWO. A First Try at Understanding the Geometry of  -1, pg. 31*CHAPTER THREE. The Puzzles Start to Clear, pg. 48*CHAPTER FOUR. Using Complex Numbers, pg. 84*CHAPTER FIVE. More Uses of Complex Numbers, pg. 105*CHAPTER SIX. Wizard Mathematics, pg. 142*CHAPTER SEVEN. The Nineteenth Century, Cauchy, and the Beginning of Complex Function Theory, pg. 187*APPENDIX A. The Fundamental Theorem of Algebra, pg. 227*APPENDIX B. The Complex Roots of a Transcendental Equation, pg. 230*APPENDIX C. ( -1)( -1) to 135 Decimal Places, and How It Was Computed, pg. 235*APPENDIX D. Solving Clausen's Puzzle, pg. 238*APPENDIX E. Deriving the Differential Equation for the Phase-Shift Oscillator, pg. 240*APPENDIX F. The Value of the Gamma Function on the Critical Line, pg. 244*Notes, pg. 247*Name Index, pg. 261*Subject Index, pg. 265*Acknowledgments, pg. 269","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":48865534017879,"sku":"9780691169248","price":13.29,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691169248.jpg?v=1722274434"},{"product_id":"the-irrationals-9780691247663","title":"The Irrationals","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"The insides of this book are as clever and compelling as the subtitle on the cover. Havil, a retired former master at Winchester College in England, where he taught math for decades, takes readers on a history of irrational numbers--numbers, like v2 or p, whose decimal expansion 'is neither finite nor recurring.' We start in ancient Greece with Pythagoras, whose thinking most likely helped to set the path toward the discovery of irrational numbers, and continue to the present day, pausing to ponder such questions as, 'Is the decimal expansion of an irrational number random?'\"\u003cb\u003e---Anna Kuchment, \u003ci\u003eScientific American\u003c\/i\u003e\u003c\/b\u003e\u003cbr\u003e\"\u003ci\u003eThe Irrationals\u003c\/i\u003e is a true mathematician's and historian's delight.\"\u003cb\u003e---Robert Schaefer, \u003ci\u003eNew York Journal of Books\u003c\/i\u003e\u003c\/b\u003e\u003cbr\u003e\"From its lively introduction straight through to a rousing finish this is a book which can be browsed for its collection of interesting facts or studied carefully by anyone with an interest in numbers and their history. . . . This is a wonderful book which should appeal to a broad audience. Its level of difficulty ranges nicely from ideas accessible to high school students to some very deep mathematics. Highly recommended!\"\u003cb\u003e---Richard Wilders, \u003ci\u003eMAA Reviews\u003c\/i\u003e\u003c\/b\u003e\u003cbr\u003e\"It is a book that can be warmly recommended to any mathematician or any reader who is generally interested in mathematics. One should be prepared to read some of the proofs. Skipping all the proofs would do injustice to the concept, leaving just a skinny skeleton, but skipping some of the most advanced ones is acceptable. The style, the well documented historical context and quotations mixed with references to modern situations make it a wonderful read.\"\u003cb\u003e---A. Bultheel, \u003ci\u003eEuropean Mathematical Society\u003c\/i\u003e\u003c\/b\u003e\u003cbr\u003e\"To follow the mathematical sections of the book, the reader should have at least a second-year undergraduate mathematical background, as the author does not shrink from providing some detailed arguments. However, the presentation of historical material is given in modern mathematical form. Many readers will encounter unfamiliar and surprising material in this field in which much remains to be explored.\"\u003cb\u003e---E. J. Barbeau, \u003ci\u003eMathematical Reviews Clippings\u003c\/i\u003e\u003c\/b\u003e\u003cbr\u003e\"This is a well-written book to which senior high school students who do not intend to study mathematics at university should be exposed in their last two years at school. The ideas are challenging and provocative, with numerous clear diagrams. The topics are presented with numerous examples, and unobtrusive humour which renders the exposition even more palatable. The book would be an ideal source of ideas in a mathematics course within a liberal arts college because it links not only with the historical source of mathematics problems, but also with some of the great ideas of philosophy.\"\u003cb\u003e---A. G. Shannon, \u003ci\u003eNotes on Number Theory and Discrete Mathematics\u003c\/i\u003e\u003c\/b\u003e\u003cbr\u003e\"Mathematicians and serious students of mathematics will find much to admire in this book. . . . Every mathematician and student of mathematics with appropriate background will find [it] to be a valuable resource.\"\u003cb\u003e---Pamela Gorkin, \u003ci\u003eMathematical Intelligencer\u003c\/i\u003e\u003c\/b\u003e","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":48865555186007,"sku":"9780691247663","price":16.14,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691247663.jpg?v=1722274540"},{"product_id":"mathematics-and-its-history-9781461426325","title":"Mathematics and Its History","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThe Theorem of Pythagoras.- Greek Geometry.- Greek Number Theory.- Infinity in Greek Mathematics.- Number Theory in Asia.- Polynomial Equations.- Analytic Geometry.- Projective Geometry.- Calculus.- Infinite Series.- The Number Theory Revival.- Elliptic Functions.- Mechanics.- Complex Numbers in Algebra.- Complex Numbers and Curves.- Complex Numbers and Functions.- Differential Geometry.- Non-Euclidean Geometry.- Group Theory.- Hypercomplex Numbers.- Algebraic Number Theory.- Topology.- Simple Groups.- Sets, Logic, and Computation.- Combinatorics.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e“Mathematics and Its History is an original, engaging and effective book, which I think would be enjoyed by students, lay readers with the right background, or indeed mathematicians themselves.” (Danny Yee, Danny Yee's Book Reviews, dannyreviews.com, March, 2019)\u003c\/p\u003e\u003cp\u003eFrom the reviews of the third edition:\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e\"The author’s goal for \u003ci\u003eMathematics and its History\u003c\/i\u003e is to provide a “bird’s-eye view of undergraduate mathematics.” (p. \u003ci\u003evii\u003c\/i\u003e) In that regard it succeeds admirably. ... \u003ci\u003eMathematics and its History\u003c\/i\u003e is a joy to read. The writing is clear, concise and inviting. The style is very different from a traditional text. ... The author has done a wonderful job of tying together the dominant themes of undergraduate mathematics. ... While Stillwell does a wonderful job of tying together seemingly unrelated areas of mathematics, it is possible to read each chapter independently. I would recommend this fine book for anyone who has an interest in the history of mathematics. For those who teach mathematics, it provides lots of information which could easily be used to enrich an opening lecture in most any undergraduate course. It would be an ideal gift for a department’s outstanding major or for the math club president. Pick it up at your peril — it is hard to put down!\"\u003c\/p\u003e\u003cp\u003e(Richard Wilders, MAA Reviews)\u003c\/p\u003e\u003cp\u003e“I appreciate and recommend Stillwell’s presentation of mathematics and history written in a lively style. The author’s concept (history mostly as the means of approaching mathematics) remains a matter of interest for both the mathematician and the historian … .” (Rüdiger Thiele, Zentralblatt MATH, Vol. 1207, 2011)\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eFrom the reviews of the second edition:\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\"This book covers many interesting topics not usually covered in a present day undergraduate course, as well as certain basic topics such as the development of the calculus and the solution of polynomial equations. The fact that the topics are introduced in their historical contexts will enable students to better appreciate and understand the mathematical ideas involved...If one constructs a list of topics central to a history course, then they would closely resemble those chosen here.\"\u003c\/p\u003e\u003cp\u003e(David Parrott, Australian Mathematical Society)\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\"The book...is presented in a lively style without unnecessary detail. It is very stimulating and will be appreciated not only by students. Much attention is paid to problems and to the development of mathematics before the end of the nineteenth century... This book brings to the non-specialist interested in mathematics many interesting results. It can be recommended for seminars and will be enjoyed by the broad mathematical community.\" \u003c\/p\u003e\u003cp\u003e(European Mathematical Society)\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\"Since Stillwell treats many topics, most mathematicians will learn a lot from this book as well as they will find pleasant and rather clear expositions of custom materials. The book is accessible to students that have already experienced calculus, algebra and geometry and will give them a good account of how the different branches of mathematics interact.\"\u003c\/p\u003e\u003cp\u003e(Denis Bonheure, Bulletin of the Belgian Society)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface to the Third Edition.- Preface to the Second Edition.- Preface to the First Edition.- The Theorem of Pythagoras.- Greek Geometry.- Greek Number Theory.- Infinity in Greek Mathematics.- Number Theory in Asia.- Polynomial Equations.- Analytic Geometry.- Projective Geometry.- Calculus.- Infinite Series.- The Number Theory Revival.- Elliptic Functions.- Mechanics.- Complex Numbers in Algebra.- Complex Numbers and Curves.- Complex Numbers and Functions.- Differential Geometry.- Non-Euclidean Geometry.- Group Theory.- Hypercomplex Numbers.- Algebraic Number Theory.- Topology.- Simple Groups.- Sets, Logic, and Computation.- Combinatorics.- Bibliography.- Index.-","brand":"Springer-Verlag New York Inc.","offers":[{"title":"Default Title","offer_id":48867159343447,"sku":"9781461426325","price":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781461426325.jpg?v=1722281959"},{"product_id":"topology-of-numbers-9781470456115","title":"Topology of Numbers","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eProvides an introduction to number theory at the undergraduate level, emphasizing geometric aspects of the subject. The geometric approach is exploited to explore in depth the classical topic of quadratic forms with integer coefficients, a central topic of the book.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cul\u003e\n\u003cli\u003eA preview\u003c\/li\u003e\n\u003cli\u003eThe Farey diagram\u003c\/li\u003e\n\u003cli\u003eContinued fractions\u003c\/li\u003e\n\u003cli\u003eSymmetries of the Farey diagram\u003c\/li\u003e\n\u003cli\u003eQuadratic forms\u003c\/li\u003e\n\u003cli\u003eClassification of quadratic forms\u003c\/li\u003e\n\u003cli\u003eRepresentations by quadratic forms\u003c\/li\u003e\n\u003cli\u003eThe class group for quadratic forms\u003c\/li\u003e\n\u003cli\u003eQuadratic fields\u003c\/li\u003e\n\u003cli\u003eTables\u003c\/li\u003e\n\u003cli\u003eGlossary of nonstandard terminology\u003c\/li\u003e\n\u003cli\u003eBibliography\u003c\/li\u003e\n\u003cli\u003eIndex\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"American Mathematical Society","offers":[{"title":"Default Title","offer_id":48867166355799,"sku":"9781470456115","price":46.8,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781470456115.jpg?v=1722281995"},{"product_id":"wild-fibonacci-natures-secret-code-revealed-9781582463247","title":"Wild Fibonacci: Nature's Secret Code Revealed","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e1, 1, 2, 3, 5, 8, 13, 21, 34. . . Look carefully. Do you see the pattern? Each number above is the sum of the two numbers before it. Though most of us are unfamiliar with it, this numerical series, called the Fibonacci sequence, is part of a code that can be found everywhere in nature. Count the petals on a flower or the peas in a peapod. The numbers are all part of the Fibonacci sequence. In Wild Fibonacci, readers will discover this mysterious code in a special shape called an equiangular spiral. Why so special? It mysteriously appears in the natural world: a sundial shell curves to fit the spiral. So does a parrot''s beak. . . a hawk''s talon. . . a ram''s horn. . . even our own human teeth! Joy Hulme provides a clear and accessible introduction to the Fibonacci sequence and its presence in the animal world.","brand":"Tricycle Press","offers":[{"title":"Default Title","offer_id":48867627106647,"sku":"9781582463247","price":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781582463247.jpg?v=1722284198"},{"product_id":"the-music-of-the-primes-why-an-unsolved-problem-in-mathematics-matters-9781841155807","title":"The Music of the Primes: Why an unsolved problem","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e20 years later \u003cem\u003eThe Music of the Primes\u003c\/em\u003e is still a groundbreaking popular science book. This new edition features updates from the author and a foreword by actor and director, Simon McBurney.\u003c\/p\u003e           \u003cp\u003eIn 1859, the German mathematician Bernhard Riemann presented a paper to the Berlin Academy which would change the history of mathematics. The subject was the strange and enigmatic prime numbers. At the heart of the presentation was an idea, a hypothesis, that Riemann had not yet proved but which has come to obsess mathematicians for the last 150 years. No one knows if he ever found the proof; on his death his housekeeper burnt all the personal papers. Today, the hypothesis is considered by many the holy grail of mathematics but has significance far beyond maths.\u003c\/p\u003e           \u003cp\u003eAt the of the heart of the enigma is a prize much larger than just intellectual glory; not only is there a $1 million reward for the person who can crack it but also is the key to all banking and e-commerce security. It is the idea that brings together many other areas of science and has ramifications within Quantum Mechanics, Chaos Theory and the future of computing.\u003c\/p\u003e           \u003cp\u003eIn 'The Music of the Primes', one of Britain's leading mathematicians, Marcus du Sautoy, recounts the history of these elusive numbers. It is a story of eccentric and brilliant men, last minute escapes from death, strange journeys, dangerous ideas and the unquenchable thirst for knowledge that drove some men mad and others to unparalleled glory. du Sautoy also tells a coruscating history of Mathematics. Combining in-depth knowledge as a practitioner in the field with narrative flair, this book will become a classic of popular science writing and will rank alongside 'Chaos' and 'Fermat's Last Theorem' within the genre.\u003c\/p\u003e           \u003cp\u003eThe Riemann Hypothesis:\u003cbr\u003e• Compared to Fermat's Last Theorem, the Hypothesis is mathematicians’ real Holy Grail\u003cbr\u003e• Is the only problem from Hilbert's 1900 Centenary Problems that was unproved in the 20th century and now has a $1 million reward for the person who cracks it.\u003cbr\u003e• The Hypothesis is the key to all Internet and e-commerce security\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e'Du Sautoy is a contagious enthusiast, a populist with a staunch faith in the public's intelligence…he has uncovered a wealth of intriguing anecdotes that he has woven into a compelling narrative.' Observer\u003c\/p\u003e           \u003cp\u003e'He laces the ideas with history, anecdote and personalia – an entertaining mix that renders an austere subject palatable…valiant and ingenious…Even those with a mathematical allergy can enjoy du Sautoy's depictions of his cast of characters' The Times\u003c\/p\u003e           \u003cp\u003e'He brings hugely enjoyable writing, full of zest and passion, to the most fundamental questions in the pursuit of true knowledge.' Sunday Times\u003c\/p\u003e           \u003cp\u003e'A mesmerising journey into the world of mathematics and its mysteries.' Daily Mail\u003c\/p\u003e           \u003cp\u003e'A brilliant storyteller.' Independent\u003c\/p\u003e","brand":"HarperCollins Publishers","offers":[{"title":"Default Title","offer_id":48868656054615,"sku":"9781841155807","price":10.44,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781841155807.jpg?v=1722289086"},{"product_id":"frontiers-of-combinatorics-number-theory-volume-3-9781628089509","title":"Frontiers of Combinatorics \u0026 Number Theory:","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis book contains papers on topics in combinatorics (including graph theory) or number theory. The subject areas within correspond to the MSC (Mathematics Subject Classification) codes 05, 11, 20D60, and 52. Some topics discussed in this compilation include restricted Eisenstein series and certain convolution sums; zeroes of the Hurwitz zeta function in the interval (O,1); prime factorization conditions providing multiplicities in coset partitions of groups; mean value formulas for twisted Edwards curves; binary matrices as morphisms of a triangular category; some diophantine triples and quadruples for quadratic polynomials; codes associated with orthogonal groups; combinatorial sums and series involving inverses of the Gaussian binomial co-effecients; full friendly index sets and full product-cordial index sets of twisted cylinders; and properly charged coloring of two-dimensional arrays.","brand":"Nova Science Publishers Inc","offers":[{"title":"Default Title","offer_id":48887071637847,"sku":"9781628089509","price":146.24,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781628089509.jpg?v=1722542868"},{"product_id":"frontiers-of-combinatorics-number-theory-volume-4-9781628089578","title":"Frontiers of Combinatorics \u0026 Number Theory:","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis book contains papers on topics in combinatorics (including graph theory) or number theory. The subject areas within correspond to the MSC (Mathematics Subject Classification) codes 05, 11, 20D60, and 52. Some topics included in this compilation are pseudorandom binary functions on rooted plane trees; class number one criteria for real quadratic fields with discriminant k2p24p; some product-to-sum identities; a zeta function for juggling sequences; divisibility properties of hypergeometric polynomials; the distance between perfect numbers; a new proof of a theorem of Hamidoune avoiding; conjectures on the monotonicity of some arithmetical sequences; complexity of trapezoidal graphs with different triangulations; applications of shuffle products of multiple zeta values in combinatorics; the invariant area formulas and lattice point bounds for the intersection of hyperbolic and elliptic regions; and product-cordial index set for Cartesian products of a graph with a path.","brand":"Nova Science Publishers Inc","offers":[{"title":"Default Title","offer_id":48887071703383,"sku":"9781628089578","price":146.24,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781628089578.jpg?v=1722542869"},{"product_id":"introduction-to-analytic-number-theory-9780387901633","title":"Introduction to Analytic Number Theory","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eHistorical Introduction.- 1 The Fundamental Theorem of Arithmetic.- 2 Arithmetical Functions and Dirichlet Multiplication.- 3 Averages of Arithmetical Functions.- 4 Some Elementary Theorems on the Distribution of Prime Numbers.- 5 Congruences.- 6 Finite Abelian Groups and Their Characters.- 7 Dirichlet's Theorem on Primes in Arithmetic Progressions.- 8 Periodic Arithmetical Functions and Gauss Sums.- 9 Quadratic Residues and the Quadratic Reciprocity Law.- 10 Primitive Roots.- 11 Dirichlet Series and Euler Products.- 12 The Functions ?(s) and L(s, ?).- 13 Analytic Proof of the Prime Number Theorem.- 14 Partitions.- Index of Special Symbols.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eFrom the reviews:\u003c\/p\u003e\u003cp\u003eT.M. Apostol\u003c\/p\u003e\u003cp\u003e\u003ci\u003eIntroduction to Analytic Number Theory\u003c\/i\u003e\u003c\/p\u003e\u003cp\u003e\"\u003ci\u003eThis 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. For this reason, the book starts with the most elementary properties of the natural integers. Nevertheless, the text succeeds in presenting an enormous amount of material in little more than 300 pages. The presentation is invariably lucid and the book is a real pleasure to read.\"\u003c\/i\u003e\u003c\/p\u003e\u003cp\u003e—MATHEMATICAL REVIEWS\u003c\/p\u003e\u003cp\u003e“After reading Introduction to Analytic Number Theory one is left with the impression that the author, Tom M. Apostal, has pulled off some magic trick. … I must admit that I love this book. The selection of topics is excellent, the exposition is fluid, the proofs are clear and nicely structured, and every chapter contains its own set of … exercises. … this book is very readable and approachable, and it would work very nicely as a text for a second course in number theory.” (Álvaro Lozano-Robledo, The Mathematical Association of America, December, 2011)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1: The Fundamental Theorem of Arithmetic. 2: Arithmetical Functions and Dirichlet Multiplication. 3: Averages of Arithmetical Function. 4: Some Elementary Theorems on the Distribution of Prime Numbers. 5: Congruences. 6: Finite Abelian Groups and Their Characters. 7: Cirichlet's Theorem on Primes in Arithmetic Progressions. 8: Periodic Arithmetical Functions and Gauss Sums. 9: Quadratic Residues and the Quadratic Reciprocity Law. 10: Primitive Roots. 11: Dirichlet Series and Euler Products. 12: The Functions. 13: Analytic Proof of the Prime Number Theorem. 14: Partitions.","brand":"Springer-Verlag New York Inc.","offers":[{"title":"Default Title","offer_id":49083495416151,"sku":"9780387901633","price":46.99,"currency_code":"GBP","in_stock":true}]},{"product_id":"davenportzannier-polynomials-and-dessins-denfants-9781470456344","title":"DavenportZannier Polynomials and Dessins dEnfants","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThe polynomials studied in this book take their origin in number theory. The authors show how, by drawing simple pictures, one can prove some long-standing conjectures and formulate new ones. The theory presented here touches upon many different fields of mathematics.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cul\u003e\n\u003cli\u003eIntroduction.\u003c\/li\u003e\n\u003cli\u003eDessins d'enfants: From polynomials through Belyi functions to weighted trees.\u003c\/li\u003e\n\u003cli\u003e Existence theorem.\u003c\/li\u003e\n\u003cli\u003e Recapitulation and perspective.\u003c\/li\u003e\n\u003cli\u003e Classification of unitrees.\u003c\/li\u003e\n\u003cli\u003e Computation of Davenport-Zannier pairs for unitrees.\u003c\/li\u003e\n\u003cli\u003e Primitive monodromy groups of weighted trees.\u003c\/li\u003e\n\u003cli\u003eTrees with primitive monodromy groups.\u003c\/li\u003e\n\u003cli\u003eA zoo of examples and constructions.\u003c\/li\u003e\n\u003cli\u003e Diophantine invariants.\u003c\/li\u003e\n\u003cli\u003eEnumeration.\u003c\/li\u003e\n\u003cli\u003e What remains to be done.\u003c\/li\u003e\n\u003cli\u003e Bibliography.\u003c\/li\u003e\n\u003cli\u003e Index.\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"American Mathematical Society","offers":[{"title":"Default Title","offer_id":49083993391447,"sku":"9781470456344","price":115.6,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781470456344.jpg?v=1725550699"},{"product_id":"a-history-of-abstract-algebra-from-algebraic-equations-to-modern-algebra-9783319947723","title":"A History of Abstract Algebra: From Algebraic","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis textbook provides an accessible account of the history of abstract algebra, tracing a range of topics in modern algebra and number theory back to their modest presence in the seventeenth and eighteenth centuries, and exploring the impact of ideas on the development of the subject.\u003c\/p\u003e  Beginning with Gauss’s theory of numbers and Galois’s ideas, the book progresses to Dedekind and Kronecker, Jordan and Klein, Steinitz, Hilbert, and Emmy Noether. Approaching mathematical topics from a historical perspective, the author explores quadratic forms, quadratic reciprocity, Fermat’s Last Theorem, cyclotomy, quintic equations, Galois theory, commutative rings, abstract fields, ideal theory, invariant theory, and group theory. Readers will learn what Galois accomplished, how difficult the proofs of his theorems were, and how important Camille Jordan and Felix Klein were in the eventual acceptance of Galois’s approach to the solution of equations. The book also describes the relationship between Kummer’s ideal numbers and Dedekind’s ideals, and discusses why Dedekind felt his solution to the divisor problem was better than Kummer’s. \u003cp\u003e\u003c\/p\u003e  \u003cp\u003eDesigned for a course in the history of modern algebra, this book is aimed at undergraduate students with an introductory background in algebra but will also appeal to researchers with a general interest in the topic. With exercises at the end of each chapter and appendices providing material difficult to find elsewhere, this book is self-contained and therefore suitable for self-study.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e“This volume is well written and nicely complements other works on the history of algebra. It can be recommended to all mathematicians and students of mathematics who want to understand how algebra turned into the rather abstract field it is today.” (C. Baxa, Monatshefte für Mathematik, Vol. 201 (4), August, 2023)\u003cbr\u003e\u003cbr\u003e“The book under review is an excellent contribution to the history of abstract algebra and the beginnings of algebraic number theory. I recommend it to everyone interested in the history of mathematics.” (Franz Lemmermeyer, zbMATH 1411.01005, 2019)\u003cbr\u003e“This is a nice book to have around; it reflects careful scholarship and is filled with interesting material. … there is much to like about this book. It is quite detailed, contains a lot of information, is meticulously researched, and has an extensive bibliography. Anyone interested in the history of mathematics, or abstract algebra, will want to make the acquaintance of this book.” (Mark Hunacek, MAA Reviews, June 24, 2019)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eIntroduction.- 1 Simple quadratic forms.- 2 Fermat’s Last Theorem.- 3 Lagrange’s theory of quadratic forms.- 4 Gauss’s Disquisitiones Arithmeticae.- 5 Cyclotomy.- 6 Two of Gauss’s proofs of quadratic reciprocity.- 7 Dirichlet’s Lectures.- 8 Is the quintic unsolvable?.- 9 The unsolvability of the quintic.- 10 Galois’s theory.- 11 After Galois – Introduction.- 12 Revision and first assignment.- 13 Jordan’s Traité.- 14 Jordan and Klein.- 15 What is ‘Galois theory’?.- 16 Algebraic number theory: cyclotomy.- 17 Dedekind’s first theory of ideals.- 18 Dedekind’s later theory of ideals.- 19 Quadratic forms and ideals.- 20 Kronecker’s algebraic number theory.- 21 Revision and second assignment.- 22 Algebra at the end of the 19th century.- 23 The concept of an abstract field.- 24 Ideal theory.- 25 Invariant theory.- 26 Hilbert’s Zahlbericht.- 27 The rise of modern algebra – group theory.- 28 Emmy Noether.- 29 From Weber to van der Waerden.- 30 Revision and final assignment.- A Polynomial equations in the 18th Century.- B Gauss and composition of forms.- C Gauss on quadratic reciprocity.- D From Jordan’s Traité.- E Klein’s Erlanger Programm.- F From Dedekind’s 11th supplement.- G Subgroups of S4 and S5.- H Curves.- I Resultants.- Bibliography.- Index.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":49084770582871,"sku":"9783319947723","price":31.34,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783319947723.jpg?v=1725553287"},{"product_id":"first-steps-in-number-theory-a-primer-on-divisibility-9788173713682","title":"First Steps in Number Theory: A Primer on","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e","brand":"Universities Press","offers":[{"title":"Default Title","offer_id":49084841558359,"sku":"9788173713682","price":20.89,"currency_code":"GBP","in_stock":false}]},{"product_id":"matrix-methods-9780128184196","title":"Matrix Methods","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1. Matrices 2. Simultaneous linear equations 3. The inverse 4. An introduction to optimization 5. Determinants 6. Eigenvalues and eigenvectors 7. Matrix calculus 8. Linear differential equations 9. Probability and Markov chains 10. Real inner products and least square 11. Sabermetrics e An introduction 12. Sabermetrics e A module Appendix: A word on technology Answers and hints to selected problems","brand":"Elsevier Science Publishing Co Inc","offers":[{"title":"Default Title","offer_id":49399838277975,"sku":"9780128184196","price":69.26,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780128184196.jpg?v=1730468871"},{"product_id":"linear-algebra-9780128234709","title":"Linear Algebra","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1. Matrices 2. Vector Spaces 3. Linear Transformations 4. Eigenvalues, Eigenvectors, and Differential Equations 5. Euclidean Inner Product   Appendix A. Determinants B. Jordan Canonical Forms C. Markov Chains D. The Simplex Method, an Example E. A Word on Numerical Techniques and Technology Answers And Hints To Selected Problems","brand":"Elsevier Science Publishing Co Inc","offers":[{"title":"Default Title","offer_id":49399840637271,"sku":"9780128234709","price":106.4,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780128234709.jpg?v=1730468879"},{"product_id":"introduction-to-cryptography-9780387207568","title":"Introduction to Cryptography","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e1 Integers.- 2 Congruences and Residue Class Rings.- 3 Encryption.- 4 Probability and Perfect Secrecy.- 5 DES.- 6 AES.- 7 Prime Number Generation.- 8 Public-Key Encryption.- 9 Factoring.- 10 Discrete Logarithms.- 11 Cryptographic Hash Functions.- 12 Digital Signatures.- 13 Other Systems.- 14 Identification.- 15 Secret Sharing.- 16 Public-Key Infrastructures.- Solutions of the exercises.- References.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eFrom the reviews:\u003c\/p\u003e \u003cp\u003eZentralblatt Math\u003c\/p\u003e \u003cp\u003e\"[......] Of the three books under review, Buchmann's is by far the most sophisticated, complete and up-to-date. It was written for computer-science majors -  German ones at that - and might be rough going for all but the best American undergraduates. It is amazing how much Buchmann is able to do in under 300 pages: self-contained explanations of the relevant mathematics (with proofs); a systematic introduction to symmetric cryptosystems, including a detailed description and discussion of DES; a good treatment of primality testing, integer factorization, and algorithms for discrete logarithms, clearly written sections describing most of the major types of cryptosystems, and explanations of basic concepts of practical cryptography such as hash functions, message authentication codes, signatures, passwords, certification authorities, and certificate chains. This book is an excellent reference, and I believe that it would also be a good textbook for a course for mathematics or computer science majors, provided that the instructor is prepared to supplement it with more leisurely treatments of some of the topics.\"\u003c\/p\u003e \u003cp\u003eN. Koblitz  (Seattle, WA)   - American Math. Society Monthly.\u003c\/p\u003e \u003cp\u003e\u003cem\u003eJ.A. Buchmann\u003c\/em\u003e\u003c\/p\u003e \u003cp\u003e\u003cem\u003eIntroduction to Cryptography\u003c\/em\u003e\u003c\/p\u003e \u003cp\u003e\u003cem\u003e\"It gives a clear and systematic introduction into the subject whose popularity is ever increasing, and can be recommended to all who would like to learn about cryptography. The book contains many exercises and examples. It can be used as a textbook and is likely to become popular among students. The necessary definitions and concepts from algebra, number theory and probability theory are formulated, illustrated by examples and applied to cryptography.\"\u003c\/em\u003e —ZENTRALBLATT MATH\u003c\/p\u003e \u003cp\u003e\"For those of use who wish to learn more about cryptography and\/or to teach it, Johannes Buchmann has written this book. … The book is mathematically complete and a satisfying read. There are plenty of homework exercises … . This is a good book for upperclassmen, graduate students, and faculty. … This book makes a superior reference and a fine textbook.\" (Robert W. Vallin, MathDL, January, 2001)\u003c\/p\u003e \u003cp\u003e\"Buchmann’s book is a text on cryptography intended to be used at the undergraduate level. … the intended audiences of this book are ‘readers who want to learn about modern cryptographic algorithms and their mathematical foundations … . I enjoy reading this book. … Readers will find a good exposition of the techniques used in developing and analyzing these algorithms. … These make Buchmann’s text an excellent choice for self study or as a text for students … in elementary number theory and algebra.\" (Andrew C. Lee, SIGACT News, Vol. 34 (4), 2003)\u003c\/p\u003e \u003cp\u003eFrom the reviews of the second edition:\u003c\/p\u003e \u003cp\u003e\"This is the english translation of the second edition of the author’s prominent german textbook ‘Einführung in die Kryptographie’. The original text grew out of several courses on cryptography given by the author at the Technical University Darmstadt; it is aimed at readers who want to learn about modern cryptographic techniques and its mathematical foundations … . As compared with the first edition the number of exercises has almost been doubled and some material … has been added.\" (R. Steinbauer, Monatshefte für Mathematik, Vol. 150 (4), 2007)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eIntegers.- Congruences and Residue Class Rings.- Encryption.- Probability and Perfect Secrecy.- DES.- AES.- Prime Number Generation.- Public-Key Encryption.- Factoring.- Discrete Logarithms.- Cryptographic Hash Functions.- Digital Signatures.- Other Systems.- Identification.- Public-Key Infrastructures.- Solutions of the Odd Exercises.- Subject Index.- Bibliography.","brand":"Springer-Verlag New York Inc.","offers":[{"title":"Default Title","offer_id":49401969082711,"sku":"9780387207568","price":56.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780387207568.jpg?v=1730479002"},{"product_id":"a-course-in-computational-number-theory-9780470412152","title":"A Course in Computational Number Theory","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003ci\u003eA Course in Computational Number Theory\u003c\/i\u003e uses the computer as a tool for motivation and explanation. The book is designed for the reader to quickly access a computer and begin doing personal experiments with the patterns of the integers. It presents and explains many of the fastest algorithms for working with integers. Traditional topics are covered, but the text also explores factoring algorithms, primality testing, the RSA public-key cryptosystem, and unusual applications such as check digit schemes and a computation of the energy that holds a salt crystal together. Advanced topics include continued fractions, Pell's equation, and the Gaussian primes.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface.  \u003cp\u003eNotation.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 1 Fundamentals.\u003c\/b\u003e\u003cbr\u003e 1.0 Introduction.\u003cbr\u003e 1.1 A Famous Sequence of Numbers.\u003cbr\u003e 1.2 The Euclidean ALgorithm.\u003cbr\u003e The Oldest Algorithm.\u003cbr\u003e Reversing the Euclidean Algorithm.\u003cbr\u003e The Extended GCD Algorithm.\u003cbr\u003e The Fundamental Theorem of Arithmetic.\u003cbr\u003e Two Applications.\u003cbr\u003e 1.3 Modular Arithmetic.\u003cbr\u003e 1.4 Fast Powers.\u003cbr\u003e A Fast Alforithm for ExponentiationPowers of Matrices, Big-O Notation.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 2 Congruences, Equations, and Powers.\u003c\/b\u003e\u003cbr\u003e 2.0 Introduction.\u003cbr\u003e 2.1 Solving Linear Congruences.\u003cbr\u003e Linear Diophantine Equations in Two Variables.\u003cbr\u003e The Conductor.\u003cbr\u003e An Importatnt Quadratic Congruence.\u003cbr\u003e 2.2 The Chinese Remainder Theorem.\u003cbr\u003e 2.3 PowerMod Patterns.\u003cbr\u003e Fermat's Little Theorem.\u003cbr\u003e More Patterns in Powers.\u003cbr\u003e 2.4 Pseudoprimes.\u003cbr\u003e Using the Pseudoprime Test.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 3 Euler's Function.\u003c\/b\u003e\u003cbr\u003e 3.0 Introduction.\u003cbr\u003e 3.1 Euler's Function.\u003cbr\u003e 3.2 Perfect Numbers and Their Relatives.\u003cbr\u003e The Sum of Divisors Function.\u003cbr\u003e Perfect Numbers.\u003cbr\u003e Amicalbe, Abundant, and Deficient Numbers.\u003cbr\u003e 3.3 Euler's Theorem.\u003cbr\u003e 3.4 Primitive Roots for Primes.\u003cbr\u003e The order of an Integer.\u003cbr\u003e Primes Have PRimitive roots.\u003cbr\u003e Repeating Decimals.\u003cbr\u003e 3.5 Primitive Roots for COmposites.\u003cbr\u003e 3.6 The Universal Exponent.\u003cbr\u003e Universal Exponents.\u003cbr\u003e Power Towers.\u003cbr\u003e The Form of Carmichael Numbers.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 4 Prime Numbers.\u003c\/b\u003e\u003cbr\u003e 4.0 Introduction.\u003cbr\u003e 4.1 The Number of Primes.\u003cbr\u003e We'll Never Run Out of Primes.\u003cbr\u003e The Sieve of Eratosthenes.\u003cbr\u003e Chebyshev's Theorem and Bertrand's Postulate.\u003cbr\u003e 4.2 Prime Testing and Certification.\u003cbr\u003e Strong Pseudoprimes.\u003cbr\u003e Industrial-Grade Primes.\u003cbr\u003e Prime Certification Via Primitive Roots.\u003cbr\u003e An Improvement.\u003cbr\u003e Pratt Certificates.\u003cbr\u003e 4.3 Refinements and Other Directions.\u003cbr\u003e Other PRimality Tests.\u003cbr\u003e Strong Liars are Scarce.\u003cbr\u003e Finding the nth Prime.\u003cbr\u003e 4.4 A Doszen Prime Mysteries.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 5 Some Applications.\u003c\/b\u003e\u003cbr\u003e 5.0 Introduction.\u003cbr\u003e 5.1 Coding Secrets.\u003cbr\u003e Tossing a Coin into a Well.\u003cbr\u003e The RSA Cryptosystem.\u003cbr\u003e Digital Signatures.\u003cbr\u003e 5.2 The Yao Millionaire Problem.\u003cbr\u003e 5.3 Check Digits.\u003cbr\u003e Basic Check Digit Schemes.\u003cbr\u003e A Perfect Check Digit Method.\u003cbr\u003e Beyond Perfection: Correcting Errors.\u003cbr\u003e 5.4 Factoring Algorithms.\u003cbr\u003e Trial Division.\u003cbr\u003e Fermat's Algorithm.\u003cbr\u003e Pollard Rho.\u003cbr\u003e Pollard p-1.\u003cbr\u003e The Current Scene.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 6 Quadratic Residues.\u003c\/b\u003e\u003cbr\u003e 6.0 Introduction.\u003cbr\u003e 6.1 Pepin's Test.\u003cbr\u003e Quadratic Residues.\u003cbr\u003e Pepin's Test.\u003cbr\u003e Primes Congruent to 1 (Mod.\u003cbr\u003e 6.2 Proof of Quadratic Reciprocity.\u003cbr\u003e Gauss's Lemma.\u003cbr\u003e Proof of Quadratic Recipocity.\u003cbr\u003e Jacobi's Extension.\u003cbr\u003e An Application to Factoring.\u003cbr\u003e 6.3 Quadratic Equations.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 7 Continuec Faction.\u003c\/b\u003e\u003cbr\u003e 7.0 Introduction.\u003cbr\u003e 7.1 FInite COntinued Fractions.\u003cbr\u003e 7.2 Infinite Continued Fractions.\u003cbr\u003e 7.3 Periodic Continued Fractions.\u003cbr\u003e 7.4 Pell's Equation.\u003cbr\u003e 7.5 Archimedes and the Sun God's Cattle.\u003cbr\u003e Wurm's Version: Using Rectangular Bulls.\u003cbr\u003e The Real Cattle Problem.\u003cbr\u003e 7.6 Factoring via Continued Fractions.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 8 Prime Testing with Lucas Sequences.\u003c\/b\u003e\u003cbr\u003e 8.0 Introduction.\u003cbr\u003e 8.1 Divisibility Properties of Lucas Sequencese.\u003cbr\u003e 8.2 Prime Tests Using Lucas Sequencesse.\u003cbr\u003e Lucas Certification.\u003cbr\u003e The Lucas-Lehmer Algorithm Explained.\u003cbr\u003e Luca Pseudoprimes.\u003cbr\u003e Strong Quadratic Pseudoprimes.\u003cbr\u003e Primality Testing's Holy Grail.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 9 Prime Imaginaries and Imaginary Primes.\u003c\/b\u003e\u003cbr\u003e 9.0 Introduction.\u003cbr\u003e 9.1 Sums of Two Squares.\u003cbr\u003e 9.2 The Gaussian Intergers.\u003cbr\u003e Complex Number Theory.\u003cbr\u003e Gaussian Primes.\u003cbr\u003e The Moat Problem.\u003cbr\u003e The Gaussian Zoo.\u003cbr\u003e 9.3 Higher Reciprocity  325.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix A. Maathematica Basics.\u003c\/b\u003e\u003cbr\u003e 1.0 Introduction.\u003cbr\u003e A.1 Plotting.\u003cbr\u003e A.2 Typesetting.\u003cbr\u003e Sending Files By E-Mail.\u003cbr\u003e A.3 Types of Functions.\u003cbr\u003e A.4 Lists.\u003cbr\u003e A.5 Programs.\u003cbr\u003e A.6 Solving Equations.\u003cbr\u003e A.7 Symbolic Algebra.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix B Lucas Certificates Exist.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eReferences.\u003c\/p\u003e \u003cp\u003eIndex of Mathematica Objects.\u003c\/p\u003e \u003cp\u003eSubject Index.\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49402328088919,"sku":"9780470412152","price":127.76,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780470412152.jpg?v=1730480082"},{"product_id":"number-theory-9780470424131","title":"Number Theory","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cb\u003e\u003ci\u003eNumber Theory: A Lively Introduction with Proofs, Applications, and Stories\u003c\/i\u003e, is a new book that provides a rigorous yet accessible introduction to elementary number theory along with relevant applications.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eReadable discussions motivate new concepts and theorems before their formal definitions and statements are presented. Many theorems are preceded by \u003ci\u003eNumerical Proof Previews\u003c\/i\u003e, which are numerical examples that will help give students a concrete understanding of both the statements of the theorems and the ideas behind their proofs, before the statement and proof are formalized in more abstract terms. In addition, many applications of number theory are explained in detail throughout the text, including some that have rarely (if ever) appeared in textbooks.\u003c\/p\u003e \u003cp\u003eA unique feature of the book is that every chapter includes a \u003ci\u003emath myth\u003c\/i\u003e, a fictional story that introduces an important number theory topic in a friendly, inviting manner. Many of the exerci\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface.  \u003c\/p\u003e\u003cp\u003eTo the Student.\u003c\/p\u003e \u003cp\u003eTo the Instructor.\u003c\/p\u003e \u003cp\u003eAcknowledgements.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e0. Prologue.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1. Numbers, Rational and Irrational.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e(Historical figures: Pythagoras and Hypatia).\u003c\/p\u003e \u003cp\u003e1.1 Numbers and the Greeks.\u003c\/p\u003e \u003cp\u003e1.2 Numbers you know.\u003c\/p\u003e \u003cp\u003e1.3 A First Look at Proofs.\u003c\/p\u003e \u003cp\u003e1.4 Irrationality of he square root of 2.\u003c\/p\u003e \u003cp\u003e1.5 Using Quantifiers.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2. Mathematical Induction.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e(Historical figure: Noether).\u003c\/p\u003e \u003cp\u003e2.1.The Principle of Mathematical Induction.\u003c\/p\u003e \u003cp\u003e2.2 Strong Induction and the Well Ordering Principle.\u003c\/p\u003e \u003cp\u003e2.3 The Fibonacci Sequence and the Golden Ratio.\u003c\/p\u003e \u003cp\u003e2.4 The Legend of the Golden Ratio.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3. Divisibility and Primes.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e(Historical figure: Eratosthenes).\u003c\/p\u003e \u003cp\u003e3.1 Basic Properties of Divisibility.\u003c\/p\u003e \u003cp\u003e3.2 Prime and Composite Numbers.\u003c\/p\u003e \u003cp\u003e3.3 Patterns in the Primes.\u003c\/p\u003e \u003cp\u003e3.4 Common Divisors and Common Multiples.\u003c\/p\u003e \u003cp\u003e3.5 The Division Theorem.\u003c\/p\u003e \u003cp\u003e3.6 Applications of gcd and lcm.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4.The Euclidean Algorithm.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e(Historical figure: Euclid).\u003c\/p\u003e \u003cp\u003e4.1 The Euclidean Algorithm.\u003c\/p\u003e \u003cp\u003e4.2 Finding the Greatest Common Divisor.\u003c\/p\u003e \u003cp\u003e4.3 A Greeker Argument that the square root of 2 is Irrational.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5. Linear Diophantine Equations.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e(Historical figure: Diophantus).\u003c\/p\u003e \u003cp\u003e5.1 The Equation \u003ci\u003eaX\u003c\/i\u003e + \u003ci\u003ebY\u003c\/i\u003e = 1.\u003c\/p\u003e \u003cp\u003e5.2 Using the Euclidean Algorithm to Find a Solution.\u003c\/p\u003e \u003cp\u003e5.3 The Diophantine Equation \u003ci\u003eaX + bY = n.\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e5.4 Finding All Solutions to a Linear Diophantine Equation.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6. The Fundamental Theorem of Arithmetic.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e(Historical figure: Mersenne).\u003c\/p\u003e \u003cp\u003e6.1 The Fundamental Theorem.\u003c\/p\u003e \u003cp\u003e6.2 Consequences of the Fundamental Theorem.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7. Modular Arithmetic.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e(Historical figure: Gauss).\u003c\/p\u003e \u003cp\u003e7.1 Congruence modulo \u003ci\u003en.\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e7.2 Arithmetic with Congruences.\u003c\/p\u003e \u003cp\u003e7.3 Check Digit Schemes.\u003c\/p\u003e \u003cp\u003e7.4 The Chinese Remainder Theorem.\u003c\/p\u003e \u003cp\u003e7.5 The Gregorian Calendar.\u003c\/p\u003e \u003cp\u003e7.6 The Mayan Calendar.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8. Modular Number Systems.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e(Historical figure: Turing).\u003c\/p\u003e \u003cp\u003e8.1 The Number System \u003cb\u003eZ\u003c\/b\u003e\u003ci\u003e\u003csub\u003en\u003c\/sub\u003e\u003c\/i\u003e: an Informal View.\u003c\/p\u003e \u003cp\u003e8.2 The Number System \u003cb\u003eZ\u003c\/b\u003e\u003ci\u003e\u003csub\u003en\u003c\/sub\u003e\u003c\/i\u003e: Definition and Basic Properties.\u003c\/p\u003e \u003cp\u003e8.3 Multiplicative Inverses in \u003cb\u003eZ\u003c\/b\u003e\u003ci\u003e\u003csub\u003en\u003c\/sub\u003e\u003c\/i\u003e.\u003c\/p\u003e \u003cp\u003e8.4 Elementary Cryptography.\u003c\/p\u003e \u003cp\u003e8.5 Encryption Using Modular Multiplication.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9. Exponents Modulo \u003ci\u003en\u003c\/i\u003e\u003c\/b\u003e.\u003c\/p\u003e \u003cp\u003e(Historical figure: Fermat).\u003c\/p\u003e \u003cp\u003e9.1 Fermat's Little Theorem.\u003c\/p\u003e \u003cp\u003e9.2 Reduced Residues and the Euler \\phi-function.\u003c\/p\u003e \u003cp\u003e9.3 Euler's Theorem.\u003c\/p\u003e \u003cp\u003e9.4 Exponentiation Ciphers with a Prime modulus.\u003c\/p\u003e \u003cp\u003e9.5 The RSA Encryption Algorithm.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10. Primitive Roots.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e(Historical figure: Lagrange).\u003c\/p\u003e \u003cp\u003e10.1 \u003cb\u003eZ\u003c\/b\u003e\u003ci\u003e\u003csub\u003en\u003c\/sub\u003e\u003c\/i\u003e.\u003c\/p\u003e \u003cp\u003e10.2 Solving Polynomial Equations in \u003cb\u003eZ\u003c\/b\u003e\u003ci\u003e\u003csub\u003en\u003c\/sub\u003e.\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e10.3 Primitive Roots.\u003c\/p\u003e \u003cp\u003e10.4 Applications of Primitive Roots.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11. Quadratic Residues.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e(Historical figure: Eisenstein)\u003c\/p\u003e \u003cp\u003e11.1 Squares Modulo \u003ci\u003en\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e11.2 Euler's Identity and the Quadratic Character of -1\u003c\/p\u003e \u003cp\u003e11.3 The Law of Quadratic Reciprocity\u003c\/p\u003e \u003cp\u003e11.4 Gauss's Lemma\u003c\/p\u003e \u003cp\u003e11.5 Quadratic Residues and Lattice Points.\u003c\/p\u003e \u003cp\u003e11.6 The Proof of Quadratic Reciprocity.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12. Primality Testing.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e(Historical figure: Erdös).\u003c\/p\u003e \u003cp\u003e12.1 Primality testing.\u003c\/p\u003e \u003cp\u003e12.2 Continued Consideration of Charmichael Numbers.\u003c\/p\u003e \u003cp\u003e12.3 The Miller-Rabin Primality test.\u003c\/p\u003e \u003cp\u003e12.4 Two Special Polynomial Equations in \u003cb\u003e\u003ci\u003eZ\u003c\/i\u003e\u003c\/b\u003e\u003ci\u003e\u003csub\u003ep\u003c\/sub\u003e.\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e12.5 Proof that Millar-Rabin is Effective.\u003c\/p\u003e \u003cp\u003e12.6 Prime Certificates.\u003c\/p\u003e \u003cp\u003e12.7 The AKS Deterministic Primality Test.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13. Gaussian Integers.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e(Historical figure: Euler).\u003c\/p\u003e \u003cp\u003e13.1 Definition of Gaussian Integers\u003c\/p\u003e \u003cp\u003e13.2 Divisibility and Primes in \u003cb\u003eZ\u003c\/b\u003e[\u003ci\u003ei\u003c\/i\u003e].\u003c\/p\u003e \u003cp\u003e13.3 The Division Theorem for the Gaussian Integers.\u003c\/p\u003e \u003cp\u003e13.4 Unique Factorization in \u003cb\u003eZ\u003c\/b\u003e[\u003ci\u003ei\u003c\/i\u003e].\u003c\/p\u003e \u003cp\u003e13.5 Gaussian Primes.\u003c\/p\u003e \u003cp\u003e13.6 Fermat's Two Squares Theorem.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e14. Continued Fractions.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e(Historical figure: Ramanujan).\u003c\/p\u003e \u003cp\u003e14.1 Expressing Rational Numbers as Continued Fractions.\u003c\/p\u003e \u003cp\u003e14.2 Expressing Irrational Numbers as Continued Fractions.\u003c\/p\u003e \u003cp\u003e14.3 Approximating Irrational Numbers Using Continued Fractions.\u003c\/p\u003e \u003cp\u003e14.4 Proving that Convergents are Fantastic Approximations.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e15. Some Nonlinear Diophantine Equations.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e(Historical figure: Germain).\u003c\/p\u003e \u003cp\u003e15.1 Pell's Equation\u003c\/p\u003e \u003cp\u003e15.2 Fermat's Last Theorem\u003c\/p\u003e \u003cp\u003e15.3 Proof of Fermat's Last Theorem for n = 4.\u003c\/p\u003e \u003cp\u003e15.4 Germain's Contributions to Fermat's Last Theorem\u003c\/p\u003e \u003cp\u003e15.5 A Geometric look at the Equation x\u003csup\u003e4\u003c\/sup\u003e + y\u003csup\u003e4\u003c\/sup\u003e = z\u003csup\u003e2\u003c\/sup\u003e.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix: Axioms of Number Theory.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eA.1 What is a Number System?\u003c\/p\u003e \u003cp\u003eA.2 Order Properties of the Integers.\u003c\/p\u003e \u003cp\u003eA.3 Building Results From Our Axioms.\u003c\/p\u003e \u003cp\u003eA.4 The Principle of Mathematical Induction.\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49402331005271,"sku":"9780470424131","price":168.1,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780470424131.jpg?v=1730480087"},{"product_id":"gauss-and-jacobi-sums-9780471128076","title":"Gauss and Jacobi Sums","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eDevised in the 19th century, Gauss and Jacobi Sums are classical formulas that form the basis for contemporary research in many of today's sciences. This book offers readers a solid grounding on the origin of these abstract, general theories.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eGauss Sums.\u003cbr\u003e \u003cbr\u003e Jacobi Sums and Cyclotomic Numbers.\u003cbr\u003e \u003cbr\u003e Evaluation of Jacobi Sums Over Fp.\u003cbr\u003e \u003cbr\u003e Determination of Gauss Sums Over Fp.\u003cbr\u003e \u003cbr\u003e Difference Sets.\u003cbr\u003e \u003cbr\u003e Jacobsthal Sums Over Fp.\u003cbr\u003e \u003cbr\u003e Residuacity.\u003cbr\u003e \u003cbr\u003e Reciprocity Laws.\u003cbr\u003e \u003cbr\u003e Congruences for Binomial Coefficients.\u003cbr\u003e \u003cbr\u003e Diagonal Equations over Finite Fields.\u003cbr\u003e \u003cbr\u003e Gauss Sums over Fq.\u003cbr\u003e \u003cbr\u003e Eisenstein Sums.\u003cbr\u003e \u003cbr\u003e Brewer Sums.\u003cbr\u003e \u003cbr\u003e A General Eisenstein Reciprocity Law.\u003cbr\u003e \u003cbr\u003e Research Problems.\u003cbr\u003e \u003cbr\u003e Bibliography.\u003cbr\u003e \u003cbr\u003e Notation.\u003cbr\u003e \u003cbr\u003e Indexes.","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49402493403479,"sku":"9780471128076","price":160.16,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780471128076.jpg?v=1730480576"},{"product_id":"elementary-number-theory-9780486469317","title":"Elementary Number Theory","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eMinimal prerequisites make this text ideal for a first course in number theory. Written in a lively, engaging style by the author of popular mathematics books, it features nearly 1,000 imaginative exercises and problems. Solutions to many of the problems are included, and a teacher''s guide is available. 1978 edition.","brand":"Dover Publications Inc.","offers":[{"title":"Default Title","offer_id":49402731888983,"sku":"9780486469317","price":13.04,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780486469317.jpg?v=1730481348"},{"product_id":"algebraic-theory-of-numbers-9780691059174","title":"Algebraic Theory of Numbers","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eExplores fundamental concepts in arithmetic. This book begins with the definitions and properties of algebraic fields. It then discusses the theory of divisibility from an axiomatic viewpoint, rather than by the use of ideals. It also gives an introduction to p-adic numbers and their uses, which are important in modern number theory.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eCh. I Algebraic Fields 1 Ch. II Theory of Divisibility (Kronecker, Dedekind) 33 Ch. III Local Primadic Analysis (Kummer, Hensel) 71 Ch. IV Algebraic Number Fields 141  Amendments 223","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":49403706048855,"sku":"9780691059174","price":63.75,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691059174.jpg?v=1730484303"},{"product_id":"weyl-group-multiple-dirichlet-series-9780691150666","title":"Weyl Group Multiple Dirichlet Series","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eWeyl group multiple Dirichlet series are generalizations of the Riemann zeta function. Like the Riemann zeta function, they are Dirichlet series with analytic continuation and functional equations, having applications to analytic number theory. This book proves foundational results about these series and develops their combinatorics.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e*FrontMatter, pg. i*Contents, pg. v*Preface, pg. vii*Chapter One. Type A Weyl Group Multiple Dirichlet Series, pg. 1*Chapter Two. Crystals and Gelfand-Tsetlin Patterns, pg. 10*Chapter Three. Duality, pg. 22*Chapter Four. Whittaker Functions, pg. 26*Chapter Five. Tokuyama's Theorem, pg. 31*Chapter Six. Outline of the Proof, pg. 36*Chapter Seven. Statement B Implies Statement A, pg. 51*Chapter Eight. Cartoons, pg. 54*Chapter Nine. Snakes, pg. 58*Chapter Ten. Noncritical Resonances, pg. 64*Chapter Eleven. Types, pg. 67*Chapter Twelve. Knowability, pg. 74*Chapter Thirteen. The Reduction to Statement D, pg. 77*Chapter Fourteen. Statement E Implies Statement D, pg. 87*Chapter Fifteen. Evaluation of LAMBDAGAMMA and LAMBDADELTA, and Statement G, pg. 89*Chapter Sixteen. Concurrence, pg. 96*Chapter Seventeen. Conclusion of the Proof, pg. 104*Chapter Eighteen. Statement B and Crystal Graphs, pg. 108*Chapter Nineteen. Statement B and the Yang-Baxter Equation, pg. 115*Chapter Twenty. Crystals and p-adic Integration, pg. 132*Bibliography, pg. 143*Notation, pg. 149*Index, pg. 155","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":49403783184727,"sku":"9780691150666","price":52.2,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691150666.jpg?v=1730484532"},{"product_id":"single-digits-9780691175690","title":"Single Digits","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"Fascinating... Chamberland offers enticing explanations that will leave readers hungry to know more. This wonderful book never loses its focus or momentum.\"--Publishers Weekly \"[B]oth amateur and professional mathematicians alike will find new items of interest here... [A] welcome, splendid, fruitful addition to my math bookshelf.\"--Math Tango blog \"The collection is outright delightful. It will agitate the minds of students and shake the sense of know-all off many a professional and most of the amateurs.\"--Alexander Bogomolny, Cut the Knot blog \"Boring deep into the innocuous-looking number one, Chamberland opens an unexpected entry point into a dizzying maze of infinities... A bracing mathematical adventure.\"--Booklist \"The exotics like pi and e have gotten their share of attention in the world of popular mathematical writing. Now it's time to give proper attention to the integers 1 through 9... [Single Digits] is consistently entertaining and well-written.\"--MAA Reviews \"Chamberland takes readers on a fascinating exploration of small numbers, from one to nine, looking at their history, applications, and connections to various areas of mathematics, including number theory, geometry, chaos theory, numerical analysis, and mathematical physics... Appealing to high-school and college students, professional mathematicians, and those mesmerized by patterns, this book shows that single digits offer a plethora of possibilities that readers can count on.\"--DVD, Lunar and Planetary Information Bulletin \"Chamberland makes this an entertaining and historical exposition, using wit and humor throughout.\"--Math Horizons \"To put it simply, this book is a delight. Chamberland has assembled a fascinating collection of vignettes, each tied to a digit from one to nine, that inform, entertain, and intrigue... This wide spectrum of ideas is consistently interesting, and the author's skill in mining each nugget is worthy of great respect.\"--Choice \"The range of topics included virtually guarantees that any reader will find new and unfamiliar material to enjoy... [Single Digits] is a very enjoyable book which, at many points, makes some very deep mathematics quite accessible. Highly recommended.\"--Keith Johnson, CMS Notes \"For instructors of math courses of all levels, the vignettes in Single Digits can provide a very readable introduction or jumping-off point for discussions and projects... In an introductory group theory course, it would be a good exercise for students to consider perfect riffle shuffles in decks of size other than 52. Finally, a statistics class collecting and analyzing real-world data sets could consider whether Benford's Law applies in their situation.\"--Matthew Welz, MAA Focus \"I highly recommend Single Digits: In Praise of Small Numbers. It would be a fine addition to any high school or math department library. As a carefully curated set of interesting topics, it would serve as a good place to start exploring the ocean of ideas in mathematics.\"--Bruce Cohen, NCTM\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e*Frontmatter, pg. i*Contents, pg. v*Preface, pg. xi*Chapter 1. The Number One, pg. 1*Chapter 2. The Number Two, pg. 24*Chapter 3. The Number Three, pg. 69*Chapter 4. The Number Four, pg. 111*Chapter 5. The Number Five, pg. 132*Chapter 6. The Number Six, pg. 156*Chapter 7. The Number Seven, pg. 170*Chapter 8. The Number Eight, pg. 191*Chapter 9. The Number Nine, pg. 205*Chapter 10. Solutions, pg. 216*Further reading, pg. 219*Credits for illustrations, pg. 223*Index, pg. 225","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":49403845542231,"sku":"9780691175690","price":16.14,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691175690.jpg?v=1730484700"}],"url":"https:\/\/bookcurl.com\/collections\/number-theory.oembed?page=5","provider":"Book Curl","version":"1.0","type":"link"}