Number theory Books
Taylor & Francis Ltd An Introduction to Number Theory with
Book SynopsisBuilding on the success of the first edition, An Introduction to Number Theory with Cryptography, Second Edition, increases coverage of the popular and important topic of cryptography, integrating it with traditional topics in number theory. The authors have written the text in an engaging style to reflect number theory''s increasing popularity. The book is designed to be used by sophomore, junior, and senior undergraduates, but it is also accessible to advanced high school students and is appropriate for independent study. It includes a few more advanced topics for students who wish to explore beyond the traditional curriculum.Features of the second edition include Over 800 exercises, projects, and computer explorations Increased coverage of cryptography, including Vigenere, Stream, Transposition,and BlockTrade Review"… provides a fine history of number theory and surveys its applications. College-level undergrads will appreciate the number theory topics, arranged in a format suitable for any standard course in the topic, and will also appreciate the inclusion of many exercises and projects to support all the theory provided. In providing a foundation text with step-by-step analysis, examples, and exercises, this is a top teaching tool recommended for any cryptography student or instructor."—California Bookwatch Table of Contents20 1. Introduction; 2 Divisibility; 3. Linear Diophantine Equations; 4. Unique Factorization; 5. Applications of Unique Factorization; 6. Conguences; 7. Classsical Cryposystems; 8. Fermat, Euler, Wilson; 9. RSA; 10. Polynomial Congruences; 11. Order and Primitive Roots; 12. More Cryptographic Applications; 13. Quadratic Reciprocity; 14. Primality and Factorization; 15. Geometry of Numbers; 16. Arithmetic Functions; 17. Continued Fractions; 18. Gaussian Integers; 19. Algebraic Integers; 20. Analytic Methods, 21. Epilogue: Fermat's Last Theorem; Appendices; Answers and Hints for Odd-Numbered Exercises; Index
£41.79
CRC Press Introduction to Modern Cryptography
Book SynopsisIntroduction to Modern Cryptography, the most relied-upon textbook in the field, provides a mathematically rigorous yet accessible treatment of this fascinating subject. The authors have kept the book up-to-date while incorporating feedback from instructors and students alike; the presentation is refined, current, and accurate.The bookâs focus is on modern cryptography, which is distinguished from classical cryptography by its emphasis on definitions, precise assumptions, and rigorous proofs of security. A unique feature of the text is that it presents theoretical foundations with an eye toward understanding cryptography as used in the real world. This revised edition fixed typos and includes all the updates made to the third edition, including: Enhanced treatment of several modern aspects of private-key cryptography, including authenticated encryption and nonce-based encryption. Coverage of widely used standards such as GMAC, Poly1305, GCM, CCM, and ChaCha20-Poly1305. New sections on the ChaCha20 stream cipher, sponge-based hash functions, and SHA-3. Increased coverage of elliptic-curve cryptography, including a discussion of various curves used in practice. A new chapter describing the impact of quantum computers on cryptography and providing examples of quantum-secure encryption and signature schemes. Containing worked examples and updated exercises, Introduction to Modern Cryptography, Revised Third Edition can serve as a textbook for undergraduate- or graduate-level courses in cryptography, a reference for graduate students, researchers, and practitioners, or a general introduction suitable for self-study.
£94.99
The Mathematical Association of America The G. H. Hardy Reader
Book SynopsisG. H. Hardy ranks among the great mathematicians of the twentieth century, doing essential research in number theory and analysis. This book is a feast of Hardy's writing, featuring articles ranging from the serious to the humorous. The G. H. Hardy Reader is a worthy introduction to an extraordinary individual.Trade Review'The editors are to be congratulated on putting together this beautiful 'reader' with material from so many different sources, which illustrates so well the life, character and work of one of the great mathematicians of the twentieth century, Godfrey Harold Hardy (1877-1947). Even if you are familiar with Hardy's masterpiece A Mathematician's Apology or his book on Ramanujan, Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work you will find a wealth of new and fascinating material in this 'reader' about Hardy.' Kenneth S. Williams, Canadian Mathematical Society NotesTable of ContentsPart I. Biography: 1. Hardy's life; 2. The letter from Ramanujan to Hardy, 16 January 1913; 3. A letter from Bertrand Russell to Lady Ottoline Morrell, 2 February 1913; 4. The Indian mathematician Ramanujan; 5. Epilogue from the man who knew infinity; 6. Posters of 'Hardy's years at Oxford'; 7. A glimpse of J. E. Littlewood; 8. A letter from Freeman Dyson to C. P. Snow, 22 May 1967, and two letters from Hardy to Dyson; 9. Miss Gertrude Hardy; Part II. Writings by and about G. H. Hardy: 10. Hardy on writing books; 11. Selections from Hardy's writings; 12. Selections from what others have said about Hardy; Part III. Mathematics: 13. An introduction to the theory of numbers; 14. Prime numbers; 15. The theory of numbers; 16. The Riemann zeta-function and lattice point problems; 17. Four Hardy gems; 18. What is geometry?; 19. The case against the mathematical tripos; 20. The mathematician on cricket; 21. Cricket for the rest of us; 22. A mathematical theorem about golf; 23. Mathematics in war-time; 24. Mathematics; 25. Asymptotic formulæ in combinatory analysis (excerpts) with S. Ramanujan; 26. A new solution of Waring's problem (excerpts), with J. E. Littlewood; 27. Some notes on certain theorems in higher trigonometry; 28. The Integral _∞0sin xx dx and further remarks on the integral _∞0sin xx dx; Part IV. Tributes: 29. Dr. Glaisher and the 'messenger of mathematics'; 30. David Hilbert; 31. Edmund Landau (with H. Heilbronn); 32. Gösta Mittag-Leffler; Part V. Book Reviews: 33. Osgood's calculus and Johnson's calculus; 34. Hadamard: the psychology of invention in the mathematical field; 35. Hulburt: differential and integral calculus; 36. Bôcher: an introduction to the study of integral equations.
£80.74
Cambridge University Press Multiplicative Number Theory I Classical Theory 97 Cambridge Studies in Advanced Mathematics Series Number 97
Book SynopsisPrime numbers are the multiplicative building blocks of natural numbers. Understanding their overall influence and especially their distribution gives rise to central questions in mathematics and physics. In this 2006 text, the authors bring their extensive and distinguished research expertise to prepare the student for intelligent reading of the more advanced research literature.Trade Review'The text is very well written and accessible to students. On many occasions the authors explicitly describe basic methods known to everyone working in the field, but too often skipped in textbooks. This book may well become the standard introduction to analytic number theory.' Zentralblatt MATHTable of ContentsPreface; Notation; 1. Dirichlet series-I; 2. The elementary theory of arithmetic functions; 3. Principles and first examples of sieve methods; 4. Primes in arithmetic progressions-I; 5. Dirichlet series-II; 6. The prime number theorem; 7. Applications of the prime number theorem; 8. Further discussion of the prime number theorem; 9. Primitive characters and Gauss sums; 10. Analytic properties of the zeta function and L-functions; 11. Primes in arithmetic progressions-II; 12. Explicit formulae; 13. Conditional estimates; 14. Zeros; 15. Oscillations of error terms; Appendix A. The Riemann-Stieltjes integral; Appendix B. Bernoulli numbers and the Euler-MacLaurin summation formula; Appendix C. The gamma function; Appendix D. Topics in harmonic analysis.
£74.99
Cambridge University Press Vorlesungen uber Zahlentheorie Cambridge Library Collection Mathematics
Book SynopsisPeter Gustav Lejeune Dirichlet (1805â59) may be considered the father of modern number theory. He studied in Paris, coming under the influence of mathematicians like Fourier and Legendre, and then taught at Berlin and GÃttingen universities, where he was the successor to Gauss. This book contains lectures on number theory given by Dirichlet in 1856â7. They include his famous proofs of the class number theorem for binary quadratic forms and the existence of an infinity of primes in every appropriate arithmetical progression. The material was first published in 1863 by Richard Dedekind (1831â1916), professor at Braunschweig, who had been a junior colleague of Dirichlet at GÃttingen. The second edition appeared in 1871; this reissue is of the third, revised and expanded, edition of 1879; a fourth edition appeared as late as 1894. The appendices contain further work by both Dirichlet and Dedekind.Table of ContentsVorwort; 1. Von der Theilbarkeit der Zahlen; 2. Von der Congruens der Zahlen; 3. Von den quadratischen Resten; 4. Von den quadratischen Formen; 5. Bestimmung der Anzahl der Classen; Supplemente.
£49.99
Cambridge University Press The Mordell Conjecture
Book SynopsisThe 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.Trade Review'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'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'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 GaucheTable of Contents1. 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.
£59.84
John Wiley & Sons Inc Primes of the Form x2ny2
Book SynopsisAn exciting approach to the history and mathematics of number theory . . . the author's style is totally lucid and very easy to read . . .the result is indeed a wonderful story. Mathematical Reviews Written in a unique and accessible style for readers of varied mathematical backgrounds, the Second Edition of Primes of the Form p = x2+ ny2 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. Primes of the Form p = x2 + ny2, Second Edition focuses on addressing the question of when a prime p is of the form x2<Table of ContentsPreface to the First Edition ixPreface to the Second Edition xiNotation xiiiIntroduction 1Chapter One: From Fermat to GaussChapter Two: Class Field TheoryChapter Three: Complex MultiplicationChapter Four: Additional TopicsRefrencesAdditional ReferencesIndex
£46.76
John Wiley & Sons Inc Fibonacci and Lucas Numbers with Applications
Book SynopsisVolume II provides an advanced approach to the extended gibonacci family, which includes Fibonacci, Lucas, Pell, Pell-Lucas, Jacobsthal, Jacobsthal-Lucas, Vieta, Vieta-Lucas, and Chebyshevpolynomials of both kinds. This volume offers a uniquely unified, extensive, and historical approach that will appeal to both students and professional mathematicians. As in Volume I, Volume II focuses on problem-solving techniques such as pattern recognition;conjecturing; proof-techniques, and applications. It offers a wealth of delightful opportunities toexplore and experiment, as well as plentiful material for group discussions, seminars, presentations, and collaboration. In addition, the material covered in this book promotes intellectual curiosity, creativity, and ingenuity. Volume II features: A wealth of examples, applications, and exercises of varying degrees of difficulty and sophistication. Numerous combinatorial and graph-theoretic proofs and techniques. A uniquely thorough discussTable of ContentsList of Symbols xiii Preface xv 31. Fibonacci and Lucas Polynomials I 1 31.1. Fibonacci and Lucas Polynomials 3 31.2. Pascal’s Triangle 18 31.3. Additional Explicit Formulas 22 31.4. Ends of the Numbers ln 25 31.5. Generating Functions 26 31.6. Pell and Pell–Lucas Polynomials 27 31.7. Composition of Lucas Polynomials 33 31.8. De Moivre-like Formulas 35 31.9. Fibonacci–Lucas Bridges 36 31.10. Applications of Identity (31.51) 37 31.11. Infinite Products 48 31.12. Putnam Delight Revisited 51 31.13. Infinite Simple Continued Fraction 54 32. Fibonacci and Lucas Polynomials II 65 32.1. Q-Matrix 65 32.2. Summation Formulas 67 32.3. Addition Formulas 71 32.4. A Recurrence for n2 76 32.5. Divisibility Properties 82 33. Combinatorial Models II 87 33.1. A Model for Fibonacci Polynomials 87 33.2. Breakability 99 33.3. A Ladder Model 101 33.4. A Model for Pell–Lucas Polynomials: Linear Boards 102 33.5. Colored Tilings 103 33.6. A New Tiling Scheme 104 33.7. A Model for Pell–Lucas Polynomials: Circular Boards 107 33.8. A Domino Model for Fibonacci Polynomials 114 33.9. Another Model for Fibonacci Polynomials 118 34. Graph-Theoretic Models II 125 34.1. Q-Matrix and Connected Graph 125 34.2. Weighted Paths 126 34.3. Q-Matrix Revisited 127 34.4. Byproducts of the Model 128 34.5. A Bijection Algorithm 136 34.6. Fibonacci and Lucas Sums 137 34.7. Fibonacci Walks 140 35. Gibonacci Polynomials 145 35.1. Gibonacci Polynomials 145 35.2. Differences of Gibonacci Products 159 35.3. Generalized Lucas and Ginsburg Identities 174 35.4. Gibonacci and Geometry 181 35.5. Additional Recurrences 184 35.6. Pythagorean Triples 188 36. Gibonacci Sums 195 36.1. Gibonacci Sums 195 36.2. Weighted Sums 206 36.3. Exponential Generating Functions 209 36.4. Infinite Gibonacci Sums 215 37. Additional Gibonacci Delights 233 37.1. Some Fundamental Identities Revisited 233 37.2. Lucas and Ginsburg Identities Revisited 238 37.3. Fibonomial Coefficients 247 37.4. Gibonomial Coefficients 250 37.5. Additional Identities 260 37.6. Strazdins’ Identity 264 38. Fibonacci and Lucas Polynomials III 269 38.1. Seiffert’s Formulas 270 38.2. Additional Formulas 294 38.3. Legendre Polynomials 314 39. Gibonacci Determinants 321 39.1. A Circulant Determinant 321 39.2. A Hybrid Determinant 323 39.3. Basin’s Determinant 333 39.4. Lower Hessenberg Matrices 339 39.5. Determinant with a Prescribed First Row 343 40. Fibonometry II 347 40.1. Fibonometric Results 347 40.2. Hyperbolic Functions 356 40.3. Inverse Hyperbolic Summation Formulas 361 41. Chebyshev Polynomials 371 41.1. Chebyshev Polynomials Tn(x) 372 41.2. Tn(x) and Trigonometry 384 41.3. Hidden Treasures in Table 41.1 386 41.4. Chebyshev Polynomials Un(x) 396 41.5. Pell’s Equation 398 41.6. Un(x) and Trigonometry 399 41.7. Addition and Cassini-like Formulas 401 41.8. Hidden Treasures in Table 41.8 402 41.9. A Chebyshev Bridge 404 41.10. Tn and Un as Products 405 41.11. Generating Functions 410 42. Chebyshev Tilings 415 42.1. Combinatorial Models for Un 415 42.2. Combinatorial Models for Tn 420 42.3. Circular Tilings 425 43. Bivariate Gibonacci Family I 429 43.1. Bivariate Gibonacci Polynomials 429 43.2. Bivariate Fibonacci and Lucas Identities 430 43.3. Candido’s Identity Revisited 439 44. Jacobsthal Family 443 44.1. Jacobsthal Family 444 44.2. Jacobsthal Occurrences 450 44.3. Jacobsthal Compositions 452 44.4. Triangular Numbers in the Family 459 44.5. Formal Languages 468 44.6. A USA Olympiad Delight 480 44.7. A Story of 1, 2, 7, 42, 429,…483 44.8. Convolutions 490 45. Jacobsthal Tilings and Graphs 499 45.1. 1 × n Tilings 499 45.2. 2 × n Tilings 505 45.3. 2 × n Tubular Tilings 510 45.4. 3 × n Tilings 514 45.5. Graph-Theoretic Models 518 45.6. Digraph Models 522 46. Bivariate Tiling Models 537 46.1. A Model for 𝑓n(x, y) 537 46.2. Breakability 539 46.3. Colored Tilings 542 46.4. A Model for ln(x, y) 543 46.5. Colored Tilings Revisited 545 46.6. Circular Tilings Again 547 47. Vieta Polynomials 553 47.1. Vieta Polynomials 554 47.2. Aurifeuille’s Identity 567 47.3. Vieta–Chebyshev Bridges 572 47.4. Jacobsthal–Chebyshev Links 573 47.5. Two Charming Vieta Identities 574 47.6. Tiling Models for Vn 576 47.7. Tiling Models for 𝑣n(x) 582 48. Bivariate Gibonacci Family II 591 48.1. Bivariate Identities 591 48.2. Additional Bivariate Identities 594 48.3. A Bivariate Lucas Counterpart 599 48.4. A Summation Formula for 𝑓2n(x, y) 600 48.5. A Summation Formula for l2n(x, y) 602 48.6. Bivariate Fibonacci Links 603 48.7. Bivariate Lucas Links 606 49. Tribonacci Polynomials 611 49.1. Tribonacci Numbers 611 49.2. Compositions with Summands 1, 2, and 3 613 49.3. Tribonacci Polynomials 616 49.4. A Combinatorial Model 618 49.5. Tribonacci Polynomials and the Q-Matrix 624 49.6. Tribonacci Walks 625 49.7. A Bijection between the Two Models 627 Appendix 631 A.1. The First 100 Fibonacci and Lucas Numbers 631 A.2. The First 100 Pell and Pell–Lucas Numbers 634 A.3. The First 100 Jacobsthal and Jacobsthal–Lucas Numbers 638 A.4. The First 100 Tribonacci Numbers 642 Abbreviations 644 Bibliography 645 Solutions to Odd-Numbered Exercises 661 Index 725
£94.95
CRC Press Handbook of Mellin Transforms Advances in Applied
Book SynopsisThe Mellin transformation is widely used in various problems of pure and applied mathematics, in particular, in the theory of differential and integral equations and the theory of Dirichlet series. It is found in extensive applications in mathematical physics, number theory, mathematical statistics, theory of asymptotic expansions, and especially, in the theory of special functions and integral transformations. It is essentially used in algorithms of integration in computer algebra systems.Since the majority of integrals encountered in applications can be reduced to the form of the corresponding Mellin transforms with specific parameters, this handbook can also be used for definite and indefinite integrals. By changes in variables, the Mellin transform can be turned into the Fourier and Laplace transforms.The appendices contain formulas of connection with other integral transformations, and an algorithm for determining regions of convergence of integrals.The Handbook of Mellin Transforms will be of interest and useful to all researchers and engineers who use mathematical methods. It will become the main source of formulas of Mellin transforms, as well as indefinite and definite integrals.Table of ContentsGeneral Formulas Elementary FunctionsSpecial Functions Appendix I: Some properties of the Mellin transformsAppnedix II: Condtions of convergence
£266.00
Springer-Verlag New York Inc. Prime Numbers
Book SynopsisIn this book, the authors concentrate on the computational aspects of prime numbers, such as recognizing primes and discovering the fundamental prime factors of a given number.Trade ReviewFrom the reviews: MATHEMATICAL REVIEWS "There are many books about the theory of prime numbers and a few about computations concerning primes. This book bridges the gap between theoretical and computational aspects of prime numbers. It considers such matters as how to recognize primes, how to compute them, how to count them, and how to test conjectures about them¿The book is clearly written and is a pleasure to read. It is largely self-contained. A first course in number theory and some knowledge of computer algorithms should be sufficient background for reading it…Each chapter concludes with a long list of interesting exercises and research problems." BULLETIN OF THE AMS "The book is an excellent resource for anyone who wants to understand these algorithms, learn how to implement them, and make them go fast. It's also a lot of fun to read! It's rare to say this of a math book, but open Prime Numbers to a random page and it's hard to put down. Crandall and Pomerance have written a terrific book." AMERICAN SCIENTIST "…a welcome addition to the literature of number theory – comprehensive, up-to-date and written with style. It will be useful to anyone interested in algorithms dealing with the arithmetic of the integers and related computational issues." SIAM REVIEW "Overall, this book by Crandall and Pomerance fills a unique niche a deserves a place on the bookshelf of anyone with more than a passing interest in prime numbers. It would provide a gold mine of information and problems for a graduate class on computationl number theory." From the reviews of the second edition: "This book is a very successful attempt of the authors to describe the current state-of-the-art of computational number theory … . One of the many attractive features of this book is the rich and beautiful set of exercises and research problems … . the authors have managed to lay down their broad and deep insight in primes into this book in a very lucid and vivid way. … The book provides excellent material for graduate and undergraduate courses on computational theory. Warmly recommended … ." (H.J.J. te Riele, Nieuw Archief voor Wiskunde, Vol. 7 (3), 2006) "An absolutely wonderful book! Written in a readable and enthusiastic style the authors try to share the elegance of the prime numbers with the readers … . Weaving together a wealth of ideas and experience from theory and practice they enable the reader to have more than a glimpse into the current state of the knowledge … . any chapter or section can be singled out for high praise. … Indeed it is destined to become a definitive text on … prime numbers and factoring." (Peter Shiu, Zentralblatt MATH, Vol. 1088 (14), 2006) "This impressive book represents a comprehensive collection of the properties of prime numbers. … in the exercises at the end of each chapter valuable hints are given how the theorems have been attained. The chapters end with research exercises. The book is up to date and carefully written. … The volume is very vividly and even entertainingly written and is best suited for students and for teachers as well." (J. Schoissengeier, Monatshefte für Mathematik, Vol. 150 (1), 2007) "The aim of this book is to bridge the gap between prime-number theory covered in many books and the relatively new area of computer experimentation and algorithms. The aim is admirably met. … There is a comprehensive and useful list of almost 500 references including many to websites. … This is an interesting, well-written and informative book neatly covering both the theoretical as well as the practical computational implementation of prime numbers and many related topics at first-year undergraduate level." (Ron Knott, The Mathematical Gazette, Vol. 92 (523), 2008)Table of ContentsPreface.- Primes!.- Number-Theoretical Tools.- Recognizing Primes and Composites.-Primality Proving.- Exponential Factoring Algorithms.- Subexponential Factoring Algorithms.- Elliptic Curve Arithmetic.- The Ubiquity of Prime Numbers.- Fast Algorithms for Large-Integer Arithmetic.- Book Pseudocode.- References.- Index.
£103.90
Springer An Introduction to Mathematical Cryptography
Book SynopsisAn Introduction to Cryptography.- Discrete Logarithms and Diffie Hellman.- Integer Factorization and RSA.- Combinatorics, Probability and Information Theory.- Elliptic Curves and Cryptography.- Lattices and Cryptography.- Digital Signatures.- Additional Topics in Cryptography.Trade ReviewFrom the reviews: "The book is devoted to public key cryptography, whose principal goal is to allow two or more people to exchange confidential information … . The material is very well organized, and it is self-contained: no prerequisites in higher mathematics are needed. In fact, everything is explained and carefully covered … . there is abundance of examples and proposed exercises at the end of each chapter. … This book is ideal as a textbook for a course aimed at undergraduate mathematics or computer science students." (Fabio Mainardi, The Mathematical Association of America, October, 2008) "This book focuses on public key cryptography … . Hoffstein, Pipher, and Silverman … provide a thorough treatment of the topics while keeping the material accessible. … The book uses examples throughout the text to illustrate the theorems, and provides a large number of exercises … . The volume includes a nice bibliography. … Summing Up: Highly recommended. Upper-division undergraduate through professional collections." (C. Bauer, Choice, Vol. 46 (7), March, 2009) "For most undergraduate students in mathematics or computer science (CS), mathematical cryptography is a challenging subject. … it is written in a way that makes you want to keep reading. … The authors officially targeted the book for advanced undergraduate or beginning graduate students. I believe that this audience is appropriate. … it could even be used with students who are just learning how to execute rigorous mathematical proofs. … I strongly believe that it finds the right tone for today’s students … ." (Burkhard Englert, ACM Computing Reviews, March, 2009) "The exercises and text would make an excellent course for undergraduate independent study. … This is an excellent book. Hoffstein, Pipher and Silverman have written as good a book as is possible to explain public key cryptography. … This book would probably be best suited for a graduate course that focused on public key cryptography, for undergraduate independent study, or for the mathematician who wants to see how mathematics is used in public key cryptography." (Jintai Ding and Chris Christensen, Mathematical Reviews, Issue 2009 m)Table of ContentsAn Introduction to Cryptography.- Discrete Logarithms and Diffie-Hellman.- Integer Factorization and RSA.- Probability Theory and Information Theory.- Elliptic Curves and Cryptography.- Lattices and Cryptography.- Digital Signatures.- Additional Topics in Cryptology.
£49.49
Springer-Verlag New York Inc. The Map of My Life
Book SynopsisIn this book, the author writes freely and often humorously about his life, beginning with his earliest childhood days. He describes his survival of American bombing raids when he was a teenager in Japan, his emergence as a researcher in a post-war university system that was seriously deficient, and his life as a mature mathematician in Princeton and in the international academic community. Every page of this memoir contains personal observations and striking stories. Such luminaries as Chevalley, Oppenheimer, Siegel, and Weil figure prominently in its anecdotes.Goro Shimura is Professor Emeritus of Mathematics at Princeton University. In 1996, he received the Leroy P. Steele Prize for Lifetime Achievement from the American Mathematical Society. He is the author of Elementary Dirichlet Series and Modular Forms (Springer 2007), Arithmeticity in the Theory of Automorphic Forms (AMS 2000), and Introduction to the Arithmetic Theory of Automorphic Functions (Princeton UniveTrade ReviewFrom the reviews:"This volume is an exciting autobiography of Goro Shimura … . The author relates not only his life and his significant mathematical achievements but also many aspects outside mathematics. The book is organized into four chapters … and an appendix. … The volume contains many personal feelings of the author towards the reaction of the mathematical community with respect to his work. … This book is certainly exciting for any reader interested in mathematics or Japanese civilization." (Doru Stefanescu, Mathematical Reviews, Issue 2009 i)“Goro Shimura, who was born in 1930, is famous for his work in algebraic geometry and number theory, extending over several decades. … the book gives an unusual insight into the mind of a famous contemporary mathematician and can be read with interest and, mostly, pleasure.” (Peter J. Giblin, The Mathematical Gazette, Vol. 94 (531), November, 2010)Table of ContentsChildhood.- As a Student.- As a Mathematician.- A Long Epilogue.
£67.49
Springer Introduction to Analytic Number Theory
Book SynopsisHistorical 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.Trade ReviewFrom the reviews:T.M. ApostolIntroduction to Analytic Number Theory"This book is the first volume of a two-volume textbook for undergraduates and is indeed the crystallization of a course offered by the author at the California Institute of Technology to undergraduates without any previous knowledge of number theory. 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."—MATHEMATICAL REVIEWS“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)Table of Contents1: 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.
£52.24
Springer New York A Course in padic Analysis
Book SynopsisIt offers many features rarely treated in introductory p-adic texts such as topological models of p-adic spaces inside Euclidian space, a special case of Hazewinkel’s functional equation lemma, and a treatment of analytic elements.Trade Review“This well-written book, complete with all proofs and a wealth of exercises, is perfectly suited as a text book for introductory courses.” (Wim Schikhof, zbMATH 0947.11035, 2022)From the reviews: MATHEMATICAL REVIEWS "The text ends with a large number of exercises. The writing is extremely clear and very meticulous. The bibliography, which does not attempt to be comprehensive, is adequate. I recommend A. Robert’s book without reservation to anyone who wants to have a reference text on one-variable p-adic analysis that is clear, complete and pleasant to read." MATHSCINET "Robert's book is aimed at an intermediate level between the very specialized monographs and the elementary texts. It has no equal in the marketplace, because it covers practically all of p-adic analysis of one variable (except the rationality of the zeta function of an algebraic variety over a finite field and the theory of p-adic differential equations) and contains numerous results that were accessible only in articles or even in preprints. ...I recommend A. Robert's book without reservation to anyone who wants to have a reference text on one-variable p-adic analysis that is clear, complete and pleasant to read."D. Barsky in MathSciNet, August 2001Table of Contents1 p-adic Numbers.- 2 Finite Extensions of the Field of p-adic Numbers.- 3 Construction of Universal p-adic Fields.- 4 Continuous Functions on Zp.- 5 Differentiation.- 6 Analytic Functions and Elements.- 7 Special Functions, Congruences.- Specific References for the Text.- Tables.- Basic Principles of Ultrametric Analysis.- Conventions, Notation, Terminology.
£49.49
Springer Us Primality Testing and Integer Factorization in PublicKey Cryptography 11 Advances in Information Security
Book SynopsisIntended for advanced level students in computer science and mathematics, this key text, now in a brand new edition, provides a survey of recent progress in primality testing and integer factorization, with implications for factoring based public key cryptography.Trade ReviewFrom the reviews of the second edition:"The well-written and self-contained second edition ‘is designed for a professional audience composed of researchers practitioners in industry.’ In addition, ‘this book is also suitable as a secondary text for graduate-level students in computer science, mathematics, and engineering,’ as it contains about 300 problems. … Overall … ‘this monograph provides a survey of recent progress in Primality Testing and Integer Factorization, with implications in factoring-based Public Key Cryptography.’" (Hao Wang, ACM Computing Reviews, April, 2009)“This is the second edition of a book originally published in 2004. … I used it as a reference in preparing lectures for an advanced cryptography course for undergraduates, and it proved to be a wonderful source for a general description of the algorithms. … the book will be a valuable addition to any good reference library on cryptography and number theory … . It contains descriptions of all the main algorithms, together with explanations of the key ideas behind them.” (S. C. Coutinho, SIGACT News, April, 2012)Table of ContentsPreface to the Second Edition.- Preface to the First Edition.- Number-Theoretic Preliminaries.- Problems in Number Theory. Divisibility Properties. Euclid's Algorithm and Continued Fractions. Arithmetic Functions. Linear Congruences. Quadratic Congruences. Primitive Roots and Power Residues. Arithmetic of Elliptic Curves. Chapter Notes and Further Reading.- Primality Testing and Prime Generation.- Computing with Numbers and Curves. Riemann Zeta and Dirichlet L Functions. Rigorous Primality Tests. Compositeness and Pseudoprimality Tests. Lucas Pseudoprimality Test. Elliptic Curve Primality Tests. Superpolynomial-Time Tests. Polynomial-Time Tests. Primality Tests for Special Numbers. Prime Number Generation. Chapter Notes and Further Reading.- Integer Factorization and Discrete Logarithms.- Introduction. Simple Factoring Methods. Elliptic Curve Method (ECM). General Factoring Congruence. Continued FRACtion Method (CFRAC). Quadratic Sieve (QS). Number Field Sieve (NFS). Quantum Factoring Algorithm. Discrete Logarithms. kth Roots. Elliptic Curve Discrete Logarithms. Chapter Notes and Further Reading.- Number-Theoretic Cryptography.- Public-Key Cryptography. RSA Cryptosystem. Rabin Cryptography. Quadratic Residuosity Cryptography. Discrete Logarithm Cryptography. Elliptic Curve Cryptography. Zero-Knowledge Techniques. Deniable Authentication. Non-Factoring Based Cryptography. Chapter Notes and Further Reading.- Bibliography.- Index.- About the Author.
£123.25
Springer-Verlag New York Inc. Mathematics and Its History
Book SynopsisFrom a review of the second edition:"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."(David Parrott, Australian Mathematical Society)This book offers a collection of historical essays detailing a large variety of mathematical disciplines and issues; it's accessible to a broad audience. This third edition includes new chapters on simple groups and new sections on alternating groups and the Poincare conjecture. Many more exercises have been added as well as commentary that helps place the exercises in context.Trade Review“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)From the reviews of the third edition:"The author’s goal for Mathematics and its History is to provide a “bird’s-eye view of undergraduate mathematics.” (p. vii) In that regard it succeeds admirably. ... Mathematics and its History 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!"(Richard Wilders, MAA Reviews)“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)From the reviews of the second edition:"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."(David Parrott, Australian Mathematical Society)"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." (European Mathematical Society)"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."(Denis Bonheure, Bulletin of the Belgian Society)Table of ContentsPreface 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.-
£44.99
Springer New York Algebraic Number Theory
Book SynopsisOne General Basic Theory.- I Algebraic Integers.- II Completions.- III The Different and Discriminant.- IV Cyclotomic Fields.- V Parallelotopes.- VI The Ideal Function.- VII Ideles and Adeles.- VIII Elementary Properties of the Zeta Function and L-series.- Two Class Field Theory.- IX Norm Index Computations.- X The Artin Symbol, Reciprocity Law, and Class Field Theory.- XI The Existence Theorem and Local Class Field Theory.- XII L-series Again.- Three Analytic Theory.- XIII Functional Equation of the Zeta Function, Hecke's Proof.- XIV Functional Equation, Tate's Thesis.- XV Density of Primes and Tauberian Theorem.- XVI The Brauer-Siegel Theorem.- XVII Explicit Formulas.Trade ReviewSecond Edition S. Lang Algebraic Number Theory "This book is the second edition of Lang's famous and indispensable book on algebraic number theory. The major change from the previous edition is that the last chapter on explicit formulas has been completely rewritten. In addition, a few new sections have been added to the other chapters . . . Lang's books are always of great value for the graduate student and the research mathematician. This updated edition of Algebraic number theory is no exception."—MATHEMATICAL REVIEWSTable of ContentsOne General Basic Theory.- I Algebraic Integers.- II Completions.- III The Different and Discriminant.- IV Cyclotomic Fields.- V Parallelotopes.- VI The Ideal Function.- VII Ideles and Adeles.- VIII Elementary Properties of the Zeta Function and L-series.- Two Class Field Theory.- IX Norm Index Computations.- X The Artin Symbol, Reciprocity Law, and Class Field Theory.- XI The Existence Theorem and Local Class Field Theory.- XII L-series Again.- Three Analytic Theory.- XIII Functional Equation of the Zeta Function, Hecke’s Proof.- XIV Functional Equation, Tate’s Thesis.- XV Density of Primes and Tauberian Theorem.- XVI The Brauer-Siegel Theorem.- XVII Explicit Formulas.
£42.29
Copernicus The Book of Numbers
Book Synopsis1 The Romance of Numbers.- 2 Figures from Figures: Doing Arithmetic and Algebra by Geometry.- 3 What Comes Next?.- 4 Famous Families of Numbers.- 5 The Primacy of Primes.- 6 Further Fruitfulness of Fractions.- 7 Geometric Problems and Algebraic Numbers.- 8 Imagining Imaginary Numbers.- 9 Some Transcendental Numbers.- 10 Infinite and Infinitesimal Numbers.Trade ReviewFrom the reviews: "This is a really fascinating book either to read or to browse in, or for reference - there is a good index, and I can strongly recommend it - it should be in every school and college library!" The Mathematical Gazette "… A delightful look at numbers and their roles in everything from language to flowers to the imagination." Science News "… The great feature of the book is that anyone can read it without excessive head scratching … You'll find plenty here to keep you occupied, amused, and informed. Buy, dip in, wallow." New ScientistTable of Contents1. The Romance of Numbers 2. Figures from Figures Doing Arithmetic and Algebra by Geometry 3. What Comes Next? 4. Famous Families of Numbers 5. The Primacy of Primes 6. Further Fruitfulness of Fractions 7. Geometric Problems and Algebraic Numbers 8. Imagining Imaginary Numbers 9. Some Transcendental Numbers 10. Infinite and Infinitesimal Numbers
£43.99
Springer-Verlag New York Inc. Mathematics and Its History
Book SynopsisThe 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.Trade Review“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)From the reviews of the third edition:"The author’s goal for Mathematics and its History is to provide a “bird’s-eye view of undergraduate mathematics.” (p. vii) In that regard it succeeds admirably. ... Mathematics and its History 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!"(Richard Wilders, MAA Reviews)“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)From the reviews of the second edition:"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."(David Parrott, Australian Mathematical Society)"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." (European Mathematical Society)"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."(Denis Bonheure, Bulletin of the Belgian Society)Table of ContentsPreface 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.-
£47.49
Springer Introduction to Mathematical Structures and Proofs
Book SynopsisPreface to the Second Edition.- Preface to the First Edition.- 1. Logic.- 2. Sets.- 3. Functions.- 4. Finite and Infinite Sets.- 5. Combinatorics.- 6. Number Theory.- 7. Complex Numbers.- Hints and Partial Solutions to Selected Odd-Numbered Exercises.- Index.Table of Contents-Preface.- 1. Logic.- 2. Sets.- 3. Functions.- 4. Finite and Infinite Sets. - 5. Permutations and Combinations.- 6. Number Theory.- 7. Complex Numbers.- Hints and Partial Solutions to Selected Odd-Numbered Exercises.- Index
£38.94
Springer New York Hidden HarmonyGeometric Fantasies The Rise of
Book SynopsisThis book is a history of complex function theory from its origins to 1914, when the essential features of the modern theory were in place.Trade Review“There is much in this book that will educate, be appreciated by, and no doubt provoke mathematicians as well as historians of mathematics and of science. … It stands its ground as a scholarly treatise that fills many lacunae in the extant historical literature. It will surely provoke further debate and research. As a bonus, it comes filled with treasures for both the specialist and the novice.” (Tushar Das, MAA Reviews, July, 2015)“The book is devoted to the history of complex (analytic) function theory from its origins to 1914. … The book is highly recommended for historians of mathematics, mathematicians with historical interests, and everyone who is interested in complex function theory and its history. It offers a wealth of information that is well documented.” (Karl-Heinz Schlote, Mathematical Reviews, October, 2014)“This comprehensive, massively researched volume … is a detailed historical account of the development of analytic function theory in the 19th century, tracing its rise and ramification through that period up until about 1910. … It is a very dense and scholarly work, suitable for specialists. Summing Up: Recommended. Graduate students, researchers/faculty, and professionals/practitioners.” (D. Robbins, Choice, Vol. 51 (9), May, 2014)“This book is the first one devoted to the history of complex function theory. The authors present the rise of analytic function theory from its origins to 1914. … This book is of great interest and help, not only for mathematicians interested in complex function theory, but also for everyone who likes the history of mathematics.” (Agnieszka Wisniowska-Wajnryb, zbMATH, Vol. 1276, 2014)Table of ContentsList of Figures.- Introduction.- 1. Elliptic Functions.- 2. From real to complex.- 3. Cauch.- 4. Elliptic integrals.- 5. Riemann.- 6. Weierstrass.- 7. Differential equations.- 8. Advanced topics.- 9. Several variables.- 10. Textbooks.
£179.99
MP-AMM American Mathematical Complex Multiplication and Lifting Problems
Book SynopsisTable of Contents Introduction Algebraic theory of complex multiplication CM lifting over a discrete valuation ring CM lifting of $p$-divisible groups CM lifting of abelian varieties up to isogeny Some arithmetic results for abelian varieties CM lifting via $p$-adic Hodge theory Notes on quotes Glossary of notations Bibliography Index
£103.50
MP-AMM American Mathematical Arakelov Geometry
Book SynopsisThe main goal of this book is to present the so-called birational Arakelov geometry, which can be viewed as an arithmetic analog of the classical birational geometry. After explaining classical results about the geometry of numbers, the author starts with Arakelov geometry for arithmetic curves, and continues with Arakelov geometry of arithmetic surfaces and higher-dimensional varieties.Table of Contents Preliminaries Geometry of numbers Arakelov geometry on arithmetic curves Arakelov geometry on arithmetic surfaces Arakelov geometry on general arithmetic varieties Arithmetic volume function and its continuity Nakai-Moishezon criterion on an arithmetic variety Arithmetic Bogomolov inequality Lang-Bogomolov conjecture Bibliography Index
£129.60
MP-AMM American Mathematical The Dynamical MordellLang Conjecture
Book SynopsisThe Dynamical Mordell-Lang Conjecture is an analogue of the classical Mordell-Lang conjecture in the context of arithmetic dynamics. This volume presents all known results of the Dynamical Mordell-Lang Conjecture, focusing mainly on a $p$-adic approach which provides a parametrization of the orbit of a point under an endomorphism of a variety.Table of Contents Introduction Background material The dynamical Mordell-Lang problem A geometric Skolem-Mahler-Lech theorem Linear relations between points in polynomial orbits Parametrization of orbits The split case in the dynamical Mordell-Lang conjecture Heuristics for avoiding ramification Higher dimensional results Additional results towards the dynamical Mordell-Lang conjecture Sparse sets in the dynamical Mordell-Lang conjecture Denis-Mordell-Lang conjecture Dynamical Mordell-Lang conjecture in positive characteristic Related problems in arithmetic dynamics Future directions Bibliography Index
£103.50
MP-AMM American Mathematical Differential Galois Theory through RiemannHilbert
Book SynopsisOffers a hands-on transcendental approach to differential Galois theory, based on the Riemann-Hilbert correspondence. Along the way, it provides a smooth, down-to-earth introduction to algebraic geometry, category theory and tannakian duality. A large variety of examples, exercises, and theoretical constructions offers an accessible entry into this exciting area.Trade ReviewJacques Sauloy's book is an introduction to differential Galois theory, an important area of mathematics having different powerful applications (for example, to the classical problem of integrability of dynamical systems in mechanics and physics)...Sauloy offers an alternative approach to the subject which is based on the monodromy representation...Enriching the understanding of differential Galois theory, this point of view also brings new solutions, which makes the book especially valuable...There are a lot of nice exercises, both inside and at the end of each chapter." — Renat R. Gontsov, Mathematical Reviews"The book is an elementary introduction to the differential Galois theory and is intended for undergraduate students of mathematical departments. It is not overloaded with redundant definitions, constructs and results. Everything that is minimally necessary for understanding the whole presentation is given in full. The reader can find the rest [of the] details from a well-designed references system. And at the same time, the book contains quite a lot of carefully selected examples and exercises." — Mykola Grygorenko, Zentralblatt MATH"It's an excellent book about a beautiful and deep subject...There are loads of exercises, and I think the book is very well-paced, as well as very clearly written. It's a fabulous entry in the AMS GSM series." — Michael Berg, MAA ReviewsTable of Contents Part 1. A quick introduction to complex analytic functions: The complex exponential function Power series Analytic functions The complex logarithm From the local to the global Part 2. Complex linear differential equations and their monodromy: Two basic equations and their monodromy Linear complex analytic differential equations A functorial point of view on analytic continuation: Local systems Part 3. The Riemann-Hilbert correspondence: Regular singular points and the local Riemann-Hilbert correspondence Local Riemann-Hilbert correspondence as an equivalence of categories Hypergeometric series and equations The global Riemann-Hilbert correspondence Part 4. Differential Galois theory: Local differential Galois theory The local Schlesinger density theorem The universal (Fuchsian local) Galois group The universal group as proalgebraic hull of the fundamental group Beyond local Fuchsian differential Galois theory Appendix A. Another proof of the surjectivity of $\mathrm{exp}:\mathrm{Mat}_n(\mathbf{C})\rightarrow \mathrm{GL}_n(\mathbf{C})$ Appendix B. Another construction of the logarithm of a matrix Appendix C. Jordan decomposition in a linear algebraic group Appendix D. Tannaka duality without schemes Appendix E. Duality for diagonalizable algebraic groups Appendix F. Revision problems Bibliography Index.
£108.00
MP-AMM American Mathematical Analytic Methods in Arithmetic Geometry
Book SynopsisContains the proceedings of the Arizona Winter School 2016, held in March 2016 at The University of Arizona. The School provided a unique opportunity to introduce graduate students to analytic methods in arithmetic geometry.Table of Contents A. C. Cojocaru, Primes, elliptic curves and cyclic groups H. A. Helfgott, Growth and expansion in algebraic groups over finite fields E. Fouvry, E. Kowalski, P. Michel, and W. Sawin, Lectures on applied $\ell$-adic cohomology A. V. Sutherland, Sato-Tate distributions.
£102.60
MP-AMM American Mathematical Arithmetic Geometry
Book SynopsisPresents original research articles covering a large range of topics, including weight enumerators for codes, function field analogs of the Brauer-Siegel theorem, the computation of cohomological invariants of curves, the trace distributions of algebraic groups, and applications of the computation of zeta functions of curves.Table of Contents J. D. Achter and E. W. Howe, Hasse-Witt and Cartier-Manin matrices: A warning and a request M. Hindry, Analogues of Brauer-Siegel theorem in arithmetic geometry J. Javanpeykar and J. Voight, The Belyi degree of a curve is computable N. Kaplan, Weight enumerators of Reed-Muller codes from cubic curves and their duals G. Lachaud, The distribution of the trace in the compact group of type $G_2$ B. Malmskog, R. Pries, and C. Weir, The de Rham cohomology of the Suzuki curves F. Pazuki, Decompositions en hauteurs locales B. Poonen, Using zeta functions to factor polynomials over finite fields J. Sijsling, Canonical models of arithmetic $(1;\infty)$-curves A. V. Sutherland and J. F. Voloch, Maps between curves and arithmetic obstructions.
£103.50
MP-AMM American Mathematical Dynamics Topology and Numbers
Book SynopsisContains the proceedings of the conference Dynamics: Topology and Numbers, held in July 2018. The papers cover diverse fields of mathematics with a unifying theme of relation to dynamical systems. These include arithmetic geometry, flat geometry, complex dynamics, graph theory, relations to number theory, and topological dynamics.Table of Contents L. Snoha, The life and mathematics of Sergii Kolyada I. Kolyada, A. Blokh, and L. Snoha, Recollections about Sergii Kolyada P. Moree, Sergiy and the MPIM Y. I. Manin and M. Marcolli, Homotopy types and geometries below ${\rm Spec}(\mathbb{Z})$ A. Fel'shtyn and M. Zietek, Dynamical zeta functions of Riedemeister type and representations spaces O. Jenkinson and M. Pollicott, Rigorous dimension estimates for Cantor sets arising in Zaremba theory P. Colognese and M. Pollicott, Volume growth for infinite graphs and translation surfaces J. Byszewski, G. Cornelissen, M. Houben, and L. Van Der Meijden, Dynamically affine maps in positive characteristic S. Kolyada, M. Misiurewicz, and L. Snoha, Special $\alpha$-limit sets E. Shi and X. Ye, Equicontinuity of minimal sets for amenable group actions on dendrites E. Akin, E. Glasner, and B. Weiss, On weak rigidity and weakly mixing enveloping semigroups A. Ganguly and A. Ghosh, The inhomogenous Sprindzhuk conjecture over a local field of positive characteristic A. Blokh, L. Oversteegen, and V. Timorin, Dynamical generation of parameter laminations P. Oprocha, T. Yu, and Guohua Zhang, Multi-sensitivity, multi-transitivity and $\delta$-transitivity R. Sharp, Convergence of zeta functions for amenable group extensions of shifts S. Bezuglyi and O. Karpel, Invariant measures for Cantor dynamical systems M. Kapovich, Periods of abelian differentials and dynamics J. Riedl and D. Schleicher, Crossed renormalization of quadratic polynomials.
£94.50
MP-AMM American Mathematical Local Lp BrunnMinkowski Inequalities for p 1
Book Synopsis
£67.50
American Mathematical Society Topology of Numbers
Book SynopsisProvides 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.Table of Contents A preview The Farey diagram Continued fractions Symmetries of the Farey diagram Quadratic forms Classification of quadratic forms Representations by quadratic forms The class group for quadratic forms Quadratic fields Tables Glossary of nonstandard terminology Bibliography Index
£46.80
American Mathematical Society DavenportZannier Polynomials and Dessins dEnfants
Book SynopsisThe 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.Table of Contents Introduction. Dessins d'enfants: From polynomials through Belyi functions to weighted trees. Existence theorem. Recapitulation and perspective. Classification of unitrees. Computation of Davenport-Zannier pairs for unitrees. Primitive monodromy groups of weighted trees. Trees with primitive monodromy groups. A zoo of examples and constructions. Diophantine invariants. Enumeration. What remains to be done. Bibliography. Index.
£115.60
MP-AMM American Mathematical Conversational Problem Solving
Book SynopsisPresents a dialogue between a professor and eight students in a summer problem solving camp and allows for a conversational approach to the problems as well as some mathematical humour and a few non-mathematical digressions. The problems have been selected for their entertainment value, elegance, trickiness, and unexpectedness.Table of Contents The first day Polynomials Base mathematics A mysterious visitor Set theory Triangles Independence day Independence aftermath Amanda An aesthetical error Miraculous cancellation Probability theory Geometry Hodegepodge Self-referential mathematics All good things must come to an end Bibliography Index.
£39.56
American Mathematical Society Iwasawa Theory and Its Perspective Volume 1
Book SynopsisThe goal of this publication is to explain the theory of ideal class groups, including its algebraic aspect (the Iwasawa class number formula), its analytic aspect (Leopoldt-Kubota $L$-functions), and the Iwasawa main conjecture, which is a bridge between the algebraic and the analytic aspects.Table of Contents Motivation and utility of Iwasawa theory $\mathbb{Z}_p$-extension and Iwasawa algebra Cyclotomic Iwasawa theory for ideal class groups Bookguide Appendix A References Index
£96.30
MP-AMM American Mathematical Numerical Algorithms for Number Theory Using
Book SynopsisPresents multiprecision algorithms used in number theory and elsewhere, such as extrapolation, numerical integration, numerical summation (including multiple zeta values and the Riemann-Siegel formula), evaluation and speed of convergence of continued fractions, Euler products and Euler sums, inverse Mellin transforms, and complex $L$-functions.Table of Contents Introduction Numerical extrapolation Numerical integration Numerical summation Euler products and Euler sums Gauss and Jacobi sums Numerical computation of continued fractions Computation of inverse Mellin transforms Computation of $L$-functions List of relevant GP programs Bibliography Index of programs General index.
£98.10
MP-AMM American Mathematical Perfectoid Spaces Lectures from the 2017 Arizona
Book SynopsisProvides a broad introduction to perfectoid spaces. The book will be an invaluable asset for any graduate student or researcher interested in the theory of perfectoid spaces and their applications.Table of Contents J. Weinstein, Arizona Winter School 2017: Adic spaces K. S. Kedlaya, Sheaves, stacks, and shtukas B. Bhatt, The Hodge-Tate decomposition via perfectoid spaces A. Caraiani, Perfectoid Shimura varieties
£78.30
MP-AMM American Mathematical pAdic Analysis Arithmetic and Singularities
Book SynopsisProvides an introduction to an active area of research that lies at the intersection of number theory, $p$-adic analysis, algebraic geometry, singularity theory, and theoretical physics. The book introduces $p$-adic analysis, the theory of zeta functions, Archimedean, $p$-adic, motivic, singularities of plane curves and their Poincare series.Table of Contents Surveys: E. Leon-Cardenal, Archimedean zeta functions and oscillatory integrals J. J. Moyano-Fernandez, Generalized Poincare series for plane curve singularities N. Potemans and W. Veys, Introduction to $p$-adic Igusa zeta functions J. Viu-Sos, An introduction to $p$-adic and motivic integration, zeta functions and invariants of singularities W. A. Zuniga-Galindo, $p$-adic analysis: A quick introduction Articles: E. Artal Bartolo and M. Gonzalez Villa, On maximal order poles of generalized topological zeta functions J. I. Cogolludo-Agustin, T. Laszlo, J. Martin-Morales, and A. Nemethi, Local invariants of minimal generic curves on rational surfaces J. Nagy and A. Nemethi, Motivic Poincare series of cusp surface singularities C. D. Sinclair, Non-Archimedean electrostatics
£98.10
American Mathematical Society Numbers and Figures
Book SynopsisOne of the great charms of mathematics is uncovering unexpected connections. In Numbers and Figures, Giancarlo Travaglini provides six conversations that do exactly that by talking about several topics in elementary number theory and some of their connections to geometry, calculus, and real-life problems such as COVID-19 vaccines.Table of Contents Integer points, polygons, and polyhedra Simpson's paradox, Farey sequences, and Diophantine approximation A coin problem and generating functions Pythagorean triples and sums of squares Benford's law, uniform distribution and normal numbers Sums and integrals Index
£46.80
MP-AMM American Mathematical Integer and Polynomial Algebra
Book SynopsisOffers a concrete introduction to abstract algebra and number theory. Starting from the basics, it develops the rich parallels between the integers and polynomials, covering topics such as Unique Factorization, arithmetic over quadratic number fields, the RSA encryption scheme, and finite fields.Table of Contents The integers Modular arithmetic Diophantine equations and quadratic number domains Codes and factoring Real and complex numbers The ring of polynomials Finite fields Bibliography Index
£52.20
Taylor & Francis Inc Algebraic Operads
Book SynopsisAlgebraic Operads: An Algorithmic Companion presents a systematic treatment of Gröbner bases in several contexts. The book builds up to the theory of Gröbner bases for operads due to the second author and Khoroshkin as well as various applications of the corresponding diamond lemmas in algebra. The authors present a variety of topics including: noncommutative Gröbner bases and their applications to the construction of universal enveloping algebras; Gröbner bases for shuffle algebras which can be used to solve questions about combinatorics of permutations; and operadic Gröbner bases, important for applications to algebraic topology, and homological and homotopical algebra. The last chapters of the book combine classical commutative Gröbner bases with operadic ones to approach some classification problems for operads. Throughout the book, both the mathematical theory and computational methods are emphasized and numerous algorithms, examples, and exerciseTrade Review"This book presents a systematic treatment of Gröbner bases, and more generally of the problem of normal forms, departing from linear algebra, going through commutative and noncommutative algebra, to operads. The algorithmic aspects are especially developed, with numerous examples and exercises."- Loϊc Foissy"By balancing computational methods and abstract reasoning, the authors of the book under review have written an excellent up-to-date introduction to Grobner basis methods applicable to associative structures, especially including operads. The book will be of interest to a wide range of readers, from undergraduates to experts in the field."~ Ralf Holtkamp, Mathematical Reviews, March 2018"This book presents a systematic treatment of Gröbner bases, and more generally of the problem of normal forms, departing from linear algebra, going through commutative and noncommutative algebra, to operads. The algorithmic aspects are especially developed, with numerous examples and exercises."- Loϊc Foissy"By balancing computational methods and abstract reasoning, the authors of the book under review have written an excellent up-to-date introduction to Grobner basis methods applicable to associative structures, especially including operads. The book will be of interest to a wide range of readers, from undergraduates to experts in the field."~ Ralf Holtkamp, Mathematical Reviews, March 2018Table of ContentsNormal Forms for Vectors and Univariate Polynomials. Noncommutative Associative Algebras. Nonsymmetric Operads. Twisted Associative Algebras and Shuffle Algebras. Symmetric Operads and Shuffle Operads. Operadic Homological Algebra and Gröbner Bases. Commutative Gröbner Bases. Linear Algebra over Polynomial Rings. Case Study of Nonsymmetric Binary Cubic Operads. Case Study of Nonsymmetric Ternary Quadratic Operads. Appendices: Maple Code for Buchberger’s Algorithm.
£114.00
Springer-Verlag New York Inc. An Introduction to Mathematical Cryptography
Book SynopsisPreface.- 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.Trade Review“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)“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)Table of ContentsPreface.- 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.
£56.69
Springer Computing the Continuous Discretely
Trade Review“This book is an outstanding book on counting integer points of polytopes … . The book contains lots of exercises with very helpful hints. Another essential feature of the book is a vast collection of open problems on different aspects of integer point counting and related areas. … The book is reader-friendly written, self-contained and contains numerous beautiful illustrations. The reader is always accompanied with deep research jokes by famous researchers and valuable historical notes.” (Oleg Karpenkov, zbMATH 1339.52002, 2016)Reviews of the first edition:“You owe it to yourself to pick up a copy of Computing the Continuous Discretely to read about a number of interesting problems in geometry, number theory, and combinatorics.”— MAA Reviews“The book is written as an accessible and engaging textbook, with many examples, historical notes, pithy quotes, commentary integrating the material, exercises, open problems and an extensive bibliography.”— Zentralblatt MATH“This beautiful book presents, at a level suitable for advanced undergraduates, a fairly complete introduction to the problem of counting lattice points inside a convex polyhedron.”— Mathematical Reviews“Many departments recognize the need for capstone courses in which graduating students can see the tools they have acquired come together in some satisfying way. Beck and Robins have written the perfect text for such a course.”— CHOICETable of ContentsPreface.- The Coin-Exchange Problem of Frobenius.- A Gallery of Discrete Volumes.- Counting Lattice Points in Polytopes: The Ehrhart Theory.- Reciprocity.- Face Numbers and the Dehn-Sommerville Relations in Ehrhartian Terms.- Magic Squares.- Finite Fourier Analysis.- Dedekind Sums.- The Decomposition of a Polytope into Its Cones.- Euler-MacLaurin Summation in Rd.- Solid Angles.- A Discrete Version of Green's Theorem Using Elliptic Functions.- Appendix A: Triangulations of Polytopes.- Appendix B: Hints for Selected Exercises.- References.- Index.- List of Symbols.-
£41.24
Springer An Introduction to Mathematical Cryptography
Book SynopsisPreface.- 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.Trade Review“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)“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)Table of ContentsPreface.- 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.
£59.84
Springer-Verlag New York Inc. Selected Papers I
Book SynopsisThis volume contains a collection of 30 of the 51 papers that David Mumford wrote in algebraic geometry. The volume divides Mumford's papers into three broad areas, each preceded by an easy summarizing the results and outlining their influence on further developmentsby David Gieseker, George Kempf, Herbert Lange and Eckart Viehweg.Further generations of researchers in this field, graduate students, mathematical physicists, and mathematical historians will profit a great deal from this collection of selected papers.Trade ReviewFrom the reviews: "The present volume contains thirty selected articles of D. Mumford on topics in algebraic geometry … . must be seen as a highly valuable and welcome collection for every researcher in the field. … Further generations of researchers in this field, graduate students, mathematical physicists, and mathematical historians will profit a great deal from this collection of selected papers … . this is why this volume is at least a must for any relevant library." (Werner Kleinert, Zentralblatt MATH, Vol. 1051) "Springer has recently released … a collection of 30 of the 51 papers that Mumford wrote in algebraic geometry. The papers are divided into three sections, each of which comes with commentary and annotation by Mumford … which give nice summaries and introductions to much of his work. … Reading these papers is exciting both for their mathematical content and to watch the evolution of the ideas … . a book that most algebraic geometers – and all libraries – will not want to do without." (Darren Glass, MathDL, January, 2005) "The Editors of this volume of Selected Papers, published by Springer Verlag, have made the choice of grouping his articles under three distinct headings … . This is a book is not going to get dust on a shelf: it will more likely spend its life on desks, read more often than a Graduate Text or a Monograph. Algebraic geometers of every generation will certainly welcome it." (E. Sernesi, Jahresbericht der Deutschen Mathematiker-Vereinigung, Vol. 107 (1), 2007) "This book contains a selection of the papers of David Mumford (born in 1937) in algebraic geometry. Even today, his papers are a rich source of information, of truly new ideas, and of inspiration. … His style is unique and fascinating. … Young algebraic geometers would do well to study these papers. They contain a wealth of ideas waiting to be developed." (Frans Oort, Nieuw Archief voor Wiskunde, Vol. 8 (3), 2007) "I am quiet happy to keep this volume on my self, and I will surely find many more seeds in it that grew so large that by now there origins are hard to recognize. The volume under review divides Mumford’s papers into three broad areas, each preceded by an easy summarizing the results and outlining their influence on further developments." (János Kollár, Bulletin of the American Math Society, Vol. 43 (1), 2005) Table of ContentsPart I. Geometric Invariant Theory and the Moduli of Curves * Commentary by David Gieseker * An elementary theorem in geometric invariant theory (1961) * Projective invariants of projective structures and applications (1962) * Periods of a moduli space of bundles on curves (with P. Newstead) (1968) * The structure of the moduli spaces of curves and abelian varieties (1970) * An analytic construction of degenerating curves over complete local rings (1972) * Pathologies IV (1975) * Stability of projective varieties (1977) * On the Kodaira dimension of the moduli space of curves (with J. Harris) (1982) * Towards an enumerative geometry of the moduli space of curves (1983) * Part II. Theta Functions and the Moduli of Abelian Varieties * Commentary by George Kempf and Herbert Lange * On the equations defining abelian varieties. I (1966)* On the equations defining abelian varieties. II (1967) * On the equations defining abelian varieties. III (1967) * Families of abelian varieties (1966) * A note on Shimura’s paper 'Discontinuous groups and abelian varieties' (1969) * Theta characteristics of an algebraic curve (1971) * An analytic construction of degenerating abelian varieties over complete rings (1972) * A rank 2 vector bundle of P^4 with 15,000 symmetries (with G. Horrocks) (1973) * Prym Varieties I (1974) * A new approach to compactifying locally symmetric varieties (1973) * Hirzebruch’s Proportionality Theorem in the Non-Compact Case (1977) * On the Kodaira dimension of the Siegel modular variety (1983) * Part III. The Classification of Surfaces and Other Varieties * Commentary by Eckart Viehweg * Enriques’ classification of surfaces in char p: I (1969) * Enriques’ classification of surfaces in char p: II (with E. Bombieri) (1979) * Enriques’ classification of surfaces in char p: III (with E. Bombieri) (1976) * Pathologies of modular algebraicsurfaces (1961) * Further pathologies in algebraic geometry (1962) * Pathologies III (1967) * Rational equivalence of 0-cycles on surfaces (1969) * Some elementary examples of unirational varieties which are not rational (with M. Artin) (1972) * An algebraic surface with K ample, (K^2) = 9, p_g = q = 0 (1979)
£49.49
Taylor & Francis Inc Introduction to Abelian Model Structures and
Book SynopsisIntroduction to Abelian Model Structures and Gorenstein Homological Dimensions provides a starting point to study the relationship between homological and homotopical algebra, a very active branch of mathematics. The book shows how to obtain new model structures in homological algebra by constructing a pair of compatible complete cotorsion pairs related to a specific homological dimension and then applying the Hovey Correspondence to generate an abelian model structure. The first part of the book introduces the definitions and notations of the universal constructions most often used in category theory. The next part presents a proof of the Eklof and Trlifaj theorem in Grothedieck categories and covers M. Hovey's work that connects the theories of cotorsion pairs and model categories. The final two parts study the relationship between model structures and classical and Gorenstein homological dimensions and explore special types of Grothendieck categorieTrade Review"This book is a worthy addition to the relative homological algebra literature. Graduate students can use it to introduce themselves in the topic and it is also a useful reference's book for specialists in the field of homological algebra." - Blas Torrecillas"The main goal of this book is to provide a multitude of model category structures for categories such as categories of chain complexes, categories of modules, and more specifically, Gorenstein categories (a Grothendieck category with extra properties). The author provides these model category structures by making use of the Hovey Correspondence, which allows one to associate a model category structure to a complete cotorsion pair in an abelian category […]This text is based on the thesis of the author and the majority of original results presented here are related to the model category structures coming from homological dimensions. The intended audience includes graduate students pursuing a degree in the field and researchers interested in the development of model category structures associated to Gorenstein homological dimensions. It is well written and is well suited for the target audience."- Bruce R. Corrigan-Salter, Mathematical Reviews, August 2017"The main goal of this book is to provide a multitude of model category structures for categories such as categories of chain complexes, categories of modules, and more specifically, Gorenstein categories (a Grothendieck category with extra properties). The author provides these model category structures by making use of the Hovey Correspondence, which allows one to associate a model category structure to a complete cotorsion pair in an abelian category […]This text is based on the thesis of the author and the majority of original results presented here are related to the model category structures coming from homological dimensions. The intended audience includes graduate students pursuing a degree in the field and researchers interested in the development of model category structures associated to Gorenstein homological dimensions. It is well written and is well suited for the target audience."- Bruce R. Corrigan-Salter, Mathematical Reviews, August 2017Table of ContentsCategorical and algebraic preliminaries. Interactions between homological algebra and homotopy theory. Classical homological dimensions and abelian model structures on chain complexes. Gorenstein homological dimensions and abelian model structures. Bibliography. Index.
£147.25
Taylor & Francis Inc An Invitation to the RogersRamanujan Identities
Book SynopsisThe Rogers--Ramanujan identities are a pair of infinite seriesinfinite product identities that were first discovered in 1894. Over the past several decades these identities, and identities of similar type, have found applications in number theory, combinatorics, Lie algebra and vertex operator algebra theory, physics (especially statistical mechanics), and computer science (especially algorithmic proof theory). Presented in a coherant and clear way, this will be the first book entirely devoted to the RogersRamanujan identities and will include related historical material that is unavailable elsewhere.Trade ReviewThis one-of-a-kind text, best suited for graduate level students and above, focuses exclusively on the Rogers-Ramanujan identities and their history. These two identities from number theory involve both infinite series and infinite products. The identities were independently discovered by Leonard James Rogers (1894 with proof), Srinivasa Ramanujan (before 1913 without proof), and Issai Schur (1917 with proof). The identities are relevant to the study of integer partitions, Lie algebras, statistical mechanics, computer science, and several other areas. Sills (Georgia Southern Univ.) begins with a review of partition theory and hypergeometric series. In the next two chapters, he moves on to prove the Rogers-Ramanujan identities and to explain their combinatorial aspects, as well as related identities and extensions. The final two chapters treat applications including continued fractions and knot theory. One appendix lists 236 related identities. A second appendix enhances the book's historical utility by providing transcriptions of letters between key researchers from 1943 to 1961. The book also includes more than 60 enlightening exercises.—D. P. Turner, Faulkner University, CHOICE Reviews"In recent years ¿-series have arisen in knot theory, and Sills discusses a few ¿-series that arise in the study of certain simple fundamental knots. While there have been systematic discussions of many of the topics mentioned above in various books, monographs, and survey articles, Sills’s book is the first comprehensive discussion of R-R type identities in all their forms, describing the state of the art. Since the subject is so vast, he does not provide proofs for most of the identities discussed, but he provides an interesting and illuminating historical context for each topic, gives good motivation, and describes the key ideas underlying the proofs. He also provides a substantial number of references that will lead both the studenTable of ContentsBackground and the Pre-History. The Golden Age and its Modern Legacy. Infinite Families...Everywhere! From Infinite to Finite. Motivated Proofs, Connections to Lie Algebras, and More Identities. But wait...there's more!
£99.75
Taylor & Francis Inc Beyond First Order Model Theory Volume I
Book SynopsisModel theory is one of the central branches of mathematical logic. The field has evolved rapidly in the last few decades. This book is an introduction to current trends in model theory, and contains a collection of articles authored by top researchers in the field. It is intended as a reference for students as well as senior researchers.Table of ContentsAbstract elementary classes. Generalized logics in set theory. Topological methods in abstract model theory. Randomizations of structures. First Order logics with dependent sorts. Applications of infinitary logics.
£175.75
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£9.42
Taylor & Francis Inc The Mathematics of Ciphers: Number Theory and RSA
Book SynopsisThis book is an introduction to the algorithmic aspects of number theory and its applications to cryptography, with special emphasis on the RSA cryptosys-tem. It covers many of the familiar topics of elementary number theory, all with an algorithmic twist. The text also includes many interesting historical notes.Table of ContentsPreface, Introduction, Chapter 1. Fundamental algorithms, Chapter 2. Unique factorization, Chapter 3. Prime numbers, Chapter 4. Modular arithmetic, Chapter 5. Induction and Fermat, Chapter 6. Pseudoprimes, Chapter 7. Systems of Congruences, Chapter 8. Groups, Chapter 9. Mersenne and Fermat, Chapter 10. Primality tests and primitive roots, Chapter 11. The RSA cryptosystem, Coda, Appendix. Roots and powers, Bibliography, Index of the main algorithms, Index of the main results, Index
£161.50
