Mathematics Books
Springer Verlag, Singapore Introduction to Stochastic Processes
Book SynopsisThis is an essential textbook for senior undergraduate and graduate students of statistics, stochastic processes, stochastic finance, and probability theory. It thoroughly discusses the concepts of stochastic processes, both Markov and non-Markov processes, as well as stochastic calculus.
£64.99
Elsevier Science An Introduction to Discrete Mathematics
Book Synopsis
£73.79
Elsevier Science Approximation Theory and Applications
Book Synopsis
£80.00
Cambridge University Press Error and Inference Recent Exchanges on
Book SynopsisBy means of a series of exchanges between the editors and leaders from the philosophy of science, statistics and economics, this volume offers a cumulative introduction connecting problems of traditional philosophy of science to problems of inference in statistical and empirical modelling practice.Trade Review'Mayo and Spanos's collection has injected new ideas into the study of scientific inference. This book offers a welcome bridge between current philosophy of science and scientific practice, providing the reader with new insights on important topics such as statistical inference, reliability, theory testing, causal modeling, and the relation between theory and experiment. The book will have a wide and enthusiastic readership among philosophers and scientists.' Cristina Bicchieri, University of Pennsylvania'Error and Inference straddles philosophy and practice; its lessons should be taken seriously in both. The editors suppose that venerable philosophical problems surrounding induction, scientific inference, and objectivity can be solved. The essays in the book give support to that perspective. They also show that pressing practical problems of scientific inference and testing gain marked benefit from careful attention to philosophers' accounts of what makes for evidence, rationality, and objectivity.' Nancy Cartwright, London School of Economics'The error-probabilistic approach developed by Deborah Mayo and Aris Spanos is the main alternative to Bayesianism in contemporary philosophy of science. In this superb volume Mayo and Spanos face their critics and show that error-probabilism is able to solve most theoretical puzzles of statistical testing. If some issue in the field of inductive inference is bothering you, you will probably find an answer in this book.' Francesco Guala, University of Milan'Mayo, an empirically minded philosopher, and Spanos, a philosophically minded economist, have succeeded beautifully in orchestrating a lively debate over methodological issues related to statistics and empirical testing that - unlike too much of the philosophy of science - speaks to the genuine issues that the practitioners of empirical sciences face daily. Their important volume deserves a broad readership.' Kevin Hoover, Duke University'Mayo and Spanos continue their campaign to bring confirmation theory face-to-face with the methods of scientists, and now extend it to the history of science and to general theories too. This book begins with a fine introduction to Mayo's error-statistical approach that makes the book a useful teaching tool. But then it carries forward the discussion of this approach with challenging papers from Glymour, Laudan, Achinstein, Worrall, and others.' Alexander Rosenberg, Duke University'This is a wonderful volume. It contains original and stimulating essays by leading figures from both philosophy and statistics on notions of evidence and testing; on how these interact with ideas about causation, explanation, and scientific rationality; and much more besides. The volume also features detailed and illuminating exchanges between the contributors. A must-read for anyone with an interest in these topics.' Jim Woodward, California Institute of TechnologyTable of ContentsPart I. Introduction and Background: 1. Philosophy of methodological practice Deborah Mayo; 2. Error statistical philosophy Deborah Mayo and Aris Spanos; Part II: 3. Severe testing, error statistics, and the growth of theoretical knowledge Deborah Mayo; Part III: 4. Can scientific theories be warranted? Alan Chalmers; 5. Can scientific theories be warranted with severity? Exchanges with Alan Chalmers Deborah Mayo; Part IV: 6. Critical rationalism, explanation and severe tests Alan Musgrave; 7. Towards progressive critical rationalism: exchanges with Alan Musgrave Deborah Mayo; Part V: 8. Error, tests and theory-confirmation John Worrall; 9. Has Worrall saved his theory (on ad hoc saves) in a non ad hoc manner? Exchanges with Worrall Deborah Mayo; Part VI: 10. Mill's sins, or Mayo's errors? Peter Achinstein; 11. Sins of the Bayesian epistemologist: exchanges with Achinstein Deborah Mayo; Part VII: 12. Theory testing in economics and the error statistical perspective Aris Spanos; Part VIII: 13. Frequentist statistics as a theory of inductive inference Deborah Mayo and David Cox; 14. Objectivity and conditionality in Frequentist inference David Cox and Deborah Mayo; 15. An error in the argument from WCP and S to the SLP Deborah Mayo; 16. On a new philosophy of Frequentist inference: exchanges with Cox and Mayo Aris Spanos; Part IX: 17. Explanation and truth Clark Glymour; 18. Explanation and testing: exchanges with Glymour Deborah Mayo; 19. Graphical causal modeling and error statistics: exchanges with Glymour Aris Spanos; Part X: 20. Legal epistemology: the anomaly of affirmative defenses Larry Laudan; 21. Error and the law: exchanges with Laudan Deborah Mayo.
£37.99
Kogan Page Ltd Neuro Design
Book SynopsisDarren Bridger is a consultant to designers and marketers, advising on using and analyzing data that tap into consumers' non-conscious thinking and motivations. He was one of the original pioneers of the Consumer Neuroscience industry, helping to pioneer two of the first companies in the field then joining the world's largest agency, Neurofocus (now part of the Nielsen company). He is currently Head of Insights at NeuroStrata. Trade Review"A super, easy-to-read book demystifying the world of neuro design, addressing the balance between the role of human creativity and that of neuroscience in modern design. If you think neuro design is about creating bland designs by deconstructing beauty, you need to read this book. It's not about that at all. Darren Bridger introduces all the major themes, key methods and tools underlying the science in engaging, manageable chunks. Any book that explains the allure of memes has to get five stars from me." * Jamie Croggon, Design Director, SharkNinja *"With solid science as the starting point, Darren Bridger provides an eminently practical guide to designing for your customer's brain. Neuro Design is packed with actionable strategies and techniques, and is a must-read for every marketer and designer." * Roger Dooley, author of Brainfluence *"A topic which should be of great importance to anyone in the business of retailing, advertising and marketing. Darren Bridger deals with complex topics in an engaging and practical manner, covering all aspects of the interplay between brain function and product design. Such an understanding is crucial for ensuring consumers stop and buy, rather than walking on by." * Dr David Lewis, Chairman of Mindlab International & Author of The Brain Sell *Table of Contents Section - 01: What is Neuro Design?; Section - 02: Neuroaesthetics; Section - 03: Processing Fluency; Section - 04: How First Impressions Work; Section - 05: Multisensory and Emotional Design; Section - 06: Visual Saliency Maps; Section - 07: Visual Persuasion and Behavioural Economics; Section - 08: Designing for Screens; Section - 09: Viral Designs; Section - 10: Designing Presentation Slides; Section - 11: Conducting Neuro Design Research; Section - 12: Conclusion;
£24.99
Birkhauser Boston Inc Riemannian Geometry
Book SynopsisRiemannian Geometry is an expanded edition of a highly acclaimed and successful textbook (originally published in Portuguese) for first-year graduate students in mathematics and physics.Trade Review"This is one of the best (if even not just the best) book for those who want to get a good, smooth and quick, but yet thorough introduction to modern Riemannian geometry." -Publicationes Mathematicae "This is a very nice introduction to global Riemannian geometry, which leads the reader quickly to the heart of the topic. Nevertheless, classical results are also discussed on many occasions, and almost 60 pages are devoted to exercises." -Newsletter of the EMS "In the reviewer's opinion, this is a superb book which makes learning a real pleasure." -Revue Romaine de Mathematiques Pures et Appliquees "This mainstream presentation of differential geometry serves well for a course on Riemannian geometry, and it is complemented by many annotated exercises." -Monatshefte F. MathematikTable of ContentsPreface to the 1st edition * Preface to the 2nd edition * Preface to the English edition * How to use this book * 0. Differentiable Manifolds * 1. Riemannian Metrics * 2. Affine Connections; Riemannian Connections * 3. Geodesics; Convex Neighborhoods * 4. Curvature * 5. Jacobi Fields * 6. Isometric Immersions * 7. Complete Manifolds; Hopf-Rinow and Hadamard Theorems * 8. Spaces of Constant Curvature * 9. Variations of Energy * 10. The Rauch Comparison Theorem * 11. The Morse Index Theorem * 12. The Fundamental Group of Manifolds of Negative Curvature * 13. The Sphere Theorem * References * Index
£33.99
Columbia University Press Perplexing Paradoxes
Book Synopsis
£27.00
Springer-Verlag New York Inc. Advanced Mathematical Methods for Scientists and
Book SynopsisI Fundamentals.- 1 Ordinary Differential Equations.- 2 Difference Equations.- II Local Analysis.- 3 Approximate Solution of Linear Differential Equations.- 4 Approximate Solution of Nonlinear Differential Equations.- 5 Approximate Solution of Difference Equations.- 6 Asymptotic Expansion of Integrals.- III Perturbation Methods.- 7 Perturbation Series.- 8 Summation of Series.- IV Global Analysis.- 9 Boundary Layer Theory.- 10 WKB Theory.- 11 Multiple-Scale Analysis.Trade Review"This book is a reprint of the original published by McGraw-Hill \ref [MR0538168 (80d:00030)]. The only changes are the addition of the Roman numeral I to the title and the provision of a subtitle, "Asymptotic methods and perturbation theory". This latter improvement is much needed, as the original title suggested that this was a teaching book for undergraduate scientists and engineers. It is not, but is an excellent introduction to asymptotic and perturbation methods for master's degree students or beginning research students. Certain parts of it could be used for a course in asymptotics for final year undergraduates in applied mathematics or mathematical physics. This is a book that has stood the test of time and I cannot but endorse the remarks of the original reviewer. It is written in a fresh and lively style and the many graphs and tables, comparing the results of exact and approximate methods, were in advance of its time. I have owned a copy of the original for over twenty years, using it on a regular basis, and, after the original had gone out of print, lending it to my research students. Springer-Verlag has done a great service to users of, and researchers in, asymptotics and perturbation theory by reprinting this classic." (A.D. Wood, Mathematical Reviews) Table of ContentsI Preface. 1 Ordinary Differential Equations. 2 Difference Equations. 3 Approximate Solution of Linear Differential Equations. 4 Approximate Solution of Nonlinear Equations. 5 Approximate Solution of Difference Equations. 6 Asymptotic Expansion of Integrals. 7 Perturbation Series. 8 Summation of Series. 9 Boundary Layer Theory. 10 WKB Theory. 11 Multiple Scales Analysis. Appendix, References, Index
£59.99
WW Norton & Co The Colossal Book of Mathematics Classic Puzzles
Book SynopsisNo amateur or math authority can be without this ultimate compendium from America's best-loved mathematical expert.Trade Review"For more than half a century, Martin Gardner has been the single brightest beacon defending rationality and good science. . . . He is also one of the most brilliant men and gracious writers I have known." -- Stephen Jay Gould
£31.99
Princeton University Press ThreeDimensional Geometry and Topology Volume 1
Book SynopsisHyperbolic geometry is the star. A strong effort has been made to convey not just denatured formal reasoning, but a living feeling for the subject. There are many figures, examples, and exercises of varying difficulty. This book develops some of the power of geometry in two and three dimensions, and the strong connection of geometry with topology.Trade ReviewWinner of the 2005 Book Prize, American Mathematical Society Winner of the 1997 for the Best Professional/Scholarly Book in Mathematics, Association of American Publishers "The present volume represents the culmination of nearly two decades of honoring his famous but difficult 1978 lecture notes. This beautifully produced, exquisitely organized volume now reads as easily as one could possibly hope given the profundity of the material. An instant classic."--ChoiceTable of ContentsPreface Reader's Advisory Ch. 1. What Is a Manifold? 3 Ch. 2. Hyperbolic Geometry and Its Friends 43 Ch. 3. Geometric Manifolds 109 Ch. 4. The Structure of Discrete Groups 209 Glossary 289 Bibliography 295 Index 301
£89.25
Princeton University Press Fashion Faith and Fantasy in the New Physics of
Book SynopsisNobel Prize–winning physicist Roger Penrose questions some of the most fashionable ideas in physics today, including string theoryWhat can fashionable ideas, blind faith, or pure fantasy possibly have to do with the scientific quest to understand the universe? Surely, theoretical physicists are immune to mere trends, dogmatic beliefs, or flights of fancy? In fact, acclaimed physicist and bestselling author Roger Penrose argues that researchers working at the extreme frontiers of physics are just as susceptible to these forces as anyone else. In this provocative book, he argues that fashion, faith, and fantasy, while sometimes productive and even essential in physics, may be leading today''s researchers astray in three of the field''s most important areas—string theory, quantum mechanics, and cosmology.Arguing that string theory has veered away from physical reality by positing six extra hidden dimensions, Penrose cautions that the fashionable nature of a theory can cloud our judgment of its plausibility. In the case of quantum mechanics, its stunning success in explaining the atomic universe has led to an uncritical faith that it must also apply to reasonably massive objects, and Penrose responds by suggesting possible changes in quantum theory. Turning to cosmology, he argues that most of the current fantastical ideas about the origins of the universe cannot be true, but that an even wilder reality may lie behind them. Finally, Penrose describes how fashion, faith, and fantasy have ironically also shaped his own work, from twistor theory, a possible alternative to string theory that is beginning to acquire a fashionable status, to 'conformal cyclic cosmology,' an idea so fantastic that it could be called 'conformal crazy cosmology.'The result is an important critique of some of the most significant developments in physics today from one of its most eminent figures.Trade ReviewWinner of the 2017 PROSE Award in Chemistry & Physics, Association of American Publishers "Physics has been at an awkward impasse for the past century. Two theories--quantum mechanics and general relativity--are widely believed to be true... But they contradict each other in basic ways--they cannot both be entirely true. InFashion, Faith, and Fantasy in the New Physics of the Universe... Roger Penrose, an elder statesman of physics, considers the problem. As intellectually offbeat as he is eminent... he ventures here some novel ways in which the two theories might be reconciled."--Wall Street Journal "Penrose gets to the heart of modern physics' problem with subjectivity in this insightful and provocative pop-sci title... [A] rewarding discussion of scientific stumbles in the search for truth."--Publishers Weekly "It is always inspiring to read Penrose's uncompromisingly independent perspec-tive on physics."--Richard Dawid, Nature "An extremely original, rich, and thoughtful survey of today's most fashionable attempts to decipher the cosmos on its smallest and largest scales."--Science "I can't recommend [Fashion, Faith, and Fantasy in the New Physics of the Universe] too highly to anyone with a serious interest in fundamental questions about physics."--Peter Woit, Not Even Wrong blog "In standing outside the fray and criticising the central dogmas of fundamental physics, Penrose is playing the role of Einstein, who forced quantum theorists to defend and hone their ideas, and Sir Fred Hoyle, who persistently challenged Big Bang theorists to sharpen their ideas. This is an extremely important role, and long may Penrose fulfill it."--Times Higher Education "[A] beautifully produced, beautifully laid-out and diagrammed book... There is possibly no better or more original expositor than Penrose to draw from. If modern physics theory is of interest to you, you certainly won't want to ignore this book."--Math Frolic "The book is replete with phenomenal visual representations of the physics under discussion, a reminder of Penrose's ability to see and describe physics in a unique way... Ultimately, what is most valuable about the book is the excellent example he offers in how to ask questions."--Chanda Prescod-Weinstein, Physics World "Something is rotten in the state of physics... The eminent mathematician and physicist Roger Penrose identifies several possible sources of the rot... He is not one to be intimidated by an overwhelming majority, no matter how illustrious and vocal it is. He sets out his objections politely and with exemplary patience towards the keepers of physics orthodoxy... Time will tell whether any of his judgments are correct. In the meantime, his critics would do well to remember George Bernard Shaw's warning: 'The minority is sometimes right; the majority is always wrong.'"--Graham Farmelo, Guardian "A valuable insight into what one of the most prominent theoretical physicists of recent times makes of reality's relationship to ideas in quantum theory, standard cosmology, and theories that pretend to replace them."--Richard Webb, New Scientist "The strength of this book is how the reader can appreciate science as a human undertaking."--Choice "The most important thing is not exactly what he writes about string theory, cosmology and quantum mechanics in his latest book ... but that a book so wide and deep in its erudition could be written at all. If his successors cannot do the same, science will be all the poorer."--Philip Ball, ProspectTable of ContentsAcknowledgements ix Preface xi Are fashion, faith, or fantasy relevant to fundamental science? xi 1 Fashion 1 1.1 Mathematical elegance as a driving force 1 1.2 Some fashionable physics of the past 10 1.3 Particle-physics background to string theory 17 1.4 The superposition principle in QFT 20 1.5 The power of Feynman diagrams 25 1.6 The original key ideas of string theory 32 1.7 Time in Einstein's general relativity 42 1.8 Weyl's gauge theory of electromagnetism 52 1.9 Functional freedom in Kaluza-Klein and string models 59 1.10 Quantum obstructions to functional freedom? 69 1.11 Classical instability of higher-dimensional string theory 77 1.12 The fashionable status of string theory 82 1.13 M-theory 90 1.14 Supersymmetry 95 1.15 AdS/CFT 104 1.16 Brane-worlds and the landscape 117 2 Faith 121 2.1 The quantum revelation 121 2.2 Max Planck's E = hnu 126 2.3 The wave-particle paradox 133 2.4 Quantum and classical levels: C, U, and R 138 2.5 Wave function of a point-like particle 145 2.6 Wave function of a photon 153 2.7 Quantum linearity 158 2.8 Quantum measurement 164 2.9 The geometry of quantum spin 174 2.10 Quantum entanglement and EPR effects 182 2.11 Quantum functional freedom 188 2.12 Quantum reality 198 2.13 Objective quantum state reduction: a limit to the quantum faith? 204 3 Fantasy 216 3.1 The Big Bang and FLRW cosmologies 216 3.2 Black holes and local irregularities 230 3.3 The second law of thermodynamics 241 3.4 The Big Bang paradox 250 3.5 Horizons, comoving volumes, and conformal diagrams 258 3.6 The phenomenal precision in the Big Bang 270 3.7 Cosmological entropy? 275 3.8 Vacuum energy 285 3.9 Inflationary cosmology 294 3.10 The anthropic principle 310 3.11 Some more fantastical cosmologies 323 4 A New Physics for the Universe? 334 4.1 Twistor theory: an alternative to strings? 334 4.2 Whither quantum foundations? 353 4.3 Conformal crazy cosmology? 371 4.4 A personal coda 391 Appendix A Mathematical Appendix 397 A.1 Iterated exponents 397 A.2 Functional freedom of fields 401 A.3 Vector spaces 407 A.4 Vector bases, coordinates, and duals 413 A.5 Mathematics of manifolds 417 A.6 Manifolds in physics 425 A.7 Bundles 431 A.8 Functional freedom via bundles 439 A.9 Complex numbers 445 A.10 Complex geometry 448 A.11 Harmonic analysis 458 References 469 Index 491
£22.50
Princeton University Press Quadrangular Algebras
Book SynopsisBased on their relationship to exceptional algebraic groups, quadrangular algebras belong in a series together with alternative and Jordan division algebras, this book introduces a class of non-associative algebras related to exceptional algebraic groups and their associated buildings.Trade Review"[T]here have been many results on finite generalized quadrangles that fill a well-needed gap in the mathematical literature, but this monograph is much deeper and will enable progress to be made in a difficult technical area where some exotic forms of algebraic groups have hitherto been little understood."--Robert L. Devaney, Bulletin of the AMSTable of ContentsPreface vii Chapter 1. Basic Definitions 1 Chapter 2. Quadratic Forms 11 Chapter 3. Quadrangular Algebras 21 Chapter 4. Proper Quadrangular Algebras 29 Chapter 5. Special Quadrangular Algebras 37 Chapter 6. Regular Quadrangular Algebras 45 Chapter 7. Defective Quadrangular Algebras 59 Chapter 8. Isotopes 77 Ch apter 9. Improp er Quadrangu lar Algebras 83 Chapter 10. Existence 95 Chapter 11. Moufang Quadrangles 109 Chapter 12. The Structure Group 125 Bibliography 133 Index 134
£59.50
Princeton University Press Convolution and Equidistribution
Book SynopsisExplores an important aspect of number theory - the theory of exponential sums over finite fields and their Mellin transforms - from a categorical point of view. This book presents fundamentally important results and a plethora of examples, opening up new directions in the subject.Trade Review"The book is written in a clear and enlightening style. The author provides the reader with many examples that are developed throughout a dozen chapters. These examples help understand and clarify the depth and the variety of applications of the beautiful main equidistribution statement that relies on rather complicated and subtle algebrageometric arguments."--Florent Jouve, Mathematical Reviews Clippings "The book provides the reader with much material around the question of the equidistribution of the angles if one fixes f and varies over the multiplicative character x. More than one hundred pages of examples provide the reader with great insight in the different applications of the main theorem. This turns the book into a very good basis for research in this area."--Manfred G. Madritsch, Zentralblatt MATH "Once a certain basic understanding is reached, this book, like the others written by N. Katz, reveals itself to be very precisely and sharply written, and to be full of riches. And finally, this theory shows spectacularly how some of the most abstract ideas of algebra and algebraic geometry may be essential to solving extremely concrete problems."--Emmanuel Kowalski, Bulletin of the American Mathematical SocietyTable of Contents*FrontMatter, pg. i*Contents, pg. vi*Introduction, pg. 1*CHAPTER 1. Overview, pg. 7*CHAPTER 2. Convolution of Perverse Sheaves, pg. 19*CHAPTER 3. Fibre Functors, pg. 21*CHAPTER 4. The Situation over a Finite Field, pg. 25*CHAPTER 5. Frobenius Conjugacy Classes, pg. 31*CHAPTER 6. Group-Theoretic Facts about Ggeom and Garith, pg. 33*CHAPTER 7. The Main Theorem, pg. 39*CHAPTER 8. Isogenies, Connectedness, and Lie-Irreducibility, pg. 45*CHAPTER 9. Autodualities and Signs, pg. 49*CHAPTER 10. A First Construction of Autodual Objects, pg. 53*CHAPTER 11. A Second Construction of Autodual Objects, pg. 55*CHAPTER 12. The Previous Construction in the Nonsplit Case, pg. 61*CHAPTER 13. Results of Goursat-Kolchin-Ribet Type, pg. 63*CHAPTER 14. The Case of SL(2); the Examples of Evans and Rudnick, pg. 67*CHAPTER 15. Further SL(2) Examples, Based on the Legendre Family, pg. 73*CHAPTER 16. Frobenius Tori and Weights; Getting Elements of Garith, pg. 77*CHAPTER 17. GL(n) Examples, pg. 81*CHAPTER 18. Symplectic Examples, pg. 89*CHAPTER 19. Orthogonal Examples, Especially SO(n) Examples, pg. 103*CHAPTER 20. GL(n) x GL(n) x ... x GL(n) Examples, pg. 113*CHAPTER 21. SL(n) Examples, for n an Odd Prime, pg. 125*CHAPTER 22. SL(n) Examples with Slightly Composite n, pg. 135*CHAPTER 23. Other SL(n) Examples, pg. 141*CHAPTER 24. An O(2n) Example, pg. 145*CHAPTER 25. G2 Examples: the Overall Strategy, pg. 147*CHAPTER 26. G2 Examples: Construction in Characteristic Two, pg. 155*CHAPTER 27. G2 Examples: Construction in Odd Characteristic, pg. 163*CHAPTER 28. The Situation over Z: Results, pg. 173*CHAPTER 29. The Situation over Z: Questions, pg. 181*CHAPTER 30. Appendix: Deligne's Fibre Functor, pg. 187*Bibliography, pg. 193*Index, pg. 197
£74.80
Princeton University Press The Seduction of Curves
Book SynopsisA lavishly illustrated book that explores the language of curves that spans the human body, science, engineering, and artCurves are seductive. These smooth, organic lines and surfaces-like those of the human body-appeal to us in an instinctive, visceral way that straight lines or the perfect shapes of classical geometry never could. In this large-fTrade Review"One of Choice Reviews' Outstanding Academic Titles of 2018""I have never encountered anything quite like [The Seduction of Curves], which I view as genuinely sui generis. . . . The (excellent) prose descriptions are accompanied by lots of illustrations, both photographs and drawings, quite a few of which are in color. . . . An unusual and eclectic book, and one that taught me a lot of things that I did not know before."---Mark Hunacek, MAA Reviews"To illustrate this little-known branch of mathematics, [Allan McRobie] draws on the art of David Hockney, Henry Moore and Salvador Dalí, as well as Helena Weightman's superb photographs of mountains, mushrooms, reflections on water and naked bodies."---Matthew Reisz, Times Higher Education"Stunning. . . . The balance is such that it should appeal both to art lovers and those with a real interest in the mathematical basis."---Brian Clegg, Popular Science"Marvelous."---Adhemar Bultheel, European Mathematical Society"Can you find your own butterflies, swallowtails and wigwams? They are right there on your body: the geometrical figures that appear when smoothly curved surfaces are viewed from the right angle. Structural engineer Allan McRobie's The Seduction of Curves is your guide to these most intimate of mathematical objects."---Philip Ball, New Scientist"A delightful journey beyond disciplines. . . . The book intends to lead readers to see the world differently and I believe that in many cases it will, linking subtle mathematical ideas to the world they are surrounded by."---Edmund O. Harriss, MathSciNet"This book is a bold attempt at evoking multiple feelings towards curves. Allan McRobie deserves praise for sensually drawing parallels between the natural and constructed worlds."---Sudhirendar Sharma, Current Science"Both immediate and analytical, beautiful and informative, The Seduction of Curves is a successful hybrid of art book, representation of descriptive geometry, and explanation of mathematical concepts . . . . a book that entertains and teaches, pleases and challenges in equal measure."---Hans J. Rindisbach, European Legacy"Remarkable. . . . Successful . . . due to the erudition of the author plus the quality of the production both in the illustrations used and in the general elegance of the book itself. It would grace the grandest of coffee tables and provide the basis for interesting debates."---Phil Dyke, Leonardo ReviewsTable of Contents1 The Alphabet of Beautiful Curves 12 The Fold 53 The Cusp 144 The Swallowtail 225 The Butterfly 316 The Wigwam 357 Lips, Beaks, Gull, Goose 378 The Persistence of Cusps 439 Moire and Dupin 4710 The Umbilics 6111 Catastrophe Optics 6712 The Rainbow 7313 Gravitational Lenses 7714 Stability 8515 Morphogenesis 8816 Gabo 9417 The Pregnance of Curves 11718 Thom 12519 Dali 135Notes 147Bibliography 151Image Credits 153Index 157
£27.00
Princeton University Press The Doctrine of Triangles
Book SynopsisTrade Review"Glen van Brummelen has prepared a highly recommended, accessible and definitive history of the subject that will serve as a resource for scholars for decades to come."---Daniel Otero, MAA Reviews"The Doctrine of Triangles is an informative and valuable reference work."---Wallace A Ferguson, Institute of Mathematics and its Applications"A guided tour through the museum of mathematics. . . . [The Doctrine of Triangles] takes the history of trigonometry, which is a formidable subject in its scope and size, and transforms it into something readable."---Daniel Mansfield, The Mathematical Intelligencer"Very easy to read, and there are lots of helpful diagrams, especially for the spherical trigonometry . . . [The Doctrine of Triangles] is deeply enriched by extracts from contemporary texts, given first in fairly literal English translations, often accompanied by the original diagrams, and then explained in modern terms. So mathematical readers (and, I hope, their students) can experience a little of what trigonometry was actually like at each stage in its history."---John Hannah, Aestimatio
£29.75
Princeton University Press Leonhard Euler
Book SynopsisTrade Review"One of Choice's Outstanding Academic Titles for 2016"
£31.50
Princeton University Press Stochastic Thermodynamics
Book Synopsis
£999.99
Princeton University Press Curves for the Mathematically Curious
Book SynopsisTrade Review"This is not your father’s – or grandfather’s – standard collection of conic sections."---Jim Stein, New Books Network"Undoubtedly [this book], written in the same entertaining unmistakable style of the author and containing a lot of information - mathematical, historical and general - will attract, as the previous ones, a large audience."---S. Cobzas, Studia Mathematica"What a beautiful book!"---Jonathan Shock, Mathemafrica.org"A wonderful addition to libraries where the mathematically curious find their reading." * Choice *"Havil’s narrative for each curve is a cornucopia of fun facts and rigorous explanation."---Andrew J. Simoson, Mathematical Intelligencer"Overall, the book was a delight to read. The writing is witty and entertaining, the history is at times peculiar and surprising, and the mathematics is rich and engaging. It would make a fine addition to a classroom bookcase or home coffee table, but while there are plenty of elegant diagrams and intriguing stories to give every curious reader the chance to glimpse mathematical beauty, only those with the ability to dig beneath the surface will understand just how much beauty this book has to offer."---Samuel Hewitt, Mathematical Gazette
£18.04
Princeton University Press The Enjoyment of Math
Book Synopsis
£15.29
Johns Hopkins University Press Deep Down Things The Breathtaking Beauty of
Book SynopsisIntroducing readers to the world of particle physics, Deep Down Things opens new realms within which are many clues to unraveling the mysteries of the universe.Trade ReviewA fascinating journey into the bizarre, subatomic world of particle physics. PhysOrg.com 2004 Quantum field theory, group theory, Lie algebras, internal symmetry spaces and gauge theory. [Schumm] does a remarkably good job of explaining all this, with a style that is mercifully plain. -- Peter de Groot New Scientist 2005 Explores the world of particle physics in terms laymen can understand. Santa Cruz Sentinel 2005 I expect that any physics undergraduate, bewildered by textbooks and lectures, would find this a delight. -- Stephen Battersby New Scientist 2005 One of several recently published books attempting to provide for interested nonphysicists a relatively nonmathematical account of what has come to be called the standard model of particle physics... Schumm's treatment is perhaps more detailed. Choice 2005 This is definitely a book for your Christmas list, and if it doesn't excite your mathematics colleagues too, they'll miss a treat. -- Rick Marshall School Science Review 2006 This book is beautifully written and is a didactic masterpiece. -- David Watts Science and Christian Belief 2006Table of ContentsPreface1. Introduction2. The True Movers & Shakers: The Forces of Nature3. The Great Reawakening: The Modern Physics Revolution4. The Marriage of Relativity & Quantum Theory: Relativistic Quantum Field Theory5. Patterns in Nature: The Fundamental Building Blocks6. Mathematical Patterns: Lie Groups7. The World Within: Internal Symmetries8. Physics by Pure Thought: Gauge Theory9. The Current Paradigm: Hidden Symmetry, the Standard Model & the Higgs Boson10. Into the Unknown: What Lies AheadAppendix: Exponential NotationNotesIndex
£29.92
National Council of Teachers of Mathematics,U.S. On the Money Math Activites to Build Financial
Book SynopsisProvides elementary teachers with the opportunity to integrate lessons into their classroom that use mathematics to model financial literacy concepts and skills, while also using financial concepts and skills to appropriately model mathematics.
£30.56
Springer-Verlag New York Inc. Geometry
Book SynopsisThis text is the fifth and final in the series of educational books written by Israel Gelfand with his colleagues for high school students. These books cover the basics of mathematics in a clear and simple format - the style Gelfand was known for internationally. Gelfand prepared these materials so as to be suitable for independent studies, thus allowing students to learn and practice the material at their own pace without a class. Geometry takes a different approach to presenting basic geometry for high-school students and others new to the subject. Rather than following the traditional axiomatic method that emphasizes formulae and logical deduction, it focuses on geometric constructions. Illustrations and problems are abundant throughout, and readers are encouraged to draw figures and move them in the plane, allowing them to develop and enhance their geometrical vision, imagination, and creativity. Chapters are structured so that only certaiTrade Review“This book is intended to engage the reader visually, tactilely, and kinesthetically. … It has a good set of material to enliven more traditional geometry instruction. … There are problems and exercises throughout. The exercises are accompanied by solutions.” (MAA Reviews, October 10, 2020) Table of ContentsPoints and Lines: A Look at Projective Geometry.- Parallel Lines: A Look at Affine Geometry.- Area: A Look at Symplectic Geometry.- Circles: A Look at Euclidean Geometry.
£31.49
Springer-Verlag New York Inc. An Introduction to Statistical Learning
Book SynopsisAn Introduction to Statistical Learning provides an accessible overview of the field of statistical learning, an essential toolset for making sense of the vast and complex data sets that have emerged in fields ranging from biology to finance to marketing to astrophysics in the past twenty years. This book presents some of the most important modeling and prediction techniques, along with relevant applications. Topics include linear regression, classification, resampling methods, shrinkage approaches, tree-based methods, support vector machines, clustering, deep learning, survival analysis, multiple testing, and more. Color graphics and real-world examples are used to illustrate the methods presented. Since the goal of this textbook is to facilitate the use of these statistical learning techniques by practitioners in science, industry, and other fields, each chapter contains a tutorial on implementing the analyses and methods presented in R, an extremely popular open source statistical sTable of ContentsPreface.- 1 Introduction.- 2 Statistical Learning.- 3 Linear Regression.- 4 Classification.- 5 Resampling Methods.- 6 Linear Model Selection and Regularization.- 7 Moving Beyond Linearity.- 8 Tree-Based Methods.- 9 Support Vector Machines.- 10 Deep Learning.- 11 Survival Analysis and Censored Data.- 12 Unsupervised Learning.- 13 Multiple Testing.- Index.
£59.99
Johns Hopkins University Press Mathematical Expeditions
Book SynopsisAlong the way, he tells us what various cultures knew about math and how they came to learn it, providing instructors with a wonderful way to incorporate multicultural mathematics into the middle school, high school, and college classroom.Trade ReviewSwetz has collected word problems, or story problems, used to teach mathematics around the world and throughout history, so mathematics teachers in middle and secondary schools can use them today. University students of mathematics and its history might also find them useful as well as entertaining. Reference and Research Book News Mathematical Expeditions is a wonderful resource for any teacher who would like to use old problems in a course to help students understand the context of mathematical ideas. -- Victor J. Katz Mathematical Reviews The book is well thought-out and is recommended to readers interested in the history of mathematics. -- E. Keith Lloyd London Mathematical Society Newsletter One of my graduate students, who is majoring in mathematics, was excited when I showed her a sample of problems in the book. A month later, she asked whether I had finished my review-she wanted to borrow the book! -- Winifred A. Mallam Mathematics TeacherTable of ContentsPreface1. Word Problems: Footprints from the History of Mathematics2. Problems, Problems: A Resource for Teaching3. Ancient Babylonia (2002–1000 BCE)4. Ancient Egypt5. Ancient Greece6. Ancient China7. India8. Islam9. Medieval Europe10. Renaissance Europe11. Japanese Temple Problems12. The Ladies Diary (1704–1841)13. Nineteenth-Century Victorian Problems14. Eighteenth- and Nineteenth-Century American Problems15. Problems from the Farmer's Almanac16. Nineteenth-Century Calculus Problems17. Some Sample Problem Solution Methods18. Where to from Here? Where Do You Want to Go?AcknowledgmentsAnswers to Numbered ProblemsGlossary of Strange and Exotic Terms: Measurements, Monetary Units, and Culturally Relevant WordsBibliographyIndex
£26.10
Springer-Verlag New York Inc. Monte Carlo Methods in Financial Engineering
Book SynopsisFrom the reviews: Paul Glasserman has written an astonishingly good book that bridges financial engineering and the Monte Carlo method. The book will appeal to graduate students, researchers, and most of all, practicing financial engineers [...] So often, financial engineering texts are very theoretical. This book is not. --Glyn Holton, Contingency AnalysisTrade Review"Paul Glasserman has written an astonishingly good book that bridges financial engineering and the Monte Carlo method. The book will appeal to graduate students, researchers, and most of all, practicing financial engineers … You will want to have prior knowledge of both the Monte Carlo method and financial engineering. If you do, you will find the book to be a goldmine … So often, financial engineering texts are very theoretical. This book is not. The Monte Carlo method serves as a unifying theme that motivates practical discussions of how to implement real models on real trading floors. You will learn plenty of financial engineering amidst these pages. The writing is a pleasure to read. Topics are timely and relevant. Glasserman's is a must-have book for financial engineers." -Glyn Holton, Contingency AnalysisMathematical Reviews, 2004: "... this book is very comprehensive, up-to-date and useful tool for those who are interested in implementing Monte Carlo methods in a financial context." From the reviews: "This recent book is a valuable addition to the references devoted to Monte Carlo methods. … the author succeeded in choosing the most actual topics in financial engineering and in presenting them in an appropriate way by keeping a suitable balance between mathematical rigour and an audience friendly language. … To help the reader, three appendices provide basic results on convergence concepts … . A large bibliography of 358 entries accompanies this text. In short, the reader will find this book extremely lucid and useful." (Radu Theodorescu, Zentralblatt MATH, Vol. 1038 (13), 2004) "To keep it short, let me summarize the recension in one phrase: Paul Glausserman’s book is a ‘strong buy’ for everybody in the financial community. … one gets 596 pages full of valuable information on all aspects of Monte Carlo simulation. … Altogether, I can encourage everyone interested in Monte Carlo methods in finance to read the book. It is very well written … comes with a carefully selected bibliography (358 references) and a helpful index, thus making it really worth the buy." (Ralf Werner, OR – Spectrum Operations Research Spectrum, Issue 27, 2005) "Glasserman’s new book is a remarkable presentation of the current state of the art of Monte Carlo Methods in Financial Engineering. … lot of material which is sometimes hard to access has been composed into one volume. … a high quality monograph which is both suitable as a reference for practitioners and researchers as well as a textbook … . The list of references is by itself a valuable aspect. The refreshing writing style of the author is tailor-made for the thirsty reader … ." (Uwe Wystup, www.mathfinance.de, November, 2003) "Paul Glasserman has written an astonishingly good book that bridges financial engineering and the Monte Carlo method. The book will appeal to graduate students, researchers, and most of all, practicing financial engineers. It is an advanced book. … The presentation is masterful. … You will learn plenty of financial engineering amidst the pages. The writing is a pleasure to read. Topics are timely and relevant. Glasserman’s is a must-have book for financial engineers." (www.riskbook.com, Dezember, 2003) "This book is divided into three parts. … the aim of the author is … to give a precise description of the different techniques in order to facilitate their implementation. In my opinion, this book is a very comprehensive, up-to-date and useful tool for those who are interested in implementing Monte Carlo methods in a financial context." (Benjamin Jourdain, Mathematical Reviews, 2004g) "The publication of this book is an important event in computational finance. For many years, Monte Carlo methods have been successfully applied to solve diverse problems in financial mathematics. By publishing this book the author deserves much credit for a very good attempt to lift such applications to a new level. … the book may well become a major reference in the field of applications of Monte Carlo methods in financial engineering. This is because the book is well structured and well written … ." (A Zhigljavsky, Journal of the Operational Research Society, Vol. 57, 2006)Table of ContentsFoundations.- Generating Random Numbers and Random Variables.- Generating Sample Paths.- Variance Reduction Techniques.- Quasi-Monte Carlo Methods.- Discretization Methods.- Estimating Sensitivities.- Pricing American Options.- Applications in Risk Management.- Appendices
£44.99
Springer-Verlag New York Inc. Introduction to Topological Manifolds
Book SynopsisThis book is an introduction to manifolds at the beginning graduate level, and accessible to any student who has completed a solid undergraduate degree in mathematics. It contains the essential topological ideas that are needed for the further study of manifolds, particularly in the context of differential geometry, algebraic topology, and related fields.Although this second edition has the same basic structure as the first edition, it has been extensively revised and clarified; not a single page has been left untouched. The major changes include a new introduction to CW complexes (replacing most of the material on simplicial complexes in Chapter 5); expanded treatments of manifolds with boundary, local compactness, group actions, and proper maps; and a new section on paracompactness.Trade ReviewFrom the reviews of the second edition:“An excellent introduction to both point-set and algebraic topology at the early-graduate level, using manifolds as a primary source of examples and motivation. … The author has … fulfilled his objective of integrating a study of manifolds into an introductory course in general and algebraic topology. This text is well-organized and clearly written, with a good blend of motivational discussion and mathematical rigor. … Any student who has gone through this book should be well-prepared to pursue the study of differential geometry … .” (Mark Hunacek, The Mathematical Association of America, March, 2011)“This book is designed for first year graduate students as an introduction to the topology of manifolds. … The book can be read with advantage by any graduate student with a good undergraduate background, and indeed by many upper class undergraduates. It can be used for self study or as a text book for a fine geometrically flavored introduction to manifolds. One which provides excellent motivation for studying the machinery needed for more advanced work.” (Jonathan Hodgson, Zentralblatt MATH, Vol. 1209, 2011)Table of ContentsPreface.- 1 Introduction.- 2 Topological Spaces.- 3 New Spaces from Old.- 4 Connectedness and Compactness.- 5 Cell Complexes.- 6 Compact Surfaces.- 7 Homotopy and the Fundamental Group.- 8 The Circle.- 9 Some Group Theory.- 10 The Seifert-Van Kampen Theorem.- 11 Covering Maps.- 12 Group Actions and Covering Maps.- 13 Homology.- Appendix A: Review of Set Theory.- Appendix B: Review of Metric Spaces.- Appendix C: Review of Group Theory.- References.- Notation Index.- Subject Index.
£53.99
American Mathematical Society Knots Molecules and the Universe An Introduction
Book SynopsisProvides an elementary introduction to geometric topology and its applications to chemistry, molecular biology, and cosmology. It does not assume any mathematical or scientific background, sophistication, or even motivation to study mathematics. It is meant to be fun and engaging while drawing students in to learn about fundamental topological and geometric ideas.Trade Review[T]his is a wonderful introduction to geometry and topology and their applications to the sciences. The book contains a unique collection of topics that might entice young readers to continue their academic careers by learning more about the world of mathematics." - Claus Ernst, Zentralblatt MATHTable of Contents Universes: An introduction to the shape of the universe Visualizing four dimensions Geometry and topology of different universes Orientability Flat manifolds Connected sums of spaces Products of spaces Geometries of surfaces Knots: Introduction to knot theory Invariants of knots and links Knot polynomials Molecules: Mirror image symmetry from different viewpoints Techniques to prove topological chirality The topology and geometry of DNA The topology of proteins Index
£62.10
University of Toronto Press The Flawed Genius of William Playfair
Book SynopsisThis book shares the life story of William Playfair, the father of statistical graphics, who experienced extreme ups and downs in his various careers, including as a statistician, economist, and fraudster.Table of ContentsPreface: Playfair Is Introduced 1. Playfair Is Sent to Newgate Prison 2. Playfair Goes to Birmingham to Work for Boulton and Watt 3. Playfair Goes to London to Set Up His Own Business 4. Playfair Evolves into a Writer by Profession 5. Playfair Expresses His Early Political Views 6. Playfair Makes His Mark on Statistical Graphics 7. Playfair Goes to Paris 8. Playfair Tries to Take Advantage of the French Revolution 9. Playfair Escapes from France and Returns to England 10. Playfair Becomes an Avid Anti-Jacobin Propagandist 11. Playfair Gets Involved with Forged Assignats 12. Playfair Starts a Bank and Goes Bankrupt 13. Playfair Ekes Out a Living as a Bankrupt 14. Playfair Has a Good Year during 1805 with Hints of Ending Badly 15. Playfair Has Serious Legal and Other Problems 16. Playfair Dabbles Deeply into Family History and Political Biography 17. Playfair Continues Writing and Tries a Few More Scams to Get to Paris 18. Playfair Returns to Paris 19. Playfair Spends His Last Few Years in England in Poverty Afterword: Playfair Avoids a Shakespearean Epitaph Appendix: Assignat Forging by French Emigres in England Notes Index
£38.70
O'Reilly Media Tidy Modeling with R
Book SynopsisGet going with tidymodels, a collection of R packages for modeling and machine learning. Whether you're just starting out or have years of experience with modeling, this practical introduction shows data analysts, business analysts, and data scientists how the tidymodels framework offers a consistent, flexible approach for your work.
£39.74
Templeton Foundation Press,U.S. Mathematics and Religion: Our Languages of Sign
Book SynopsisMathematics and Religion: Our Languages of Sign and Symbol is the sixth title published in the Templeton Science and Religion Series, in which scientists from a wide range of fields distill their experience and knowledge into brief tours of their respective specialties. In this volume, Javier Leach, a mathematician and Jesuit priest, leads a fascinating study of the historical development of mathematical language and its influence on the evolution of metaphysical and theological languages.Leach traces three historical moments of change in this evolution: the introduction of the deductive method in Greece, the use of mathematics as a language of science in modern times, and the formalization of mathematical languages in the nineteenth and twentieth centuries. As he unfolds this fascinating history, Leach notes the striking differences and interrelations between the two languages of science and religion. Until now there has been little reflection on these similarities and differences, or about how both languages can complement and enrich each other.Table of ContentsPreface viiChapter 1: Mathematics and Natural Sciences 3Chapter 2: Metaphysical Language 16Chapter 3: Origins of Mathematics 35Chapter 4: Euclid and Beyond 44Chapter 5: Dawn of Science 55Chapter 6: Mathematics Formalized 67Chapter 7: Propositional Logic 93Chapter 8: Language and Meaning 106Chapter 9: Science, Language, and Religion 120Appendix 1: Syntax of Propositional Logic 133Appendix 2: Semantics of Propositional Logic 136Appendix 3: Syntax of First-Order Logic 139Appendix 4: Semantics of First-Order Logic 143Appendix 5: Numerical Systems:Their Role in First-Order Logic 147
£17.99
Society for Industrial & Applied Mathematics,U.S. Nonlocal Modeling, Analysis, and Computation
Book SynopsisStudies of complexity, singularity, and anomaly using nonlocal continuum models are steadily gaining popularity. This monograph provides an introduction to basic analytical, computational, and modeling issues and to some of the latest developments in these areas.Nonlocal Modeling, Analysis, and Computation includes motivational examples of nonlocal models, basic building blocks of nonlocal vector calculus, elements of theory for well-posedness and nonlocal spaces, connections to and coupling with local models, convergence and compatibility of numerical approximations, and various applications, such as nonlocal dynamics of anomalous diffusion and nonlocal peridynamic models of elasticity and fracture mechanics.A particular focus is on nonlocal systems with a finite range of interaction to illustrate their connection to traditional local systems represented by partial differential equations and fractional PDEs. These models are designed to represent nonlocal interactions explicitly and to remain valid for complex systems involving possible singular solutions and they have the potential to be alternatives to as well as bridges to existing local continuum and discrete models.The author discusses ongoing studies of nonlocal models to encourage the discovery of new mathematical theory for nonlocal continuum models and offer new perspectives on existing discrete models and local continuum models and the connections between them.
£51.85
National Council of Teachers of Mathematics,U.S. The Living Tree of Mathematics: Mathematics of
Book SynopsisThis book explores the key concepts of middle school mathematics such as fractions, negative numbers, arithmetical operations, variables, the coordinate plane, and measurement formulas. It also highlights the rarely examined notions of the tree of mathematics and language of mathematics. The practical content knowledge is scaffolded using the history of the concepts in mathematics of various cultures around the world. The rich material for culturally responsive pedagogy is provided by relevant historical vignettes and alternative mathematical approaches.
£35.10
Springer Nature Switzerland AG Notes on the Stationary p-Laplace Equation
Book SynopsisThis book in the BCAM SpringerBriefs series is a treatise on the p-Laplace equation. It is based on lectures by the author that were originally delivered at the Summer School in Jyväskylä, Finland, in August 2005 and have since been updated and extended to cover various new topics, including viscosity solutions and asymptotic mean values. The p-Laplace equation is a far-reaching generalization of the ordinary Laplace equation, but it is non-linear and degenerate (p>2) or singular (p<2). Thus it requires advanced methods. Many fascinating properties of the Laplace equation are, in some modified version, extended to the p-Laplace equation. Nowadays the theory is almost complete, although some challenging problems remain open.Trade Review“The book will provide the reader with an up-to-date overview on the p-Laplace equation and will uncover ideas behind some concepts and involved results in the field.” (Vladimir Bobkov, Mathematical Reviews, December, 2019)“The book is a very useful contribution to the growing literature on this circle of ideas. I wholeheartedly recommend this book both as a textbook, as well as for independent study.” (Vicenţiu D. Rădulescu, zbMATH 1421.35002, 2019)Table of Contents1 Introduction.- 2 The Dirichlet problem and weak solutions.- 3 Regularity theory.- 4 Differentiability.- 5 On p-superharmonic functions.- 6 Perron's method.- 7 Some remarks in the complex plane.- 8 The infinity Laplacian.- 9 Viscosity solutions.- 10 Asymptotic mean values.- 11 Some open problems.- 12 Inequalities for vectors.
£43.99
Springer Nature Switzerland AG Machine Learning in Finance: From Theory to
Book SynopsisThis book introduces machine learning methods in finance. It presents a unified treatment of machine learning and various statistical and computational disciplines in quantitative finance, such as financial econometrics and discrete time stochastic control, with an emphasis on how theory and hypothesis tests inform the choice of algorithm for financial data modeling and decision making. With the trend towards increasing computational resources and larger datasets, machine learning has grown into an important skillset for the finance industry. This book is written for advanced graduate students and academics in financial econometrics, mathematical finance and applied statistics, in addition to quants and data scientists in the field of quantitative finance. Machine Learning in Finance: From Theory to Practice is divided into three parts, each part covering theory and applications. The first presents supervised learning for cross-sectional data from both a Bayesian and frequentist perspective. The more advanced material places a firm emphasis on neural networks, including deep learning, as well as Gaussian processes, with examples in investment management and derivative modeling. The second part presents supervised learning for time series data, arguably the most common data type used in finance with examples in trading, stochastic volatility and fixed income modeling. Finally, the third part presents reinforcement learning and its applications in trading, investment and wealth management. Python code examples are provided to support the readers' understanding of the methodologies and applications. The book also includes more than 80 mathematical and programming exercises, with worked solutions available to instructors. As a bridge to research in this emergent field, the final chapter presents the frontiers of machine learning in finance from a researcher's perspective, highlighting how many well-known concepts in statistical physics are likely to emerge as important methodologies for machine learning in finance.Trade Review“This book is, however, a well-structured and self-contained graduate textbook on ML applications in finance. Exercises and some applications are included at the end of each chapter and the Python code used in this book makes use of the Python Tensor Flow library. This book could also serve as a useful reference book for researchers and practitioners in quantitative finance.” (Gilles Teyssière, Mathematical Reviews, February, 2023)“Each part is introduced with background information, examples of relevant practical applications, and references to the most recent scientific literature. … The book covers all essential areas of machine learning with relevance to quantitative finance. … An additional strong advantage of this book is the clear and consistent structure of its chapters. … Overall, the book covers multiple machine learning approaches with advanced technical exposition and is therefore especially suitable as an academic reference point, especially on Reinforcement Learning.” (Antoniya Shivarova, Financial Markets and Portfolio Management, Issue 35, 2021)“This volume aims to present a broad yet technical treatment of (ML) algorithms used by financial practitioners and scholars alike. … the book fills a large void. … This encourages reproducibility as well as learning by doing, which is highly appreciated.” (Guillaume Coqueret, Quantitative Finance, October 15, 2020)Table of ContentsChapter 1. Introduction.- Chapter 2. Probabilistic Modeling.- Chapter 3. Bayesian Regression & Gaussian Processes.- Chapter 4. Feed Forward Neural Networks.- Chapter 5. Interpretability.- Chapter 6. Sequence Modeling.- Chapter 7. Probabilistic Sequence Modeling.- Chapter 8. Advanced Neural Networks.- Chapter 9. Introduction to Reinforcement learning.- Chapter 10. Applications of Reinforcement Learning.- Chapter 11. Inverse Reinforcement Learning and Imitation Learning.- Chapter 12. Frontiers of Machine Learning and Finance.
£71.99
Springer Nature Switzerland AG Ideals of Powers and Powers of Ideals:
Book SynopsisThis book discusses regular powers and symbolic powers of ideals from three perspectives– algebra, combinatorics and geometry – and examines the interactions between them. It invites readers to explore the evolution of the set of associated primes of higher and higher powers of an ideal and explains the evolution of ideals associated with combinatorial objects like graphs or hypergraphs in terms of the original combinatorial objects. It also addresses similar questions concerning our understanding of the Castelnuovo-Mumford regularity of powers of combinatorially defined ideals in terms of the associated combinatorial data. From a more geometric point of view, the book considers how the relations between symbolic and regular powers can be interpreted in geometrical terms. Other topics covered include aspects of Waring type problems, symbolic powers of an ideal and their invariants (e.g., the Waldschmidt constant, the resurgence), and the persistence of associated primes.Trade Review“This is a very interesting monograph providing a fast introduction to different fields of research devoted to modern aspects and develompents of commutative algebra, algebraic geometry, combinatorics, etc.” (Piotr Pokora, zbMATH 1445.13001, 2020)Table of Contents- Part I Associated Primes of Powers of Ideals - Associated Primes of Powers of Ideals. - Associated Primes of Powers of Squarefree Monomial Ideals. - Final Comments and Further Reading. - Part II Regularity of Powers of Ideals. - Regularity of Powers of Ideals and the Combinatorial Framework. - Problems, Questions, and Inductive Techniques. - Examples of the Inductive Techniques. - Final Comments and Further Reading. - Part III The Containment Problem. - The Containment Problem: Background. - The Containment Problem. - The Waldschmidt Constant of Squarefree Monomial Ideals. - Symbolic Defect. - Final Comments and Further Reading. - Part IV Unexpected Hypersurfaces. - Unexpected Hypersurfaces. - Final Comments and Further Reading.
£50.99
Springer Nature Switzerland AG Quaternion Algebras
Book SynopsisThis 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. 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. Quaternion Algebras 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.Trade Review“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)Table of Contents1. 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.
£26.99
Springer Nature Switzerland AG Introduction to Python in Earth Science Data
Book SynopsisThis textbook introduces the use of Python programming for exploring and modelling data in the field of Earth Sciences. It drives the reader from his very first steps with Python, like setting up the environment and starting writing the first lines of codes, to proficient use in visualizing, analyzing, and modelling data in the field of Earth Science. Each chapter contains explicative examples of code, and each script is commented in detail. The book is minded for very beginners in Python programming, and it can be used in teaching courses at master or PhD levels. Also, Early careers and experienced researchers who would like to start learning Python programming for the solution of geological problems will benefit the reading of the book.Table of ContentsPart I Python for Geologists, a kick-off; 1. Setting Up Your Python Environment, Easily; 2. Python Essentials for a Geologist; 3. Start Solving Geological Problems Using Python; Part II Describing Geological Data; 4. Graphical Visualization of a Geological Dataset; 5. Descriptive Statistics; Part III Integrals and Differential Equations in Geology; 6. Numerical Integration; 7. Ordinary Differential Equations (ODE); 8. Partial Differential Equations (PDE); Part IV Probability Density Functions and Error Analysis; 9. Probability Density Functions and their Use in Geology; 10. Error Analysis; Part V Robust Statistics and Machine Learning; 11. Introduction to Robust Statistics; 12. Machine Learning;
£49.49
Springer Nature Switzerland AG Recent Advances in Industrial and Applied
Book SynopsisThis open access book contains review papers authored by thirteen plenary invited speakers to the 9th International Congress on Industrial and Applied Mathematics (Valencia, July 15-19, 2019). Written by top-level scientists recognized worldwide, the scientific contributions cover a wide range of cutting-edge topics of industrial and applied mathematics: mathematical modeling, industrial and environmental mathematics, mathematical biology and medicine, reduced-order modeling and cryptography. The book also includes an introductory chapter summarizing the main features of the congress. This is the first volume of a thematic series dedicated to research results presented at ICIAM 2019-Valencia Congress.Table of Contents1 M. Berger, Asteroid-Generated Tsunamis: A Review.- 2 A. Bermúdez, Some Case Studies in Environmental and Industrial Mathematics.- 3 Z. Cai et al., Hyperbolic Model Reduction for Kinetic Equations.- 4 A. Cohen et al., State Estimation - The Role of Reduced Models.- 5 C. Conca, Modelling Our Sense Of Smell.- 6 L. Edelstein-Keshet, Pattern formation inside living cells.- 7 M. Garzon et al., Efficient Algorithms for Tracking Moving Interfaces.- 8 K. Lauter, Private AI: Machine Learning on Encrypted Data.- 9 C. Le Bris, Mathematical approaches for contemporary materials science: Addressing defects in the microstructure.- 10 H. Leng et al., An iterative thresholding method for topology optimization for the Navier-Stokes flow.- 11 K. Sako, Cryptography and Digital Transformation.- 12 H. Suito et al., Numerical Study for Blood Flows in Thoracic Aorta.- 13 J.A.C. Weideman, Dynamics of Complex Singularities of Nonlinear PDEs: Analysis and Computation.
£29.74
Springer Nature Switzerland AG Convex Analysis and Beyond: Volume I: Basic Theory
Book SynopsisThis book presents a unified theory of convex functions, sets, and set-valued mappings in topological vector spaces with its specifications to locally convex, Banach and finite-dimensional settings. These developments and expositions are based on the powerful geometric approach of variational analysis, which resides on set extremality with its characterizations and specifications in the presence of convexity. Using this approach, the text consolidates the device of fundamental facts of generalized differential calculus to obtain novel results for convex sets, functions, and set-valued mappings in finite and infinite dimensions. It also explores topics beyond convexity using the fundamental machinery of convex analysis to develop nonconvex generalized differentiation and its applications. The text utilizes an adaptable framework designed with researchers as well as multiple levels of students in mind. It includes many exercises and figures suited to graduate classes in mathematical sciences that are also accessible to advanced students in economics, engineering, and other applications. In addition, it includes chapters on convex analysis and optimization in finite-dimensional spaces that will be useful to upper undergraduate students, whereas the work as a whole provides an ample resource to mathematicians and applied scientists, particularly experts in convex and variational analysis, optimization, and their applications.Trade Review“Each chapter ends with an exercise section … . While primarily addressed to researchers, the book can be used for graduate courses in optimization, by undergraduate and graduate students for theses and projects as well as by researchers and practitioners from other fields where tools from convex analysis, variational analysis and optimization play a role. All in one, the reviewer warmly recommends this book to anyone interested.” (Sorin-Mihai Grad, zbMATH 1506.90001, 2023)“This outstanding book will certainly be useful to anyone interested to learn convex analysis, in particular to graduate students and researchers in the field. Most parts of it can also serve as the basis of advanced courses on a variety of topics. In view of the excellence of this first volume, one can expect the best of the announced second one, which will deal with applications of convex analysis.” (Juan Enrique Martínez-Legaz, Mathematical Reviews, February, 2023)“Every chapter of the book has one section of exercises and one section of commentaries. These sections provide the reader with a lot of information and give him/her great benefits in self-learning. … The book under review has many things to offer and, surely, it will play an important role in the development of convex analysis … . The book is very useful for theoretical research and practical use. Thanks to the art of writing of the authors … .” (Nguyen Dong Yen, Journal of Global Optimization, Vol. 85, 2023)Table of ContentsFundamentals.- Basic theory of convexity.- Convex generalized differentiation.- Enhanced calculus and fenchel duality.- Variational techniques and further subgradient study.- Miscellaneous topics on convexity.- Convexified Lipschitzian analysis.- List of Figures.- Glossary of Notation and Acronyms.- Subject Index.
£51.99
Springer Nature Switzerland AG Modeling Reality with Mathematics
Book SynopsisSimulating the behavior of a human heart, predicting tomorrow's weather, optimizing the aerodynamics of a sailboat, finding the ideal cooking time for a hamburger: to solve these problems, cardiologists, meteorologists, sportsmen, and engineers can count on math help. This book will lead you to the discovery of a magical world, made up of equations, in which a huge variety of important problems for our life can find useful answers.Trade Review“By providing tools and current examples on modeling issues ... the book makes a contribution answering the becoming more and more prevalent presence of Mathematics in our daily lives. The examples come essentially from the physical and natural sciences, but the book can be relied on in other areas, including the humanities, aside seminal works on mathematical modeling ... . The journey consists in eight rigorous and enjoying chapters.” (Lisa Morhaim, zbMATH 1519.00001, 2023)Table of Contents1 The model, aka the magic box.- 2 Weather Forecast Models.- 3 Epidemics: the Mathematics of Contagion.- 4 Mathematical Hearth.- 5 Mathematics in the Wind.- 6 Flying on Sun Power.- 7 The taste for Mathematics.- 8 Conclusions.
£17.99
Springer Nature Switzerland AG Novel Mathematics Inspired by Industrial
Book SynopsisThis contributed volume convenes a rich selection of works with a focus on innovative mathematical methods with applications in real-world, industrial problems. Studies included in this book are all motivated by a relevant industrial challenge, and demonstrate that mathematics for industry can be extremely rewarding, leading to new mathematical methods and sometimes even to entirely new fields within mathematics.The book is organized into two parts: Computational Sciences and Engineering, and Data Analysis and Finance. In every chapter, readers will find a brief description of why such work fits into this volume; an explanation on which industrial challenges have been instrumental for their inspiration; and which methods have been developed as a result. All these contribute to a greater unity of the text, benefiting not only practitioners and professionals seeking information on novel techniques but also graduate students in applied mathematics, engineering, and related fields.Table of ContentsPart I: Computational Science and Engineering.- Multirate Schemes — An Answer of Numerical Analysis to a Demand from Applications.- Electronic Circuit Simulation and the Development of New Krylov-Subspace Methods.- Modular time integration of coupled problems in system dynamics.- Differential-Algebraic Equations and Beyond: From Smooth to Nonsmooth Constrained Dynamical Systems.- Fast Numerical Methods to Compute Periodic Solutions of Electromagnetic Models.- Challenges in the Simulation of Radio Frequency Circuits.- An integrated data-driven computational pipeline with model order reduction for industrial and applied mathematics.- From rotating fluid masses and Ziegler’s paradox to Pontryagin- and Krein spaces and bifurcation theory.- Part II: Data Analysis and finance.- Topological Data Analysis.- Prediction Models with Functional Data for Variables related with Energy Production.- Quantization Methods for Stochastic Differential Equations.
£63.74
Springer International Publishing AG Graph and Network Theory: An Applied Approach
Book SynopsisThis textbook covers a diversity of topics in graph and network theory, both from a theoretical standpoint, and from an applied modelling point of view. Mathematica® is used to demonstrate much of the modelling aspects. Graph theory and model building tools are developed in tandem with effective techniques for solving practical problems via computer implementation. The book is designed with three primary readerships in mind. Individual syllabi or suggested sequences for study are provided for each of three student audiences: mathematics, applied mathematics/operations research, and computer science. In addition to the visual appeal of each page, the text contains an abundance of gems. Most chapters open with real-life problem descriptions which serve as motivation for the theoretical development of the subject matter. Each chapter concludes with three different sets of exercises. The first set of exercises are standard and geared toward the more mathematically inclined reader. Many of these are routine exercises, designed to test understanding of the material in the text, but some are more challenging. The second set of exercises is earmarked for the computer technologically savvy reader and offer computer exercises using Mathematica. The final set consists of larger projects aimed at equipping those readers with backgrounds in the applied sciences to apply the necessary skills learned in the chapter in the context of real-world problem solving. Additionally, each chapter offers biographical notes as well as pictures of graph theorists and mathematicians who have contributed significantly to the development of the results documented in the chapter. These notes are meant to bring the topics covered to life, allowing the reader to associate faces with some of the important discoveries and results presented. In total, approximately 100 biographical notes are presented throughout the book. The material in this book has been organized into three distinct parts, each with a different focus. The first part is devoted to topics in network optimization, with a focus on basic notions in algorithmic complexity and the computation of optimal paths, shortest spanning trees, maximum flows and minimum-cost flows in networks, as well as the solution of network location problems. The second part is devoted to a variety of classical problems in graph theory, including problems related to matchings, edge and vertex traversal, connectivity, planarity, edge and vertex coloring, and orientations of graphs. Finally, the focus in the third part is on modern areas of study in graph theory, covering graph domination, Ramsey theory, extremal graph theory, graph enumeration, and application of the probabilistic method.Table of ContentsPreface.- List of Algorithms.- List of Bibliographical Notes.- Part 1. Topics in network optimisation.- 1. An introduction to graphs.- 2. Graph connectedness.- 3. Algorithmic complexity.- 4. Optimal paths.- 5. Trees.- 6. Location problems.- 7. Maximum flow networks.- 8. Minimum-cost network flows.- Part 2. Topics in classical graph theory.- 9. Matchings.- 10. Eulerian graphs.- 11. Hamiltonian graphs.- 12. Graph connectivity.- 13. Planarity.- 14. Graph colouring.- 15. Oriented graphs. Part 3. Topics in modern graph theory.- 16. Domination in graphs.- 17. Ramsey Theory.- 18. Extremal graph theory.- 19. Graph enumeration.- 20. The probabilistic method.- Index.
£55.99
Springer International Publishing AG VLADIMIR I. ARNOLD—Collected Works: Dynamics,
Book SynopsisThis volume 6 of the Collected Works comprises 27 papers by V.I.Arnold, one of the most outstanding mathematicians of all times, written in 1991 to 1995. During this period Arnold's interests covered Vassiliev’s theory of invariants and knots, invariants and bifurcations of plane curves, combinatorics of Bernoulli, Euler and Springer numbers, geometry of wave fronts, the Berry phase and quantum Hall effect. The articles include a list of problems in dynamical systems, a discussion of the problem of (in)solvability of equations, papers on symplectic geometry of caustics and contact geometry of wave fronts, comments on problems of A.D.Sakharov, as well as a rather unusual paper on projective topology. The interested reader will certainly enjoy Arnold’s 1994 paper on mathematical problems in physics with the opening by-now famous phrase “Mathematics is the name for those domains of theoretical physics that are temporarily unfashionable.” The book will be of interest to the wide audience from college students to professionals in mathematics or physics and in the history of science. The volume also includes translations of two interviews given by Arnold to the French and Spanish media. One can see how worried he was about the fate of Russian and world mathematics and science in general.Table of Contents1 Bernoulli–Euler updown numbers associated with function singularities, their combinatorics and arithmetics.- 2 Congruences for Euler, Bernoulli and Springer numbers of Coxeter groups.- 3 The calculus of snakes and the combinatorics of Bernoulli, Euler and Springer numbers of Coxeter groups.- 4 Springer numbers and Morsification spaces.- 5 Polyintegrable flows.- 6 Bounds for Milnor numbers of intersections in holomorphic dynamical systems.- 7 Some remarks on symplectic monodromy of Milnor fibrations.- 8 Topological properties of Legendre projections in contact geometry of wave fronts [On topological properties of Legendre projections in contact geometry of wave fronts].- 9 Sur les propriétés topologiques des projections lagrangiennes en géométrie symplectique des caustiques [On topological properties of Lagrangian projections in symplectic geometry of caustics].- 10 Plane curves, their invariants, perestroikas and classifications (with an appendix by F. Aicardi).- 11 Invariants and perestroikas of plane fronts.- 12 The Vassiliev theory of discriminants and knots.- 13 The geometry of spherical curves and the algebra of quaternions.- 14 Remarks on eigenvalues and eigenvectors of Hermitian matrices, Berry phase, adiabatic connections and quantum Hall effect.- 15 Problems on singularities and dynamical systems.- 16 Sur quelques problèmes de la théorie des systèmes dynamiques [On some problems in the theory of dynamical systems].- 17 Mathematical problems in classical physics.- 18 Problèmes résolubles et problèmes irrésolubles analytiques et géométriques [Solvable and unsolvable analytic and geometric problems].- 19 Projective topology.- 20 Questions à V.I. Arnold (an interview with M. Audin and P. Iglésias) [Questions to V.I. Arnold].- 21 En todo matemático hay un ángel y un demonio (an interview with Marimar Jiménez) [In every mathematician, there is an angel and a devil].- 22 Will Russian mathematics survive?.- 23 Will mathematics survive? Report on the Zurich Congress.- 24 Why study mathematics? What mathematicians think about it.- 25 Preface to the Russian translation of the book by M.F. Atiyah “The Geometry and Physics of Knots”.- 26 A comment on one of A.D. Sakharov’s “Amateur Problems”.- 27 Comments on two of A.D. Sakharov’s “Amateur Problems”.- Acknowledgements.
£107.99
Springer International Publishing AG Welington de Melo - Selected Works
Book SynopsisWelington de Melo (Guapé, 1946 - Rio de Janeiro, 2016) was a brazilian mathematician whose contributions were deeply connected with Smale and Palis school of dynamical systems. In particular the classification of smooth dynamical systems and the study of its generic properties are recurrent topics in his work. This book collected some of his most significant contributions, from his early work on structural stability of diffeomorphisms in the 1970's to his groundbreaking results on one-dimensional dynamics. Indeed his interest in one-dimensional dynamics is a clear distinction from early influences. An effervescent work in discrete dynamics on the interval and the circle started in the 1970s. It was soon realized that those systems have surprisingly rich dynamics. But, at the same time, an impressive set of tools were developed to study them. There are two main sets of tools. Real methods such as bounded distortion control via Schwarzian derivative and later cross-ratio estimates allows one to understand some of its features. However, often complex methods, with deep connections with Teichmuller theory, are necessary to obtain some of the most striking results. This is especially true in renormalization theory, a theme Welington was very fond of, and that appears prominently in his collected works. Welington played an important role in the development on both fronts, and this book is a testament of his influence in the field which resonates to this day.
£110.49
Springer International Publishing AG Drinfeld Modules
Book SynopsisThis textbook offers an introduction to the theory of Drinfeld modules, mathematical objects that are fundamental to modern number theory.After 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.Drinfeld Modules 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.Table of ContentsPreface.- 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.
£67.49
Springer International Publishing AG Representations of SU(2,1) in Fourier Term
Book SynopsisThis book studies the modules arising in Fourier expansions of automorphic forms, namely Fourier term modules on SU(2,1), the smallest rank one Lie group with a non-abelian unipotent subgroup. It considers the “abelian” Fourier term modules connected to characters of the maximal unipotent subgroups of SU(2,1), and also the “non-abelian” modules, described via theta functions. A complete description of the submodule structure of all Fourier term modules is given, with a discussion of the consequences for Fourier expansions of automorphic forms, automorphic forms with exponential growth included.These results can be applied to prove a completeness result for Poincaré series in spaces of square integrable automorphic forms.Aimed at researchers and graduate students interested in automorphic forms, harmonic analysis on Lie groups, and number-theoretic topics related to Poincaré series, the book will also serve as a basic reference on spectral expansion with Fourier-Jacobi coefficients. Only a background in Lie groups and their representations is assumed.Table of Contents- 1. Introduction. - 2. The Lie Group SU(2,1) and Subgroups. - 3. Fourier Term Modules. - 4. Submodule Structure. - 5. Application to Automorphic Forms.
£39.99
Birkhäuser Elementary Numerical Mathematics for Programmers
Book Synopsis
£35.99
Springer International Publishing AG Differential Geometry of Curves and Surfaces
Book SynopsisThis is a textbook on differential geometry well-suited to a variety of courses on this topic. For readers seeking an elementary text, the prerequisites are minimal and include plenty of examples and intermediate steps within proofs, while providing an invitation to more excursive applications and advanced topics. For readers bound for graduate school in math or physics, this is a clear, concise, rigorous development of the topic including the deep global theorems. For the benefit of all readers, the author employs various techniques to render the difficult abstract ideas herein more understandable and engaging.Over 300 color illustrations bring the mathematics to life, instantly clarifying concepts in ways that grayscale could not. Green-boxed definitions and purple-boxed theorems help to visually organize the mathematical content. Color is even used within the text to highlight logical relationships.Applications abound! The study of conformal and equiareal functions is grounded in its application to cartography. Evolutes, involutes and cycloids are introduced through Christiaan Huygens' fascinating story: in attempting to solve the famous longitude problem with a mathematically-improved pendulum clock, he invented mathematics that would later be applied to optics and gears. Clairaut’s Theorem is presented as a conservation law for angular momentum. Green’s Theorem makes possible a drafting tool called a planimeter. Foucault’s Pendulum helps one visualize a parallel vector field along a latitude of the earth. Even better, a south-pointing chariot helps one visualize a parallel vector field along any curve in any surface.In truth, the most profound application of differential geometry is to modern physics, which is beyond the scope of this book. The GPS in any car wouldn’t work without general relativity, formalized through the language of differential geometry. Throughout this book, applications, metaphors and visualizations are tools that motivate and clarify the rigorous mathematical content, but never replace it. Trade Review“This is the first textbook on mathematics that I see printed in color. … This book is not a usual textbook, but a very well written introduction to differential geometry, and the colors really help the reader in understanding the figures and navigating through the text. … this book will surely serve very well for students who want to learn differential geometry from the ground up no matter what their main learning goal is.” (Árpád Kurusa, Acta Scientiarum Mathematicarum, Vol. 84 (1-2), 2018)“This book is perfect for undergraduate students. ... There is also plenty of figures, examples, exercises and applications which make the differential geometry of curves and surfaces so interesting and intuitive. The author uses a rich variety of colours and techniques that help to clarify difficult abstract concepts.” (Teresa Arias-Marco, zbMATH 1375.53001, 2018)“This is a visually appealing book, replete with many diagrams, lots of them in full color. … the author’s writing style is extremely clear and well-motivated. … this is still the book I would use as a text for a beginning course on this subject. It would not surprise me if it quickly becomes the market leader.” (Mark Hunacek, MAA Reviews, July, 2017) Table of ContentsIntroduction.- Curves.- Additional topics in curves.- Surfaces.- The curvature of a surface.- Geodesics.- The Gauss–Bonnet theorem.- Appendix A: The topology of subsets of Rn.- Recommended excursions.- Index.
£43.99
