{"title":"Applied mathematics Books","description":"","products":[{"product_id":"about-time-einsteins-unfinished-revolution-9780140174618","title":"About Time Einsteins Unfinished Revolution","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cb\u003eIn \u003ci\u003eAbout Time: Einstein''s Unfinished Revolution \u003c\/i\u003ePaul Davies confronts the puzzles and paradoxes of time that have bemused the world''s greatest thinkers throughout the ages.\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003eWhen Albert Einstein formulated his theory of relativity it brought about a revolution in our understanding of time, yet also presented a new set of mysteries. Einstein''s time can be warped, leading to bizarre possibilities such as black holes and time travel, while making a nonsense of our perception of a ''now'' or a division of time into past, present and future.\u003cbr\u003e\u003cbr\u003eIn \u003ci\u003eAbout Time\u003c\/i\u003e Paul Davies tackles the tough questions about time, including the strange relationship between physical time and our psychological perception of it. He gives straightforward descriptions of topics such as the theory of relativity, the relation between time dilation and the speed of light and Hawking''s ''imaginary time''. He concludes that, despite decades of progress in unravelling the mysteries of \u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eA very brief history of time; time for a change; timewarps;  black holes - gateways to the end of time; the beginning of  time - when exactly was it?; Einstein's greatest triumph?; quantum time; imaginary time; the arrow of time; backwards in time; time travel - fact or fantasy?; but what time is it now?; experimenting with time; the unfinished revolution.\u003c\/p\u003e","brand":"Penguin Books Ltd","offers":[{"title":"Default Title","offer_id":48732347400535,"sku":"9780140174618","price":10.44,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780140174618.jpg?v=1719996509"},{"product_id":"the-ten-equations-that-rule-the-world-9780141991092","title":"The Ten Equations that Rule the World","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cb\u003eTHE INTERNATIONAL BESTSELLER\u003cbr\u003e\u003cbr\u003e''An entertaining tour that will change how you see the world'' Sean Carroll, author of \u003ci\u003eSomething Deeply Hidden\u003c\/i\u003e\u003cbr\u003e\u003cbr\u003eIs there a secret formula for improving your life? For making something a viral hit? For deciding how long to stick with your current job, Netflix series, or even relationship?\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003eThis book is all about the equations that make our world go round. Ten of them, in fact. They are integral to everything from investment banking to betting companies and social media giants. And they can help you to increase your chance of success, guard against financial loss, live more healthily and see through scaremongering. They are known only by mathematicians - until now.\u003cbr\u003e\u003cbr\u003eWith wit and clarity, mathematician David Sumpter shows that it isn''t the technical details which make these formulas so successful. It is the way they allow mathematicians to view problems from a different angle - a way of seeing the world that anyone c\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cb\u003eSometimes books about numbers come along and we're so ecstatic that we just pop with delight. One such book is \u003ci\u003eThe Ten Equations that Rule The World\u003c\/i\u003e\u003c\/b\u003e -- Tim Harford * More or Less BBC4 *\u003cbr\u003eHugely entertaining, erudite and at times genuinely witty . . . \u003cb\u003eit's nice to be spoken to in grown-up language by a genius\u003c\/b\u003e. You will come away from Sumpter's book with a much clearer idea of why the world is less messy than it appears * E\u0026amp;T Magazine *\u003cbr\u003eThese aren't the equations of Newton or Einstein -- crisp relations describing the evolution of a clockwork universe. These are the equations of randomness, expectation, and imperfect information. The equations, in other words, of the real world. David Sumpter provides \u003cb\u003ean entertaining tour that will change how you see the world \u003c\/b\u003e -- Sean Carroll author of Something Deeply Hidden\u003cbr\u003e\u003cb\u003eSumpter writes fascinatingly\u003c\/b\u003e about his experiences as a consulting mathematician. . .  I will encourage my mathematics undergraduates to read this book since it will inspire them by showing the relevance of mathematics to today's world and make them think about the moral issues they will face as mathematicians * Times Higher Education *\u003c\/p\u003e","brand":"Penguin Books Ltd","offers":[{"title":"Default Title","offer_id":48732512878935,"sku":"9780141991092","price":10.44,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780141991092.jpg?v=1719997210"},{"product_id":"multilayer-networks-structure-and-function-9780192865540","title":"Multilayer Networks Structure and Function","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eMultilayer networks has become a central topic in Network Science. The book presents a comprehensive account of this emerging field. Multilayer networks are formed by several networks and include social networks, financial markets, multi-modal transportation systems, infrastructures, molecular networks, and the brain.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePart I: Single and multilayer networks 1: Complex systems as multilayer networks Part II: Single networks 2: The structure of single networks 3: The dynamics on single networks Part III: Multilayer networks 4: Multilayer networks in nature, society and infrastructures 5: The mathematical definition 6: Basic structural properties 7: Structural correlations of multiplex networks 8: Communities 9: Centrality measures 10: Multilayer network models 11: Interdependent multilayer networks 12: Classical percolation, generalized percolation and cascades 13: Epidemic spreading 14: Diffusion 15: Synchronization, non-linear dynamics and control 16: Opinion dynamics and game theory Appendix A: The Barabasi Albert model: the master equation Appendix B: Entropy and null models of single networks Appendix C: Growing multiplex networks: the master equation Appendix D: Percolation of interdependent networks Appendix E: Directed percolation of interdependent networks Appendix F: Immunization strategies on multiplex networks Appendix G: Spectrum of the Supra-Laplacian Part I: Single and multilayer networks 1: Complex systems as multilayer networks Part II: Single networks 2: The structure of single networks 3: The dynamics on single networks Part III: Multilayer networks 4: Multilayer networks in nature, society and infrastuctures 5: The mathematical definition 6: Basic structural properties 7: Structural correlations of multiplex networks 8: Communities 9: Centrality measures 10: Multilayer network models 11: Interdependent multilayer networks 12: Classical percolation, generalized percolation and cascades 13: Epidemic spreading 14: Diffusion 15: Synchronization, non-linear dynamics and control 16: Opinion dynamics and game theory Appendix A: The Barabasi Albert model: the master equation Appendix B: Entropy and null models of single networks Appendix C: Growing multiplex networks: the master equation Appendix D: Percolation of interdependent networks Appendix E: Directed percolation of interdependent networks Appendix F: Immunization strategies on multiplex networks Appendix G: Spectrum of the Supra-Laplacian","brand":"Oxford University Press","offers":[{"title":"Default Title","offer_id":48732604301655,"sku":"9780192865540","price":33.24,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780192865540.jpg?v=1719997613"},{"product_id":"mathematical-physics-with-differential-equations-9780192872623","title":"Mathematical Physics with Differential Equations","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis textbook uses insight from differential equations to analyse fundamental subjects of modern theoretical physics, including classical and quantum mechanics, thermodynamics, electromagnetism, superconductivity, gravitational physics, and quantum field theories.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface Notation and Convention 1: Hamiltonian Systems and Applications 2: Schrödinger Equation and Quantum Mechanics 3: Maxwell Equations, Dirac Monopole, and Gauge Fields 4: Special Relativity 5: Abelian Gauge Field Equations 6: Dirac Equations 7: GinzburgDSLandau Equations for Superconductivity 8: Magnetic Vortices in Abelian Higgs Theory 9: Non-Abelian Gauge Field Equations 10: Einstein Equations and Related Topics 11: Charged Vortices and ChernDSSimons Equations 12: Skyrme Model and Related Topics 13: Strings and Branes 14: BornDSInfeld Theory of Electromagnetism 15: Canonical Quantization of Fields Appendices Bibliography Index","brand":"Oxford University Press","offers":[{"title":"Default Title","offer_id":48732608463191,"sku":"9780192872623","price":38.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780192872623.jpg?v=1719997631"},{"product_id":"50-visions-of-mathematics-9780198701811","title":"50 Visions of Mathematics","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eRelax: no one understands technical mathematics without lengthy training but we all have an intuitive grasp of the ideas behind the symbols. To celebrate the 50th anniversary of the founding of the Institute of Mathematics and its Applications (IMA), this book is designed to showcase the beauty of mathematics - including images inspired by mathematical problems - together with its unreasonable effectiveness and applicability, without frying your brain. The book is a collection of 50 original essays contributed by a wide variety of authors. It contains articles by some of the best expositors of the subject (du Sautoy, Singh and Stewart for example) together with entertaining biographical pieces and articles of relevance to our everyday lives (such as Spiegelhalter on risk and Elwes on medical imaging). The topics covered are deliberately diverse and involve concepts from simple numerology to the very cutting edge of mathematics research. Each article is designed to be read in one sittin\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003eMotorways; Sherlock Holmes; networks; mysterious numbers; sweets; champagne; interviews; mathematical poetry; ravens and even The Simpsons - this book has them all and more! Don't miss it! * Alan Stevens, Mathematics Today *\u003cbr\u003eThe 50 essays in the book cover both pure and applied topics, and even the most esoteric subjects are addressed in an accessible way. * Physics World *\u003cbr\u003eWarmly recommended as recreational and stimulating reading to all mathematics aficionado! * Yuriy V. Rogovchenko, Zentralblatt MATH *\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1. What's the problem with mathematics? ; 2. The mathematics of messages ; 3. Decathlon: The art of scoring points ; 4. Queen Dido and the mathematics of the extreme ; 5. Can strings tie things together? ; 6. Grooves and knuckleballs ; 7. Pigs didn't fly but swine flu ; 8. Bill Tutte: Unsung Bletchley hero ; 9. What's the use of a quadratic equation? ; 10. Tony Hilton Royle Skyrme ; 11. The mathematics of obesity ; 12. It's a small world really ; 13. How does mathematics help at a murder scene? ; 14. Mathematics: The language of the universe ; 15. The troublesome geometry of CAT scanning ; 16. The mathematics of sports gambling ; Pythagoras's Theorem: a2 ; 17. A conversation with Freeman Dyson ; 18. A glass of bubbly ; 19. The influenza virus: It's all in the packaging ; 20. Mathematicians at the movies: Sherlock Holmes vs Professor Moriarty ; 21. Solving the Bristol bridge problem ; 22. All ravens are black: Puzzles and paradoxes in probability and statistics ; 23. The Tower of Hanoi: Where mathematics meets psychology ; 24. Career: A sample path ; 25. Sweets in the jar ; 26. Mary Cartwright ; 27. The fallibility of mathematics ; 28. Anecdotes of Dr Barrow ; 29. Finding Apollo ; 30. The golden ratio in astronomy and astrophysics ; 31. The high-power hypar ; 32. This is not a carrot: Paraconsistent mathematics ; 33. The mystery of Groombridge Place ; Pythagoras's Theorem: b2 ; 34. Mysterious number 6174 ; 35. Percolating possibilities ; 36. Milestones on a non-Euclidean journey ; 37. Simpson's rule ; 38. Risking your life ; 39. Networks and illusions ; 40. Emmy Noether: Against the odds ; 41. Of catastrophes and creodes: How maths benefits from collaboration with other fields ; 42. Conic section hide and seek ; 43. Sir James Lighthill: A life in waves ; 44. Fail safe or fail dangerous ; 45. Leapfrogging into the future: How child's play is at the heart of weather and climate models ; 46. Motorway mathematics ; 47. The philosophy of applied mathematics ; 48. Mighty Morphogenesis ; 49. Called to the barcode ; 50. Roughly fifty-fifty? ; Pythagoras's Theorem: c2","brand":"Oxford University Press","offers":[{"title":"Default Title","offer_id":48732765618519,"sku":"9780198701811","price":999.99,"currency_code":"GBP","in_stock":false}]},{"product_id":"mathematical-finance-9780198787945","title":"Mathematical Finance","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eIn recent years the finance industry has mushroomed to become an important part of modern economies, and many science and engineering graduates have joined the industry as quantitative analysts, with mathematical and computational skills that are needed to solve complex problems of asset valuation and risk management. An important parallel story exists of scientific endeavour. Between 1965-1995, insightful ideas in economics about asset valuation were turned into a mathematical ''theory of arbitrage'', an enterprise whose first achievement was the famous 1973 Black-Scholes formula, followed by extensive investigations using all the resources of modern analysis and probability. The growth of the finance industry proceeded hand-in-hand with these developments. Now new challenges arise to deal with the fallout from the 2008 financial crisis and to take advantage of new technology, which has revolutionized the practice of trading. This Very Short Introduction introduces readers with no previous background in this area to arbitrage theory and why it works the way it does. Illuminating pricing theory, Mark Davis explains its applications to interest rates, credit trading, fund management and risk management. He concludes with a survey of the most pressing issues in mathematical finance today.ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003eOnly a scholar of the highest order could provide the depth, breadth, clarity, precision, and brevity to be found in this work. Enjoy the resulting gem. * Dilip B. Madan, Professor of Finance, Robert H. Smith School of Business *\u003cbr\u003eThis elegant little book will enthral readers looking for a clear sense of what mathematical finance is all about. Each chapter captures the essential ideas within a different aspect of the subject, without burying readers in abstruse models. Davis knows the subject so well, from both the mathematical and practical viewpoints, that he can make it accessible, relevant, and correct, all at the same time. * Darrell Duffie, Dean Witter Distinguished Professor of Finance, Stanford University *\u003cbr\u003eWith concise explanations of the most important financial mathematical correlations and the mathematical formulas necessary for them, this book represents a successful very short introduction into this complex topic. * zbMATH *\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface 1: Money, banking, and financial markets 2: Quantifying risks 3: The classical theory of option pricing 4: Interest rates 5: Credit risk 6: Fund management 7: Risk management 8: The banking crisis and its aftermatch Epilogue Further reading Index","brand":"Oxford University Press","offers":[{"title":"Default Title","offer_id":48732784230743,"sku":"9780198787945","price":9.49,"currency_code":"GBP","in_stock":true}]},{"product_id":"foundations-of-science-mathematics-ocp-2e-oxford-chemistry-primers-9780198797548","title":"Foundations of Science Mathematics OCP 2e Oxford","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eMathematics plays a key part in every quantitative and theoretical subject, and is taught to all science and engineering students. Foundations of Science Mathematics bridges the gap between school and university, and spans a large range of topics, from basic arithmetic and algebra to calculus, Fourier transforms, and elementary data analysis. Problems and worked solutions are presented in an informal and readable tutorial style, making the text accessible to the novice, while its concise nature ensures that it is a useful reference for the experienced professional.The first edition primer and its companion ''Worked Problems'' workbook are combined in this new edition, and a new chapter on data analysis has been added to ensure the book remains as comprehensive and useful to students as possible.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003eThe answers to the worked examples are superb, very instructive, and include detailed sketches. * Dr Athanasia Dervisi, Cardiff University *\u003cbr\u003eThere is a selection of worked examples in a chemistry context which help students to apply maths more efficiently in their chemistry modules. * Dr Gita Sedghi, University of Liverpool *\u003cbr\u003eExcellent, concise coverage of basic algebra. * Prof Scott Woodley, University College London *\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1: Basic algebra and arithmetic 2: Curves and graphs 3: Trigonometry 4: Differentiation 5: Integration 6: Taylor series 7: Complex numbers 8: Vectors 9: Matricies 10: Partial differentiation 11: Line integrals 12: Multiple integrals 13: Ordinary differential equations 14: Partial differential equations 15: Fourier series and transforms 16: Data analysis","brand":"Oxford University Press","offers":[{"title":"Default Title","offer_id":48732787147095,"sku":"9780198797548","price":32.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780198797548.jpg?v=1719998398"},{"product_id":"fluid-mechanics-a-very-short-introduction-very-short-introductions-9780198831006","title":"Fluid Mechanics A Very Short Introduction Very","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cb\u003eVery Short Introductions\u003cb\u003e: Brilliant, Sharp, Inspiring \u003c\/b\u003eFluid mechanics is an important branch of physics concerned with the way in which fluids, such as liquids and gases, behave when in motion and at rest. A quintessential interdisciplinary field of science, it interacts with many other scientific disciplines, from chemistry and biology to mathematics and engineering.This Very Short Introduction presents the field of fluid mechanics by focusing on the underlying physical ideas and using everyday phenomena to demonstrate them, from dripping taps to swimming ducks. Eric Lauga shows how this set of fundamental physical concepts can be applied to a wide range of flow behaviours and highlights the role of fluid motion in both the natural and industrial worlds. This book also considers future applications of fluid mechanics in science.ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003eOverall, the book should definitely be an individual's go-to source when seeking an authoritative perspective on the field of fluid mechanics. * Anita T. Layton, Society for Industrial and Applied Mathematics Vol 65.4 *\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1: Fluids 2: Viscosity 3: Pipes 4: Dimensions 5: Boundary layers 6: Vortices 7: Instabilities 8: Researching fluids and flows Further Reading Index\u003c\/b\u003e","brand":"Oxford University Press","offers":[{"title":"Default Title","offer_id":48732801368407,"sku":"9780198831006","price":9.49,"currency_code":"GBP","in_stock":true}]},{"product_id":"topology-9780198832683","title":"Topology","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eHow is a subway map different from other maps? What makes a knot knotted? What makes the Möbius strip one-sided? These are questions of topology, the mathematical study of properties preserved by twisting or stretching objects. In the 20th century topology became as broad and fundamental as algebra and geometry, with important implications for science, especially physics.In this Very Short Introduction Richard Earl gives a sense of the more visual elements of topology (looking at surfaces) as well as covering the formal definition of continuity. Considering some of the eye-opening examples that led mathematicians to recognize a need for studying topology, he pays homage to the historical people, problems, and surprises that have propelled the growth of this field. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003eThe book is written in an intuitive, informal and motivating style, with emphasis on concepts, ideas, examples and historical comments, and can be recommended as parallel reading for students of a basic course in topology. * Bruno Zimmermann, zbMATH *\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1: What is Topology? 2: Making Surfaces 3: Thinking Continuously 4: The Plane and Other Spaces 5: Flavours of Topology 6: More on Surfaces 7:  Knot to Be Historical Timeline Further Reading Index","brand":"Oxford University Press","offers":[{"title":"Default Title","offer_id":48732802482519,"sku":"9780198832683","price":9.49,"currency_code":"GBP","in_stock":true}]},{"product_id":"core-maths-for-the-biosciences-9780199216345","title":"Core Maths for the Biosciences","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eCore Maths for the Biosciences introduces the range of mathematical concepts that bioscience students need to master during thier studies. Starting from fundamental concepts, it blends clear explanations and biological examples throughout as it equips the reader with the full range of mathematical tools required by biologists today.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003eExactly the sort of thing that will be helpful in showing those with biological problems how mathematics can be very useful - and that what is really important is maintaining an intuitive understanding between the mathematics - which is essentially no more, but no less, than a way of thinking very precisely - and the actual phenomena they are dealing with...Very fine indeed. * Professor Lord May of Oxford, Department of Zoology, University of Oxford *\u003cbr\u003eFantastic. Easy to understand, interactive, biologically relevant and dictated in a way that seemed as though you are almost having a conversation with the author. * James Sleigh, Student, University of Oxford *\u003cbr\u003eCoherent and clear. The best I have seen this kind of material treated. * Stephen Hubbard, University of Dundee *\u003cbr\u003eThis book is by far the best of its kind, a spectacular diamond in the rough. * Helen Smith, student, University of Salford *\u003cbr\u003eThe interactive spreadsheets are a work of genius. * Stuart Fisk, student, University of Essex *\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePART 1: ARITHMETIC, ALGEBRA \u0026amp; FUNCTIONS; PART 2: CALCULUS AND DIFFERENTIAL EQUATIONS","brand":"Oxford University Press","offers":[{"title":"Default Title","offer_id":48732835774807,"sku":"9780199216345","price":50.34,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780199216345.jpg?v=1719998603"},{"product_id":"mathematical-techniques-an-introduction-for-the-engineering-physical-and-mathematical-sciences-9780199282012","title":"Mathematical Techniques An Introduction for the","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eMathematical Techniques provides a complete course in mathematics, covering all the essential topics with which a physical sciences or engineering student should be familiar. It introduces and builds on concepts in a progressive, carefully-layered way, and features over 2000 end of chapter problems, plus additional self-check questions.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003eReview from previous edition This textbook offers an accessible and comprehensive grounding in many of the mathematical techniques required in the early stages of an engineering or science degree and also for the routine methods needed by first and second year mathematics students. * Engineering Designer March\/April 2003 *\u003cbr\u003eThere are also significant changes in content in the opening chapter, where the foundation material has been expanded usefully. The authors do not attempt to dodge theoretical hurdles. They are careful to explain many of the less intuitive properties of functions and to highlight generalisations without becoming over abstract. * Times Higher Education Supplement, November 2002 *\u003cbr\u003eThoroughly recommended. * Zentralblatt MATH, 993:2002 *\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePART 1. ELEMENTARY METHODS, DIFFERENTIATION, COMPLEX NUMBERS; PART 2. MATRIX AND VECTOR ALGEBRA; PART 3. INTEGRATION AND DIFFERENTIAL EQUATIONS; PART 4. TRANSFORMS AND FOURIER SERIES; PART 5. MULTIVARIABLE CALCULUS; PART 6. DISCRETE MATHEMATICS; PART 7. PROBABILITY AND STATISTICS; PART 8. PROJECTS; SELF-TESTS: SELECTED ANSWERS; ANSWERS TO SELECTED PROBLEMS; APPENDICES; FURTHER READING; INDEX","brand":"Oxford University Press","offers":[{"title":"Default Title","offer_id":48732839969111,"sku":"9780199282012","price":60.79,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780199282012.jpg?v=1719998620"},{"product_id":"explanation-in-causal-inference-9780199325870","title":"Explanation in Causal Inference","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003eYes, mediation is an important topic. It has longed been used in the social sciences especially psychology. Of late there has been interest in many different fields including economics, sociology, epidemiology, political science and education, among other fields. Tyler VanderWeele is very qualified to author this book. He has contributed important work to the development of this topic and is a talented and careful researcher. I think there is potential for adoption in graduate courses in the social and biomedical sciences. I also think it could be widely purchased by applied researchers as a reference. I recommend publication. * Luke Keele, Associate Professor, Department of Political Science, Penn State University   *\u003cbr\u003eMediation is about understanding pathways between a treatment and an outcome that lead to the outcome, i.e., mechanisms. Mechanisms are a central thing in science and statisticians have been providing new principled methods for studying these topics over especially the last 10 years. Especially in the social and behavioral sciences and in epidemiology there has been great interest in these methods, and the methodology the author wants to write about is the new stuff from the last 10 years. [VanderWeele] is the key player in statistical literature these days. He's a good communicator… Primary market: applied researchers doing mediation in epidemiology, social and behavioral sciences. Secondary market: applied statisticians teaching causal inference and\/or working in the area.\" \" * Michael Sobel, Dept Sociology, Columbia *\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePART I: MEDIATION ANALYSIS ; Chapter 1. Explanation and Mechanism ; Chapter 2. Mediation: Introduction and Regression-Based Approaches ; Chapter 3. Sensitivity Analysis for Mediation ; Chapter 4. Mediation Analysis with Survival Data ; Chapter 5. Multiple Mediators ; Chapter 6. Mediation Analysis with Time-Varying Exposures and Mediators ; Chapter 7. Selected Topics in Mediation Analysis ; Chapter 8. Other Topics Related to Intermediates ; PART II: INTERACTION ANALYSIS ; Chapter 9. An Introduction to Interaction Analysis ; Chapter 10. Mechanistic Interaction ; Chapter 11. Bias Analysis for Interactions ; Chapter 12. Interaction in Genetics: Independence and Boosting Power ; Chapter 13. Power and Sample-Size Calculations for Interaction Analysis ; PART III: SYNTHESIS AND SPILLOVER EFFECTS ; Chapter 14. A Unification of Mediation and Interaction ; Chapter 15. Social Interactions and Spillover Effects ; Chapter 16. Mediation and Interaction: Future and Context ; Appendix. Technical Details and Proofs ; References","brand":"Oxford University Press Inc","offers":[{"title":"Default Title","offer_id":48732840919383,"sku":"9780199325870","price":115.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780199325870.jpg?v=1719998624"},{"product_id":"networks-9780199588077","title":"Networks","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eFrom ecosystems to Facebook, from the Internet to the global financial market, some of the most important and familiar natural systems and social phenomena are based on a networked structure. It is impossible to understand the spread of an epidemic, a computer virus, large-scale blackouts, or massive extinctions without taking into account the network structure that underlies all these phenomena.In this Very Short Introduction, Guido Caldarelli and Michele Catanzaro discuss the nature and variety of networks, using everyday examples from society, technology, nature, and history to explain and understand the science of network theory. They show the ubiquitous role of networks; how networks self-organize; why the rich get richer; and how networks can spontaneously collapse. They conclude by highlighting how the findings of complex network theory have very wide and important applications in genetics, ecology, communications, economics, and sociology. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1. A network point of view on the world ; 2. A fruitful approach ; 3. A world of networks ; 4. Connected and close ; 5. Superconnectors ; 6. Emergence of networks ; 7. Digging deeper into networks ; 8. Perfect storms on networks ; 9. All the world's a net. Or not? ; Further reading","brand":"Oxford University Press","offers":[{"title":"Default Title","offer_id":48732870672727,"sku":"9780199588077","price":9.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780199588077.jpg?v=1719998749"},{"product_id":"linear-algebra-9780199654444","title":"Linear Algebra","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eLinear algebra is a fundamental area of mathematics, and is arguably the most powerful mathematical tool ever developed. It is a core topic of study within fields as diverse as: business, economics, engineering, physics, computer science, ecology, sociology, demography and genetics. For an example of linear algebra at work, one needs to look no further than the Google search engine, which relies upon linear algebra to rank the results of a search with respect to relevance. The strength of the text is in the large number of examples and the step-by-step explanation of each topic as it is introduced. It is compiled in a way that allows distance learning, with explicit solutions to set problems freely available online. The miscellaneous exercises at the end of each chapter comprise questions from past exam papers from various universities, helping to reinforce the reader''s confidence. Also included, generally at the beginning of sections, are short historical biographies of the leading p\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003eThis book gives an introduction to linear algebra for students with limited mathematical preparation. ... The steady pace of the book is so gentle that no student need be left behind. * Peter Macgregor, Mathematical Gazette *\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1. Linear Equations and Matrices ; 2. Euclidean Space ; 3. General Vector Spaces ; 4. Inner Product Spaces ; 5. Linear Transformation ; 6. Determinants ; 7. Eigenvalues and Eigenvectors","brand":"Oxford University Press","offers":[{"title":"Default Title","offer_id":48732876439895,"sku":"9780199654444","price":32.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780199654444.jpg?v=1719998775"},{"product_id":"classification-parameter-estimation-and-state-estimation-an-engineering-approach-using-matlab-9781119152439","title":"Classification Parameter Estimation and State","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eA practical introduction to intelligent computer vision theory, design, implementation, and technology     The past decade has witnessed epic growth in image processing and intelligent computer vision technology.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePreface xi\u003c\/p\u003e \u003cp\u003eAbout the Companion Website xv\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Introduction 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 The Scope of the Book 2\u003c\/p\u003e \u003cp\u003e1.1.1 Classification 3\u003c\/p\u003e \u003cp\u003e1.1.2 Parameter Estimation 4\u003c\/p\u003e \u003cp\u003e1.1.3 State Estimation 5\u003c\/p\u003e \u003cp\u003e1.1.4 Relations between the Subjects 7\u003c\/p\u003e \u003cp\u003e1.2 Engineering 10\u003c\/p\u003e \u003cp\u003e1.3 The Organization of the Book 12\u003c\/p\u003e \u003cp\u003e1.4 Changes from First Edition 14\u003c\/p\u003e \u003cp\u003e1.5 References 15\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 PRTools Introduction 17\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Motivation 17\u003c\/p\u003e \u003cp\u003e2.2 Essential Concepts 18\u003c\/p\u003e \u003cp\u003e2.3 PRTools Organization Structure and Implementation 22\u003c\/p\u003e \u003cp\u003e2.4 Some Details about PRTools 26\u003c\/p\u003e \u003cp\u003e2.4.1 Datasets 26\u003c\/p\u003e \u003cp\u003e2.4.2 Datafiles 30\u003c\/p\u003e \u003cp\u003e2.4.3 Datafiles Help Information 31\u003c\/p\u003e \u003cp\u003e2.4.4 Classifiers and Mappings 34\u003c\/p\u003e \u003cp\u003e2.4.5 Mappings Help Information 36\u003c\/p\u003e \u003cp\u003e2.4.6 How to Write Your Own Mapping 38\u003c\/p\u003e \u003cp\u003e2.5 Selected Bibliography 42\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Detection and Classification 43\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Bayesian Classification 46\u003c\/p\u003e \u003cp\u003e3.1.1 Uniform Cost Function and Minimum Error Rate 53\u003c\/p\u003e \u003cp\u003e3.1.2 Normal Distributed Measurements; Linear and Quadratic Classifiers 56\u003c\/p\u003e \u003cp\u003e3.2 Rejection 62\u003c\/p\u003e \u003cp\u003e3.2.1 Minimum Error Rate Classification with Reject Option 63\u003c\/p\u003e \u003cp\u003e3.3 Detection: The Two-Class Case 66\u003c\/p\u003e \u003cp\u003e3.4 Selected Bibliography 74\u003c\/p\u003e \u003cp\u003eExercises 74\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Parameter Estimation 77\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Bayesian Estimation 79\u003c\/p\u003e \u003cp\u003e4.1.1 MMSE Estimation 86\u003c\/p\u003e \u003cp\u003e4.1.2 MAP Estimation 87\u003c\/p\u003e \u003cp\u003e4.1.3 The Gaussian Case with Linear Sensors 88\u003c\/p\u003e \u003cp\u003e4.1.4 Maximum Likelihood Estimation 89\u003c\/p\u003e \u003cp\u003e4.1.5 Unbiased Linear MMSE Estimation 91\u003c\/p\u003e \u003cp\u003e4.2 Performance Estimators 94\u003c\/p\u003e \u003cp\u003e4.2.1 Bias and Covariance 95\u003c\/p\u003e \u003cp\u003e4.2.2 The Error Covariance of the Unbiased Linear MMSE Estimator 99\u003c\/p\u003e \u003cp\u003e4.3 Data Fitting 100\u003c\/p\u003e \u003cp\u003e4.3.1 Least Squares Fitting 101\u003c\/p\u003e \u003cp\u003e4.3.2 Fitting Using a Robust Error Norm 104\u003c\/p\u003e \u003cp\u003e4.3.3 Regression 107\u003c\/p\u003e \u003cp\u003e4.4 Overview of the Family of Estimators 110\u003c\/p\u003e \u003cp\u003e4.5 Selected Bibliography 111\u003c\/p\u003e \u003cp\u003eExercises 112\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 State Estimation 115\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 A General Framework for Online Estimation 117\u003c\/p\u003e \u003cp\u003e5.1.1 Models 117\u003c\/p\u003e \u003cp\u003e5.1.2 Optimal Online Estimation 123\u003c\/p\u003e \u003cp\u003e5.2 Infinite Discrete-Time State Variables 125\u003c\/p\u003e \u003cp\u003e5.2.1 Optimal Online Estimation in Linear-Gaussian Systems 125\u003c\/p\u003e \u003cp\u003e5.2.2 Suboptimal Solutions for Non-linear Systems 133\u003c\/p\u003e \u003cp\u003e5.3 Finite Discrete-Time State Variables 147\u003c\/p\u003e \u003cp\u003e5.3.1 Hidden Markov Models 148\u003c\/p\u003e \u003cp\u003e5.3.2 Online State Estimation 152\u003c\/p\u003e \u003cp\u003e5.3.3 Offline State Estimation 156\u003c\/p\u003e \u003cp\u003e5.4 Mixed States and the Particle Filter 163\u003c\/p\u003e \u003cp\u003e5.4.1 Importance Sampling 164\u003c\/p\u003e \u003cp\u003e5.4.2 Resampling by Selection 166\u003c\/p\u003e \u003cp\u003e5.4.3 The Condensation Algorithm 167\u003c\/p\u003e \u003cp\u003e5.5 Genetic State Estimation 170\u003c\/p\u003e \u003cp\u003e5.5.1 The Genetic Algorithm 170\u003c\/p\u003e \u003cp\u003e5.5.2 Genetic State Estimation 176\u003c\/p\u003e \u003cp\u003e5.5.3 Computational Issues 177\u003c\/p\u003e \u003cp\u003e5.6 State Estimation in Practice 183\u003c\/p\u003e \u003cp\u003e5.6.1 System Identification 185\u003c\/p\u003e \u003cp\u003e5.6.2 Observability, Controllability and Stability 188\u003c\/p\u003e \u003cp\u003e5.6.3 Computational Issues 193\u003c\/p\u003e \u003cp\u003e5.6.4 Consistency Checks 196\u003c\/p\u003e \u003cp\u003e5.7 Selected Bibliography 201\u003c\/p\u003e \u003cp\u003eExercises 204\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Supervised Learning 207\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Training Sets 208\u003c\/p\u003e \u003cp\u003e6.2 Parametric Learning 210\u003c\/p\u003e \u003cp\u003e6.2.1 Gaussian Distribution, Mean Unknown 211\u003c\/p\u003e \u003cp\u003e6.2.2 Gaussian Distribution, Covariance Matrix Unknown 212\u003c\/p\u003e \u003cp\u003e6.2.3 Gaussian Distribution, Mean and Covariance Matrix Both Unknown 213\u003c\/p\u003e \u003cp\u003e6.2.4 Estimation of the Prior Probabilities 215\u003c\/p\u003e \u003cp\u003e6.2.5 Binary Measurements 216\u003c\/p\u003e \u003cp\u003e6.3 Non-parametric Learning 217\u003c\/p\u003e \u003cp\u003e6.3.1 Parzen Estimation and Histogramming 218\u003c\/p\u003e \u003cp\u003e6.3.2 Nearest Neighbour Classification 223\u003c\/p\u003e \u003cp\u003e6.3.3 Linear Discriminant Functions 230\u003c\/p\u003e \u003cp\u003e6.3.4 The Support Vector Classifier 237\u003c\/p\u003e \u003cp\u003e6.3.5 The Feedforward Neural Network 242\u003c\/p\u003e \u003cp\u003e6.4 Adaptive Boosting – Adaboost 245\u003c\/p\u003e \u003cp\u003e6.5 Convolutional Neural Networks (CNNs) 249\u003c\/p\u003e \u003cp\u003e6.5.1 Convolutional Neural Network Structure 249\u003c\/p\u003e \u003cp\u003e6.5.2 Computation and Training of CNNs 251\u003c\/p\u003e \u003cp\u003e6.6 Empirical Evaluation 252\u003c\/p\u003e \u003cp\u003e6.7 Selected Bibliography 257\u003c\/p\u003e \u003cp\u003eExercises 257\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Feature Extraction and Selection 259\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Criteria for Selection and Extraction 261\u003c\/p\u003e \u003cp\u003e7.1.1 Interclass\/Intraclass Distance 262\u003c\/p\u003e \u003cp\u003e7.1.2 Chernoff–Bhattacharyya Distance 267\u003c\/p\u003e \u003cp\u003e7.1.3 Other Criteria 270\u003c\/p\u003e \u003cp\u003e7.2 Feature Selection 272\u003c\/p\u003e \u003cp\u003e7.2.1 Branch-and-Bound 273\u003c\/p\u003e \u003cp\u003e7.2.2 Suboptimal Search 275\u003c\/p\u003e \u003cp\u003e7.2.3 Several New Methods of Feature Selection 278\u003c\/p\u003e \u003cp\u003e7.2.4 Implementation Issues 287\u003c\/p\u003e \u003cp\u003e7.3 Linear Feature Extraction 288\u003c\/p\u003e \u003cp\u003e7.3.1 Feature Extraction Based on the Bhattacharyya Distance with Gaussian Distributions 291\u003c\/p\u003e \u003cp\u003e7.3.2 Feature Extraction Based on Inter\/Intra Class Distance 296\u003c\/p\u003e \u003cp\u003e7.4 References 300\u003c\/p\u003e \u003cp\u003eExercises 300\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Unsupervised Learning 303\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Feature Reduction 304\u003c\/p\u003e \u003cp\u003e8.1.1 Principal Component Analysis 304\u003c\/p\u003e \u003cp\u003e8.1.2 Multidimensional Scaling 309\u003c\/p\u003e \u003cp\u003e8.1.3 Kernel Principal Component Analysis 315\u003c\/p\u003e \u003cp\u003e8.2 Clustering 320\u003c\/p\u003e \u003cp\u003e8.2.1 Hierarchical Clustering 323\u003c\/p\u003e \u003cp\u003e8.2.2 K-Means Clustering 327\u003c\/p\u003e \u003cp\u003e8.2.3 Mixture of Gaussians 329\u003c\/p\u003e \u003cp\u003e8.2.4 Mixture of probabilistic PCA 335\u003c\/p\u003e \u003cp\u003e8.2.5 Self-Organizing Maps 336\u003c\/p\u003e \u003cp\u003e8.2.6 Generative Topographic Mapping 342\u003c\/p\u003e \u003cp\u003e8.3 References 345\u003c\/p\u003e \u003cp\u003eExercises 346\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Worked Out Examples 349\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Example on Image Classification with PRTools 349\u003c\/p\u003e \u003cp\u003e9.1.1 Example on Image Classification 349\u003c\/p\u003e \u003cp\u003e9.1.2 Example on Face Classification 354\u003c\/p\u003e \u003cp\u003e9.1.3 Example on Silhouette Classification 357\u003c\/p\u003e \u003cp\u003e9.2 Boston Housing Classification Problem 361\u003c\/p\u003e \u003cp\u003e9.2.1 Dataset Description 361\u003c\/p\u003e \u003cp\u003e9.2.2 Simple Classification Methods 363\u003c\/p\u003e \u003cp\u003e9.2.3 Feature Extraction 365\u003c\/p\u003e \u003cp\u003e9.2.4 Feature Selection 367\u003c\/p\u003e \u003cp\u003e9.2.5 Complex Classifiers 368\u003c\/p\u003e \u003cp\u003e9.2.6 Conclusions 371\u003c\/p\u003e \u003cp\u003e9.3 Time-of-Flight Estimation of an Acoustic Tone Burst 372\u003c\/p\u003e \u003cp\u003e9.3.1 Models of the Observed Waveform 374\u003c\/p\u003e \u003cp\u003e9.3.2 Heuristic Methods for Determining the ToF 376\u003c\/p\u003e \u003cp\u003e9.3.3 Curve Fitting 377\u003c\/p\u003e \u003cp\u003e9.3.4 Matched Filtering 379\u003c\/p\u003e \u003cp\u003e9.3.5 ml Estimation Using Covariance Models for the Reflections 380\u003c\/p\u003e \u003cp\u003e9.3.6 Optimization and Evaluation 385\u003c\/p\u003e \u003cp\u003e9.4 Online Level Estimation in a Hydraulic System 392\u003c\/p\u003e \u003cp\u003e9.4.1 Linearized Kalman Filtering 394\u003c\/p\u003e \u003cp\u003e9.4.2 Extended Kalman Filtering 397\u003c\/p\u003e \u003cp\u003e9.4.3 Particle Filtering 398\u003c\/p\u003e \u003cp\u003e9.4.4 Discussion 403\u003c\/p\u003e \u003cp\u003e9.5 References 406\u003c\/p\u003e \u003cp\u003eAppendix A: Topics Selected from Functional Analysis 407\u003c\/p\u003e \u003cp\u003eAppendix B: Topics Selected from Linear Algebra and Matrix Theory 421\u003c\/p\u003e \u003cp\u003eAppendix C: Probability Theory 437\u003c\/p\u003e \u003cp\u003eAppendix D: Discrete-Time Dynamic Systems 453\u003c\/p\u003e \u003cp\u003eIndex 459\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":48738357281111,"sku":"9781119152439","price":89.96,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781119152439.jpg?v=1723811969"},{"product_id":"fluid-dynamics-via-examples-and-solutions-9781439888827","title":"Fluid Dynamics via Examples and Solutions","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cstrong\u003eFluid Dynamics via Examples and Solutions\u003c\/strong\u003e provides a substantial set of example problems and detailed model solutions covering various phenomena and effects in fluids. The book is ideal as a supplement or exam review for undergraduate and graduate courses in fluid dynamics, continuum mechanics, turbulence, ocean and atmospheric sciences, and related areas. It is also suitable as a main text for fluid dynamics courses with an emphasis on learning by example and as a self-study resource for practicing scientists who need to learn the basics of fluid dynamics.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThe author covers several sub-areas of fluid dynamics, types of flows, and applications. He also includes supplementary theoretical material when necessary. Each chapter presents the background, an extended list of references for further reading, numerous problems, and a complete set of model solutions.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\"There is no better way to fall in love with a particular subject then to learn it through problem solving. Sergey Nazarenko has created an important resource for mathematics and physics students and young researchers by introducing basics and techniques of fluid dynamics. Anyone involved in teaching fluid dynamics will treasure this book because it provides a clear path to help convey the beauty, elegance, and sophistication of this enticing area of science.\"\u003cbr\u003e—Professor Natalia Berloff, Department of Applied Mathematics and Theoretical Physics, University of Cambridge and Skolkovo Institute of Science and Technology\u003c\/p\u003e\u003cp\u003e\"This is an excellent book for fluid dynamics students. It gives a good overview of the theory through a large set of worthy example problems. After many classical textbooks on the subject, there is finally one with solved exercises. I fully appreciate the selection of topics.\"\u003cbr\u003e—Professor Miguel Onorato, Physics Department, University of Torino\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eFluid Equations and Different Regimes of Fluid Flows. Conservation Laws in Incompressible Fluid Flows. Fluid with Free Surface. Waves and Instabilities. Boundary Layers. Two-Dimensional Flows. Point Vortices and Point Sources. Turbulence. Compressible Flow. Bibliography. Index.","brand":"Taylor \u0026 Francis Inc","offers":[{"title":"Default Title","offer_id":48739203154263,"sku":"9781439888827","price":58.89,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781439888827.jpg?v=1720051472"},{"product_id":"advanced-calculus-9781441973313","title":"Advanced Calculus","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eWith a fresh geometric approach that incorporates more than 250  illustrations, this textbook sets itself apart from all others in  advanced calculus.  Besides the classical  capstones--the change of variables formula, implicit and inverse  function theorems, the integral theorems of Gauss and Stokes--the text  treats other important topics in differential analysis, such as Morse''s  lemma and the Poincaré lemma.  The ideas behind  most topics can be understood with just two or three variables.  The book  incorporates modern computational tools to give visualization real  power.  Using 2D and 3D graphics, the book offers new  insights into fundamental elements of the calculus of differentiable  maps.  The geometric theme  continues with an analysis of the physical meaning of the divergence and  the curl at a level of detail not found in other advanced calculus  books.  This is a  textbook for undergraduates and graduate students in mathematics, the  physical sciences, and economics.  Prerequisites  are an introduction to linear algebra and multivariable calculus.  There is enough material for a year-long course on  advanced calculus and for a variety of semester courses--including  topics in geometry.  The measured pace of  the book, with its extensive examples and illustrations, make it  especially suitable for independent study.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eFrom the reviews:\u003c\/p\u003e\u003cp\u003e“Many concepts in calculus and linear algebra have obvious geometric interpretations. … This book differs from other advanced calculus works … it can serve as a useful reference for professors. … it is the adopted course resource, its inclusion in a college library’s collection should be determined by the size and interests of the mathematics faculty. Summing Up … . Upper-division undergraduate through professional collections.” (C. Bauer, Choice, Vol. 48 (8), April, 2011)\u003c\/p\u003e\u003cp\u003e“The author of this book sees an opportunity to bring back a more geometric, visual and physically-motivated approach to the subject. … The author makes exceptionally good use of two and three-dimensional graphics. Drawings and figures are abundant and strongly support his exposition. Exercises are plentiful and they cover a range from routine computational work to proofs and extensions of results from the text. … Strong students … are likely to be attracted by the approach and the serious meaty content.” (William J. Satzer, The Mathematical Association of America, January, 2011)\u003c\/p\u003e\u003cp\u003e“A new geometric and visual approach to advanced calculus is presented. … The book can be useful a textbook for beginners as well as a source of supplementary material for university teachers in calculus and analysis. … the book meets a wide auditorium among undergraduate and graduate students in mathematics, physics, economics and in other fields which essentially use mathematical models. It is also very interesting for teachers and instructors in Calculus and Mathematical Analysis.” (Sergei V. Rogosin, Zentralblatt MATH, Vol. 1205, 2011)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1 Starting Points.-1.1 Substitution.- Exercises.- 1.2 Work and path integrals.- Exercises.- 1.3 Polar coordinates.- Exercises.- 2 Geometry of Linear Maps.- 2.1 Maps from R2 to R2.- Exercises.- 2.2 Maps from Rn to Rn.- Exercises.- 2.3 Maps from Rn to Rp, n 6= p.- Exercises.- 3 Approximations.- 3.1 Mean-value theorems.- Exercises.- 3.2 Taylor polynomials in one variable.- Exercises.- 3.3 Taylor polynomials in several variables.- Exercises.- 4 The Derivative.- 4.1 Differentiability.- Exercises.- 4.2 Maps of the plane.- Exercises.- 4.3 Parametrized surfaces.- Exercises.- 4.4 The chain rule.- Exercises.- 5 Inverses.- 5.1 Solving equations.- Exercises.- 5.2 Coordinate Changes.- Exercises.- 5.3 The Inverse Function Theorem.- Exercises.- 6 Implicit Functions.- 6.1 A single equation.- Exercises.- 6.2 A pair of equations.- Exercises.- 6.3 The general case.- Exercises.- 7 Critical Points.- 7.1 Functions of one variable.- Exercises.- 7.2 Functions of two variables.- Exercises.- 7.3 Morse’s lemma.- Exercises.- 8 Double Integrals.- 8.1 Example: gravitational attraction.- Exercises.- 8.2 Area and Jordan content.- Exercises.- 8.3 Riemann and Darboux integrals.- Exercises.- 9 Evaluating Double Integrals.- 9.1 Iterated integrals.- Exercises.- 9.2 Improper integrals.- Exercises.- 9.3 The change of variables formula.- 9.4 Orientation.- Exercises.- 9.5 Green’s Theorem.- Exercises.- 10 Surface Integrals.- 10.1 Measuring flux.- Exercises.- 10.2 Surface area and scalar integrals.- Exercises.- 10.3 Differential forms.- Exercises.- 11 Stokes’ Theorem.- 11.1 Divergence.- Exercises.- 11.2 Circulation and Vorticity.- Exercises.- 11.3 Stokes’ Theorem.- 11.4 Closed and Exact Forms.- Exercises","brand":"Springer-Verlag New York Inc.","offers":[{"title":"Default Title","offer_id":48739210068311,"sku":"9781441973313","price":53.09,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781441973313.jpg?v=1720051499"},{"product_id":"pluses-and-minuses-9781474612487","title":"Pluses and Minuses","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eA concise guide to the wonderful world of mathematics, that makes connections with the world around us\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003eAn illuminating history of mathematics that also touches on fascinating philosophical questions surrounding maths. * Publishers Weekly *","brand":"Orion Publishing Co","offers":[{"title":"Default Title","offer_id":48739608625495,"sku":"9781474612487","price":9.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781474612487.jpg?v=1720052727"},{"product_id":"theoretical-and-computational-research-in-the-21st-century-9781771880336","title":"Theoretical and Computational Research in the","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis book focuses mainly on the recent developments of all types of theoretical, mathematical, and computational conceptions, as well as modelling and simulation of specific research themes covering all scientific and technical disciplines from chemistry, physics, and engineering to biology and medicine. The book contains timely reviews and research covering fundamental and applied research aspects in all disciplines of natural sciences, including their historical representations and philosophical perspectives. \u003c\/p\u003e\u003cp\u003eThe book discusses the fact that the largest and smallest values of the fukui function and local softness do not necessarily correspond to the softness and hardness regions of the molecules such as porphyrins. The authors have adopted two popular calculation procedures for this venture. One is the very old Hückel molecular orbital calculation, and the other is one of best semi-empirical AM-1 procedures for such systems. Our finding is that neither the fukui functions nor the local softnesses can predict the preferred donor sites of porphyrins toward metal ions. \u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePreface. The Time Evolution of the Hard and Soft Acids and Bases (HSAB) Theory. Magneto Hydrodynamic Effects on an Atherosclerotic Artery: A Theoretical Study. A Fast Solver for the Backward Heat Conduction Problem in Unbounded Domains. Steganographic Method for Color Images Using Variance Field Estimation and Scaling Factor for Energy Conservation. Breviary of Quantum Computation. Classical Charged Particles in Arbitrary Motion. Second Order Linear Differential Equation in Its Exact Form. On the Operator Exp( 2 Λ (P + Q)). Quantum Computational Studies on Porphycene. The Evaluation of Protonation Energy of Molecules in Terms of Quantum Theoretical Descriptors. Analysis of Casson Fluid Model for Blood Flow in Externally Applied Magnetic Field. Index.\u003c\/p\u003e","brand":"Apple Academic Press Inc.","offers":[{"title":"Default Title","offer_id":48740962566487,"sku":"9781771880336","price":114.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781771880336.jpg?v=1720056149"},{"product_id":"applied-mathematics-for-ccea-as-level-9781780733456","title":"Applied Mathematics for CCEA AS Level","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis resource has been developed to fully cover unit AS 2: Applied Mathematics of the CCEA specification, addressing both mechanics and statistics.\u003cbr\u003e\u003cbr\u003eFor each topic, the book begins with a logical explanation of the theory, examples to reinforce the explanation, and any key words and definitions that are required. Examples and definitions are clearly differentiated to ease revision and progression through the book. The material then flows into exercises, before introducing the next topic. In this way, the student is guided through the subject.\u003cbr\u003e\u003cbr\u003eThe book contains a large number of exercises in order to provide teachers with as much flexibility as possible for their students. Answers to the questions are included at the back of the book.   \u003cstrong\u003eContents:\u003c\/strong\u003e 1 Concepts in Mechanics; 2 Kinematics; Constant Acceleration; 3 Motion Graphs; 4 Forces; 5 Newton's Laws; 6 Friction; 7 Connected Bodies; 8 Statistical Sampling; 9 Data Presentation and Interpretation; 10 Central Tendency and Variation; 11 Correlation and Regression; 12 Data Cleaning; 13 Probability; 14 Binomial Distribution","brand":"Colourpoint Creative Ltd","offers":[{"title":"Default Title","offer_id":48741014045015,"sku":"9781780733456","price":32.47,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781780733456.jpg?v=1720056317"},{"product_id":"applied-mathematics-for-ccea-a2-level-9781780733470","title":"Applied Mathematics for CCEA A2 Level","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis resource has been developed to fully cover unit A2 2: Applied Mathematics of the CCEA specification, addressing both mechanics and statistics.\u003cbr\u003e\u003cbr\u003eFor each topic, the book begins with a logical explanation of the theory, examples to reinforce the explanation, and any key words and definitions that are required. Examples and definitions are clearly differentiated to ease revision and progression through the book. The material then flows into exercises, before introducing the next topic. In this way, the student is guided through the subject.\u003cbr\u003e\u003cbr\u003eThe book contains a large number of exercises in order to provide teachers with as much flexibility as possible for their students. Answers to the questions are included at the back of the book.   \u003cstrong\u003eContents:\u003c\/strong\u003e 1 Kinematics; 2 Projectiles; 3 Moments; 4 Impulse and Momentum; 5 Probability; 6 Statistical Distributions; 7 Statistical Hypothesis Testing","brand":"Colourpoint Creative Ltd","offers":[{"title":"Default Title","offer_id":48741014241623,"sku":"9781780733470","price":999.99,"currency_code":"GBP","in_stock":false}]},{"product_id":"mathematical-methods-and-models-in-composites-9781800611870","title":"Mathematical Methods And Models In Composites","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eMathematical Methods and Models in Composites (Second Edition) provides an in-depth treatment of modern and rigorous mathematical methods and models applied to composites modeling on the micro-, meso-, and macro scale. There has been a steady growth in the diversity of such methods and models that are used in the analysis and characterization of composites, their behavior, and their associated phenomena and processes. This second edition expands upon the success of the first edition, and has been substantially revised and updated.Written by well-known experts in different areas of applied mathematics, physics, and composite engineering, this book is mainly focused on continuous fiber reinforced composites and their ever increasing range of applications (for example, in the aerospace industry), though it also covers other kind of composites. The chapters cover a range of topics including, but not limited to: scaling and homogenization procedures in composites, thin plate and wave solutions in anisotropic materials, laminated structures, fiber-reinforced nonlinearly elastic solids, buckling and postbuckling, fracture and damage analysis of composites, and highly efficient methods for simulation of composites manufacturing such as resin transfer molding. The results presented are useful for the design, fabrication, testing and industrial applications of composite components and structures.This book is an essential reference for graduate and doctoral students, as well as researchers in mathematics, physics and composite engineering. Explanations and references in the book are sufficiently detailed so as to provide the necessary background to further investigate the fascinating subject of composites modeling and explore relevant research literature. It is also suitable for non-experts who wish to have an overview of the mathematical methods and models used for composites, and of the open problems in this area that require further research.","brand":"World Scientific Europe Ltd","offers":[{"title":"Default Title","offer_id":48741754044759,"sku":"9781800611870","price":157.5,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781800611870.jpg?v=1720058694"},{"product_id":"quantum-mechanics-for-pedestrians-2-applications-and-extensions-9783030004668","title":"Quantum Mechanics for Pedestrians 2: Applications","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis book, the second in a two-volume set, provides an introduction to the basics of (mainly) non-relativistic quantum mechanics. While the first volume addresses the basic principles, this second volume discusses applications and extensions to more complex problems. In addition to topics dealt with in traditional quantum mechanics texts, such as symmetries or many-body problems, it also treats issues of current interest such as entanglement, Bell’s inequality, decoherence and various aspects of quantum information in detail. Furthermore, questions concerning the basis of quantum mechanics and epistemological issues which are relevant e.g. to the realism debate are discussed explicitly. A chapter on the interpretations of quantum mechanics rounds out the book. \u003c\/p\u003e  Readers are introduced to the requisite mathematical tools step by step. In the appendix, the most relevant mathematics is compiled in compact form, and more advanced topics such as the Lenz vector, Hardy’s experiment and Shor’s algorithm are treated in more detail. As an essential aid to learning and teaching, 130 exercises are included, most of them with solutions.\u003cp\u003e\u003c\/p\u003e  \u003cp\u003eThis revised second edition is expanded by an introduction into some ideas and problems of relativistic quantum mechanics. In this second volume, an overview of quantum field theory is given and basic conceptions of quantum electrodynamics are treated in some detail. \u003c\/p\u003e  \u003cp\u003eOriginally written as a course for students of science education, the book addresses all those science students and others who are looking for a reasonably simple, fresh and modern introduction to the field.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e“This book continues the excellent introduction to quantum mechanics of the first volume ... suited for beginners to get first insights which may be deepened reading the appendices. The two volumes can be best recommended generally and especially for self studies.” (K.-E. Hellwig, zbMATH 1445.81002, 2020)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eOne-Dimensional Piecewise-Constant Potentials.- Angular Momentum.- The Hydrogen Atom.- The Harmonic Oscillator.- Perturbation Theory.- Entanglement, EPR, Bell.- Symmetries and Conservation Laws.- The Density Operator.- Identical Particles.- Decoherence.- Scattering.- Quantum Information.- Is Quantum Mechanics Complete?.- Interpretations of Quantum Mechanics.\u003cp\u003e\u003c\/p\u003e","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":48743021052247,"sku":"9783030004668","price":54.99,"currency_code":"GBP","in_stock":true}]},{"product_id":"continuous-time-asset-pricing-theory-a-martingale-based-approach-9783030744090","title":"Continuous-Time Asset Pricing Theory: A","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eAsset pricing theory yields deep insights into crucial market phenomena such as stock market bubbles. Now in a newly revised and updated edition, this textbook guides the reader through this theory and its applications to markets. The new edition features ​new results on state dependent preferences, a characterization of market efficiency and a more general presentation of multiple-factor models using only the assumptions of no arbitrage and no dominance. \u003c\/p\u003e\u003cp\u003eTaking an innovative approach based on martingales, the book presents advanced techniques of mathematical finance in a business and economics context, covering a range of relevant topics such as derivatives pricing and hedging, systematic risk, portfolio optimization, market efficiency, and equilibrium pricing models. For applications to high dimensional statistics and machine learning, new multi-factor models are given. This new edition integrates suicide trading strategies into the understanding of asset price bubbles, greatly enriching the overall presentation and further strengthening the book’s underlying theme of economic bubbles.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eWritten by a leading expert in risk management, \u003ci\u003eContinuous-Time Asset Pricing Theory\u003c\/i\u003e is the first textbook on asset pricing theory with a martingale approach. Based on the author’s extensive teaching and research experience on the topic, it is particularly well suited for graduate students in business and economics with a strong mathematical background.\u003c\/p\u003e   \u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":48743048053079,"sku":"9783030744090","price":54.99,"currency_code":"GBP","in_stock":true}]},{"product_id":"foundation-mathematics-for-science-and-engineering-students-9783030919627","title":"Foundation Mathematics for Science and","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis compact textbook provides a foundation in mathematics for STEM students entering university. The book helps students from different disciplines and backgrounds make the transition to university.  Based on the author’s teaching for many years, the book can be used as a textbook and a resource for lecturers and professors. Its accessibility is such that it is can also be used by students in their final year in school before university and help them continue their mathematical studies at college. The book is designed so that students will return to the book repeatedly as their undergraduate careers progress. Although compact and concise, it loses no rigour. All the topics are carefully explained meaningfully, not just presented as a set of rules or rote-learned procedures.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eTrigonometry.- Real and Complex Numbers.- Vector Algebra.- Matrices.- Differentiation.\u003c\/p\u003e","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":48743058440535,"sku":"9783030919627","price":58.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030919627.jpg?v=1720063928"},{"product_id":"a-brief-history-of-mathematics-a-promenade-through-the-civilizations-of-our-world-9783031268403","title":"A Brief History of Mathematics: A Promenade","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis volume, originally published in China and translated into four other languages, presents a fascinating and unique account of the history of mathematics, divided into eight chronologically organized chapters. Tracing the development of mathematics across disparate regions and peoples, with particular emphasis on the relationship between mathematics and civilization, it examines mathematical sources and inspirations leading from Egypt, Babylon and ancient Greece and expanding to include Chinese, Indian and Arabic mathematics, the European Renaissance and the French revolution up through the Nineteenth and Twentieth Centuries. Each chapter explores connections among mathematics and cultural elements of the time and place treated, accompanying the reader in a varied and exciting journey through human civilizations. The book contemplates the intersections of mathematics with other disciplines, including the relationship between modern mathematics and modern art, and the resulting applications, with the aid of images and photographs, often taken by the author, which further enhance the enjoyment for the reader.  \u003cbr\u003eWritten for a general audience, this book will be of interest to anyone who's studied mathematics in university or even high school, while also benefiting researchers in mathematics and the humanities. \u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1. The Middle East, or the Beginning.- 2. The Sages of Ancient Greece.- 3. The Chinese Middle Ages.- 4. India and Persia.- 5. From the Renaissance to the Birth of Calculus.- 6. The Age of Analysis and the French Revolution.- 7. Modern Mathematics, Modern Art.- 8. Abstraction: Mathematics Since the Twentieth Century.","brand":"Birkhauser Verlag AG","offers":[{"title":"Default Title","offer_id":48743077970263,"sku":"9783031268403","price":28.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031268403.jpg?v=1720064014"},{"product_id":"dark-and-bright-mathematics-hidden-harmony-in-art-history-and-culture-9783031362545","title":"Dark and Bright Mathematics: Hidden Harmony in","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eWas it necessary for a 17th century painter to know principles of optics to hide a skull in one of his masterpieces? Is it possible the violent deaths of Roman emperors obey a statistical law? Are there connections between market trends and geometry? How did Islamic artists draw almost perfectly regular nine-sided polygons, when these cannot be traced with the use of compasses? Dirk Huylebrouk asks these and other exciting questions in this collection of essays, originally written for the science magazine EOS, a Dutch equivalent of Scientific American, distributed in Belgium and in The Netherlands. Every chapter can be read independently, as some subjects are repeated, and not strictly interconnected. Such is the case for instance of the golden section, an often-recurring topic in general mathematics. The reader will appreciate the original point of view expressed through each chapter, which makes this book stand out against the general information one can find by browsing the general media. The subtly provocative character of some parts is meant to stimulate the reader for further exploration. The book's title itself may already generate surprise. Sure, to many, mathematics seems to come from hell, but the darkness in the title in fact refers to the lugubrious stories about math and skulls, murders or World War II. There is also a more down-to-earth part about math and maps, money, Facebook, folding paper, shapes in ice and the most earthly yet unsolved math problems. ‘Bright mathematics’ alludes to Vedic, Islam, New Age, a meta-divine section, and is concluded by an interview with a top mathematician who also wrote about the existence of God.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eHell, Earth and Heaven in One Painting.- Hitler’s Math.- Guernica.- Architect-Alchemist.- War Hero, Math Genius, Martyr.- Murder and Higher Math.- Murdering Emperors.- When the Dead Talk in Code.\u003c\/p\u003e","brand":"Birkhauser Verlag AG","offers":[{"title":"Default Title","offer_id":48743082099031,"sku":"9783031362545","price":20.9,"currency_code":"GBP","in_stock":false}]},{"product_id":"mathematical-principles-of-topological-and-geometric-data-analysis-9783031334399","title":"Mathematical Principles of Topological and","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis book explores and demonstrates how geometric tools can be used in data analysis. Beginning with a systematic exposition of the mathematical prerequisites, covering topics ranging from category theory to algebraic topology, Riemannian geometry, operator theory and network analysis, it goes on to describe and analyze some of the most important machine learning techniques for dimension reduction, including the different types of manifold learning and kernel methods. It also develops a new notion of curvature of generalized metric spaces, based on the notion of hyperconvexity, which can be used for the topological representation of geometric information.\u003c\/p\u003e\u003cp\u003eIn recent years there has been a fascinating development: concepts and methods originally created in the context of research in pure mathematics, and in particular in geometry, have become powerful tools in machine learning for the analysis of data. The underlying reason for this is that data are typically equipped with some kind of notion of distance, quantifying the differences between data points. Of course, to be successfully applied, the geometric tools usually need to be redefined, generalized, or extended appropriately.\u003c\/p\u003e\u003cp\u003ePrimarily aimed at mathematicians seeking an overview of the geometric concepts and methods that are useful for data analysis, the book will also be of interest to researchers in machine learning and data analysis who want to see a systematic mathematical foundation of the methods that they use.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eIntroduction.- Topological foundations, hypercomplexes and homology.- Weighted complexes, cohomology and Laplace operators.- The Laplace operator and the geometry of graphs.- Metric spaces and manifolds.- Linear methods: Kernels, variations, and averaging.- Nonlinear schemes: Clustering, feature extraction and dimension reduction.- Manifold learning, the scheme of Laplacian eigenmaps.- Metrics and curvature.\u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743082164567,"sku":"9783031334399","price":53.99,"currency_code":"GBP","in_stock":true}]},{"product_id":"music-and-astronomy-from-pythagoras-to-steven-spielberg-9783031415234","title":"Music and Astronomy: From Pythagoras to Steven","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis book explores the profound and ancient relationship between music and astronomy. Throughout history, Music has occupied a significant place among the disciplines of the \u003ci\u003eQuadrivium\u003c\/i\u003e, which also include Geometry, Arithmetic, and Astronomy. The captivating bond between these two realms has not only inspired eminent scientists like Kepler, Newton, and Einstein, but has also captured the imagination of NASA and astronauts in modern times.\u003c\/p\u003e  \u003cp\u003eThe author delves into various aspects of the intersection between music and astronomy, encompassing everything from ancient cosmological beliefs to groundbreaking discoveries such as the cosmic background radiation and gravitational waves. This enthralling theme has not only stimulated renowned artists like David Bowie and Elton John, but has also served as a muse for movies like \u003ci\u003eClose Encounters of the Third Kind\u003c\/i\u003e.\u003c\/p\u003e  \u003cp\u003eWithin the book, readers will find an extensive photo gallery and a specially curated soundtrack that enhances the reading experience. It caters to a broad audience, appealing to those with a general interest in both music and astronomy, as well as to specialized individuals in either field of study.\u003c\/p\u003e\u003cbr\u003e\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eForeword.- Preface.- ToC.- Introduction.- The Universe Born of Sound.- Everything Is Number. Pythagoras and the Pythagoreans.- The Music of the Spheres in Kepler’s Cosmos.- Musicians and Scientists.- From Newton to Einstein.- The Music of the Cosmos.- The Universe Is Teeming with Music.- Songs of the Space Race.- Space, the Music of the Spheres, and Movies.- Close Encounters of the Third Kind.- Conclusion.- Appendix.- Index of names.\u003c\/p\u003e","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743085375831,"sku":"9783031415234","price":21.84,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031415234.jpg?v=1720064047"},{"product_id":"brownian-motion-martingales-and-stochastic-calculus-9783319310886","title":"Brownian Motion, Martingales, and Stochastic","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis book offers a rigorous and self-contained presentation of stochastic integration and stochastic calculus within the general framework of continuous semimartingales. The main tools of stochastic calculus, including Itô’s formula, the optional stopping theorem and Girsanov’s theorem, are treated in detail alongside many illustrative examples. The book also contains an introduction to Markov processes, with applications to solutions of stochastic differential equations and to connections between Brownian motion and partial differential equations. The theory of local times of semimartingales is discussed in the last chapter.\u003cbr\u003eSince its invention by Itô, stochastic calculus has proven to be one of the most important techniques of modern probability theory, and has been used in the most recent theoretical advances as well as in applications to other fields such as mathematical finance. \u003ci\u003eBrownian Motion, Martingales, and Stochastic Calculus\u003c\/i\u003e provides a strong theoretical background to the reader interested in such developments.\u003cbr\u003eBeginning graduate or advanced undergraduate students will benefit from this detailed approach to an essential area of probability theory. The emphasis is on concise and efficient presentation, without any concession to mathematical rigor. The material has been taught by the author for several years in graduate courses at two of the most prestigious French universities. The fact that proofs are given with full details makes the book particularly suitable for self-study. The numerous exercises help the reader to get acquainted with the tools of stochastic calculus.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e“‘The aim of this book is to provide a rigorous introduction to the theory of stochastic calculus for continuous semi-martingales putting a special emphasis on Brownian motion.’ … If the reader has the background and needs a rigorous treatment of the subject this book would be a good choice. Le Gall writes clearly and gets to the point quickly … .” (Richard Durrett, MAA Reviews, March, 2017) \u003cp\u003e\u003c\/p\u003e\u003cp\u003e“The purpose of this book is to provide concise but rigorous introduction to the theory of stochastic calculus for continuous semimartingales, putting a special emphasis on Brownian motion. … The book is written very clearly, it is interesting both for its construction and maintenance, mostly it is self-contained. It can be recommended to everybody who wants to study stochastic calculus, including those who is interested to its applications in other fields.” (Yuliya S. Mishura, zbMATH, 2017)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eGaussian variables and Gaussian processes.- Brownian motion.- Filtrations and martingales.- Continuous semimartingales.- Stochastic integration.- General theory of Markov processes.- Brownian motion and partial differential equations.- Stochastic differential equations.- Local times.- The monotone class lemma.- Discrete martingales.- References.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743094124887,"sku":"9783319310886","price":38.69,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783319310886.jpg?v=1720064084"},{"product_id":"multivariable-calculus-with-applications-9783319740720","title":"Multivariable Calculus with Applications","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis text in multivariable calculus fosters comprehension through meaningful explanations. Written with students in mathematics, the physical sciences, and engineering in mind, it extends concepts from single variable calculus such as derivative, integral, and important theorems to partial derivatives, multiple integrals, Stokes’ and divergence theorems. Students with a background in single variable calculus are guided through a variety of problem solving techniques and practice problems.\u003c\/p\u003e  Examples from the physical sciences are utilized to highlight the essential relationship between calculus and modern science. The symbiotic relationship between science and mathematics is shown by deriving and discussing several conservation laws, and vector calculus is utilized to describe a number of physical theories via partial differential equations. Students will learn that mathematics is the language that enables scientific ideas to be precisely formulated and that science is a source for the development of mathematics. \u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e“The presentation of the material is guided by applications so that physics and engineering students will find the text engaging and see the relevance of multivariable calculus to their work. The text contains over 500 exercises with answers and\/or solutions to half provided at the back of the book, enabling students to gauge their understanding of the content as they proceed. A well-written, engaging text. Summing Up: Highly recommended. Upper-division undergraduates and professionals.” (J. T. Zerger, Choice, Vol. 56 (03), November, 2018)\u003cbr\u003e“This book belongs to a collection aimed at third- and fourth-year undergraduate mathematics students at North American universities. … There are more than 200 figures to help the reader to understand the explanations and about 500 problems. … I think this book can be recommended since, moreover, it is very pedagogical.” (Richard Becker, Mathematical Reviews, October, 2018)\u003cbr\u003e“Lax and Terrell’s sequel to their Calculus With Applications presents a first course in multivariable calculus that fits in just over 400 pages. Even instructors who use standard texts will find much of value in this refreshing first edition. The book is written with a wide range of STEM students in mind, and its exposition remains remarkably fluid without scarificing precision. Every section of each chapter ends with an excellent collection of exercises, which should be graciously welcomed by independent learners and instructors alike.” (Tushar Das, MAA Reviews, September, 2018)\u003cbr\u003e“The main achievement of the authors is that they essentially have simplified the teaching of the old topics to make a place for new ones. The proofs are exposited to encourage understanding, not meaningless rigor. … the presented book is a useful tool for all mathematicians (not only for students) and I find it regrettable that this book was not written when I was a student.” (Andrey Zahariev, zbMATH 1396.26002, 2018)\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e1. Vectors and matrices.- 2. Functions.- 3. Differentiation.- 4. More about differentiation.- 5. Applications to motion.- 6. Integration.- 7. Line and surface integrals.- 8.  Divergence and Stokes’ Theorems and conservation laws.- 9. Partial differential equations.-  Answers to selected problems.- Index. \u003c\/p\u003e","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743103758679,"sku":"9783319740720","price":50.99,"currency_code":"GBP","in_stock":true}]},{"product_id":"probability-essentials-9783540438717","title":"Probability Essentials","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis introduction can be used, at the beginning graduate level, for a one-semester course on probability theory or for self-direction without benefit of a formal course; the measure theory needed is developed in the text. It will also be useful for students and teachers in related areas such as finance theory, electrical engineering, and operations research. The text covers the essentials in a directed and lean way with 28 short chapters, and assumes only an undergraduate background in mathematics. Readers are taken right up to a knowledge of the basics of Martingale Theory, and the interested student will be ready to continue with the study of more advanced topics, such as Brownian Motion and Ito Calculus, or Statistical Inference.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"(The book is) a lean and largely self-contained introduction to the modern theory of probability, aimed at advanced undergraduate or beginning graduate students. The 28 short chapters belie the book's genesis as polished lecture notes; the exposition is sleek and rigorous and each chapter ends with a supporting collection of mainly routine exercises. ... The authors make it clear what luggage is required for this exhilarating trek,... a good knowledge of advanced calculus, some linear algebra, and some \"mathematical sophistication\". With this understood, the itinerary is immaculately paced and planned with just the right balances of technical ascents and pauses to admire the scenery. Within the constraints of a slim volume, it is hard to imagine how the authors could have done a more effective or more attractive job.\" The Mathematical Gazette, Vol. 84, No 500, 2000 \"The authors provide the shortest path through the twenty-eight chapter headings. The topics are treated in a mathematically and pedagogically digestible way. The writing is concise and crisp: the average chapter length is about eight pages. ... Numerous exercises add to the value of the text as a teaching tool. In conclusion, this is an excellent text for the intended audience.\"\u003cbr\u003eShort Book Reviews, Vol. 21, No. 2, 2001\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1. Introduction 2. Axioms of Probability 3. Conditional Probability and Independence 4. Probabilities on a Countable Space 5. Random Variables on a Countable Space 6. Construction of a Probability Measure 7. Construction of a Probability Measure on R 8. Random Variables 9. Integration with Respect to a Probability Measure 10. Independent Random Variables 11. Probability Distributions on R 12. Probability Distributions on Rn 13. Characteristic Functions 14. Properties of Characteristic Functions 15. Sums of Independent Random Variables 16. Gaussian Random Variables (The Normal and the Multivariate Normal Distributions) 17. Convergence of Random Variables 18. Weak Convergence 19. Weak Convergence and Characteristic Functions 20. The Laws of Large Numbers 21. The Central Limit Theorem 22. L2 and Hilbert Spaces 23. Conditional Expectation 24. Martingales 25. Supermartingales and Submartingales 26. Martingale Inequalities 27. Martingales Convergence Theorems 28. The Radon-Nikodym Theorem","brand":"Springer-Verlag Berlin and Heidelberg GmbH \u0026 Co. KG","offers":[{"title":"Default Title","offer_id":48743130759511,"sku":"9783540438717","price":54.99,"currency_code":"GBP","in_stock":true}]},{"product_id":"geometry-of-minkowski-space-time-9783642179761","title":"Geometry of Minkowski Space-Time","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis book provides an original introduction to the geometry of Minkowski space-time. A hundred years after the space-time formulation of special relativity by Hermann Minkowski, it is shown that the kinematical consequences of special relativity are merely a manifestation of space-time geometry.\u003c\/p\u003e\u003cp\u003eThe book is written with the intention of providing students (and teachers) of the first years of University courses with a tool which is easy to be applied and allows the solution of any problem of relativistic kinematics at the same time. The book treats in a rigorous way, but using a non-sophisticated mathematics, the Kinematics of Special Relativity. As an example, the famous \"Twin Paradox\" is completely solved for all kinds of motions.\u003c\/p\u003e\u003cp\u003eThe novelty of the presentation in this book consists in the extensive use of hyperbolic numbers, the simplest extension of complex numbers, for a complete formalization of the kinematics in the Minkowski space-time.\u003c\/p\u003e\u003cp\u003eMoreover, from this formalization the understanding of gravity comes as a manifestation of curvature of space-time, suggesting new research fields.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eIntroduction.- Hyperbolic Numbers.- Geometrical Representation of Hyperbolic Numbers.- Trigonometry in the Hyperbolic (Minkowski) Plane.- Equilateral Hyperbolas and Triangles in the Hyperbolic Plane.- The Motions in Minkowski Space-Time (Twin Paradox).- Some Final Considerations.","brand":"Springer-Verlag Berlin and Heidelberg GmbH \u0026 Co. KG","offers":[{"title":"Default Title","offer_id":48743134331223,"sku":"9783642179761","price":49.99,"currency_code":"GBP","in_stock":true}]},{"product_id":"financial-math-for-business-and-economics-compendium-of-essential-formulas-9783662676455","title":"Financial Math for Business and Economics:","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThis compendium contains and explains essential mathematical formulas for financial economics and finance. A broad range of aids and supportive examples will help readers to understand the formulas and their practical applications. This mathematical formulary is presented in a practice-oriented, clear, and understandable manner, as it is needed for meaningful and relevant application in global business, as well as in the academic setting and economic practice. \u003c\/p\u003e\u003cp\u003eThe topics presented include but are not limited to accumulation, discounting, annuity, interest calculation, redemption, investment, effective interest rates, ICMA, depreciation, and present value.\u003cbr\u003e\u003c\/p\u003e\u003cp\u003eGiven its scope, the book offers an indispensable reference guide and is a must-read for undergraduate and graduate students, as well as managers, scholars, and lecturers in financial economics and business.\u003cbr\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e  \u003cp\u003e\u003cbr\u003e\u003c\/p\u003e","brand":"Springer-Verlag Berlin and Heidelberg GmbH \u0026 Co. KG","offers":[{"title":"Default Title","offer_id":48743143932247,"sku":"9783662676455","price":66.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783662676455.jpg?v=1720064302"},{"product_id":"mathematical-game-theory-9789811246692","title":"Mathematical Game Theory","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eWhat is a game? Classically, a game is perceived as something played by human beings. Its mathematical analysis is human-centered, explores the structures of particular games, economic or social environments and tries to model supposedly 'rational' human behavior in search of appropriate 'winning strategies'. This point of view places game theory into a very special scientific corner where mathematics, economics and psychology overlap and mingle.This book takes a novel approach to the subject.  Its focus is on mathematical models that apply  to game theory in particular but exhibit a universal character and thus extend the scope of game theory considerably.This textbook addresses anyone interested in a general game-theoretic view of the world. The reader should have mathematical knowledge at the level of a first course in real analysis and linear algebra. However, possibly more specialized aspects are further elaborated and pointers to relevant supplementary literature are given. Moreover, many examples  invite the reader to participate 'actively' when going through the material. The scope of the book can be covered in one course on Mathematical Game Theory at advanced undergraduate or graduate level.","brand":"World Scientific Publishing Co Pte Ltd","offers":[{"title":"Default Title","offer_id":48743282311511,"sku":"9789811246692","price":63.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789811246692.jpg?v=1720064912"},{"product_id":"ordinary-differential-equations-with-applications-third-edition-9789811250743","title":"Ordinary Differential Equations With Applications","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eWritten in a straightforward and easily accessible style, this volume is suitable as a textbook for advanced undergraduate or first-year graduate students in mathematics, physical sciences, and engineering. The aim is to provide students with a strong background in the theories of Ordinary Differential Equations, Dynamical Systems and Boundary Value Problems, including regular and singular perturbations. It is also a valuable resource for researchers.This volume presents an abundance of examples in physical and biological sciences, and engineering to illustrate the applications of the theorems in the text. Readers are introduced to some important theorems in Nonlinear Analysis, for example, Brouwer fixed point theorem and fundamental theorem of algebras.  A chapter on Monotone Dynamical Systems takes care of the new developments in Ordinary Differential Equations and Dynamical Systems.In this third edition, an introduction to Hamiltonian Systems is included to enhance and complete its coverage on Ordinary Differential Equations with applications in Mathematical Biology and Classical Mechanics.","brand":"World Scientific Publishing Co Pte Ltd","offers":[{"title":"Default Title","offer_id":48743283884375,"sku":"9789811250743","price":58.5,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789811250743.jpg?v=1720064919"},{"product_id":"modern-cryptography-volume-1-a-classical-introduction-to-informational-and-mathematical-principle-9789811909191","title":"Modern Cryptography Volume 1: A Classical","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis open access book systematically explores the statistical characteristics of cryptographic systems, the computational complexity theory of cryptographic algorithms and the mathematical principles behind various encryption and decryption algorithms. The theory stems from technology. Based on Shannon's information theory, this book systematically introduces the information theory, statistical characteristics and computational complexity theory of public key cryptography, focusing on the three main algorithms of public key cryptography, RSA, discrete logarithm and elliptic curve cryptosystem. It aims to indicate what it is and why it is. It systematically simplifies and combs the theory and technology of lattice cryptography, which is the greatest feature of this book.\u003cbr\u003eIt requires a good knowledge in algebra, number theory and probability statistics for readers to read this book. The senior students majoring in mathematics, compulsory for cryptography and science and engineering postgraduates will find this book helpful. It can also be used as the main reference book for researchers in cryptography and cryptographic engineering areas.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eChapter 1. Preparatory knowledge.- Chapter 2. The basis of code theory.- Chapter 3. Shannon theory.- Chapter 4. Cryptosystem and authentication system.- Chapter 5. Prime test.- Chapter 6. Elliptic curve.- Chapter 7. Lattice-based cryptography.","brand":"Springer Verlag, Singapore","offers":[{"title":"Default Title","offer_id":48743292993879,"sku":"9789811909191","price":999.99,"currency_code":"GBP","in_stock":false}]},{"product_id":"modern-cryptography-volume-2-a-classical-introduction-to-informational-and-mathematical-principle-9789811976438","title":"Modern Cryptography Volume 2: A Classical","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis open access book covers the most cutting-edge and hot research topics and fields of post-quantum cryptography. The main purpose of this book is to focus on the computational complexity theory of lattice ciphers, especially the reduction principle of Ajtai, in order to fill the gap that post-quantum ciphers focus on the implementation of encryption and decryption algorithms, but the theoretical proof is insufficient. In Chapter 3, Chapter 4 and Chapter 6, author introduces the theory and technology of LWE distribution, LWE cipher and homomorphic encryption in detail. When using random analysis tools, there is a problem of \"ambiguity\" in both definition and algorithm. The greatest feature of this book is to use probability distribution to carry out rigorous mathematical definition and mathematical demonstration for various unclear or imprecise expressions, so as to make it a rigorous theoretical system for classroom teaching and dissemination. Chapters 5 and 7 further expand and improve the theory of cyclic lattice, ideal lattice and generalized NTRU cryptography.\u003cbr\u003eThis book is used as a professional book for graduate students majoring in mathematics and cryptography, as well as a reference book for scientific and technological personnel engaged in cryptography research.\u003cbr\u003e\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eChapter 1. Gauss lattice theory.- Chapter 2. Reduction principle of Ajtai.- Chapter 3. Learning with errors.- Chapter 4. LWE cryptosystem.- Chapter 5. Cyclic lattice and Ideal lattice.- Chapter 6. Fully Homomorphic Encryption.- Chapter 7. General NTRU cryptosystem.","brand":"Springer Verlag, Singapore","offers":[{"title":"Default Title","offer_id":48743294959959,"sku":"9789811976438","price":40.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789811976438.jpg?v=1720064967"},{"product_id":"doing-bayesian-data-analysis-9780124058880","title":"Doing Bayesian Data Analysis","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"Both textbook and practical guide, this work is an accessible account of Bayesian data analysis starting from the basics…This edition is truly an expanded work and includes all new programs in JAGS and Stan designed to be easier to use than the scripts of the first edition, including when running the programs on your own data sets.\" --MAA Reviews   \"fills a gaping hole in what is currently available, and will serve to create its own market\" --Prof. Michael Lee, U. of Cal., Irvine; pres. Society for Mathematical Psych   \"has the potential to change the way most cognitive scientists and experimental psychologists approach the planning and analysis of their experiments\" --Prof. Geoffrey Iverson, U. of Cal., Irvine; past pres. Society for Mathematical Psych.   \"better than others for reasons stylistic.... buy it -- it’s truly amazin’!\" --James L. (Jay) McClelland, Lucie Stern Prof. \u0026amp; Chair, Dept. of Psych., Stanford U.   \"the best introductory textbook on Bayesian MCMC techniques\" --J. of Mathematical Psych.   \"potential to change the methodological toolbox of a new generation of social scientists\" --J. of Economic Psych.   \"revolutionary\" --British J. of Mathematical and Statistical Psych.   \"writing for real people with real data. From the very first chapter, the engaging writing style will get readers excited about this topic\" --PsycCritiques\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1. What’s in This Book (Read This First!)   PART I The Basics: Models, Probability, Bayes’ Rule, and R 2. Introduction: Credibility, Models, and Parameters 3. The R Programming Language 4. What Is This Stuff Called Probability? 5. Bayes’ Rule   PART II All the Fundamentals Applied to Inferring a Binomial Probability 6. Inferring a Binomial Probability via Exact Mathematical Analysis 7. Markov Chain Monte Carlo 8. JAGS 9. Hierarchical Models 10. Model Comparison and Hierarchical Modeling 11. Null Hypothesis Significance Testing 12. Bayesian Approaches to Testing a Point (\"Null\") Hypothesis 13. Goals, Power, and Sample Size 14. Stan   PART III The Generalized Linear Model 15. Overview of the Generalized Linear Model 16. Metric-Predicted Variable on One or Two Groups 17. Metric Predicted Variable with One Metric Predictor 18. Metric Predicted Variable with Multiple Metric Predictors 19. Metric Predicted Variable with One Nominal Predictor 20. Metric Predicted Variable with Multiple Nominal Predictors 21. Dichotomous Predicted Variable 22. Nominal Predicted Variable 23. Ordinal Predicted Variable 24. Count Predicted Variable 25. Tools in the Trunk","brand":"Elsevier Science Publishing Co Inc","offers":[{"title":"Default Title","offer_id":48864158417239,"sku":"9780124058880","price":63.89,"currency_code":"GBP","in_stock":true}]},{"product_id":"things-to-make-and-do-in-the-fourth-dimension-9780141975863","title":"Things to Make and Do in the Fourth Dimension","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cb\u003e''Maths at its most playful and multifarious'' Jordan Ellenberg\u003cbr\u003e\u003cbr\u003eMatt Parker, author of the No.1 bestseller \u003ci\u003eHumble Pi\u003c\/i\u003e, takes us on a riotous journey through the possibilities of numbers \u003cbr\u003e\u003c\/b\u003e\u003cbr\u003eMathematician Matt Parker uses bizarre Klein Bottles, unimaginably small pizza slices, knots no one can untie and computers built from dominoes to reveal some of the most exotic and fascinating ideas in mathematics. Starting with simple numbers and algebra, this book goes on to deal with inconceivably big numbers in more dimensions than you ever knew existed. And always with something for you to make or do along the way.  \u003cbr\u003e\u003cbr\u003e''The book oozes with sheer joy'' \u003ci\u003eNew Scientist\u003cbr\u003e\u003c\/i\u003e\u003cbr\u003e''Matt Parker is some sort of unholy fusion of a prankster, wizard and brilliant nerd - clever, funny and ever so slightly naughty'' Adam Rutherford, author of \u003ci\u003eCreation\u003c\/i\u003e\u003cbr\u003e\u003cbr\u003e''Matt Parker never got the memo about maths being boring ... he seeks to reconnect us to the numbers around us'' Simon Usborne, \u003ci\u003eIndependent\u003c\/i\u003e\u003cbr\u003e\u003cbr\u003e''Essential reading'' \u003ci\u003eObserver\u003c\/i\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003eAn unusual, in-depth but highly accessible popular-maths book by a member of the London Mathematical Society who also has a sideline in stand-up comedy -- Books of the Year * Economist *\u003cbr\u003eMatt Parker is some sort of unholy fusion of a prankster, wizard and brilliant nerd - clever, funny and ever so slightly naughty -- Adam Rutherford, author of CREATION\u003cbr\u003eEssential reading * Observer *\u003cbr\u003eMatt Parker is a lovely, funny, big, dork -- Ben Goldacre\u003cbr\u003eShows off maths at its most playful and multifarious, ranging from classics like knot theory and ruler-and-compass constructions to more whimsical topics like the topology of beer logos and error-correcting scarves -- Jordan Ellenberg, author of HOW NOT TO BE WRONG\u003cbr\u003eThis is the best book on recreational mathematics since Martin Gardner's \u003ci\u003eMy Best Mathematical and Logic Puzzles\u003c\/i\u003e -- Harold D. Shane, Mathematics Emeritus, Baruch Coll., CUNY * Library Journal *","brand":"Penguin Books Ltd","offers":[{"title":"Default Title","offer_id":48864184664407,"sku":"9780141975863","price":12.34,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780141975863.jpg?v=1722270791"},{"product_id":"how-to-think-about-abstract-algebra-9780198843382","title":"How to Think About Abstract Algebra","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eHow to Think about Abstract Algebra provides an engaging and readable introduction to its subject, which encompasses group theory and ring theory.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003eI'd very strongly recommend it to undergraduates studying maths, Sixth formers about to study maths, and anyone who did a maths degree a while ago and wants to revisit groups, rings and fields. I also recommend that any first year pure maths lecturers reading this should add this book to their course's reading list. * Chalkdust *\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e1: What is Abstract Algebra? 2: Axioms and Denitions 3: Theorems and Proofs 4: Studying Abstract Algebra 5: Binary Operations 6: Groups and Subgroups 7: Quotient Groups 8: Isomorphisms and Homomorphisms 9: Rings References","brand":"Oxford University Press","offers":[{"title":"Default Title","offer_id":48864218349911,"sku":"9780198843382","price":21.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780198843382.jpg?v=1722270944"},{"product_id":"love-triangle-9780241505700","title":"Love Triangle","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cb\u003eA #1 SUNDAY TIMES BESTSELLER\u003cbr\u003e \u003cbr\u003e Explore the life-changing magic of trigonometry with Matt Parker, stand-up mathematician and No. 1 bestselling author of \u003ci\u003eHumble Pi\u003c\/i\u003e\u003c\/b\u003e\u003cbr\u003e \u003cbr\u003e Why can no two people ever see the same rainbow? What happens when you pull a pop song apart into pure sine waves and play it back on a piano? Why does the wake behind a duck always form an angle of exactly 39 degrees? And what did mathematicians have to do with the great pig stampede of 2012? The answer to each of these questions can be found in the triangle.\u003cbr\u003e \u003cbr\u003e In \u003ci\u003eLove Triangle\u003c\/i\u003e, stand-up comedian, ex-maths teacher and \u003ci\u003eSunday Times\u003c\/i\u003e number one bestselling author Matt Parker is on a mission to prove why we should all show a lot more love for triangles, along with the useful trigonometry and geometry they enable. To make his point, he uses triangles to create his own digital avatar, survive a harrowing motorcycle ride, cut a sandwich into three equal parts, and measure tall bu\u003c\/p\u003e","brand":"Penguin Books Ltd","offers":[{"title":"Default Title","offer_id":48864274121047,"sku":"9780241505700","price":15.29,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780241505700.jpg?v=1722271185"},{"product_id":"evidencebased-technical-analysis-9780470008744","title":"EvidenceBased Technical Analysis","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003ci\u003eEvidence-Based Technical Analysis\u003c\/i\u003e examines how you can apply the scientific method, and recently developed statistical tests, to determine the true effectiveness of technical trading signals. Throughout the book, expert David Aronson provides you with comprehensive coverage of this new methodology, which is specifically designed for evaluating the performance of rules\/signals that are discovered by data mining.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003ci\u003e\"…\u003c\/i\u003ehis book is well written and contains a great deal of information that is of value….\" (\u003ci\u003eThe Technical Analyst,\u003c\/i\u003e May\/June 2007)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eAcknowledgments.  \u003cp\u003eAbout the Author.\u003c\/p\u003e \u003cp\u003eIntroduction.\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePART I Methodological, Psychological, Philosophical, and Statistical Foundations.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eCHAPTER 1 Objective Rules and Their Evaluation.\u003c\/p\u003e \u003cp\u003eCHAPTER 2 The Illusory Validity of Subjective Technical Analysis.\u003c\/p\u003e \u003cp\u003eCHAPTER 3 The Scientific Method and Technical Analysis.\u003c\/p\u003e \u003cp\u003eCHAPTER 4 Statistical Analysis.\u003c\/p\u003e \u003cp\u003eCHAPTER 5 Hypothesis Tests and Confidence Intervals.\u003c\/p\u003e \u003cp\u003eCHAPTER 6 Data-Mining Bias: The Fool’s Gold of Objective TA.\u003c\/p\u003e \u003cp\u003eCHAPTER 7 Theories of Nonrandom Price Motion.\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePART II Case Study: Signal Rules for the S\u0026amp;P 500 Index.\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eCHAPTER 8 Case Study of Rule Data Mining for the S\u0026amp;P 500.\u003c\/p\u003e \u003cp\u003eCHAPTER 9 Case Study Results and the Future of TA.\u003c\/p\u003e \u003cp\u003eAPPENDIX Proof That Detrending Is Equivalent to Benchmarking Based on Position Bias.\u003c\/p\u003e \u003cp\u003eNotes.\u003c\/p\u003e \u003cp\u003eIndex.\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":48864620740951,"sku":"9780470008744","price":63.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780470008744.jpg?v=1722272762"},{"product_id":"applied-multivariate-techniques-9780471310648","title":"Applied Multivariate Techniques","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis book focuses on when to use the various analytic techniques and how to interpret the resulting output from the most widely used statistical packages (e.g. , SAS, SPSS).\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eGeometric Concepts of Data Manipulation.\u003cbr\u003e \u003cbr\u003e Fundamentals of Data Manipulation.\u003cbr\u003e \u003cbr\u003e Principal Components Analysis.\u003cbr\u003e \u003cbr\u003e Factor Analysis.\u003cbr\u003e \u003cbr\u003e Confirmatory Factor Analysis.\u003cbr\u003e \u003cbr\u003e Cluster Analysis.\u003cbr\u003e \u003cbr\u003e Two-Group Discriminant Analysis.\u003cbr\u003e \u003cbr\u003e Multiple-Group Discriminant Analysis.\u003cbr\u003e \u003cbr\u003e Logistic Regression.\u003cbr\u003e \u003cbr\u003e Multivariate Analysis of Variance.\u003cbr\u003e \u003cbr\u003e Assumptions.\u003cbr\u003e \u003cbr\u003e Canonical Correlation.\u003cbr\u003e \u003cbr\u003e Covariance Structure Models.\u003cbr\u003e \u003cbr\u003e Statistical Tables.\u003cbr\u003e \u003cbr\u003e References.\u003cbr\u003e \u003cbr\u003e Tables, Figures, and Exhibits.\u003cbr\u003e \u003cbr\u003e Index.","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":48864647020887,"sku":"9780471310648","price":223.16,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780471310648.jpg?v=1722272882"},{"product_id":"information-theory-9780486665214","title":"Information Theory","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e","brand":"Dover Publications Inc.","offers":[{"title":"Default Title","offer_id":48864740344151,"sku":"9780486665214","price":13.04,"currency_code":"GBP","in_stock":true}]},{"product_id":"viewpoints-9780691125923","title":"Viewpoints","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eSuitable for students of all mathematics and art levels, this title focuses on two mathematical areas: perspective related to drawing man-made forms and fractal geometry related to drawing natural forms. It encourages experimentation and collaboration, and captures the essence of artistic and mathematical creation and discovery.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"The book goes a long way trying to convey to its audience--through both theory and practice--professional techniques that could not fail but empower students to make accurate, sophisticated drawings. The book presents an elegant fusion of mathematical ideas and practical aspects of fine art.\"--Cut the Knot \"[T]his is an excellent text that I will certainly consider using for a future class. The material on perspective is accessible, thorough and well-written, and the text is designed for a hands-on pedagogy that is well-suited to the intended audience. And as an elementary, but thorough, discussion of both the mathematics and practice of perspective drawing, it deserves a place in any collection of books on mathematics and the arts.\"--Blake Mellor, Journal of Mathematics and the Arts \"The writing is extremely clear, the material is fresh, and the many excellent diagrams clarify the ideas under discussion. The authors use relevant artwork to illustrate the mathematical principles... The exercises are original and promote active learning... This is an excellent work for academic curricula and an outstanding resource for self-study in mathematical perspective, fractals, and the relationship between art and mathematics.\"--Choice \"This is not a book to read passively and, indeed, you will want to read this book with a pencil in hand. The text is designed to be experienced first hand, sketching out examples whilst following the text, as well as doing the exercises at the end of each chapter that develop the material well... Prerequisites for this book are a minimum, effectively being an understanding of basic coordinate geometry. I would recommend this book to anyone who is interested in the interplay between mathematics and art.\"--George Matthews, Mathematics Today\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface vii Acknowledgments ix   Chapter 1: Introduction to Perspective and Space Coordinates 1 Artist Vignette: Sherry Stone 9   Chapter 2: Perspective by the Numbers 13 Artist Vignette: Peter Galante 25   Chapter 3: Vanishing Points and Viewpoints 29 Artist Vignette: Jim Rose 39   Chapter 4: Rectangles in One-Point Perspective 43 What's My Line?: A Perspective Game 55   Chapter 5: Two-Point Perspective 59 Artist Vignette: Robert Bosch 77   Chapter 6: Three-Point Perspective and Beyond 85 Artist Vignette: Dick Termes 113   Chapter 7: Anamorphic Art 117 Viewpoints at the Movies: The Hitchcock Zoom 135 Plates follow page 138   Chapter 8: Introduction to Fractal Geometry 139 Artist Vignette: Teri Wagner 157   Chapter 9: Fractal Dimension 161 Artist Vignette: Kerry Mitchell 193 Answers to Selected Exercises 197   Appendix: Information for Instructors 215 Annotated References 223 Index 229","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":48865518879063,"sku":"9780691125923","price":46.75,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691125923.jpg?v=1722274359"},{"product_id":"complex-adaptive-systems-9780691127026","title":"Complex Adaptive Systems","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eProvides an account of complex adaptive social systems, by two of the field's leading authorities. This work focuses on the key tools and ideas that have emerged in the field since the mid-1990s, as well as the techniques needed to investigate such systems. It also demonstrates how the usual extremes used in modeling can be fruitfully transcended.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"The use of computational, especially agent-based, models has already shown its value in illuminating the study of economic and other social processes. Miller and Page have written an orientation to this field that is a model of motivation and insight, making clear the underlying thinking and illustrating it by varied and thoughtful examples. It conveys with remarkable clarity the essentials of the complex systems approach to the embarking researcher.\"\u003cb\u003e—Kenneth J. Arrow, winner of the Nobel Prize in economics\u003c\/b\u003e\u003cbr\u003e\"In \u003ci\u003eComplex Adaptive Systems\u003c\/i\u003e, two masters of this burgeoning field provide a highly readable and novel restatement of the logic of social interactions, linking individually based micro processes to macrosocial outcomes, ranging from Adam Smith's invisible hand to Thomas Schelling's models of standing ovations. The book combines the vision of a new Santa Fe school of computational, social, and behavioral science with essential 'how to' advice for apprentice modelers.\"\u003cb\u003e—Samuel Bowles, author of \u003ci\u003eMicroeconomics: Behavior, Institutions, Evolution\u003c\/i\u003e\u003c\/b\u003e\u003cbr\u003e\"This is a wonderful book that will be read by graduate students, faculty, and policymakers. The authors write in an extraordinarily clear manner about topics that are very technical and difficult for many people. I sat down to begin thumbing through and found myself deeply engaged.\"\u003cb\u003e—Elinor Ostrom, author of \u003ci\u003eUnderstanding Institutional Diversity\u003c\/i\u003e\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eList of Figures xiii  List of Tables xv  Preface xvii      Part I: Introduction 1      Chapter 1: Introduction 3      Chapter 2: Complexity in Social Worlds 9  2.1 The Standing Ovation Problem 10  2.2 What's the Buzz? 14  2.2.1 Stay Cool 14  2.2.2 Attack of the Killer Bees 15  2.2.3 Averaging Out Average Behavior 16  2.3 A Tale of Two Cities 17  2.3.1 Adding Complexity 20  2.4 New Directions 26  2.5 Complex Social Worlds Redux 27  2.5.1 Questioning Complexity 27      Part II: Preliminaries 33      Chapter 3: Modeling 35  3.1 Models as Maps 36  3.2 A More Formal Approach to Modeling 38  3.3 Modeling Complex Systems 40  3.4 Modeling Modeling 42      Chapter 4: On Emergence 44  4.1 A Theory of Emergence 46  4.2 Beyond Disorganized Complexity 48  4.2.1 Feedback and Organized Complexity 50      Part III: Computational Modeling 55      Chapter 5: Computation as Theory 57  5.1 Theory versus Tools 59  5.1.1 Physics Envy: A Pseudo-Freudian Analysis 62  5.2 Computation and Theory 64  5.2.1 Computation in Theory 64  5.2.2 Computation as Theory 67  5.3 Objections to Computation as Theory 68  5.3.1 Computations Build in Their Results 69  5.3.2 Computations Lack Discipline 70  5.3.3 Computational Models Are Only Approximations to Specific Circumstances 71  5.3.4 Computational Models Are Brittle 72  5.3.5 Computational Models Are Hard to Test 73  5.3.6 Computational Models Are Hard to Understand 76  5.4 New Directions 76      Chapter 6: Why Agent-Based Objects? 78  6.1 Flexibility versus Precision 78  6.2 Process Oriented 80  6.3 Adaptive Agents 81  6.4 Inherently Dynamic 83  6.5 Heterogeneous Agents and Asymmetry 84  6.6 Scalability 85  6.7 Repeatable and Recoverable 86  6.8 Constructive 86  6.9 Low Cost 87  6.10 Economic E. coli (E. coni?) 88      Part IV: Models of Complex Adaptive Social Systems 91      Chapter 7: A Basic Framework 93  7.1 The Eightfold Way 93  7.1.1 Right View 94  7.1.2 Right Intention 95  7.1.3 Right Speech 96  7.1.4 Right Action 96  7.1.5 Right Livelihood 97  7.1.6 Right Effort 98  7.1.7 Right Mindfulness 100  7.1.8 Right Concentration 101  7.2 Smoke and Mirrors: The Forest Fire Model 102  7.2.1 A Simple Model of Forest Fires 102  7.2.2 Fixed, Homogeneous Rules 102  7.2.3 Homogeneous Adaptation 104  7.2.4 Heterogeneous Adaptation 105  7.2.5 Adding More Intelligence: Internal Models 107  7.2.6 Omniscient Closure 108  7.2.7 Banks 109  7.3 Eight Folding into One 110  7.4 Conclusion 113      Chapter 8: Complex Adaptive Social Systems in One Dimension 114  8.1 Cellular Automata 115  8.2 Social Cellular Automata 119  8.2.1 Socially Acceptable Rules 120  8.3 Majority Rules 124  8.3.1 The Zen of Mistakes in Majority Rule 128  8.4 The Edge of Chaos 129  8.4.1 Is There an Edge? 130  8.4.2 Computation at the Edge of Chaos 137  8.4.3 The Edge of Robustness 139      Chapter 9: Social Dynamics 141  9.1 A Roving Agent 141  9.2 Segregation 143  9.3 The Beach Problem 146  9.4 City Formation 151  9.5 Networks 154  9.5.1 Majority Rule and Network Structures 158  9.5.2 Schelling's Segregation Model and Network Structures 163  9.6 Self-Organized Criticality and Power Laws 165  9.6.1 The Sand Pile Model 167  9.6.2 A Minimalist Sand Pile 169  9.6.3 Fat-Tailed Avalanches 171  9.6.4 Purposive Agents 175  9.6.5 The Forest Fire Model Redux 176  9.6.6 Criticality in Social Systems 177      Chapter 10: Evolving Automata 178  10.1 Agent Behavior 178  10.2 Adaptation 180  10.3 A Taxonomy of 2 x 2 Games 185  10.3.1 Methodology 187  10.3.2 Results 189  10.4 Games Theory: One Agent, Many Games 191  10.5 Evolving Communication 192  10.5.1 Results 194  10.5.2 Furthering Communication 197  10.6 The Full Monty 198      Chapter 11: Some Fundamentals of Organizational Decision Making 200  11.1 Organizations and Boolean Functions 201  11.2 Some Results 203  11.3 Do Organizations Just Find Solvable Problems? 206  11.3.1 Imperfection 207  11.4 Future Directions 210      Part V: Conclusions 211      Chapter 12: Social Science in Between 213  12.1 Some Contributions 214  12.2 The Interest in Between 218  12.2.1 In between Simple and Strategic Behavior 219  12.2.2 In between Pairs and Infinities of Agents 221  12.2.3 In between Equilibrium and Chaos 222  12.2.4 In between Richness and Rigor 223  12.2.5 In between Anarchy and Control 225  12.3 Here Be Dragons 225      Epilogue 227  The Interest in Between 227  Social Complexity 228  The Faraway Nearby 230      Appendixes  A An Open Agenda For Complex Adaptive Social Systems 231  A.1 Whither Complexity 231  A.2 What Does it Take for a System to Exhibit Complex Behavior? 233  A.3 Is There an Objective Basis for Recognizing Emergence and Complexity? 233  A.4 Is There a Mathematics of Complex Adaptive Social Systems? 234  A.5 What Mechanisms Exist for Tuning the Performance of Complex Systems? 235  A.6 Do Productive Complex Systems Have Unusual Properties? 235  A.7 Do Social Systems Become More Complex over Time 236  A.8 What Makes a System Robust? 236  A.9 Causality in Complex Systems? 237  A.10 When Does Coevolution Work? 237  A.11 When Does Updating Matter? 238  A.12 When Does Heterogeneity Matter? 238  A.13 How Sophisticated Must Agents Be Before They Are Interesting? 239  A.14 What Are the Equivalence Classes of Adaptive Behavior? 240  A.15 When Does Adaptation Lead to Optimization and Equilibrium? 241  A.16 How Important Is Communication to Complex Adaptive Social Systems? 242  A.17 How Do Decentralized Markets Equilibrate? 243  A.18 When Do Organizations Arise? 243  A.19 What Are the Origins of Social Life? 244      B Practices for Computational Modeling 245  B.1 Keep the Model Simple 246  B.2 Focus on the Science, Not the Computer 246  B.3 The Old Computer Test 247  B.4 Avoid Black Boxes 247  B.5 Nest Your Models 248  B.6 Have Tunable Dials 248  B.7 Construct Flexible Frameworks 249  B.8 Create Multiple Implementations 249  B.9 Check the Parameters 250  B.10 Document Code 250  B.11 Know the Source of Random Numbers 251  B.12 Beware of Debugging Bias 251  B.13 Write Good Code 251  B.14 Avoid False Precision 252  B.15 Distribute Your Code 253  B.16 Keep a Lab Notebook 253  B.17 Prove Your Results 253  B.18 Reward the Right Things 254      Bibliography 255  Index 261","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":48865519042903,"sku":"9780691127026","price":31.5,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691127026.jpg?v=1722274359"},{"product_id":"mathematics-in-nature-9780691127965","title":"Mathematics in Nature","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eFrom rainbows, river meanders, and shadows to spider webs, honeycombs, the visible world is full of patterns that can be described mathematically. Examining such readily observable phenomena, this book introduces readers to the beauty of nature as revealed by mathematics and the beauty of mathematics as revealed in nature.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003eWinner of the 2003 for Professional\/Scholarly Award in Mathematics and Statistics, Association of American Publishers One of Choice's Outstanding Academic Titles for 2004 \"Mathematics in Nature is an excellent resource for bringing a greater variety of patterns into the mathematical study of nature, as well as for teaching students to think about describing natural phenomena mathematically... [T]he breadth of patterns studied is phenomenal.\"--Will Wilson, American Scientist \"John Adam has combined his interest in the great outdoors and applied mathematics to compile one surprising example after another of how mathematics can be used to explain natural phenomena. And what examples! ... [He] has done a great deal of reading and exposition, indulging his passions to create this compilation of mathematical models of natural phenomena, and the sheer number of examples he manages to cram into this book is testament to his efforts. There are other texts on the market which explore the connection between mathematics and nature ... but none this wide-ranging.\"--Steven Morics, MAA Online \"Adam has laced his mathematical models with popular descriptions of the phenomena selected... Mathematics in Nature can accordingly be read for pleasure and instruction by the select laity who are not afraid of reading between the lines of equations.\"--Philip J. Davis, SIAM News \"John Adam's quest is a very simple one: that is, to invite one to look around and observe the wonders of nature, both natural and biological; to ponder them; and to try to explain them at various levels with, for the most part, quite elementary mathematical concepts and techniques.\"--Brian D. Sleeman, Notices of the American Mathematical Association \"Reading this book progressively creates a course in mathematical modeling built around familiar, tangible, human-scale examples, with a trajectory that takes readers from dimensional estimates through geometrical modeling, linear and nonlinear dynamics, to pattern formation.\"--Choice \"John Adam's Mathematics in Nature illustrates how, in a friendly and lucid manner, mathematicians think about nature. Adam lets us see how mathematics is not only an ally, but is perhaps the very language that nature uses to express the beautiful... This is a book that will challenge while it intrigues and excites.\"--Stanley David Gedzelman, Weatherwise \"Although Mathematics in Nature has not been written as a textbook, availability of such a manual shall help instructors who choose this delightful book for teaching a course in applied mathematics or mathematical modeling.\"--Yuri V. Rogovchenko, Zentralblatt Math \"Spanning a range of mathematical levels, this book can be used as an undergraduate textbook, a source of high school math enrichment, or can be read for pleasure by folks with an appreciation of nature but without advanced mathematical background.\"--Southeastern Naturalist\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface: The motivation for the book; Acknowledgments; Credits xiii  Prologue: Why I Might Never Have Written This Book xxi  CHAPTER ONE: The Confluence of Nature and Mathematical Modeling 1  CHAPTER TWO: Estimation: The Power of Arithmetic in Solving Fermi Problems 17  CHAPTER THREE: Shape, Size, and Similarity: The Problem of Scale 31  CHAPTER FOUR: Meteorological Optics I: Shadows, Crepuscular Rays, and Related Optical Phenomena 57  CHAPTER FIVE: Meteorological Optics II: A \"Calculus I\" Approach to Rainbows, Halos, and Glories 80  CHAPTER SIX: Clouds, Sand Dunes, and Hurricanes 118  CHAPTER SEVEN: (Linear) Waves of All Kinds 139  CHAPTER EIGHT: Stability 173  CHAPTER NINE: Bores and Nonlinear Waves 194  CHAPTER TEN: The Fibonacci Sequence and the Golden Ratio 213  CHAPTER ELEVEN: Bees, Honeycombs, Bubbles, and Mud Cracks 231  CHAPTER TWELVE: River Meanders, Branching Patterns, and Trees 254  CHAPTER THIRTEEN: Bird Flight 295  CHAPTER FOURTEEN: HowDid the Leopard Get Its Spots? 309  APPENDIX: Fractals: An Appetite Whetter... 336  BIBLIOGRAPHY 341  INDEX 357","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":48865519239511,"sku":"9780691127965","price":40.5,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691127965.jpg?v=1722274360"},{"product_id":"optimization-algorithms-on-matrix-manifolds-9780691132983","title":"Optimization Algorithms on Matrix Manifolds","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eMany problems in the sciences and engineering can be rephrased as optimization problems on matrix search spaces endowed with a so-called manifold structure. This book shows how to exploit the special structure of such problems to develop efficient numerical algorithms. It is of interest to applied mathematicians, and computer scientists.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"This book is succinct but essentially self-contained; it includes an appendix with background material as well as an extensive bibliography. The algorithmic techniques developed may be useful anytime a model leads to a mathematical optimization problem where the domain naturally is a manifold, particularly if the manifold is a matrix manifold. The book follows the usual definition-theorem-proof style but it is not intended for traditional course work so there are no exercises. A reader with limited exposure to manifold theory and differential geometry most likely will benefit from consulting standard texts on those subjects first.\"--Anders Linner, Mathematical Reviews \"[T]his book is succinct but essentially self-contained; it includes an appendix with background material as well as an extensive bibliography. The algorithmic techniques developed may be useful anytime a model leads to a mathematical optimization problem where the domain naturally is a manifold, particularly if the manifold is a matrix manifold. The book follows the usual definition-theorem-proof style but it is not intended for traditional course work so there are no exercises. A reader with limited exposure to manifold theory and differential geometry most likely will benefit from consulting standard texts on those subjects first.\"--Anders Linner, American Mathematical Society \"The book is very well and carefully written. Every chapter starts with a page-long introduction clearly outlining its goals and how they are achieved together with possible relations to other chapters. I find the material very well explained and supported with appropriate examples. It is a pleasure to work with such a book.\"--Nickolay T. Trendafilov, Foundations of Computational Mathematics\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eList of Algorithms xi  Foreword, by Paul Van Dooren xiii  Notation Conventions xv      Chapter 1. Introduction 1  Chapter 2. Motivation and Applications 5  2.1 A case study: the eigenvalue problem 5  2.1.1 The eigenvalue problem as an optimization problem 7  2.1.2 Some benefits of an optimization framework 9  2.2 Research problems 10  2.2.1 Singular value problem 10  2.2.2 Matrix approximations 12  2.2.3 Independent component analysis 13  2.2.4 Pose estimation and motion recovery 14  2.3 Notes and references 16      Chapter 3. Matrix Manifolds: First-Order Geometry 17  3.1 Manifolds 18  3.1.1 Definitions: charts, atlases, manifolds 18  3.1.2 The topology of a manifold* 20  3.1.3 How to recognize a manifold 21  3.1.4 Vector spaces as manifolds 22  3.1.5 The manifolds Rn x p and Rn x p 22  3.1.6 Product manifolds 23  3.2 Differentiable functions 24  3.2.1 Immersions and submersions 24  3.3 Embedded submanifolds 25  3.3.1 General theory 25  3.3.2 The Stiefel manifold 26  3.4 Quotient manifolds 27  3.4.1 Theory of quotient manifolds 27  3.4.2 Functions on quotient manifolds 29  3.4.3 The real projective space RPn x 1 30  3.4.4 The Grassmann manifold Grass(p, n) 30  3.5 Tangent vectors and differential maps 32  3.5.1 Tangent vectors 33  3.5.2 Tangent vectors to a vector space 35  3.5.3 Tangent bundle 36  3.5.4 Vector fields 36  3.5.5 Tangent vectors as derivations? 37  3.5.6 Differential of a mapping 38  3.5.7 Tangent vectors to embedded submanifolds 39  3.5.8 Tangent vectors to quotient manifolds 42  3.6 Riemannian metric, distance, and gradients 45  3.6.1 Riemannian submanifolds 47  3.6.2 Riemannian quotient manifolds 48  3.7 Notes and references 51      Chapter 4. Line-Search Algorithms on Manifolds 54  4.1 Retractions 54  4.1.1 Retractions on embedded submanifolds 56  4.1.2 Retractions on quotient manifolds 59  4.1.3 Retractions and local coordinates* 61  4.2 Line-search methods 62  4.3 Convergence analysis 63  4.3.1 Convergence on manifolds 63  4.3.2 A topological curiosity* 64  4.3.3 Convergence of line-search methods 65  4.4 Stability of fixed points 66  4.5 Speed of convergence 68  4.5.1 Order of convergence 68  4.5.2 Rate of convergence of line-search methods* 70  4.6 Rayleigh quotient minimization on the sphere 73  4.6.1 Cost function and gradient calculation 74  4.6.2 Critical points of the Rayleigh quotient 74  4.6.3 Armijo line search 76  4.6.4 Exact line search 78  4.6.5 Accelerated line search: locally optimal conjugate gradient 78  4.6.6 Links with the power method and inverse iteration 78  4.7 Refining eigenvector estimates 80  4.8 Brockett cost function on the Stiefel manifold 80  4.8.1 Cost function and search direction 80  4.8.2 Critical points 81  4.9 Rayleigh quotient minimization on the Grassmann manifold 83  4.9.1 Cost function and gradient calculation 83  4.9.2 Line-search algorithm 85  4.10 Notes and references 86      Chapter 5. Matrix Manifolds: Second-Order Geometry 91  5.1 Newton's method in Rn 91  5.2 Affine connections 93  5.3 Riemannian connection 96  5.3.1 Symmetric connections 96  5.3.2 Definition of the Riemannian connection 97  5.3.3 Riemannian connection on Riemannian submanifolds 98  5.3.4 Riemannian connection on quotient manifolds 100  5.4 Geodesics, exponential mapping, and parallel translation 101  5.5 Riemannian Hessian operator 104  5.6 Second covariant derivative* 108  5.7 Notes and references 110      Chapter 6. Newton's Method 111  6.1 Newton's method on manifolds 111  6.2 Riemannian Newton method for real-valued functions 113  6.3 Local convergence 114  6.3.1 Calculus approach to local convergence analysis 117  6.4 Rayleigh quotient algorithms 118  6.4.1 Rayleigh quotient on the sphere 118  6.4.2 Rayleigh quotient on the Grassmann manifold 120  6.4.3 Generalized eigenvalue problem 121  6.4.4 The nonsymmetric eigenvalue problem 125  6.4.5 Newton with subspace acceleration: Jacobi-Davidson 126  6.5 Analysis of Rayleigh quotient algorithms 128  6.5.1 Convergence analysis 128  6.5.2 Numerical implementation 129  6.6 Notes and references 131      Chapter 7. Trust-Region Methods 136  7.1 Models 137  7.1.1 Models in Rn 137  7.1.2 Models in general Euclidean spaces 137  7.1.3 Models on Riemannian manifolds 138  7.2 Trust-region methods 140  7.2.1 Trust-region methods in Rn 140  7.2.2 Trust-region methods on Riemannian manifolds 140  7.3 Computing a trust-region step 141  7.3.1 Computing a nearly exact solution 142  7.3.2 Improving on the Cauchy point 143  7.4 Convergence analysis 145  7.4.1 Global convergence 145  7.4.2 Local convergence 152  7.4.3 Discussion 158  7.5 Applications 159  7.5.1 Checklist 159  7.5.2 Symmetric eigenvalue decomposition 160  7.5.3 Computing an extreme eigenspace 161  7.6 Notes and references 165      Chapter 8. A Constellation of Superlinear Algorithms 168  8.1 Vector transport 168  8.1.1 Vector transport and affine connections 170  8.1.2 Vector transport by differentiated retraction 172  8.1.3 Vector transport on Riemannian submanifolds 174  8.1.4 Vector transport on quotient manifolds 174  8.2 Approximate Newton methods 175  8.2.1 Finite difference approximations 176  8.2.2 Secant methods 178  8.3 Conjugate gradients 180  8.3.1 Application: Rayleigh quotient minimization 183  8.4 Least-square methods 184  8.4.1 Gauss-Newton methods 186  8.4.2 Levenberg-Marquardt methods 187  8.5 Notes and references 188      A. Elements of Linear Algebra, Topology, and Calculus 189  A.1 Linear algebra 189  A.2 Topology 191  A.3 Functions 193  A.4 Asymptotic notation 194  A.5 Derivatives 195  A.6 Taylor's formula 198      Bibliography 201  Index 221","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":48865519829335,"sku":"9780691132983","price":63.75,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691132983.jpg?v=1722274364"},{"product_id":"benfords-law-9780691147611","title":"Benfords Law","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eBenford's law states that the leading digits of many data sets are not uniformly distributed from one through nine, but rather exhibit a profound bias. This bias is evident in everything from electricity bills and street addresses to stock prices, population numbers, mortality rates, and the lengths of rivers. Here, Steven Miller brings together ma\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"This book will prove to be both a valuable reference and a first source to turn to for whoever is interested in the mathematical genesis and empirical usefulness of Benford's law.\"--Walter Kramer, Statistical Papers\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e*Frontmatter, pg. i*Contents, pg. vii*Foreword, pg. xiii*Preface, pg. xvii*Notation, pg. xxiii*Chapter One. A Quick Introduction to Benford's Law, pg. 3*Chapter Two. A Short Introduction to the Mathematical Theory of Benford's Law, pg. 23*Chapter Three. Fourier Analysis and Benford's Law, pg. 68*Chapter Four. Benford's Law Geometry, pg. 109*Chapter Five. Explicit Error Bounds via Total Variation, pg. 119*Chapter Six. Levy Processes and Benford's Law, pg. 135*Chapter Seven. Benford's Law as a Bridge between Statistics and Accounting, pg. 177*Chapter Eight. Detecting Fraud and Errors Using Benford's Law, pg. 191*Chapter Nine. Can Vote Counts' Digits and Benford's Law Diagnose Elections?, pg. 212*Chapter Ten. Complementing Benford's Law for Small N: A Local Bootstrap, pg. 223*Chapter Eleven. Measuring the Quality of European Statistics, pg. 235*Chapter Twelve. Benford's Law and Fraud in Economic Research, pg. 244*Chapter Thirteen. Testing for Strategic Manipulation of Economic and Financial Data, pg. 257*Chapter Fourteen. Psychology and Benford's Law, pg. 267*Chapter Fifteen. Managing Risk in Numbers Games, pg. 276*Chapter Sixteen. Benford's Law in the Natural Sciences, pg. 290*Chapter Seventeen. Generalizing Benford's Law, pg. 304*Chapter Eighteen. PV Modeling of Medical Imaging Systems, pg. 319*Chapter Nineteen. Application of Benford's Law to Images, pg. 338*Chapter Twenty. Exercises, pg. 373*Bibliography, pg. 402*Index, pg. 433","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":48865523827031,"sku":"9780691147611","price":63.75,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691147611.jpg?v=1722274380"}],"url":"https:\/\/bookcurl.com\/collections\/applied-mathematics.oembed?page=6","provider":"Book Curl","version":"1.0","type":"link"}