Mathematics Books

Book SynopsisTrade Review"In The Mathematics of Secrets, Joshua Holden takes the reader on a chronological journey from Julius Caesar’s substitution cipher to modern day public-key algorithms and beyond. . . . Written for anyone with an interest in cryptography." —Noel-Ann Bradshaw, Times Higher Education "Complete in surveying cryptography. . . . This is a marvelous way of illustrating the use of simple mathematics in an important application that has triggered the wit of the designers and the ingenuity of the attackers since antiquity." —Adhemar Bultheel, European Mathematical Society "The best book I have seen on this subject." —Phil Dyke, Leonardo Reviews "This is a fascinating tour of the mathematics behind cryptography, showing how its principles underpin the ways that different codes and ciphers operate. . . . While it’s all about maths, the book is accessible—basic high school algebra is all that’s needed to understand and enjoy it." —Cosmos Magazine

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Book SynopsisTrade Review"Avi Wigderson, Co-Winner of the Abel Prize, Norwegian Academy of Science and Letters""Avi Wigderson's new 440-page book, Mathematics and Computation: A Theory Revolutionizing Technology and Science (Princeton University Press, October 2019), lays out a commanding overview of the theory of computing and argues for its central role in human thought."---Allyn Jackson, Communications of the ACM"This must-read book provides a high-level, enjoyable overview of numerous parts of mathematics that are related to computation in general, and computational complexity in particular." * Choice *

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Book SynopsisTrade Review"The field has been due for a general treatment accessible to undergraduates and to mathematicians in other areas. . . . With Reverse Mathematics, John Stillwell provides exactly that kind of introduction."—Carl Mummert, Notices of the American Mathematical Society"Stillwell carefully situates the field in the broader context of the history of mathematics and its foundations, and does a fine job of making the whole endeavor accessible to a general mathematical audience."—Jeremy Avigad, Carnegie Mellon University"Filling an important niche, this book gives readers a good picture of the basics of reverse mathematics while suggesting several directions for further reading and study."—Denis Hirschfeldt, University of Chicago"Stillwell's book is self-contained and includes much background material in analysis, mathematical logic, combinatorics, and computability. I heartily commend this very readable and accessible book."—Stephen Simpson, Vanderbilt University

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Book SynopsisTrade Review"Nahin’s style is entertaining, directly addressing his readers. . . . Highly recommended."---Adhemar Bultheel, MAA Reviews"This book will be both enjoyable and a rich source of useful as well as intriguing information to a wide range of readers."---Michael Th. Rassias, zbMATH Open"I thoroughly enjoyed this book!"---Jonathan Shock, Mathemafrica.org"N/A"---Andrew Simoson, The Mathematical Intelligencer

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Book SynopsisTrade Review"[A] treat . . . I think that students studying this material would not only find Paul’s treatments easy to follow, but would benefit greatly by learning something of the history that surrounds the development of the analysis and applications of the heat equation."---Jim Stein, New Books in Mathematics"Nahin knows how to write a book mixing physics and (a lot of) mathematics and (still) make it readable."---Adhemar Bultheel, European Mathematical Society"Hot Molecules, Cold Electrons has provided me with a new perspective on what I thought to be a rather tedious topic. . . . I would recommend it to anyone who wants to work out their maths muscles and learn something along the way."---Louis Ammon, Chemistry World

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Book SynopsisTrade Review"Winner of the PROSE Award for Excellence in Physical Sciences and Mathematics, Association of American Publishers""Winner of the PROSE Award in Mathematics, Association of American Publishers""A Choice Outstanding Academic Title of the Year""This book is an insightful addition to mathematical literature."---Robert Maddox-Harle, Leonardo Reviews"Ording presents ninety-nine proofs that a specific cubic equation has two real roots. The theorem itself is fairly uninteresting, but the proofs are the stars and each of them seeks to show a different aspect of the theory, history, or culture of mathematics."---Geoffrey Dietz, MAA Reviews"These proofs’ playfulness at the boundary of sense and nonsense surely expands the limits of mathematical exposition as well as readerly response to mathematical ideas. I think Queneau would have been proud."---Dan Rockmore, New York Review of Books"This rather unusual book shows that . . . the essentials for communicating mathematical contents is not formulas, let alone numbers, but a more or less precise reasoning in a convincing language."---Jürgen Appell, Zentralblatt MATH"A deep and thoughtful examination of the nature of mathematical arguments, of mathematical style, and of proof itself."---Chris Sangwin, London Mathematical Newsletter"[A] fascinating book. . . . The book can be recommended as light reading and, in particular, for everyone who wants to become more aware of the different styles used in mathematical writing."---C. Fuchs, International Mathematical News"[99 Variations on a Proof] is certainly beautifully produced and invites dipping into rather than reading from cover to cover."---Nick Lord, Mathematical Gazette ​​​​​​​"In his marvelous book 99 Variations on a Proof, Philip Ording demonstrates in a creative, often amusing, and always illuminating way that there are many, many good styles for writing mathematical proofs. Mathematicians (in fact, almost all writers) have much to learn about their craft from this book, and mathematical literature much to gain."---John J. Watkins, Mathematical Intelligencer ​​​​​​​

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Book SynopsisTrade Review"The insides of this book are as clever and compelling as the subtitle on the cover. Havil, a retired former master at Winchester College in England, where he taught math for decades, takes readers on a history of irrational numbers--numbers, like v2 or p, whose decimal expansion 'is neither finite nor recurring.' We start in ancient Greece with Pythagoras, whose thinking most likely helped to set the path toward the discovery of irrational numbers, and continue to the present day, pausing to ponder such questions as, 'Is the decimal expansion of an irrational number random?'"---Anna Kuchment, Scientific American"The Irrationals is a true mathematician's and historian's delight."---Robert Schaefer, New York Journal of Books"From its lively introduction straight through to a rousing finish this is a book which can be browsed for its collection of interesting facts or studied carefully by anyone with an interest in numbers and their history. . . . This is a wonderful book which should appeal to a broad audience. Its level of difficulty ranges nicely from ideas accessible to high school students to some very deep mathematics. Highly recommended!"---Richard Wilders, MAA Reviews"It is a book that can be warmly recommended to any mathematician or any reader who is generally interested in mathematics. One should be prepared to read some of the proofs. Skipping all the proofs would do injustice to the concept, leaving just a skinny skeleton, but skipping some of the most advanced ones is acceptable. The style, the well documented historical context and quotations mixed with references to modern situations make it a wonderful read."---A. Bultheel, European Mathematical Society"To follow the mathematical sections of the book, the reader should have at least a second-year undergraduate mathematical background, as the author does not shrink from providing some detailed arguments. However, the presentation of historical material is given in modern mathematical form. Many readers will encounter unfamiliar and surprising material in this field in which much remains to be explored."---E. J. Barbeau, Mathematical Reviews Clippings"This is a well-written book to which senior high school students who do not intend to study mathematics at university should be exposed in their last two years at school. The ideas are challenging and provocative, with numerous clear diagrams. The topics are presented with numerous examples, and unobtrusive humour which renders the exposition even more palatable. The book would be an ideal source of ideas in a mathematics course within a liberal arts college because it links not only with the historical source of mathematics problems, but also with some of the great ideas of philosophy."---A. G. Shannon, Notes on Number Theory and Discrete Mathematics"Mathematicians and serious students of mathematics will find much to admire in this book. . . . Every mathematician and student of mathematics with appropriate background will find [it] to be a valuable resource."---Pamela Gorkin, Mathematical Intelligencer

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Book SynopsisFeaturing strategies for solving the puzzles and computations illustrated using the SAGE open-source computer algebra system, the second edition of Adventures in Group Theory is perfect for mathematics enthusiasts and for use as a supplementary textbook.Trade Review"Adventures in Group Theory is a tour through the algebra of several 'permutation puzzles'... If you like puzzles, this is a somewhat fun book. If you like algebra, this is a fun book. If you like puzzles and algebra, this is a really fun book." - MAA Online "Joyner has collated all the Rubik lore and integrated it with a self-contained introduction to group theory that equals or, more likely, exceeds what is available in typical dedicated elementary texts." - Choice "Joyner does convey some of the excitement and adventure in picking up knowledge of group theory by trying to understand Rubik's Cube. Enthusiastic students will learn a lot of mathematics from this book." - American Scientist"Table of ContentsPrefaceAcknowledgmentsWhere to Begin...1. Elementary, my dear Watson2. 'And you do addition?'3. Bell ringing and other permutations4. A procession of permutation puzzles5. What's commutative and purple?6. Welcome to the machine7. 'God's algorithm' and graphs8. Symmetry and the Platonic solids9. The illegal cube group10. Words which move11. The (legal) Rubik's Cube group12. Squares, two-faces, and other subgroups13. Other Rubik-like puzzle groups14. Crossing the Rubicon15. Some solution strategies16. Coda: Questions and other directionsBibliographyIndex

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Book SynopsisHolland, this persuasively argued and firmly scientific book exposes some of history's most persistent bamboozling. Be forewarned, you may never be taken in again!Trade ReviewWhat stands out in this book is that Broch allows the facts of his arguments to impress on their own, and they are impressive. Moreover, readers will be wowed by what he has dug up. -- Norm Goldman BookPleasures.com 2009 Backed up by easily understood charts and diagrams, Exposed! is witty but substantial science for the layman. -- Ken Lauderdale AUTHOR Magazine 2009 Offers some great material for conversation! Bluesci 2010Table of ContentsForeword: Charlatanism or Science: Which Will Prevail?Introduction1. DowsingSticks That Move on Their OwnBrilliant WavesUnconscious Movements?Dowsing and Waterwheels2. Become ClairvoyantExtrasensory PerceptionPsychokinesisPerception at a DistanceHypnosis and TelepathyClairvoyanceMusculokinesis3. How to Recognize Deceptive Techniques in ArgumentThe Circularity TechniqueThe Snowball TechniqueThe Escalation TechniqueThe "Little Streams" EffectAccounting and Errors4. Cast Your HoroscopeQuiet Please, Turning in Progress!SerpentariusLaplanders without Horoscopes?Whom to Believe?The Effects of Mars, Jupiter, Saturn, and All the RestDouble or Nothing5. Miracle or Fraud?Holy Hemoglobin!A Do-It-Yourself Shroud of TurinA 3-D ImageWhat If Jesus Wasn't Naked?The Holy Shroud of Turin Is Not a ForgeryThe Body of ChristMade in France and Stolen from the Religious6. Develop Your PowersGlowing Embers Held in Bare HandsThe Uses of Short ArmsThe Life Force Energy, QiMeasuring the Vital ForceThe Ouija GlassTurn the TablesMarvelous MechanismsMiraculous VasesBetter than The Da Vinci Code7. More MysteriesPlace Your BetsThe Haunted HouseThe Dog Who Could Measure DistancesInitiated by a Tibetan MasterConclusionIndex

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Book SynopsisLearning Data Science is the first book to cover foundational skills in both programming and statistics that encompass the entire data science lifecycle: the process of collecting, wrangling, analyzing, and drawing conclusions from data.

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Book SynopsisIntroductory Statistics, 10th edition, is written for a one- or two-semester first course in applied statistics and is intended for students who do not have a strong background in mathematics. The only prerequisite is knowledge of elementary algebra. Known for its realistic examples and exercises, clarity and brevity of presentation, and soundness of pedagogical approach, the book encourages statistical interpretation and literacy regardless of student background. The book employs a clear and straightforward writing style and uses abundant visuals and figures, which reinforce key concepts and relate new ideas to prior sections for a smooth transition between topics. This international edition offers new and updated materials and focuses on strengthening the coverage by including new sections on types of scales, negative binomial distribution, and two-way analysis of variance. Additionally, discussions on ogive curves, geometric mean, and harmonic mean have also been added. Many examTable of Contents1 Introduction 1 1.1 Statistics and Types of Statistics 1 Case Study 1.1 Deaths Due to Red-Light Running in the United States 3 Case Study 1.2 Is Anxiety and Depression a Major Problem Among Teens? 4 1.2 Basic Terms 5 1.3 Types of Variables 7 1.4 Types of Scales 10 1.5 Cross-Section Versus Time-Series Data 12 1.6 Population Versus Sample 13 1.7 Design of Experiments 22 1.8 Summation Notation 26 Uses and Misuses of Statistics / Glossary / Exercises / Self-Review Test / Mini-Project / Decide for ourself / Chapter 1 Technology Instructions 2 Organizing and Graphing Data 41 2.1 Organizing and Graphing Qualitative Data 42 Case Study 2.1 Confidence in Charitable and Nongovernmental Organizations 46 Case Study 2.2 Single-Payer Health-Care System Where the Federal Government Provides Coverage for Everyone 47 2.2 Organizing and Graphing Quantitative Data 48 Case Study 2.3 Average Starting Salaries of Teachers in the United States 53 Case Study 2.4 Mom, I Am Hungry 54 Case Study 2.5 How Many Cups of Coffee Do You Drink a Day? 58 2.3 Stem-and-Leaf Displays 66 2.4 Dotplots 71 Uses and Misuses of Statistics / Glossary / Exercises / Self-Review Test / Mini-Projects / Decide for Yourself / Chapter 2 Technology Instructions 3 Numerical Descriptive Measures 87 3.1 Measures of Center for Ungrouped Data 88 Case Study 3.1 Coffee Consumption Statistics 91 Case Study 3.2 Median Prices of Homes in Selected Metro Areas of the United States 94 3.2 Measures of Dispersion for Ungrouped Data 103 3.3 Mean, Variance, and Standard Deviation for Grouped Data 111 3.4 Use of Standard Deviation 117 Case Study 3.3 Does Spread Mean the Same as Variability and Dispersion? 121 3.5 Measures of Position 122 3.6 Box-and-Whisker Plot 127 Uses and Misuses of Statistics / Glossary / Exercises / Appendix 3.1 / Self-Review Test / Mini-Projects / Decide for Yourself / Chapter 3 Technology Instructions 4 Probability 147 4.1 Experiment, Outcome, and Sample Space 148 4.2 Calculating Probability 153 4.3 Marginal Probability, Conditional Probability, and Related Probability Concepts 160 Case Study 4.1 Vegetarians, Gender, and Ideology 163 4.4 Intersection of Events and the Multiplication Rule 171 4.5 Union of Events and the Addition Rule 177 4.6 Counting Rule, Factorials, Combinations, and Permutations 184 Case Study 4.2 Probability of Winning a Mega Millions Lottery Jackpot 189 Uses and Misuses of Statistics / Glossary / Exercises / Self-Review Test / Mini-Projects / Decide for Yourself / Chapter 4 Technology Instructions 5 Discrete Random Variables and Their Probability Distributions 203 5.1 Random Variables 204 5.2 Probability Distribution of a Discrete Random Variable 206 5.3 Mean and Standard Deviation of a Discrete Random Variable 212 Case Study 5.1 All State Lottery 214 5.4 The Binomial Probability Distribution 219 5.5 Negative Binomial Probability Distribution 230 5.6 The Hypergeometric Probability Distribution 234 5.7 The Poisson Probability Distribution 237 Case Study 5.2 Global Birth and Death Rates 240 Uses and Misuses of Statistics / Glossary / Exercises / Self-Review Test / Mini-Projects / Decide for Yourself / Chapter 5 Technology Instructions 6 Continuous Random Variables and the Normal Distribution 257 6.1 Continuous Probability Distribution and the Normal Probability Distribution 258 Case Study 6.1 Distribution of Time Taken to Run a Road Race 261 6.2 Standardizing a Normal Distribution 272 6.3 Applications of the Normal Distribution 278 6.4 Determining the Z and X Values When An Area Under the Normal Distribution Curve Is Known 283 6.5 The Normal Approximation to the Binomial Distribution 288 Uses and Misuses of Statistics / Glossary / Exercises /Appendix 6.1 / Self-Review Test / Mini-Projects / Decide for Yourself / Chapter 6 Technology Instructions 7 Sampling Distributions 309 7.1 Sampling Distribution, Sampling Error, and Nonsampling Errors 310 7.2 Mean and Standard Deviation of ​x̄ 315 7.3 Shape of the Sampling Distribution of ​x̄ 318 7.4 Applications _ of the Sampling Distribution of ​ x̄ 324 7.5 Population and Sample Proportions; and the Mean, Standard Deviation, and Shape of the Sampling Distribution of ​p̂ 329 Case Study 7.1 2016 U.S. Election and Sampling Error 331 7.6 Applications of the Sampling Distribution of ​p̂​ 336 Uses and Misuses of Statistics / Glossary / Exercises / Self- Review Test / Mini-Projects / Decide for Yourself /Chapter 7 Technology Instructions 8 Estimation of the Mean and Proportion 349 8.1 Estimation, Point Estimate, and Interval Estimate 349 8.2 Estimation of a Population Mean: σ Known 353 Case Study 8.1 2019 National Average Salaries of U.S. Doctors 357 8.3 Estimation of a Population Mean: σ Not Known 362 8.4 Estimation of a Population Proportion: Large Samples 370 Case Study 8.2 Is Government, Poor Leadership, or Politicians the Most Important Problem Facing the United States? 373 Uses and Misuses of Statistics / Glossary / Exercises / Self-Review Test / Mini-Projects / Decide for Yourself /Chapter 8 Technology Instructions 9 Hypothesis Tests About the Mean and Proportion 389 9.1 Hypothesis Tests: An Introduction 390 9.2 Hypothesis Tests About μ: σ Known 397 Case Study 9.1 Class of 2018 Average Loan Debt for U.S. Students 407 9.3 Hypothesis Tests About μ: σ Not Known 410 9.4 Hypothesis Tests About a Population Proportion: Large Samples 419 Case Study 9.2 Are Parents Doing Too Much for Their Adult Children? 425 Uses and Misuses of Statistics / Glossary / Exercises /Self-Review Test / Mini-Projects / Decide for Yourself / Chapter 9 Technology Instructions 10 Estimation and Hypothesis Testing: Two Populations 441 10.1 Inferences About the Difference Between Two Population Means for Independent Samples: σ1 and σ2Known 442 10.2 Inferences About the Difference Between Two Population Means for Independent Samples: σ1 and σ2 Unknown but Equal 449 10.3 Inferences About the Difference Between Two Population Means for Independent Samples: σ1 and σ2 Unknown and Unequal 457 10.4 Inferences About the Mean of Paired Samples (Dependent Samples) 462 10.5 Inferences About the Difference Between Two Population Proportions for Large and Independent Samples 471 Uses and Misuses of Statistics / Glossary / Exercises /Self-Review Test / Mini-Projects / Decide for Yourself /Chapter 10 Technology Instructions 11 Chi-Square Tests 497 11.1 The Chi-Square Distribution 498 11.2 A Goodness-of-Fit Test 501 Case Study 11.1 How Are the Economic Conditions in the United States Affecting the Middle Class? 507 11.3 A Test of Independence or Homogeneity 509 11.4 Inferences About the Population Variance 519 Uses and Misuses of Statistics / Glossary / Exercises /Self-Review Test / Mini-Projects / Decide for Yourself /Chapter 11 Technology Instructions 12 Analysis of Variance 537 12.1 The F Distribution 538 12.2 One-Way Analysis of Variance 540 12.3 Two-Way Analysis of Variance 550 Uses and Misuses of Statistics / Glossary / Exercises /Self-Review Test / Mini-Projects / Decide for Yourself /Chapter 12 Technology Instructions 13 Simple Linear Regression 573 13.1 Simple Linear Regression 573 Case Study 13.1 Regression of Weights on Heights for NFL Players 583 13.2 Standard Deviation of Errors and Coefficient of Determination 588 13.3 Inferences About B 594 13.4 Linear Correlation 599 13.5 Regression Analysis: A Complete Example 604 13.6 Using the Regression Model 610 Uses and Misuses of Statistics / Glossary / Exercises /Self-Review Test / Mini-Projects / Decide for Yourself /Chapter 13 Technology Instructions 14 Multiple Regression 629 14.1 Multiple Regression Analysis 629 14.2 Assumptions of the Multiple Regression Model 631 14.3 Standard Deviation of Errors 632 14.4 Coefficient of Multiple Determination 633 14.5 Computer Solution of Multiple Regression 634 Uses and Misuses of Statistics / Glossary / Self-Review Test / Mini-Project / Decide for Yourself / Chapter 14 Technology Instructions 15 Nonparametric Methods 649 This chapter is not included in this text but is available in the book’s product page on www.wiley.com. 15.1 The Sign Test 650 15.2 The Wilcoxon Signed-Rank Test for Two Dependent Samples 663 15.3 The Wilcoxon Rank Sum Test for Two Independent Samples 669 15.4 The Kruskal-Wallis Test 675 15.5 The Spearman Rho Rank Correlation Coefficient Test 680 15.6 The Runs Test for Randomness 683 Uses and Misuses of Statistics / Glossary / Exercises / Self-Review Test / Mini-Projects / Decide for Yourself /Chapter 15 Technology Instructions Appendix A Explanation of Data Sets A- 1 Appendix B Statistical Tables B- 1 Appendix C Lists of Formulas C- 1 Answers to Selected Odd-numbered Exercises And Self-review Tests An- 1 Index I- 1

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Book SynopsisFrom the first chapter through the last, readers eager to learn more about the connections between mathematics and music will find a comprehensive textbook designed to satisfy their natural curiosity.Trade ReviewOverall, From Music to Mathematics is a pleasing and well-written book that is accessible for everyone who wants to explore the connections between music and mathematics. Gareth Roberts does a great job of making numerous suggestions on how music can be used to illuminate mathematical concepts... From Music to Mathematics is very enjoyable to read - not only for students, but for anyone who loves music and mathematics. Musicae Scientiae Overall, I strongly recommend this as an excellent basis for teaching. MathSciNetTable of ContentsPrefaceAcknowledgmentsIntroduction1. Rhythm1.1. Musical Notation and a Geometric Property1.1.1. Duration1.1.2. Dots1.2. Time Signatures1.2.1. Musical examples1.2.2. Rhythmic repetition1.3. Polyrhythmic Music1.3.1. The least common multiple1.3.2. Musical examples1.4. A Connection with Sanskrit PoetryReferences for Chapter 12. Introduction to Music Theory2.1. Musical Notation2.1.1. The common clefs2.1.2. The piano keyboard2.2. Scales2.2.1. Chromatic scale2.2.2. Whole-tone scale2.2.3. Major scales2.2.4. Minor scales2.2.5. Why are there 12 major scales?2.3. Intervals and Chords2.3.1. Major and perfect intervals2.3.2. Minor intervals and the tritone2.3.3. Chords2.4. Tonality, Key Signatures, and the Circle of Fifths2.4.1. The critical tonic-dominant relationship2.4.2. Key signatures2.4.3. The circle of fifths2.4.4. Transposition2.4.5. The evolution of polyphonyReferences for Chapter 23. The Science of Sound3.1. How We Hear3.1.1. The magnificent ear-brain system3.2. Attributes of Sound3.2.1. Loudness and decibels3.2.2. Frequency3.3. Sine Waves3.3.1. The sine function3.3.2. Graphing sinusoids3.3.3. The harmonic oscillator3.4. Understanding Pitch3.4.1. Residue pitch3.4.2. A vibrating string3.4.3. The overtone series3.4.4. The starting transient3.4.5. Resonance and beats3.5. The Monochord LabReferences for Chapter 34. Tuning and Temperament4.1. The Pythagorean Scale4.1.1. Consonance and integer ratios4.1.2. The spiral of fifths4.1.3. The overtone series revisited4.2. Just Intonation4.2.1. Problems with just intonation4.2.2. Major versus minor4.3. Equal Temperament4.3.1. A conundrum and a compromise4.3.2. Rational and irrational numbers4.3.3. Cents4.4. Comparing the Three Systems4.5. Strähle's Guitar4.5.1. An ingenious construction4.5.2. Continued fractions4.5.3. On the accuracy of Strähle's method4.6. Alternative Tuning Systems4.6.1. The significance of log2(3/2)4.6.2. Meantone scales4.6.3. Other equally tempered scalesReferences for Chapter 45. Musical Group Theory5.1. Symmetry in Music5.1.1. Symmetric transformations5.1.2. Inversions5.1.3. Other examples5.2. The Bartók Controversy5.2.1. The Fibonacci numbers and nature5.2.2. The golden ratio5.2.3. Music for Strings, Percussion and Celesta5.3. Group Theory5.3.1. Some examples of groups5.3.2. Multiplication tables5.3.3. Symmetries of the square5.3.4. The musical subgroup of D4References for Chapter 56. Change Ringing6.1. Basic Theory, Practice, and Examples6.1.1. Nomenclature6.1.2. Rules of an extent6.1.3. Three bells6.1.4. The number of permissible moves6.1.5. Example6.1.6. Example6.2. Group Theory Revisited6.2.1. The symmetric group Sn6.2.2. The dihedral group revisited6.2.3. Ringing the cosets6.2.4. ExampleReferences for Chapter 67. Twelve-Tone Music7.1. Schoenberg's Twelve-Tone Method of Composition7.1.1. Notation and terminology7.1.2. The tone row matrix7.2. Schoenberg's Suite für Klavier, Op. 257.3. Tone Row Invariance7.3.1. Using numbers instead of pitches7.3.2. Further analysis7.3.3. Tritone symmetry7.3.4. The number of distinct tone rows7.3.5. Twelve-tone music and group theoryReferences for Chapter 78. Mathematical Modern Music8.1. Sir Peter Maxwell Davies8.1.1. Magic squares8.1.2. Some examples8.1.3. The magic constant8.1.4. A Mirror of Whitening Light8.2. Steve Reich8.2.1. Clapping Music8.2.2. Phase shifts8.3. Xenakis8.3.1. A Greek architect8.3.2. Metastasis and the Philips Pavilion8.3.3. Pithoprakta8.4. Final Project8.4. References for Chapter 8CreditsIndex

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Book SynopsisThis eighth volume of Imagine Math is different from all the previous ones. The reason is very clear: in the last two years, the world changed, and we still do not know what the world of tomorrow will look like. Difficult to make predictions. This volume has a subtitle Dreaming Venice. Venice, the dream city of dreams, that miraculous image of a city on water that resisted for hundreds of years, has become in the last two years truly unreachable. Many things tie this book to the previous ones. Once again, this volume also starts like Imagine Math 7, with a homage to the Italian artist Mimmo Paladino who created exclusively for the Imagine Math 8 volume a new series of ten original and unique works of art dedicated to Piero della Francesca. Many artists, art historians, designers and musicians are involved in the new book, including Linda D. Henderson and Marco Pierini, Claudio Ambrosini and Davide Amodio. Space also for comics and mathematics in a Disney key. Many applications, from Origami to mathematical models for world hunger. Particular attention to classical and modern architecture, with Tullia Iori.As usual, the topics are treated in a way that is rigorous but captivating, detailed and full of evocations. This is an all-embracing look at the world of mathematics and culture.Table of ContentsPart I Homage to Mimmo Paladino: 1 Michele Emmer, 8 Works by Mimmo Paladino.- Part II Dreaming in Venice: 2 Michele Emmer, Dreaming Venice.- 3 Sandro G. Franchini, The Napoleonic Fresco in Palazzo Loredan, Thinking of the Bicentennial.- 4 Giovanni Zarotti, MOSE, the Defence System to Safeguard Venice and its Lagoon.- Part III Art and Mathematics: 5 Marco Andreatta, The Rise of Abstractionism: Art and Mathematics.- 6 Clemena Antonova, Aestheticizing an Einsteinian World: The Idea of Space-time in Russian Literary Theory and in Art Criticism.- 7 Michele Emmer, Cagli, Olson, Coxeter.- 8 Emanuela Fiorelli, A Fault in the Order: Thoughts on Frayed Wires.- 9 Linda Dalrymple Henderson, The Multivalent Fourth Dimension and the Impact of Claude Bragdon’s A Primer of Higher Space on Twentieth and Twenty-First Century Art.- 10 Martin Kemp, “Where Natural Law Holds No Sway”. Geometrical Optics and Divine Light in Dante, Michelangelo and Raphael.- 11 Marco Pierini, On The Classification and Recording of Colours According to the Methods of the Painter Adolfo Ferraris: A Brief Note.- 12 Anthony Phillips, Colored Figurative Tilings in Pre-Incan Textiles.- 13 Tony Robbin, The Artistic (and Practical) Utility of Hyperspace.- 14 Carla Scagliosi, From Vision to Perception: Chardin’s Eighteenth Century Cultural and Scientific Approach to Painting (and Soap Bubbles).- Part IV Architecture and Mathematics: 15 Michele Emmer and Fulvio Wirz, Andrea Palladio and Zaha Hadid.- Tullia Iori, 16 Sergio Musmeci and the Calculation of the Form.- 17 Enrico Giusti, Twenty Years of Il Giardino di Archimede.- Part V Design and Mathematics: 18 George W. Hart, The Multifaceted Abraham Sharp.- 19 Giordano Bruno, Massimo Ciafrei, Claudia Iannilli, Giacomo Fabbri, and Marzia Lupi, Learning by Metadesigning.- Part VI Homage to Roger Penrose: 20 Michele Emmer, A Little Homage to Roger Penrose.- Part VII Mathematics and Physics: 21 Amaury Mouchet, Identity and Difference: How Topology Helps to Understand Quantum Indiscernability.- 22 Denis Weaire, Stefan Hutzler, Ali Irannezhad and Kym Cox, Physics in a Small Bedroom.- Part VIII Mathematics and Applications: 23 Maurizio Falcone, The Train of Artificial Intelligence.- 24 Paolo Marcellini and Emanuele Paolini, Origami and Fractal Solutions of Differential Systems.- 25 Gian Marco Todesco, The Tangled Allure of Recursion.- 26 Marcela Villarreal, Desert Locusts: Can Mathematical Models Help to Control Them?.- Part IX Literature and Mathematics: 27 Marco Abate, Soul Searchin’.- 28 Francesca M. Dovetto, Geometric Metaphors and Linguistic Genealogy.- 29 Jean-Marc Lévy-Leblond, A Mathematical Physicist in Hell. Galileo on the Geometry of Dante's Inferno.- 30 Luca Viganò, Don’t Tell Me the Cybersecurity Moon is Shining... Cybersecurity Show and Tell.- Part X Music and Mathematics: 31 Claudio Ambrosini, Sounds, Numbers and Other Fancies.- 32 Davide Amodio, Euler and Music Musing Euler’s Identity.- 33 Francesco Ciccone, The Shapes of Violin.- Part XI Women and Mathematics: 34 Chiara de Fabritiis, Women, Academia, Math: an Ephemeral Golden Braid.- 35 Elisabetta Strickland, Women in Charge of Mathematics.- Part XII Comics and Mathematics: 36 Valerio Held , Without Title.- 37 Roberto Natalini and Andrea Plazzi, A Comics & Science Experience.- 38 Alberto Saracco, Is Math Useful?.

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Book SynopsisThe principle aim of this unique text is to illuminate the beauty of the subject both with abstractions like proofs and mathematical text, and with visuals, such as abundant illustrations and diagrams. With few mathematical prerequisites, geometry is presented through the lens of linear fractional transformations. The exposition is motivational and the well-placed examples and exercises give students ample opportunity to pause and digest the material. The subject builds from the fundamentals of Euclidean geometry, to inversive geometry, and, finally, to hyperbolic geometry at the end. Throughout, the author aims to express the underlying philosophy behind the definitions and mathematical reasoning. This text may be used as primary for an undergraduate geometry course or a freshman seminar in geometry, or as supplemental to instructors in their undergraduate courses in complex analysis, algebra, and number theory. There are elective courses that bring together seemingly disparate topics and this text would be a welcome accompaniment.Table of ContentsMotivation.- I Euclidean and Inversive Geometry.- Euclidean Isometries and Similarities.- Inversive Geometry.- Applications of Inversive Geometry.- II Non-Euclidean Geometry.- Spherical Geometry.- Appendix: Set Theory.

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Book SynopsisPreface.- 1. Running.- 2. Throwing.- 3. Balls.- 4. Water, Wind and Cold.- 5. Rotating.- 6. Counting.

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Book SynopsisThis is the second (revised and enlarged) edition of the book originally published in 2003. It introduces the first concepts of Algebraic Topology like general simplicial complexes, simplicial homology theory, fundamental groups, covering spaces and singular homology theory in detail. The text has been designed for undergraduate and beginning graduate students of Mathematics. It assumes a minimal background of linear algebra, group theory and topological spaces. The author has dealt with the basic concepts and ideas in a very lucid manner giving suitable motivations and illustrations. As an application of the tools developed in this book, some classical theorems like Brouwer’s fixed point theorem, the Lefschetz fixed point theorem, the Borsuk-Ulam theorem, Brouwer’s separation theorem and the theorem on invariance of domain have been proved and illustrated. Most of the exercises are elementary but some are more challenging and will help the readers in their understanding of the subject.Table of Contents 1 Basic Topology: A review 2 The Fundamental Group 3 Simplicial Complexes 4 Simplicial Homology 5 Covering Projections 6 Singular Homology 7 Appendix References Index

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Book SynopsisThis book helps the reader make use of the mathematical models of biological phenomena starting from the basics of programming and computer simulation. Computer simulations based on a mathematical model enable us to find a novel biological mechanism and predict an unknown biological phenomenon. Mathematical biology could further expand the progress of modern life sciences. Although many biologists are interested in mathematical biology, they do not have experience in mathematics and computer science. An educational course that combines biology, mathematics, and computer science is very rare to date. Published books for mathematical biology usually explain the theories of established mathematical models, but they do not provide a practical explanation for how to solve the differential equations included in the models, or to establish such a model that fits with a phenomenon of interest. MATLAB is an ideal programming platform for the beginners of computer science. This book starts from the very basics about how to write a programming code for MATLAB (or Octave), explains how to solve ordinary and partial differential equations, and how to apply mathematical models to various biological phenomena such as diabetes, infectious diseases, and heartbeats. Some of them are original models, newly developed for this book. Because MATLAB codes are embedded and explained throughout the book, it will be easy to catch up with the text. In the final chapter, the book focuses on the mathematical model of the proneural wave, a phenomenon that guarantees the sequential differentiation of neurons in the brain. This model was published as a paper from the author’s lab (Sato et al., PNAS 113, E5153, 2016), and was intensively explained in the book chapter “Notch Signaling in Embryology and Cancer”, published by Springer in 2020. This book provides the reader who has a biological background with invaluable opportunities to learn and practice mathematical biology.Table of Contents1. Preparation.- 2. Introduction to MATLAB programming .- 3. Simulating time variations in life phenomena.- 4. Simulating temporal and spatial changes in biological phenomena.

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Book SynopsisComprehensive, up-to-date textbook, integrating recent experimental results, including discovery of the Higgs boson, to convey the excitement of the field to undergraduate and graduate students. Physical theory is made accessible with coverage of underlying principles, full mathematical derivations, worked examples of experimental applications, and end-of-chapter problems.Trade Review'This advanced undergraduate textbook provides an excellent introduction to one of the most exciting areas of modern physics. It combines a pedagogical 'from first principles' approach with a comprehensive survey of the latest developments in particle physics, including the recent discovery of the Higgs boson. Thoroughly recommended for both students and teachers alike.' James Stirling, Imperial College London'Professor Thomson has written a great textbook on modern particle physics (including a masterful exposition of the discovery of the Higgs boson) that provides a professional introduction to the field, suitable for upper-division undergraduate as well as graduate courses. His distinctive presentation style combines clarity with [an] admirable level of rigor. The book is richly illustrated with helpful diagrams and tables, and is destined to be a favorite of both students and instructors alike.' Dmitry Budker, University of California, Berkeley'Mark Thomson has written a wonderful new introductory textbook on particle physics … [it] is well written … easy to read, with clear pedagogical lines of reasoning, and the layout is pleasing … as I am teaching an introduction to theory this autumn, I will definitely be using this book.' CERN Courier'… gem of a book … excellent and highly readable … well structured with useful chapter summaries and many good student exercises with on-line solutions. It is thoroughly recommended.' The Observatory'… this book has my highest recommendation. In its effective, clear and comprehensive treatment of so much detailed material, it represents a remarkable achievement on the part of its author, and is likely to become a standard work to put into the hands of new graduate students in particle physics. Their supervisors will do well to buy it too!' Peter J. Bussey, Contemporary PhysicsTable of Contents1. Introduction; 2. Underlying concepts; 3. Decay rates and cross sections; 4. The Dirac equation; 5. Interaction by particle exchange; 6. Electron-positron annihilation; 7. Electron-proton elastic scattering; 8. Deep inelastic scattering; 9. Symmetries and the quark model; 10. Quantum chromodynamics; 11. The weak interaction; 12. The weak interactions of leptons; 13. Neutrinos and neutrino oscillations; 14. CP violation and weak hadronic interactions; 15. Electroweak unification; 16. Tests of the Standard Model; 17. The Higgs boson; 18. The Standard Model and beyond; Appendixes; References; Further reading; Index.

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Book SynopsisIs there any connection between the vastness of the universes of stars and galaxies and the existence of life on a small planet out in the suburbs of the Milky Way? This book shows that there is. In their classic work, John Barrow and Frank Tipler examine the question of Mankind''s place in the Universe, taking the reader on a tour of many scientific disciplines and offering fascinating insights into issues such as the nature of life, the serach for extraterrestrial intelligence, and the past history and fate of our universe.Trade Reviewan engaging book ... practically a universal education in both the history of modern science and the history of the Universe ... will be much quoted, much debated and much praised * Nature *a feast: the kind of book which tells you everything you want to know about everything * The Economist *

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Book SynopsisTrade ReviewOne of the Top 10 Technical Books on Financial Engineering by Financial Engineering News for 2006 Praise for the previous edition: "This book provides a state-of-the-art discussion of the three main categories of risk in financial markets, market risk, ... credit risk ... and operational risk... This is a high level, but well-written treatment, rigorous (sometimes succinct), complete with theorems and proofs."--D.L. McLeish, Short Book Reviews of the International Statistical Institute Praise for the previous edition: "A great summary of the latest techniques available within quantitative risk measurement... [I]t is an excellent text to have on the shelf as a reference when your day job covers the whole spectrum of quantitative techniques in risk management."--Financial Engineering News Praise for the previous edition: "Alexander McNeil, Rudiger Frey and Paul Embrechts have written a beautiful book... [T]here is no book that can provide the type of rigorous, detailed, well balanced and relevant coverage of quantitative risk management topics that Quantitative Risk Management: Concepts, Techniques, and Tools offers... I believe that this work may become the book on quantitative risk management... [N]o book that I know of can provide better guidance."--Dr. Riccardo Rebonato, Global Association of Risk Professionals (GARP) Review Praise for the previous edition: "This is a very impressive book on a rapidly growing field. It certainly helps to discover the forest in an area where a lot of trees are popping up daily."--Hans Buhlmann, SIAM Review Praise for the previous edition: "This book is a compendium of the statistical arrows that should be in any quantitative risk manager's quiver. It includes extensive discussion of dynamic volatility models, extreme value theory, copulas and credit risk. Academics, PhD students and quantitative practitioners will find many new and useful results in this important volume."--Robert F. Engle III, 2003 Nobel Laureate in Economic Sciences, Michael Armellino Professor in the Management of Financial Services at New York University's Stern School of Business Praise for the previous edition: "Quantitative Risk Management can be highly recommended to anyone looking for an excellent survey of the most important techniques and tools used in this rapidly growing field."--Holger Drees, Risk Praise for the previous edition: "Quantitative Risk Management is highly recommended for financial regulators. The statistical and mathematical tools facilitate a better understanding of the strengths and weaknesses of a useful range of advanced risk-management concepts and models, while the focus on aggregate risk enhances the publication's value to banking and insurance supervisors."--Hans Blommestein, Financial Regulator Praise for the previous edition: "This book provides a framework and a useful toolkit for analysis of a wide variety of risk management problems. Common pitfalls are pointed out, and mathematical sophistication is used in pursuit of useful and usable solutions. Every financial institution has a risk management department that looks at aggregated portfolio-wide risks on longer time scales, and at risk exposure to large, or extreme, market movements. Risk managers are always on the lookout for good techniques to help them do their jobs. This very good book provides these techniques and addresses an important, and under-developed, area of practical research."--Martin Baxter, Nomura International

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Book SynopsisThe latest volume in the hugely popular Killer Su Doku series from The Times, featuring the highest-quality puzzles with an extra element of arithmetic.This addition to the successful Times Killer Su Doku series will test your skills to the limit, adding the challenge of arithmetic and taking Su Doku to a new and even deadlier level of difficulty.The puzzles use the same 9x9 grid as Su Doku but with an added mathematical challenge. The aim is not only to complete every row, column and cube so that it contains the numbers 1-9, it is also necessary to ensure that the outlined cubes add up to the same number as well.With 200 new Moderate, Tricky, Tough and Deadly Killer Su Doku puzzles, there is no chance to ease yourself in with simple puzzles. For those who like to live dangerously and push beyond their mental comfort zone, steel yourself for The Times'' next, terribly tough instalment.

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Book SynopsisStewart/Redlin/Watson's best-selling PRECALCULUS: MATHEMATICS FOR CALCULUS, 8th INTERNATIONAL METRIC EDITION with WebAssign digital resources prepares students to succeed in future calculus courses. This best-selling author team emphasizes problem-solving and mathematical modeling as this edition presents concepts with unparalleled clarity and precision. Updated content and revised learning features remove barriers for a carefully planned, inclusive learning experience. The authors' attention to detail and clarity makes this resource a proven market leader. Accompanying WebAssign digital resources further reinforce comprehension with a rich variety of exercise types and learning resources.Table of Contents1. Fundamentals 2. Functions 3. Polynomial and Rational Functions 4. Exponential and Logarithmic Functions 5. Trigonometric Functions: Unit Circle Approach 6. Trigonometric Functions: Right Triangle Approach 7. Analytical Trigonometry 8. Polar Coordinates, Parametric Equations, and Vectors 9. Systems of Equations and Inequalities 10. Conic Sections 11. Sequences and Series 12. Limits: A Preview of Calculus APPENDIX A: Geometry Review APPENDIX B: Calculations and Significant Figures (available on website) APPENDIX C: Graphing with a Graphing Calculator (available on website) APPENDIX D: Using the TI-83/84 Graphing Calculator (available on website) Additional Topics: Vectors in Three-Dimensions (available on website)

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Book SynopsisHow do you remember more and forget less?How can you earn more and become more creative just by moving house?And how do you pack a car boot most efficiently?This is your shortcut to the art of the shortcut.Mathematics is full of better ways of thinking, and with over 2,000 years of knowledge to draw on, Oxford mathematician Marcus du Sautoy interrogates his passion for shortcuts in this fresh and fascinating guide. After all, shortcuts have enabled so much of human progress, whether in constructing the first cities around the Euphrates 5,000 years ago, using calculus to determine the scale of the universe or in writing today's algorithms that help us find a new life partner.As well as looking at the most useful shortcuts in history such as measuring the circumference of the earth in 240 BC to diagrams that illustrate how modern GPS works Marcus also looks at how you can use shortcuts in investing or how to learn a musical instrument to memory techniques. He talks to, among many, the Trade Review‘enjoyably clever …with vividly illustrated chapters about the real-world applications of algebra, geometry, probability theory…It’s Du Sautoy, in the end, who provides the wisest commentary’ Steven Poole, Guardian ‘If you thought Maths was all about long stuff, like long division and long multiplication and taking a long, long time to figure things out, Marcus du Sautoy shows that it's just the opposite. Full of humour, stories and the lightest of touches, this is a sight-seeing tour of some of the world's greatest neat dodges, unexpected turns and useful cut-throughs. Prepare to be caught short’ Michael Rosen ‘This book will change the way you look at the world. It's chock full of stories, ideas and clever tricks – I loved it. Marcus is a maestro at making big ideas come alive – he deserves his place alongside Richard Dawkins, E. O. Wilson and Carlo Rovelli in the pantheon of great modern science writers’ Rohan Silva, CEO and founder of Second Home ‘If mathematics has proved anything, it is that shortcuts can change the world. Marcus du Sautoy has come up with a smart, well written and entertaining guide to the connecting tunnels, underpasses and other tricks to traverse the trials of everyday life’ Roger Highfield, author, broadcaster and Science Director at the Science Museum ‘The joy of du Sautoy’s book isn’t really the art of the real-world shortcut at all. It is the romp through mathematical ideas, from place value to non Euclidean geometry to probability theory…There are vivid historical examples of scientists and others using mathematical ideas to solve problems’ Tim Harford, Financial Times

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Book SynopsisComplex Analysis is the powerful fusion of the complex numbers (involving the ''imaginary'' square root of -1) with ordinary calculus, resulting in a tool that has been of central importance to science for more than 200 years.This book brings this majestic and powerful subject to life by consistently using geometry (not calculation) as the means of explanation. The 501 diagrams of the original edition embodied geometrical arguments that (for the first time) replaced the long and often opaque computations of the standard approach, in force for the previous 200 years, providing direct, intuitive, visual access to the underlying mathematical reality.This new 25th Anniversary Edition introduces brand-new captions that fully explain the geometrical reasoning, making it possible to read the work in an entirely new wayas a highbrow comic book!Trade ReviewVisual Complex Analysis is a delight, and a book after my own heart. By his innovative and exclusive use of the geometrical perspective, Tristan Needham uncovers many surprising and largely unappreciated aspects of the beauty of complex analysis. * Sir Roger Penrose *...it is comparable with Feynman's Lectures on Physics. At every point it asks "why" and finds a beautiful visual answer. * Newsletter of the European Mathematical Society *Newton would have approved... a fascinating and refreshing look at a familiar subject... essential reading for anybody with any interest at all in this absorbing area of mathematics. * Times Higher Education Supplement *One of the saddest developments in school mathematics has been the downgrading of the visual for the formal. I'm not lamenting the loss of traditional Euclidean geometry, despite its virtues, because it too emphasised stilted formalities. But to replace our rich visual tradition by silly games with 2 x 2 matrices has always seemed to me to be the height of folly. It is therefore a special pleasure to see Tristan Needham's Visual Complex Analysis with its elegantly illustrated visual approach. Yes, he has 2 x 2 matrices--but his are interesting. * Ian Stewart, New Scientist *an engaging, broad, thorough, and often deep, development of undergraduate complex analysis and related areas from a geometric point of view. The style is lucid, informal, reader-friendly, and rich with helpful images (e.g. the complex derivative as an "amplitwist"). A truly unusual and notably creative look at a classical subject. * Paul Zorn, American Mathematical Monthly *If your budget limits you to only buying one mathematics book in a year then make sure that this is the one that you buy. * Mathematical Gazette *I was delighted when I came across Visual Complex Analysis. As soon as I thumbed through it, I realized that this was the book I was looking for ten years ago. * Ed Catmull, former president of Pixar and Disney Animation Studios *The new ideas and exercises bring together a body of information potentially invaluable to researchers in fields from topology to number theory... this is only the beginning of a long list of famous facts for which Needham offers attractive visual proofs: Cauchy's theorem is a satisfying example: you can see the contribution to the integral from each infinitesimal square vanish before your eyes. * Frank Farris, American Mathematical Monthly *This informal style is excellently judged and works extremely well. Many of the arguments presented will be new even to experts, and the book will be of great interest to professionals working in either complex analysis or in any field where complex analysis is used. * David Armitage, Mathematical Reviews *The arguments constructed are highly innovative; even veterans of the field will find new ideas here. This is a special book. Tristan Needham has not only completely rethought a classical field of mathematics, but has presented it in a clear and compelling way. Visual Complex Analysis is worthy of the accolades it has received * MAA Reviews *This new edition of Visual Complex Analysis applies Newton's geometrical methods from the Principia and his concept of ultimate equality to Complex Analysis. * MathSciNet *Table of Contents1: Geometry and Complex Arithmetic 2: Complex Functions as Transformations 3: Möbius Transformations and Inversion 4: Differentiation: The Amplitwist Concept 5: Further Geometry of Differentiation 6: Non-Euclidean Geometry 7: Winding Numbers and Topology 8: Complex Integration: Cauchy's Theorem 9: Cauchy's Formula and Its Applications 10: Vector Fields: Physics and Topology 11: Vector Fields and Complex Integration 12: Flows and Harmonic Functions

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Book SynopsisThe twenty-first century has seen a breathtaking expansion of statistical methodology, both in scope and influence. ''Data science'' and ''machine learning'' have become familiar terms in the news, as statistical methods are brought to bear upon the enormous data sets of modern science and commerce. How did we get here? And where are we going? How does it all fit together? Now in paperback and fortified with exercises, this book delivers a concentrated course in modern statistical thinking. Beginning with classical inferential theories - Bayesian, frequentist, Fisherian - individual chapters take up a series of influential topics: survival analysis, logistic regression, empirical Bayes, the jackknife and bootstrap, random forests, neural networks, Markov Chain Monte Carlo, inference after model selection, and dozens more. The distinctly modern approach integrates methodology and algorithms with statistical inference. Each chapter ends with class-tested exercises, and the book concludes with speculation on the future direction of statistics and data science.Table of ContentsPart I. Classic Statistical Inference: 1. Algorithms and inference; 2. Frequentist inference; 3. Bayesian inference; 4. Fisherian inference and maximum likelihood estimation; 5. Parametric models and exponential families; Part II. Early Computer-Age Methods: 6. Empirical Bayes; 7. James–Stein estimation and ridge regression; 8. Generalized linear models and regression trees; 9. Survival analysis and the EM algorithm; 10. The jackknife and the bootstrap; 11. Bootstrap confidence intervals; 12. Cross-validation and Cp estimates of prediction error; 13. Objective Bayes inference and Markov chain Monte Carlo; 14. Statistical inference and methodology in the postwar era; Part III. Twenty-First-Century Topics: 15. Large-scale hypothesis testing and false-discovery rates; 16. Sparse modeling and the lasso; 17. Random forests and boosting; 18. Neural networks and deep learning; 19. Support-vector machines and kernel methods; 20. Inference after model selection; 21. Empirical Bayes estimation strategies; Epilogue; References; Author Index; Subject Index.

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Book SynopsisThe study of networks, including computer networks, social networks, and biological networks, has attracted enormous interest in the last few years. The rise of the Internet and the wide availability of inexpensive computers have made it possible to gather and analyze network data on an unprecedented scale, and the development of new theoretical tools has allowed us to extract knowledge from networks of many different kinds. The study of networks is broadly interdisciplinary and central developments have occurred in many fields, including mathematics, physics, computer and information sciences, biology, and the social sciences. This book brings together the most important breakthroughs in each of these fields and presents them in a coherent fashion, highlighting the strong interconnections between work in different areas.Topics covered include the measurement of networks; methods for analyzing network data, including methods developed in physics, statistics, and sociology; fundamentals of graph theory; computer algorithms; mathematical models of networks, including random graph models and generative models; and theories of dynamical processes taking place on networks.Trade ReviewThis is the definitive book on networks, friendly enough for anyone to read and serious enough for researchers to find their way. [Newman] is one of the founders and leaders of the field and has updated the book with cutting-edge topics. * Professor Cris Moore, Santa Fe Institute *This is the definitive book on network science, by one of its most brilliant researchers and graceful expositors. The second edition of Mark Newman's Networks is clear, comprehensive, and fascinating. * Steven Strogatz, Department of Mathematics, Cornell University, USA *This is an excellent textbook by one of the preeminent scholars in the study of networks. I draw heavily from it when teaching my undergraduate course on networks, and I am very pleased to see a new edition of the book. Newman's clear exposition shines through in this textbook. * Mason Porter, Department of Mathematics, UCLA, USA *An extraordinarily comprehensive and clear exposition of network science from one of the giants in the field. Newman succeeds in making accessible to a broad readership even the most technical content. * Santo Fortunato, School of Informatics and Computing, Indiana University *Reviews from previous edition:Networks accomplishes two key goals: It provides a comprehensive introduction and presents the theoretic backbone of network science. [] The book is balanced in its presentation of theoretical concepts, computational techniques, and algorithms. The level of difficulty increases which each chapter [which] makes the book particularly valuable to physics students who wish to acquire a solid foundation based on their knowledge of basic linear algebra, calculus, and differential equations. * Physics Today *Newman has written a wonderful book that gives an extensive overview of the broadly interdisciplinary network-related developments that have occured in many fields, including mathematics, physics, computer science, biology, and the social sciences ... Overall, a valuable resource covering a wide-randing field. * Choice *Likely to become the standard introductory textbook for the study of networks [...] Overall, this is an excellent textbook for the growing field of networks. It is cleverly written and suitable as both an introduction for undergraduate students (particularly Parts 1 to 3) and as a roadmap for graduate students. [...] Being highly self-contained, computer scientists and professionals from other fields can also use the book - in fact, the author himself is a physicist. In short, this book is a delight for the inquisitive mind. * Computing Reviews *This book brings together, for the first time, the most important breakthroughs in each of these fields and presents them in a coherent fashion, highlighting the strong connections between work in different subject areas. * CERN Courier *Table of Contents1: Introduction Part I: The empirical study of networks 2: Technological networks 3: Networks of information 4: Social networks 5: Biological networks Part II: Fundamentals of network theory 6: Mathematics of networks 7: Measures and metrics 8: Computer algorithms 9: Network statistics and measurement error 10: The structure of real-world networks Part III: Network models 11: Random graphs 12: The configuration model 13: Models of network formation Part IV: Applications 14: Community structure 15: Percolation and network resilience 16: Epidemics on networks 17: Dynamical systems on networks 18: Network search

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Book SynopsisThis book reveals glimpses of how the quantum physics of atoms and molecules influences, and even controls, the way our cells function and how we and our fellow animals interact with our environment. Simply put, how birds fly and why grass grows.Certainly, biochemistry and molecular biology are the foundations for the biology of living cells, but there is more—quantum coherence and entanglement influencing the functioning of proteins and enzymes, and strictly speaking, without the quantum phenomena we wouldn’t even be here.In the end, however, this book is based on the solid ground of science, presenting the many fascinating phenomena of how quantum physics makes life possible without any unwarranted mystification.Table of Contents1. Life and Quantum Physics 2. Our World Is Just a Small Part of the Whole 3. The Gecko and Life Upside Down 4. The Quantized World 5. Evolution: About the Origin of Life 6. From the Big Bang to Black Holes 7. As Time Goes By: The Arrow of Time 8. The Art of Finding Your Way Back Home 9. The Vision in New Light 10. Photosynthesis and the Golf Putt 11. The Respiratory Chain Sustains Our Lives 12. A Sense of Smell 13. DNA Repair: A Matter of Survival and Development 14. Quantum Physics in Diagnostics and Therapy 15. Not More Mysterious Than Necessary 16. Consciousness: The Greatest Mystery 17. A Glance at the Future of Quantum and Life

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Book SynopsisVery Short Introductions: Brilliant, sharp, inspiringThe 17th-century calculus of Newton and Leibniz was built on shaky foundations, and it wasn''t until the 18th and 19th centuries that mathematicians--especially Bolzano, Cauchy, and Weierstrass--began to establish a rigorous basis for the subject. The resulting discipline is now known to mathematicians as analysis.This book, aimed at readers with some grounding in mathematics, describes the nascent evolution of mathematical analysis, its development as a subject in its own right, and its wide-ranging applications in mathematics and science, modelling reality from acoustics to fluid dynamics, from biological systems to quantum theory.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.Table of ContentsAcknowledgements 1: Taming Infinity 2: All change... 3: Should I believe my computer? 4: Dimensions aplenty 5: I'll name that tune in... 6: Putting the i in analysis 7: But there's more... Appendix Historical timeline References Further Reading Index

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Book SynopsisCalculus is important for first-year undergraduate students pursuing mathematics, physics, economics, engineering, and other disciplines where mathematics plays a significant role. The book provides a thorough reintroduction to calculus with an emphasis on logical development arising out of geometric intuition. The author has restructured the subject matter in the book by using Tarski''s version of the completeness axiom, introducing integration before differentiation and limits, and emphasizing benefits of monotonicity before continuity. The standard transcendental functions are developed early in a rigorous manner and the monotonicity theorem is proved before the mean value theorem. Each concept is supported by diverse exercises which will help the reader to understand applications and take them nearer to real and complex analysis.Table of ContentsIntroduction; 1. Real Numbers and Functions; 2. Integration; 3. Limits and Continuity; 4. Differentiation; 5. Techniques of Integration; 6. Mean Value Theorems and Applications; 7. Sequences and Series; 8. Taylor and Fourier Series; A. Solutions to Odd-Numbered Exercises; Bibliography; Index.

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Book SynopsisAlgebra is like a foreign language for many students. They have difficulty translating the words, their definitions and how it applies to problem-solving. Tussy/Gustafson''s ELEMENTARY AND INTERMEDIATE ALGEBRA, 6th Edition, addresses these concerns, giving you the tools needed to understand the language of algebra. Strategy and Why explanations in the worked examples show the how and the why behind problem-solving. Algebra is not just about the x -- it''s also about the WHY. The text contains many opportunities to apply the algebraic skills you have learned to solve a wide variety of interesting real-life applications using a six-step problem-solving strategy. In combination, the text and WebAssign will guide you through an integrated learning process that will expand your reasoning abilities as it teaches you how to read, write and think mathematically using the language of Algebra.

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Book SynopsisThe Shape of Space, Third Edition maintains the standard of excellence set by the previous editions. This lighthearted textbook covers the basic geometry and topology of two- and three-dimensional spacesâstretching studentsâ minds as they learn to visualize new possibilities for the shape of our universe.Written by a master expositor, leading researcher in the field, and MacArthur Fellow, its informal exposition and engaging exercises appeal to an exceptionally broad audience, from liberal arts students to math undergraduate and graduate students looking for a clear intuitive understanding to supplement more formal texts, and even to laypeople seeking an entertaining self-study book to expand their understanding of space.Features of the Third Edition: Full-color figures throughout Picture proofs have replaced algebraic proofs Simpler handles-and-crosscaps approach to surfaces Updated discussiTable of ContentsPart I Surfaces and Three-Manifolds Flatland Gluing Vocabulary Orientability Classification of Surfaces Products Flat Manifolds Orientability vs. Two-Sidedness Part II Geometries on Surfaces The Sphere The Hyperbolic Plane Geometries on Surfaces Gauss-Bonnet Formula and Euler Number Part III Geometries on Three-Manifolds Four-Dimensional Space The Hypersphere Hyperbolic Space Geometries on Three-Manifolds I Bundles Geometries on Three-Manifolds II Part IV The Universe The Universe The History of Space Appendix A: Answers Appendix B: Bibliography Appendix C: Conway’s ZIP Proof

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Book SynopsisTrade Review“A clear analysis of systems ranging from radiation to human brains”—Nature“Many people might not bother to define complexity, thinking that we know it when we see it. Scientists and philosophers have no such luxury, and for them this book will be invaluable. Ladyman and Wiesner have provided a compact but comprehensive overview of the different ways that systems can be complex, ultimately arguing that complexity comes in distinct forms, but that their commonalities are nevertheless quite real.”—Sean Carroll, author of Something Deeply Hidden: Quantum Worlds and the Emergence of Spacetime“This is an outstanding, original, and much-needed book. Ladyman and Wiesner give an accessible, engaging, and precise overview of complexity science from a panoptic perspective, spanning many different kinds of examples from a variety of disciplines”—James Owen Weatherall, coauthor of The Misinformation Age: How False Beliefs Spread“Written in a lively and readable style, What Is a Complex System? provides a clear and coherent synthesis of the myriad and sometimes contradictory descriptions and definitions of complex systems.”—Colm Connaughton, Director of the Centre for Complexity Science, University of Warwick “This is highly thoughtful incisive essay on the meaning and use of the concept of complex systems. I particularly like the attempt to formulate syntheses across fields, across features and across mechanisms.”—Didier Sornette, author of Why Stock Markets Crash: Critical Events in Complex Financial Systems“This book is a superb introduction to complex systems. Ladyman and Wiesner skillfully guide the reader from examples of complex systems all-around us, to ten common features of such systems and how to mathematically measure them, to a discussion of complexity as a scientific field by itself. Anyone interested in complex systems should read this book before any other.”—Tina Eliassi-Rad, Professor of Network Science, Northeastern University

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Book SynopsisDiscrete Mathematics with Ducks, Second Edition is a gentle introduction for students who find the proofs and abstractions of mathematics challenging. At the same time, it provides stimulating material that instructors can use for more advanced students. The first edition was widely well received, with its whimsical writing style and numerous exercises and materials that engaged students at all levels. The new, expanded edition continues to facilitate effective and active learning. It is designed to help students learn about discrete mathematics through problem-based activities. These are created to inspire students to understand mathematics by actively practicing and doing, which helps students better retain what they've learned. As such, each chapter contains a mixture of discovery-based activities, projects, expository text, in-class exercises, and homework problems. The author's lively and friendly writing style is apTable of ContentsPreface for Instructors and Other TeachersPreface for Students and Other LearnersTheme: The Basics1 Counting and Proofs2 Sets and Logic3 Graphics and Functions4 Induction5 Algorithms with CiphersTheme I Supplement6 Binomial Coefficients and Pascal’s Triangle7 Balls and Boxes and PIE: Counting Techniques8 Recurrences9 Cutting Up Food: Counting and GeometryIII Theme: Graph Theory10 Trees11 Euler’s Formula and Applications12 Graph Traversals13 Graph ColoringTheme III Supplement: Problems on the Theme of Graph TheoryIV Other Material14 Probability and Expectation15 Fun with Cardinality16 Number Theory17 Computational ComplexityA Solutions to Check Yourself ProblemsB Solutions to Bonus Check-Yourself ProblemsC The Greek Alphabet and Some Uses for Some LettersD List of SymbolsBibliographyIndex

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Book SynopsisThis is a practical guide to P-splines, a simple, flexible and powerful tool for smoothing. P-splines combine regression on B-splines with simple, discrete, roughness penalties. They were introduced by the authors in 1996 and have been used in many diverse applications. The regression basis makes it straightforward to handle non-normal data, like in generalized linear models. The authors demonstrate optimal smoothing, using mixed model technology and Bayesian estimation, in addition to classical tools like cross-validation and AIC, covering theory and applications with code in R. Going far beyond simple smoothing, they also show how to use P-splines for regression on signals, varying-coefficient models, quantile and expectile smoothing, and composite links for grouped data. Penalties are the crucial elements of P-splines; with proper modifications they can handle periodic and circular data as well as shape constraints. Combining penalties with tensor products of B-splines extends theseTrade Review'The title says it all. This is a practical book which shows how P-splines are used in an astonishingly wide range of settings. If you use P-splines already the book is indispensable; if you don't, then reading it will convince you it's time to start. Every example comes with an R-program available on the book's web-site, an important feature for the experienced user and novice alike.' Iain Currie, Heriot-Watt University'This book is an enlightening and at the same time extremely enjoyable read. It will serve the applied statistician who is looking for practical solutions but also the connoisseur in search of elegant concepts. The accompanying website offers reproducible code and invites to promptly enter the fascinating universe of P-splines.' Jutta Gampe, Max Planck Institute for Demographic Research'Everything you always wanted to know about P-splines, from the inventors themselves. Paul H.C. Eilers and Brian D. Marx make a compelling case for their claim that P-splines are the best practical smoother out there, providing intuition, methodology, applications, and R code that clearly demonstrate the power, flexibility, and wide applicability of this approach to smoothing.' Jeffrey Simonoff, New York University'This is the book that everyone working on smoothing models should keep handy. At last we have a manuscript that shows the real power of P-splines, their versatility, and the different perspectives you can take to use them. Chapters 1 to 3 will certainly appeal to those who want to start working in this field, and to researchers that need to deepen their knowledge of this technique. Scientists and practitioners from other areas will find chapters 4 to 8 very useful for the wide range of examples and applications. The companion package and the fact that all results (even figures) are reproducible is a real bonus. Thank you Paul and Brian for being truthful to your motto: 'show, don't tell'.' Maria Durbán, University Carlos III de MadridTable of Contents1. Introduction; 2. Bases, penalties, and likelihoods; 3. Optimal smoothing in action; 4. Multidimensional smoothing; 5. Smoothing of scale and shape; 6. Complex counts and composite links; 7. Signal regression; 8. Special subjects; A. P-splines for the impatient; B. P-splines and competitors; C. Computational details; D. Array algorithms; E. Mixed model equations; F. Standard errors in detail; G. The website.

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Book SynopsisThis classic by one of the 20th century''s most prominent mathematicians offers a concise introduction to set theory. Suitable for advanced undergraduates and graduate students in mathematics, it employs the language and notation of informal mathematics. Topics include the basic concepts of set theory, cardinal numbers, transfinite methods, and a good deal more in 25 brief chapters.

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Book SynopsisPraise for the First Edition An indispensable addition to any serious collection on lifetime data analysis and . . . a valuable contribution to the statistical literature. Highly recommended . . . -Choice This is an important book, which will appeal to statisticians working on survival analysis problems. -Biometrics A thorough, unified treatment of statistical models and methods used in the analysis of lifetime data . . . this is a highly competent and agreeable statistical textbook. -Statistics in Medicine The statistical analysis of lifetime or response time data is a key tool in engineering, medicine, and many other scientific and technological areas. This book provides a unified treatment of the models and statistical methods used to analyze lifetime data. Equally useful as a reference for individuals interested in the analysis of lifetime data and as a text for advanced students, Statistical Models and Methods for Lifetime Data, SecoTrade Review“...a welcome addition to the literature on survival analysis...for a unified and thorough reference of classical theory and models, this book is an excellent choice.” (Journal of the American Statistical Association, March 2004) "This book is a role-model for other who are planning to write books…every statistician and applied researcher ought to have this book in their collection." (Journal of Statistical Computation and Simulation, October 2003) "...expanded and updated with recent research...a valuable reference...this book...merits a place on the bookshelf of anyone concerned with the analysis of lifetime data from any field. (Technometrics, Vol. 45, No. 3, August 2003) "...updated version of the popular text...this excellent book will serve as either a reference or a graduate-level textbook." (Short Book Reviews, Vol. 23, No. 2, August 2003) "...excellent...provides a wealth of information for those familiar with the area." (Pharmaceutical Research, Vol. 20, No. 9, September 2003) "...the author's aim is to cover lifetime data analysis without concentrating exclusively on any field of applications...he succeeds quite well..." (Zentralblatt Math, 2003) “...rewritten to reflect new developments...” (Quarterly of Applied Mathematics, Vol. LXI, No. 2, June 2003) "Compared with the large number of other good textbooks in the this field, this is one of the best. I highly recommend that all applied statisticians add this volume to their libraries." (Applied Clinical Trials, May 2003)Table of ContentsBasic Concepts and Models. Observation Schemes, Censoring and Likelihood. Some Nonparametric and Graphical Procedures. Inference Procedures for Parametric Models. Inference procedures for Log-Location-Scale Distributions. Parametric Regression Models. Semiparametric Multiplicative Hazards Regression Models. Rank-Type and Other Semiparametric Procedures for Log-Location-Scale Models. Multiple Modes of Failure. Goodness of Fit Tests. Beyond Univariate Survival Analysis. Appendix A. Glossary of Notation and Abbreviations. Appendix B. Asymptotic Variance Formulas, Gamma Functions and Order Statistics. Appendix C. Large Sample Theory for Likelihood and Estimating Function Methods. Appendix D. Computational Methods and Simulation. Appendix E. Inference in Location-Scale Parameter Models. Appendix F. Martingales and Counting Processes. Appendix G. Data Sets. References.

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Book SynopsisHaskell is a purely functional language that allows programmers to rapidly develop clear, concise, and correct software. The language has grown in popularity in recent years, both in teaching and in industry. This book is based on the author''s experience of teaching Haskell for more than twenty years. All concepts are explained from first principles and no programming experience is required, making this book accessible to a broad spectrum of readers. While Part I focuses on basic concepts, Part II introduces the reader to more advanced topics. This new edition has been extensively updated and expanded to include recent and more advanced features of Haskell, new examples and exercises, selected solutions, and freely downloadable lecture slides and example code. The presentation is clean and simple, while also being fully compliant with the latest version of the language, including recent changes concerning applicative, monadic, foldable, and traversable types.Trade Review'The skills you acquire by studying this book will make you a much better programmer no matter what language you use to actually program in.' Erik Meijer, Facebook, from the ForewordReview of previous edition: 'The best introduction to Haskell available. There are many paths towards becoming comfortable and competent with the language but I think studying this book is the quickest path. I urge readers of this magazine to recommend Programming in Haskell to anyone who has been thinking about learning the language.' Duncan Coutts, The Monad.ReaderReview of previous edition: 'Where this book excels is in the order and style of its exposition … With its ripe selection of examples and its careful clarity of exposition, the book is a welcome addition to the introductory functional programming literature.' Journal of Functional ProgrammingTable of ContentsForeword; Preface; Part I. Basic Concepts: 1. Introduction; 2. First steps; 3. Types and classes; 4. Defining functions; 5. List comprehensions; 6. Recursive functions; 7. Higher-order functions; 8. Declaring types and classes; 9. The countdown problem; Part II. Going Further: 10. Interactive programming; 11. Unbeatable tic-tac-toe; 12. Monads and more; 13. Monadic parsing; 14. Foldables and friends; 15. Lazy evaluation; 16. Reasoning about programs; 17. Calculating compilers; Appendix A. Selected solutions; Appendix B. Standard prelude; Bibliography; Index.

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Book Synopsis* The book is written by a first-class, world-renown authority in probability and measure theory at a leading U.S. institution of higher education * The book has been class-tested at over 200 universities around the globe * Theory is first-and-foremost.Trade Review“Like the previous editions, this Anniversary edition will be well received by students of mathematics, statistics, economics, and a wide variety of disciplines that require a solid understanding of probability theory.” (Int. J. Microstructure and Materials Properties, 1 February 2013)Table of ContentsFOREWORD xi PREFACE xiii Patrick Billingsley 1925–2011 xv Chapter1 PROBABILITY 1 1. BOREL’S NORMAL NUMBER THEOREM, 1 The Unit Interval The Weak Law of Large Numbers The Strong Law of Large Numbers Strong Law Versus Weak Length The Measure Theory of Diophantine Approximation* 2. PROBABILITY MEASURES, 18 Spaces Assigning Probabilities Classes of Sets Probability Measures Lebesgue Measure on the Unit Interval Sequence Space* Constructing s-Fields* 3. EXISTENCE AND EXTENSION, 39 Construction of the Extension Uniqueness and the p–? Theorem Monotone Classes Lebesgue Measure on the Unit Interval Completeness Nonmeasurable Sets Two Impossibility Theorems* 4. DENUMERABLE PROBABILITIES, 53 General Formulas Limit Sets Independent Events Subfields The Borel-Cantelli Lemmas The Zero-One Law 5. SIMPLE RANDOM VARIABLES, 72 Definition Convergence of Random Variables Independence Existence of Independent Sequences Expected Value Inequalities 6. THE LAW OF LARGE NUMBERS, 90 The Strong Law The Weak Law Bernstein's Theorem A Refinement of the Second Borel-Cantelli Lemma 7. GAMBLING SYSTEMS, 98 Gambler's Ruin Selection Systems Gambling Policies Bold Play* Timid Play* 8. MARKOV CHAINS, 117 Definitions Higher-Order Transitions An Existence Theorem Transience and Persistence Another Criterion for Persistence Stationary Distributions Exponential Convergence* Optimal Stopping* 9. LARGE DEVIATIONS AND THE LAW OF THE ITERATED LOGARITHM, 154 Moment Generating Functions Large Deviations Chernoff's Theorem* The Law of the Iterated Logarithm Chapter2 MEASURE 167 10. GENERAL MEASURES, 167 Classes of Sets Conventions Involving 8 Measures Uniqueness 11. OUTER MEASURE, 174 Outer Measure Extension An Approximation Theorem 12. MEASURES IN EUCLIDEAN SPACE, 181 Lebesgue Measure Regularity Specifying Measures on the Line Specifying Measures in Rk Strange Euclidean Sets* 13. MEASURABLE FUNCTIONS AND MAPPINGS, 192 Measurable Mappings Mappings into Rk Limits and Measurability Transformations of Measures 14. DISTRIBUTION FUNCTIONS, 198 Distribution Functions Exponential Distributions Weak Convergence Convergence of Types* Extremal Distributions* Chapter3 INTEGRATION 211 15. THE INTEGRAL, 211 Definition Nonnegative Functions Uniqueness 16. PROPERTIES OF THE INTEGRAL, 218 Equalities and Inequalities Integration to the Limit Integration over Sets Densities Change of Variable Uniform Integrability Complex Functions 17. THE INTEGRAL WITH RESPECT TO LEBESGUE MEASURE, 234 The Lebesgue Integral on the Line The Riemann Integral The Fundamental Theorem of Calculus Change of Variable The Lebesgue Integral in Rk Stieltjes Integrals 18. PRODUCT MEASURE AND FUBINI’S THEOREM, 245 Product Spaces Product Measure Fubini's Theorem Integration by Parts Products of Higher Order 19. THE Lp SPACES*, 256 Definitions Completeness and Separability Conjugate Spaces Weak Compactness Some Decision Theory The Space L2 An Estimation Problem Chapter4 RANDOM VARIABLES AND EXPECTED VALUES 271 20. RANDOM VARIABLES AND DISTRIBUTIONS, 271 Random Variables and Vectors Subfields Distributions Multidimensional Distributions Independence Sequences of Random Variables Convolution Convergence in Probability The Glivenko-Cantelli Theorem* 21. EXPECTED VALUES, 291 Expected Value as Integral Expected Values and Limits Expected Values and Distributions Moments Inequalities Joint Integrals Independence and Expected Value Moment Generating Functions 22. SUMS OF INDEPENDENT RANDOM VARIABLES, 300 The Strong Law of Large Numbers The Weak Law and Moment Generating Functions Kolmogorov's Zero-One Law Maximal Inequalities Convergence of Random Series Random Taylor Series* 23. THE POISSON PROCESS, 316 Characterization of the Exponential Distribution The Poisson Process The Poisson Approximation Other Characterizations of the Poisson Process Stochastic Processes 24. THE ERGODIC THEOREM*, 330 Measure-Preserving Transformations Ergodicity Ergodicity of Rotations Proof of the Ergodic Theorem The Continued-Fraction Transformation Diophantine Approximation Chapter5 CONVERGENCE OF DISTRIBUTIONS 349 25. WEAK CONVERGENCE, 349 Definitions Uniform Distribution Modulo 1* Convergence in Distribution Convergence in Probability Fundamental Theorems Helly's Theorem Integration to the Limit 26. CHARACTERISTIC FUNCTIONS, 365 Definition Moments and Derivatives Independence Inversion and the Uniqueness Theorem The Continuity Theorem Fourier Series* 27. THE CENTRAL LIMIT THEOREM, 380 Identically Distributed Summands The Lindeberg and Lyapounov Theorems Dependent Variables* 28. INFINITELY DIVISIBLE DISTRIBUTIONS*, 394 Vague Convergence The Possible Limits Characterizing the Limit 29. LIMIT THEOREMS IN Rk, 402 The Basic Theorems Characteristic Functions Normal Distributions in Rk The Central Limit Theorem 30. THE METHOD OF MOMENTS*, 412 The Moment Problem Moment Generating Functions Central Limit Theorem by Moments Application to Sampling Theory Application to Number Theory Chapter6 DERIVATIVES AND CONDITIONAL PROBABILITY 425 31. DERIVATIVES ON THE LINE*, 425 The Fundamental Theorem of Calculus Derivatives of Integrals Singular Functions Integrals of Derivatives Functions of Bounded Variation 32. THE RADON–NIKODYM THEOREM, 446 Additive Set Functions The Hahn Decomposition Absolute Continuity and Singularity The Main Theorem 33. CONDITIONAL PROBABILITY, 454 The Discrete Case The General Case Properties of Conditional Probability Difficulties and Curiosities Conditional Probability Distributions 34. CONDITIONAL EXPECTATION, 472 Definition Properties of Conditional Expectation Conditional Distributions and Expectations Sufficient Subfields* Minimum-Variance Estimation* 35. MARTINGALES, 487 Definition Submartingales Gambling Functions of Martingales Stopping Times Inequalities Convergence Theorems Applications: Derivatives Likelihood Ratios Reversed Martingales Applications: de Finetti's Theorem Bayes Estimation A Central Limit Theorem* Chapter7 STOCHASTIC PROCESSES 513 36. KOLMOGOROV'S EXISTENCE THEOREM, 513 Stochastic Processes Finite-Dimensional Distributions Product Spaces Kolmogorov's Existence Theorem The Inadequacy of RT A Return to Ergodic Theory The Hewitt–Savage Theorem* 37. BROWNIAN MOTION, 530 Definition Continuity of Paths Measurable Processes Irregularity of Brownian Motion Paths The Strong Markov Property The Reflection Principle Skorohod Embedding Invariance* 38. NONDENUMERABLE PROBABILITIES, 558 Introduction Definitions Existence Theorems Consequences of Separability* APPENDIX 571 NOTES ON THE PROBLEMS 587 BIBLIOGRAPHY 617 INDEX 619

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Book SynopsisThis classic on games and how to play them intelligently is being re-issued in a new, four volume edition. This book has laid the foundation to a mathematical approach to playing games. The wise authors wield witty words, which wangle wonderfully winning ways. In Volume 1, the authors do the Spade Work, presenting theories and techniques to "dissect" games of varied structures and formats in order to develop winning strategies.Trade Review" ""Winning Ways is an absolute must have for those who are interested in mathematical game theory. It is sure to please any fan of recreational mathematics or simply anyone who is interested in games and how to play them well."" -Jacob McMillen, Math Horizons, November 2005 ""This new edition confirms the status of the book as a standard reference, which it will continue to be for at least another decade."" -Adhemar Bultheel, Bulletin of the Belgian Mathematical Society , December 2005"Table of ContentsPreface to Second Edition, Preface, Spade-Work!, 1. WhoseGame?, 2. Finding the Correct Number is Simplicity Itself, 3. Some Harder Games and How to Make Them Easier, 4. Taking and Breaking, 5. Numbers, Nimbers and Numberless Wonders, 6. The Heat of Battle, 7. Hackenbush, 8. It’s a Small Small Small Small World, Index

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Book SynopsisTable of Contents 1. Functions 2. Limits 3. Derivatives 4. Applications of the Derivative 5. Integration 6. Applications of Integration 7. Integration Techniques 8. Sequences and Infinite Series 9. Power Series 10. Parametric and Polar Curves 11. Vectors and Vector-Valued Functions 12. Functions of Several Variables 13. Multiple Integration 14. Vector Calculus Appendix A. Algebra Review Appendix B. Proofs of Selected Theorems D1. Differential Equations (online) D1.1 Basic Ideas D1.2 Direction Fields and Euler’s Method D1.3 Separable Differential Equations D1.4 Special First-Order Differential Equations D1.5 Modeling with Differential Equations D2. Second-Order Differential Equations (online) D2.1 Basic Ideas D2.2 Linear Homogeneous Equations D2.3 Linear Nonhomogeneous Equations D2.4 Applications D2.5 Complex Forcing Functions

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