Mathematics Books

Book SynopsisThis 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. 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. Trade Review“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)“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)“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)“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)Table of Contents1. 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.

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Book SynopsisThis book deals with the geometry of visual space in all its aspects. As in any branch of mathematics, the aim is to trace the hidden to the obvious; the peculiarity of geometry is that the obvious is sometimes literally before one's eyes.Starting from intuition, spatial concepts are embedded in the pre-existing mathematical framework of linear algebra and calculus. The path from visualization to mathematically exact language is itself the learning content of this book. This is intended to close an often lamented gap in understanding between descriptive preschool and school geometry and the abstract concepts of linear algebra and calculus. At the same time, descriptive geometric modes of argumentation are justified because their embedding in the strict mathematical language has been clarified.The concepts of geometry are of a very different nature; they denote, so to speak, different layers of geometric thinking: some arguments use only concepts such as point, straight line, and incidence, others require angles and distances, still others symmetry considerations. Each of these conceptual fields determines a separate subfield of geometry and a separate chapter of this book, with the exception of the last-mentioned conceptual field "symmetry", which runs through all the others: - Incidence: Projective geometry - Parallelism: Affine geometry - Angle: Conformal Geometry - Distance: Metric Geometry - Curvature: Differential Geometry - Angle as distance measure: Spherical and Hyperbolic Geometry - Symmetry: Mapping Geometry.The mathematical experience acquired in the visual space can be easily transferred to much more abstract situations with the help of the vector space notion. The generalizations beyond the visual dimension point in two directions: Extension of the number concept and transcending the three illustrative dimensions.This book is a translation of the original German 1st edition Geometrie – Anschauung und Begriffe by Jost-Hinrich Eschenburg, published by Springer Fachmedien Wiesbaden GmbH, part of Springer Nature in 2020. The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com). A subsequent human revision was done primarily in terms of content, so that the book will read stylistically differently from a conventional translation. Springer Nature works continuously to further the development of tools for the production of books and on the related technologies to support the authors.Table of ContentsWhat is geometry.- Parallelism: affine geometry.- From affine geometry to linear algebra.- Definition of affine space.- Parallelism and semiaffine mappings.- Parallel projections.- Affine coordinates and center of gravity.- Incidence: projective geometry.- Central perspective.- Far points and straight lines of projection.- Projective and affine space.-Semi-projective mappings and collineations.- Conic sections and quadrics; homogenization.- The theorems of Desargues and Brianchon.- Duality and polarity; Pascal's theorem.- The double ratio.- Distance: Euclidean geometry.- The Pythagorean theorem.- Isometries of Euclidean space.- Classification of isometries.- Platonic solids.- Symmetry groups of Platonic solids.- Finite rotation groups and crystal groups.- Metric properties of conic sections.- Curvature: differential geometry.- Smoothness.- Fundamental forms and curvatures.- Characterization of spheres and hyperplanes.- Orthogonal hyperface systems.- Angles: conformal geometry.- Conformal mappings.- Inversions.- Conformal and spherical mappings.- The stereographic projection.- The space of spheres.- Angular distance: spherical and hyperbolic geometry. The hyperbolic space. Distance on the sphere and in hyperbolic space. Models of hyperbolic geometry.- Exercises.- Solutions

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Book SynopsisThis book provides a comprehensive knowledge of linear algebra for graduate and undergraduate courses. As a self-contained text, it aims at covering all important areas of the subject, including algebraic structures, matrices and systems of linear equations, vector spaces, linear transformations, dual and inner product spaces, canonical, bilinear, quadratic, sesquilinear, Hermitian forms of operators and tensor products of vector spaces with their algebras. The last three chapters focus on empowering readers to pursue interdisciplinary applications of linear algebra in numerical methods, analytical geometry and in solving linear system of differential equations. A rich collection of examples and exercises are present at the end of each section to enhance the conceptual understanding of readers. Basic knowledge of various notions, such as sets, relations, mappings, etc., has been pre-assumed.Table of Contents1. Algebraic Structures2. Matrices and Systems of Linear Equations3. Vector Spaces4. Linear Transformations5. Dual Spaces6. Inner Product Spaces7. Canonical Forms of an Operator8. Bilinear and Quadratic Forms9. Sesquilinear and Hermitian Forms10. Applications of Linear Algebra to Numerical Methods11. Affine and Euclidean Spaces and the Applications of Linear Algebra to Geometry12. Ordinary differential equations and linear systems of ordinary differential equations

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Book SynopsisThe purpose of this book is to explain linear algebra clearly for beginners. In doing so, the author states and explains somewhat advanced topics such as Hermitian products and Jordan normal forms. Starting from the definition of matrices, it is made clear with examples that matrices and matrix operation are abstractions of tables and operations of tables. The author also maintains that systems of linear equations are the starting point of linear algebra, and linear algebra and linear equations are closely connected. The solutions to systems of linear equations are found by solving matrix equations in the row-reduction of matrices, equivalent to the Gauss elimination method of solving systems of linear equations. The row-reductions play important roles in calculation in this book. To calculate row-reductions of matrices, the matrices are arranged vertically, which is seldom seen but is convenient for calculation. Regular matrices and determinants of matrices are defined and explained. Furthermore, the resultants of polynomials are discussed as an application of determinants. Next, abstract vector spaces over a field K are defined. In the book, however, mainly vector spaces are considered over the real number field and the complex number field, in case readers are not familiar with abstract fields. Linear mappings and linear transformations of vector spaces and representation matrices of linear mappings are defined, and the characteristic polynomials and minimal polynomials are explained. The diagonalizations of linear transformations and square matrices are discussed, and inner products are defined on vector spaces over the real number field. Real symmetric matrices are considered as well, with discussion of quadratic forms. Next, there are definitions of Hermitian inner products. Hermitian transformations, unitary transformations, normal transformations and the spectral resolution of normal transformations and matrices are explained. The book ends with Jordan normal forms. It is shown that any transformations of vector spaces over the complex number field have matrices of Jordan normal forms as representation matrices.Table of ContentsPreface.- 1. Matrices.- 2. Linear Equations.- 3. Determinants.- 4. Vector Spaces.- 5. Linear Mappings.- 6. Inner Product Spaces.- 7. Hermitian Inner Product Spaces.- 8. Jordan Normal Forms.-Notation.- Answers to Exercises.- References.- Index of Theorems.- Index.

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Book SynopsisThis textbook is for those who want to learn linear algebra from the basics. After a brief mathematical introduction, it provides the standard curriculum of linear algebra based on an abstract linear space. It covers, among other aspects: linear mappings and their matrix representations, basis, and dimension; matrix invariants, inner products, and norms; eigenvalues and eigenvectors; and Jordan normal forms. Detailed and self-contained proofs as well as descriptions are given for all theorems, formulas, and algorithms. A unified overview of linear structures is presented by developing linear algebra from the perspective of functional analysis. Advanced topics such as function space are taken up, along with Fourier analysis, the Perron–Frobenius theorem, linear differential equations, the state transition matrix and the generalized inverse matrix, singular value decomposition, tensor products, and linear regression models. These all provide a bridge to more specialized theories based on linear algebra in mathematics, physics, engineering, economics, and social sciences. Python is used throughout the book to explain linear algebra. Learning with Python interactively, readers will naturally become accustomed to Python coding. By using Python’s libraries NumPy, Matplotlib, VPython, and SymPy, readers can easily perform large-scale matrix calculations, visualization of calculation results, and symbolic computations. All the codes in this book can be executed on both Windows and macOS and also on Raspberry Pi.Table of ContentsMathematics and Python.- Linear Spaces and Linear Mappings.- Basis and Dimension.- Matrices.- Elementary Operations and Matrix Invariants.- Inner Product and Fourier Expansion.- Eigenvalues and Eigenvectors.- Jordan Normal Form and Spectrum.- Dynamical Systems.- Applications and Development of Linear Algebra.

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Book SynopsisFrom Ancient Greek times, music has been seen as a mathematical art, and this relationship has fascinated generations. This new in paperback edition of diverse, comprehensive and fully-illustrated papers, authored by leading scholars, links the two fields in a lucid manner that is suitable for students of each subject as well as the general reader.Trade ReviewAn attractive volume that covers almost al of the important aspects of the interplay between mathematics and music. * Ehrhard Behrends, The Mathematical Intelligencer, Vol 28, 3 *Table of ContentsPART I: MUSIC AND MATHEMATICS THROUGH HISTORY; PART II: THE MATHEMATICS OF MUSICAL SOUND; PART III: MATHEMATICAL STRUCTURE IN MUSIC; PART IV: THE COMPOSER SPEAKS

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Book SynopsisTechnical Analysis of Stock Trends helps investors make smart, profitable trading decisions by providing proven long- and short-term stock trend analysis. It gets right to the heart of effective technical trading concepts, explaining technical theory such as The Dow Theory, reversal patterns, consolidation formations, trends and channels, technical analysis of commodity charts, and advances in investment technology. It also includes a comprehensive guide to trading tactics from long and short goals, stock selection, charting, low and high risk, trend recognition tools, balancing and diversifying the stock portfolio, application of capital, and risk management. This updated new edition includes patterns and modifiable charts that are tighter and more illustrative. Expanded material is also included on Pragmatic Portfolio Theory as a more elegant alternative to Modern Portfolio Theory; and a newer, simpler, and more powerful alternative to Dow Theory is presented.Table of ContentsPart I: Technical theory 1. The technical approach to trading and investing 2. Charts 3. The Dow Theory 4. The Dow Theory’s defects 5. Replacing Dow Theory with John Magee’s Basing points Procedure 6. Important Reversal Patterns 7. Important Reversal Patterns: continued 8. Important Reversal Patterns: the Triangles 9. More important Reversal Patterns 10. Other Reversal phenomena 11. Consolidation Formations 12. Gaps 13. Support and Resistance 14. Trendlines and Channels 15. Major Trendlines 16. Technical analysis of commodity charts 17. A summary and concluding comments Part II: Trading tactics 18. The tactical problem 19. The all-important details 20. The kind of stocks we want: the speculator’s viewpoint 21. Selection of stocks to chart 22. Selection of stocks to chart: continued 23. Choosing and managing high-risk stocks: tulip stocks, Internet sector, and speculative frenzies 24. The probable moves of your stocks 25. Two touchy questions 26. Round lots or odd lots? 27. Stop orders 28. What is a Bottom and what is a Top? 29. Trendlines in action 30. Use of Support and Resistance 31. Not all in one basket 32. Measuring implications in technical chart patterns 33. Tactical review of chart action 34. A quick summation of tactical methods 35. Effect of technical trading on market action 36. Automated trendline: the Moving Average 37. The same old patterns 38. Balanced and diversified 39. Trial and error 40. How much capital to use in trading 41. Application of capital in practice 42. Portfolio risk management 43. Stick to your guns

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Book SynopsisThis comprehensive student manual provides the perfect accompaniment to the leading textbook by Bernard Schutz, A First Course in General Relativity. Meticulously detailed solutions to almost half of Schutz's exercises and 125 brand new supplementary problems enable undergraduates, postgraduates and self-learners to master general relativity with confidence.Trade Review'Robert B. Scott has done a great service to students and instructors alike by compiling this superb Student's Manual to Bernard Schutz's A First Course in General Relativity, a classic introductory textbook on general relativity. Not only does Scott present exquisitely detailed solutions to Schutz's exercises, he also proposes a large number of his own problems to further test the student's understanding. The student will benefit greatly from this resource, and will be eased into the subject by Scott's excellent advice.' Eric Poisson, University of Guelph, Ontario'In attempting to master any subject, there is no substitute for working through problems, and this is especially true for developing an understanding of relativity. This collection of solutions to a range of selected problems from Schutz's classic textbook A First Course in General Relativity contains carefully worked model answers that should provide an invaluable resource to generations of students.' Michael Hobson, University of Cambridge'This Student's Manual, with its detailed calculations and very pedagogical explanations, is an extremely valuable tool for learning general relativity and acquiring a solid foundation in this field. I highly recommend it!' Eric Gourgoulhon, Université Paris Diderot'The textbook by Bernard Schutz, A First Course in General Relativity, is one of the best regarded on the subject, and Robert Scott's 'student's manual' is an extremely good aid… Scott provides clear and detailed explanations and algebra so that the student can navigate through these problems with confidence … It seems to me that Scott's very helpful volume - which includes a number of further problems set by himself - will prove indispensable to any student who makes use of Schutz, and it may well provide an incentive for students and course directors to base their studies on this text … It might be possible to use Scott's book, which also includes material on special relativity, as an adjunct to other books on relativity … it might be worthwhile for users of other textbooks to check its compatibility. … this is a book that all students of general relativity should be aware of.' Peter J. Bussey, Contemporary Physics'This is an excellent companion volume for anyone contemplating teaching a first course in General Relativity … this book is a perfect companion to a textbook …' Paranjape Manu, Physics in CanadaTable of ContentsPreface; 1. Special relativity; 2. Vector analysis in special relativity; 3. Tensor analysis in special relativity; 4. Perfect fluids in special relativity; 5. Preface to curvature; 6. Curved manifolds; 7. Physics in curved spacetime; 8. The Einstein field equations; 9. Gravitational radiation; 10. Spherical solutions for stars; 11. Schwarzschild geometry and black holes; 12. Cosmology; Appendix A. Acronyms and definitions; Appendix B. Useful results; References; Index.

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Book SynopsisCluster analysis finds groups in data automatically. Most methods have been heuristic and leave open such central questions as: how many clusters are there? Which method should I use? How should I handle outliers? Classification assigns new observations to groups given previously classified observations, and also has open questions about parameter tuning, robustness and uncertainty assessment. This book frames cluster analysis and classification in terms of statistical models, thus yielding principled estimation, testing and prediction methods, and sound answers to the central questions. It builds the basic ideas in an accessible but rigorous way, with extensive data examples and R code; describes modern approaches to high-dimensional data and networks; and explains such recent advances as Bayesian regularization, non-Gaussian model-based clustering, cluster merging, variable selection, semi-supervised and robust classification, clustering of functional data, text and images, and co-clTrade Review'Bouveyron, Celeux, Murphy, and Raftery pioneered the theory, computation, and application of modern model-based clustering and discriminant analysis. Here they have produced an exhaustive yet accessible text, covering both the field's state of the art as well as its intellectual development. The authors develop a unified vision of cluster analysis, rooted in the theory and computation of mixture models. Embedded R code points the way for applied readers, while graphical displays develop intuition about both model construction and the critical but often-neglected estimation process. Building on a series of running examples, the authors gradually and methodically extend their core insights into a variety of exciting data structures, including networks and functional data. This text will serve as a backbone for graduate study as well as an important reference for applied data scientists interested in working with cutting-edge tools in semi- and unsupervised machine learning.' John S. Ahlquist, University of California, San Diego'This book, written by authoritative experts in the field, gives a comprehensive and thorough introduction to model-based clustering and classification. The authors not only explain the statistical theory and methods, but also provide hands-on applications illustrating their use with the open-source statistical software R. The book also covers recent advances made for specific data structures (e.g. network data) or modeling strategies (e.g. variable selection techniques), making it a fantastic resource as an overview of the state of the field today.' Bettina Grün, Johannes Kepler Universität Linz, Austria'Four authors with diverse strengths nicely integrate their specialties to illustrate how clustering and classification methods are implemented in a wide selection of real-world applications. Their inclusion of how to use available software is an added benefit for students. The book covers foundations, challenging aspects, and some essential details of applications of clustering and classification. It is a fun and informative read!' Naisyin Wang, University of Michigan'This is a beautifully written book on a topic of fundamental importance in modern statistical science, by some of the leading researchers in the field. It is particularly effective in being an applied presentation - the reader will learn how to work with real data and at the same time clearly presenting the underlying statistical thinking. Fundamental statistical issues like model and variable selection are clearly covered as well as crucial issues in applied work such as outliers and ordinal data. The R code and graphics are particularly effective. The R code is there so you know how to do things, but it is presented in a way that does not disrupt the underlying narrative. This is not easy to do. The graphics are 'sophisticatedly simple' in that they convey complex messages without being too complex. For me, this is a 'must have' book.' Rob McCulloch, Arizona State University'This advanced text explains the underlying concepts clearly and is strong on theory … I congratulate the authors on the theoretical aspects of their book, it's a fine achievement.' Antony Unwin, International Statistical Review'In my opinion, the overall quality of this impactful and intriguing book can be expressed by concluding that it is a perfect fit to the Cambridge Series in Statistical and Probabilistic Mathematics, characterized as a series of high-quality upper-division textbooks and expository monographs containing applications and discussions of new techniques while emphasizing rigorous treatment of theoretical methods.' Zdenek Hlavka, MathSciNet'… this book not only gives the big picture of the analysis of clustering and classification but also explains recent methodological advances. Extensive real-world data examples and R code for many methods are also well summarized. This book is highly recommended to students in data science, as well as researchers and data analysts.' Li-Pang Chen, Biometrical Journal'Model-Based Clustering and Classification for Data Science: With Applications in R, written by leading statisticians in the field, provides academics and practitioners with a solid theoretical and practical foundation on the use of model-based clustering methods … this book will serve as an excellent resource for quantitative practitioners and theoreticians seeking to learn the current state of the field.' C. M. Foley, Quarterly Review of Biology'This book frames cluster analysis and classification in terms of statistical models, thus yielding principled estimation, testing and prediction methods, and sound answers to the central questions … Written for advanced undergraduates in data science, as well as researchers and practitioners, it assumes basic knowledge of multivariate calculus, linear algebra, probability and statistics.' Hans-Jürgen Schmidt, zbMATHTable of Contents1. Introduction; 2. Model-based clustering: basic ideas; 3. Dealing with difficulties; 4. Model-based classification; 5. Semi-supervised clustering and classification; 6. Discrete data clustering; 7. Variable selection; 8. High-dimensional data; 9. Non-Gaussian model-based clustering; 10. Network data; 11. Model-based clustering with covariates; 12. Other topics; List of R packages; Bibliography; Index.

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Book SynopsisNow in its second edition, this popular textbook on game theory is unrivalled in the breadth of its coverage, the thoroughness of technical explanations and the number of worked examples included. Covering non-cooperative and cooperative games, this introduction to game theory includes advanced chapters on auctions, games with incomplete information, games with vector payoffs, stable matchings and the bargaining set. This edition contains new material on stochastic games, rationalizability, and the continuity of the set of equilibrium points with respect to the data of the game. The material is presented clearly and every concept is illustrated with concrete examples from a range of disciplines. With numerous exercises, and the addition of a solution manual for instructors with this edition, the book is an extensive guide to game theory for undergraduate through graduate courses in economics, mathematics, computer science, engineering and life sciences, and will also serve as useful reTrade ReviewPraise for first edition: 'This is the book for which the world has been waiting for decades: a definitive, comprehensive account of the mathematical theory of games, by three of the world's biggest experts on the subject. Rigorous yet eminently readable, deep yet comprehensible, replete with a large variety of important real-world applications, it will remain the standard reference in game theory for a very long time.' Robert Aumann, Nobel Laureate in Economics, The Hebrew University of JerusalemPraise for first edition: 'Without any sacrifice on the depth or the clarity of the exposition, this book is amazing in its breadth of coverage of the important ideas of game theory. It covers classical game theory, including utility theory, equilibrium refinements and belief hierarchies; classical cooperative game theory, including the core, Shapley value, bargaining set and nucleolus; major applications, including social choice, auctions, matching and mechanism design; and the relevant mathematics of linear programming and fixed point theory. The comprehensive coverage combined with the depth and clarity of exposition makes it an ideal book not only to learn game theory from, but also to have on the shelves of working game theorists.' Ehud Kalai, Kellogg School of Management, Northwestern UniversityPraise for first edition: 'The best and the most comprehensive textbook for advanced courses in game theory.' David Schmeidler, Ohio State University and Tel Aviv UniversityPraise for first edition: 'There are quite a few good textbooks on game theory now, but for rigor and breadth this one stands out.' Eric S. Maskin, Nobel Laureate in Economics, Harvard University, MassachusettsPraise for first edition: 'This textbook provides an exceptionally clear and comprehensive introduction to both cooperative and noncooperative game theory. It deftly combines a rigorous exposition of the key mathematical results with a wealth of illuminating examples drawn from a wide range of subjects. It is a tour de force.' Peyton Young, University of OxfordPraise for first edition: 'This is a wonderful introduction to game theory, written in a way that allows it to serve both as a text for a course and as a reference … The book is written by leading figures in the field [whose] broad view of the field suffuses the material.' Joe Halpern, Cornell University, New YorkTable of Contents1. The game of chess; 2. Utility theory; 3. Extensive-form games; 4. Strategic-form games; 5. Mixed strategies; 6. Behavior strategies and Kuhn's theorem; 7. Equilibrium refinements; 8. Correlated equilibria; 9. Games with incomplete information and common priors; 10. Games with incomplete information: the general model; 11. The universal belief space; 12. Auctions; 13. Repeated games; 14. Repeated games with vector payoffs; 15. Social choice; 16. Bargaining games; 17. Coalitional games with transferable utility; 18. The core; 19. The Shapley value; 20. The bargaining set; 21. The nucleolus; 22. Stable matching; 23. Appendices.

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Book SynopsisENCYCLOPEDIA OF STATISTICAL SCIENCES

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Book SynopsisProvides a humorous tour through modern statistics as it is practiced in a wide variety of fields - from the humanities to the sciences. The book begins with a brief history of the subject, then proceeds to cover data analysis, probability and all topics crucial to the study of statistics.

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Book SynopsisStudy smarter and stay on top of your discrete mathematics course with the bestselling Schaumâs Outlineânow with the NEW Schaumâs app and website! Schaumâs Outline of Discrete Mathematics, Fourth Edition is the go-to study guide for more than 115,000 math majors and first- and second-year university students taking basic computer science courses. With an outline format that facilitates quick and easy review, Schaumâs Outline of Discrete Mathematics, Fourth Edition helps you understand basic concepts and get the extra practice you need to excel in these courses.Coverage includes set theory; relations; functions and algorithms; logic and propositional calculus; techniques of counting; advanced counting techniques, recursion; probability; graph theory; directed graphs; binary trees; properties of the integers; languages, automata, machines; finite state machines and Turning machines; ordered sets and lattices, and Boolean algebra.Features&

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Book SynopsisA #1 SUNDAY TIMES BESTSELLER Explore the life-changing magic of trigonometry with Matt Parker, stand-up mathematician and No. 1 bestselling author of Humble Pi 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. In Love Triangle, stand-up comedian, ex-maths teacher and Sunday Times 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

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Book SynopsisThe same five practices teachers know and love for planning and managing powerful conversations in mathematics classrooms, updated with current research and new insights on anticipating, lesson planning, and lessons learned from teachers, coaches, and school leaders. This framework for orchestrating mathematically productive discussions is rooted in student thinking to launch meaningful discussions in which important mathematical ideas are brought to the surface, contradictions are exposed, and understandings are developed or consolidated. Learn the 5 practices for facilitating effective inquiry-oriented classrooms: Anticipating what students will do and what strategies they will use in solving a problem Monitoring their work as they approach the problem in class Selecting students whose strategies are worth discussing in class Sequencing those students′ presentations to maximize their potential to increase students′ learning Connecting the strategies and ideas in a way that helps students understand the mathematics learned Table of Contents Front Matter Dedication Acknowledgments Preface Introduction Full access Chapter 1 Introducing the Five Practices Chapter 2 Laying the Groundwork: Setting Goals and Selecting Tasks Chapter 3 Investigating the Five Practices in Action Chapter 4 Getting Started: Anticipating Students’ Responses and Monitoring Their Work Chapter 5 Determining the Direction of the Discussion: Selecting, Sequencing, and Connecting Students’ Responses Chapter 6 Ensuring Active Thinking and Participation: Asking Good Questions and Holding Students Accountable Chapter 7 Putting the Five Practices in a Broader Context of Lesson Planning Chapter 8 Working in the School Environment to Improve Classroom Discussions Chapter 9 The Five Practices: Lessons Learned and Potential Benefits Appendix A Web-based Resources for Tasks and Lesson Plans Appendix B Lesson Plan for Building a Playground Task Appendix C Bag of Marbles Task Monitoring Chart References 5 Practices: Professional Development Guide

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Book SynopsisJourney through the world of abstract mathematics into category theory with popular science author Eugenia Cheng. Featuring humanizing examples and demystification of mathematical thought processes, this book is for fans of How to Bake Pi who want to dig deeper into mathematical concepts and build their mathematical background.Trade Review'This book is an educational tour de force that presents mathematical thinking as a right-brained activity. Most 'left brain/right brain' education-talk is at best a crude metaphor; but by putting the main focus on the process of (mathematical) abstraction, Eugenia Cheng supplies the reader (whatever their 'brain-type') with the mental tools to make that distinction precise and potentially useful. The book takes the reader along in small steps; but make no mistake, this is a major intellectual journey. Starting not with numbers, but everyday experiences, it develops what is regarded as a very advanced branch of abstract mathematics (category theory, though Cheng really uses this as a proxy for mathematical thinking generally). This is not watered-down math; it's the real thing. And it challenges the reader to think-deeply at times. We 'left-brainers' can learn plenty from it too.' Keith Devlin, Stanford University (Emeritus), author of The Joy of Sets'Eugenia Cheng loves mathematics—not the ordinary sort that most people encounter, but the most abstract sort that she calls 'the mathematics of mathematics.' And in this lovely excursion through her abstract world of Category Theory, she aims to give those who are willing to join her a glimpse of that world. The journey will change how they view mathematics. Cheng is a brilliant writer, with prose that feels like poetry. Her contagious enthusiasm makes her the perfect guide.' John Ewing, President, Math for America'Eugenia Cheng's singular contribution is in making abstract mathematics relevant to all through her great ingenuity in developing novel connections between logic and life. Her latest book, The Joy of Abstraction, provides a long awaited fully rigorous yet gentle introduction to the 'mathematics of mathematics,' allowing anyone to experience the joy of learning to think categorically.' Emily Riehl, Johns Hopkins University, author of Category Theory in Context'Archimedes is quoted as having said once: 'Mathematics reveals its secrets only to those who approach it with pure love, for its own beauty.' In this fascinating book, Eugenia Cheng approaches the abstract mathematical area of Category Theory with pure love, to reveal its beauty to anybody interested in learning something about contemporary mathematics.' Mario Livio, astrophysicist, author of The Golden Ratio and Brilliant Blunders'Eugenia Cheng's latest book will appeal to a remarkably broad and diverse audience, from non-mathematicians who would like to get a sense of what mathematics is really about, to experienced mathematicians who are not category theorists but would like a basic understanding of category theory. Speaking as one of the latter, I found it a real pleasure to be able to read the book without constantly having to stop and puzzle over the details. I have learnt a lot from it already, including what the famous Yoneda lemma is all about, and I look forward to learning more from it in the future.' Sir Timothy Gowers, Collège de France, Fields Medalist, main editor of The Princeton Companion to Mathematics'At last: a book that makes category theory as simple as it really is. Cheng explains the subject in a clear and friendly way, in detail, not relying on material that only mathematics majors learn. Category theory – indeed, mathematics as a whole – has been waiting for a book like this.' John Baez, University of California, Riverside'Many people speak derisively of category theory as the most abstract area of mathematics, but Eugenia Cheng succeeds in redeeming the word 'abstract'. This book is loquacious, conversational, and inviting. Reading this book convinced me I could teach category theory as an introductory course, and that is a real marvel, since it is a subject most people leave for experts.' Francis Su, Harvey Mudd College, author of Mathematics for Human Flourishing'Finally, a book about category theory that doesn't assume you already know category theory! In this inviting but rigorous introduction to what she calls 'the mathematics of mathematics', Eugenia Cheng brings the subject to us with insight, wit, and a point of view. Her story of finding joy-and advantage-in abstraction will inspire you to find it, too.' Patrick Honner, award-winning high school math teacher, columnist for Quanta Magazine, author of Painless Statistics'This higher category theory is the mathematics of the twenty-first century (at least my corner of it). If you'd like a taste of it, I recommend Dr. Cheng's book. The first half is an accessible and thought-provoking insight into categorical thinking. The second half climbs into the rarified air of theoretic math, but it is worth a read to get a feel for what some parts of modern mathematics look like.' Jonathan Kujawa, 3 Quarks Daily'… a successful addition to the literature that I am sure students will use in the future and I would be happy to recommend.' Constanze Roitzheim, Mathematische SemesterberichteTable of ContentsPrologue; Part I. Building Up to Categories: 1. Categories: the idea; 2. Abstraction; 3. Patterns; 4. Context; 5. Relationships; 6. Formalism; 7. Equivalence relations; 8. Categories: the definition; Interlude: A Tour of Math: 9. Examples we've already seen, secretly; 10. Ordered sets; 11. Small mathematical structures; 12. Sets and functions; 13. Large worlds of mathematical structures; Part II. Doing Category Theory: 14. Isomorphisms; 15. Monics and epics; 16. Universal properties; 17. Duality; 18. Products and coproducts; 19. Pullbacks and pushouts; 20. Functors; 21. Categories of categories; 22. Natural transformations; 23. Yoneda; 24. Higher dimensions; 25. Epilogue: thinking categorically; Appendices: A. Background on alphabets; B. Background on basic logic; C. Background on set theory; D. Background on topological spaces; Glossary; Further reading; Acknowledgements; Index.

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Book SynopsisFirst English translation of revolutionary paper (1931) that established that even in elementary parts of arithmetic, there are propositions which cannot be proved or disproved within the system. Introduction by R. B. Braithwaite.

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Book SynopsisUnderstanding the world of R programming and analysis has never been easier Most guides to R, whether books or online, focus on R functions and procedures.Table of ContentsIntroduction 1 About This Book 1 Similarity with This Other For Dummies Book 2 What You Can Safely Skip 2 Foolish Assumptions 2 How This Book Is Organized 3 Part 1: Getting Started with Statistical Analysis with R 3 Part 2: Describing Data 3 Part 3: Drawing Conclusions from Data 3 Part 4: Working with Probability 3 Part 5: The Part of Tens 4 Online Appendix A: More on Probability 4 Online Appendix B: Non-Parametric Statistics 4 Online Appendix C: Ten Topics That Just Didn’t Fit in Any Other Chapter 4 Icons Used in This Book 4 Where to Go from Here 5 Part 1: Getting Started with Statistical Analysis with R 7 Chapter 1: Data, Statistics, and Decisions 9 The Statistical (and Related) Notions You Just Have to Know 10 Samples and populations 10 Variables: Dependent and independent 11 Types of data 12 A little probability 13 Inferential Statistics: Testing Hypotheses 14 Null and alternative hypotheses 14 Two types of error 15 Chapter 2: R: What It Does and How It Does It 17 Downloading R and RStudio 18 A Session with R 21 The working directory 21 So let’s get started, already 22 Missing data 26 R Functions 26 User-Defined Functions 28 Comments 29 R Structures 29 Vectors 30 Numerical vectors 30 Matrices 31 Factors 33 Lists 34 Lists and statistics 35 Data frames 36 Packages 39 More Packages 42 R Formulas 43 Reading and Writing 44 Spreadsheets 44 CSV files 46 Text files 47 Part 2: Describing Data 49 Chapter 3: Getting Graphic 51 Finding Patterns 51 Graphing a distribution 52 Bar-hopping 53 Slicing the pie 54 The plot of scatter 55 Of boxes and whiskers 56 Base R Graphics 57 Histograms 57 Adding graph features 59 Bar plots 60 Pie graphs 62 Dot charts 62 Bar plots revisited 64 Scatter plots 67 Box plots 71 Graduating to ggplot2 71 Histograms 72 Bar plots 74 Dot charts 75 Bar plots re-revisited 78 Scatter plots 82 Box plots 86 Wrapping Up 89 Chapter 4: Finding Your Center 91 Means: The Lure of Averages 91 The Average in R: mean() 93 What’s your condition? 93 Eliminate $-signs forth with() 94 Exploring the data 95 Outliers: The flaw of averages 96 Other means to an end 97 Medians: Caught in the Middle 99 The Median in R: median() 100 Statistics à la Mode 101 The Mode in R 101 Chapter 5: Deviating from the Average 103 Measuring Variation 104 Averaging squared deviations: Variance and how to calculate it 104 Sample variance 107 Variance in R 107 Back to the Roots: Standard Deviation 108 Population standard deviation 108 Sample standard deviation 109 Standard Deviation in R 109 Conditions, Conditions, Conditions 110 Chapter 6: Meeting Standards and Standings 111 Catching Some Z’s 112 Characteristics of z-scores 112 Bonds versus the Bambino 113 Exam scores 114 Standard Scores in R 114 Where Do You Stand? 117 Ranking in R 117 Tied scores 117 Nth smallest, Nth largest 118 Percentiles 118 Percent ranks 120 Summarizing 121 Chapter 7: Summarizing It All 123 How Many? 123 The High and the Low 125 Living in the Moments 125 A teachable moment 126 Back to descriptives 126 Skewness 127 Kurtosis 130 Tuning in the Frequency 131 Nominal variables: table() et al 131 Numerical variables: hist() 132 Numerical variables: stem() 138 Summarizing a Data Frame 139 Chapter 8: What’s Normal? 143 Hitting the Curve 143 Digging deeper 144 Parameters of a normal distribution 145 Working with Normal Distributions 147 Distributions in R 147 Normal density function 147 Cumulative density function 152 Quantiles of normal distributions 155 Random sampling 156 A Distinguished Member of the Family 158 Part 3: Drawing Conclusions From Data 161 Chapter 9: The Confidence Game: Estimation 163 Understanding Sampling Distributions 164 An EXTREMELY Important Idea: The Central Limit Theorem 165 (Approximately) Simulating the central limit theorem 167 Predictions of the central limit theorem 171 Confidence: It Has Its Limits! 173 Finding confidence limits for a mean 173 Fit to a t 175 Chapter 10: One-Sample Hypothesis Testing 179 Hypotheses, Tests, and Errors 179 Hypothesis Tests and Sampling Distributions 181 Catching Some Z’s Again 183 Z Testing in R 185 t for One 187 t Testing in R 188 Working with t-Distributions 189 Visualizing t-Distributions 190 Plotting t in base R graphics 191 Plotting t in ggplot2 192 One more thing about ggplot2 197 Testing a Variance 198 Testing in R 199 Working with Chi-Square Distributions 201 Visualizing Chi-Square Distributions 201 Plotting chi-square in base R graphics 202 Plotting chi-square in ggplot2 203 Chapter 11: Two-Sample Hypothesis Testing 205 Hypotheses Built for Two 205 Sampling Distributions Revisited 206 Applying the central limit theorem 207 Z’s once more 208 Z-testing for two samples in R 210 t for Two 212 Like Peas in a Pod: Equal Variances 212 t-Testing in R 214 Working with two vectors 214 Working with a data frame and a formula 215 Visualizing the results 216 Like p’s and q’s: Unequal variances 219 A Matched Set: Hypothesis Testing for Paired Samples 220 Paired Sample t-testing in R 222 Testing Two Variances 222 F-testing in R 224 F in conjunction with t 225 Working with F-Distributions 226 Visualizing F-Distributions 226 Chapter 12: Testing More than Two Samples 231 Testing More Than Two 231 A thorny problem 232 A solution 233 Meaningful relationships 237 ANOVA in R 237 Visualizing the results 239 After the ANOVA 239 Contrasts in R 242 Unplanned comparisons 243 Another Kind of Hypothesis, Another Kind of Test 244 Working with repeated measures ANOVA 245 Repeated measures ANOVA in R 247 Visualizing the results 249 Getting Trendy 250 Trend Analysis in R 254 Chapter 13: More Complicated Testing 255 Cracking the Combinations 255 Interactions 257 The analysis 257 Two-Way ANOVA in R 259 Visualizing the two-way results 261 Two Kinds of Variables at Once 263 Mixed ANOVA in R 266 Visualizing the Mixed ANOVA results 268 After the Analysis 269 Multivariate Analysis of Variance 270 MANOVA in R 271 Visualizing the MANOVA results 273 After the analysis 275 Chapter 14: Regression: Linear, Multiple, and the General Linear Model 277 The Plot of Scatter 277 Graphing Lines 279 Regression: What a Line! 281 Using regression for forecasting 283 Variation around the regression line 283 Testing hypotheses about regression 285 Linear Regression in R 290 Features of the linear model 292 Making predictions 292 Visualizing the scatter plot and regression line 293 Plotting the residuals 294 Juggling Many Relationships at Once: Multiple Regression 295 Multiple regression in R 297 Making predictions 298 Visualizing the 3D scatter plot and regression plane 298 ANOVA: Another Look 301 Analysis of Covariance: The Final Component of the GLM 305 But wait — there’s more 311 Chapter 15: Correlation: The Rise and Fall of Relationships 313 Scatter plots Again 313 Understanding Correlation 314 Correlation and Regression 316 Testing Hypotheses About Correlation 319 Is a correlation coefficient greater than zero? 319 Do two correlation coefficients differ? 320 Correlation in R 322 Calculating a correlation coefficient 322 Testing a correlation coefficient 322 Testing the difference between two correlation coefficients 323 Calculating a correlation matrix 324 Visualizing correlation matrices 324 Multiple Correlation 326 Multiple correlation in R 327 Adjusting R-squared 328 Partial Correlation 329 Partial Correlation in R 330 Semipartial Correlation 331 Semipartial Correlation in R 332 Chapter 16: Curvilinear Regression: When Relationships Get Complicated 335 What Is a Logarithm? 336 What Is e? 338 Power Regression 341 Exponential Regression 346 Logarithmic Regression 350 Polynomial Regression: A Higher Power 354 Which Model Should You Use? 358 Part 4: Working with Probability 359 Chapter 17: Introducing Probability 361 What Is Probability? 361 Experiments, trials, events, and sample spaces 362 Sample spaces and probability 362 Compound Events 363 Union and intersection 363 Intersection again 364 Conditional Probability 365 Working with the probabilities 366 The foundation of hypothesis testing 366 Large Sample Spaces 366 Permutations 367 Combinations 368 R Functions for Counting Rules 369 Random Variables: Discrete and Continuous 371 Probability Distributions and Density Functions 371 The Binomial Distribution 374 The Binomial and Negative Binomial in R 375 Binomial distribution 375 Negative binomial distribution 377 Hypothesis Testing with the Binomial Distribution 378 More on Hypothesis Testing: R versus Tradition 380 Chapter 18: Introducing Modeling 383 Modeling a Distribution 383 Plunging into the Poisson distribution 384 Modeling with the Poisson distribution 385 Testing the model’s fit 388 A word about chisqtest() 391 Playing ball with a model 392 A Simulating Discussion 396 Taking a chance: The Monte Carlo method 396 Loading the dice 396 Simulating the central limit theorem 401 Part 5: The Part of Tens 405 Chapter 19: Ten Tips for Excel Emigrés 407 Defining a Vector in R Is Like Naming a Range in Excel 407 Operating on Vectors Is Like Operating on Named Ranges 408 Sometimes Statistical Functions Work the Same Way 412 And Sometimes They Don’t 412 Contrast: Excel and R Work with Different Data Formats 413 Distribution Functions Are (Somewhat) Similar 414 A Data Frame Is (Something) Like a Multicolumn Named Range 416 The sapply() Function Is Like Dragging 417 Using edit() Is (Almost) Like Editing a Spreadsheet 418 Use the Clipboard to Import a Table from Excel into R 419 Chapter 20: Ten Valuable Online R Resources 421 Websites for R Users 421 R-bloggers 421 Microsoft R Application Network 422 Quick-R 422 RStudio Online Learning 422 Stack Overflow 422 Online Books and Documentation 423 R manuals 423 R documentation 423 RDocumentation 423 YOU CANanalytics 423 The R Journal 424 Index 425

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Book SynopsisThis work develops techniques and basic results concerning the homotopy theory of enriched diagrams and enriched Mackey functors. Presentation of a category of interest as a diagram category has become a standard and powerful technique in a range of applications. Diagrams that carry enriched structures provide deeper and more robust applications. With an eye to such applications, this work provides further development of both the categorical algebra of enriched diagrams, and the homotopy theoretic applications in K-theory spectra. The title refers to certain enriched presheaves, known as Mackey functors, whose homotopy theory classifies that of equivariant spectra. More generally, certain stable model categories are classified as modules - in the form of enriched presheaves - over categories of generating objects. This text contains complete definitions, detailed proofs, and all the background material needed to understand the topic. It will be indispensable for graduate students and researchers alike.

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Book SynopsisA perennial bestseller by eminent mathematician G. Polya, How to Solve It will show anyone in any field how to think straight. In lucid and appealing prose, Polya reveals how the mathematical method of demonstrating a proof or finding an unknown can be of help in attacking any problem that can be "reasoned" out--from building a bridge to winning aTrade Review"Every prospective teacher should read it. In particular, graduate students will find it invaluable. The traditional mathematics professor who reads a paper before one of the Mathematical Societies might also learn something from the book: 'He writes a, he says b, he means c; but it should be d.' "--E. T. Bell, Mathematical Monthly "[This] elementary textbook on heuristic reasoning, shows anew how keen its author is on questions of method and the formulation of methodological principles. Exposition and illustrative material are of a disarmingly elementary character, but very carefully thought out and selected."--Herman Weyl, Mathematical Review "I recommend it highly to any person who is seriously interested in finding out methods of solving problems, and who does not object to being entertained while he does it."--Scientific Monthly "Any young person seeking a career in the sciences would do well to ponder this important contribution to the teacher's art."--A. C. Schaeffer, American Journal of Psychology "Every mathematics student should experience and live this book"--Mathematics Magazine "In an age that all solutions should be provided with the least possible effort, this book brings a very important message: mathematics and problem solving in general needs a lot of practice and experience obtained by challenging creative thinking, and certainly not by copying predefined recipes provided by others. Let's hope this classic will remain a source of inspiration for several generations to come."--A. Bultheel, European Mathematical Society

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Book Synopsis The 5th edition of Calculus: Early Transcendental Functions maintains the critical components for which this calculus text is well known: facilitating mastery of prerequisite algebra and trigonometry skills, offering an elegant presentation of calculus concepts that is rigorous yet accessible, and including classic calculus problems such as applications for STEM and business disciplines. Key features of the new edition: The new edition benefits from an accessible layout and presentation of graphs for topics like limits and continuity and area under the curve. A thorough revision has been carried out of all end-of-chapter problems and exercises and 120 new exercises have been added to the text and Connect. Introduction of âœmind mappingâ to help students understand the nature of calculus problems and develop problem-solving techniques that integrate multiple pieces of information. Improved approach to integration by starTable of ContentsCHAPTER 0: Preliminaries CHAPTER 1: Limits and ContinuityCHAPTER 2: Differentiation CHAPTER 3: Applications of Differentiation CHAPTER 4: Integration CHAPTER 5: Applications of the Definite Integral CHAPTER 6: Integration Techniques CHAPTER 7: First-Order Differential Equations CHAPTER 8: Infinite Series CHAPTER 9: Parametric Equations and Polar Coordinates CHAPTER 10: Vectors and the Geometry of Space CHAPTER 11: Vector-Valued Functions CHAPTER 12: Functions of Several Variables and Partial Differentiation CHAPTER 13: Multiple Integrals CHAPTER 14: Vector Calculus CHAPTER 15: Second-Order Differential Equations APPENDIX A: Proofs of Selected Theorems APPENDIX B: Answers to Odd-Numbered Exercises

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Book SynopsisAl-Khwarizmi was a mathematician, astronomer and geographer. He worked most of his life as a scholar in the House of Wisdom in Baghdad during the first half of the 9th century and is considered by many to be the father of algebra. This book deals with algebraic theory, and focuses on the calculation of inheritances and legacies.

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Book SynopsisEvidence-Based Technical Analysis 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.Trade Review"…his book is well written and contains a great deal of information that is of value…." (The Technical Analyst, May/June 2007)Table of ContentsAcknowledgments. About the Author. Introduction. PART I Methodological, Psychological, Philosophical, and Statistical Foundations. CHAPTER 1 Objective Rules and Their Evaluation. CHAPTER 2 The Illusory Validity of Subjective Technical Analysis. CHAPTER 3 The Scientific Method and Technical Analysis. CHAPTER 4 Statistical Analysis. CHAPTER 5 Hypothesis Tests and Confidence Intervals. CHAPTER 6 Data-Mining Bias: The Fool’s Gold of Objective TA. CHAPTER 7 Theories of Nonrandom Price Motion. PART II Case Study: Signal Rules for the S&P 500 Index. CHAPTER 8 Case Study of Rule Data Mining for the S&P 500. CHAPTER 9 Case Study Results and the Future of TA. APPENDIX Proof That Detrending Is Equivalent to Benchmarking Based on Position Bias. Notes. Index.

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Book SynopsisTrade Review"Praise for the previous edition: "Linear Systems Theory gives a good presentation of the main topics on linear systems as well as more advanced topics related to controller design. The scholarship is sound and the book is very well written and readable.""---Ian Petersen, University of New South Wales"Praise for the previous edition: "This book provides a sound basis for an excellent course on linear systems theory. It covers a breadth of material in a fast-paced and mathematically focused way. It can be used by students wishing to specialize in this subject, as well as by those interested in this topic generally.""---Geir E. Dullerud, University of Illinois, Urbana-Champaign

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a huge range and FREE tracked UK delivery on ALL orders.

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Book SynopsisTrade ReviewBestselling physicist Carlo Rovelli argues in this enjoyable and provocative little book that a little-known Greek philosopher invented the idea of the cosmos -- Tim Adams * Observer *Carlo Rovelli’s Anaximander is a knockout: there’s nobody like Rovelli for bridging the Two Cultures, and I was enlarged by his lucid, optimistic account, full of fascinating historical nuggets, of what scientists do and why it’s exciting -- Sam Leith * TLS , Best Books of the Year *Rovelli is a very good scientist and a very good writer. He explains some of the most conceptually difficult and densest areas of physics lightly and breezily. Here, he tells the story of an ancient thinker who had a revolutionary idea about the Earth's place in the cosmos -- Tom Whipple * The Times *Anaximander is a delight and so is this book -- James McConnachie * Sunday Times *As Rovelli's fans will expect, this book is excellent. It is never less than engaging, and enviably compendious -- Tim Smith-Laing * The Telegraph *A celebration of the scientific spirit of inquiry and the remarkable achievements of one man more than 2,500 years ago -- John Sellars * TLS *A bold and persuasive case that this ancient Greek philosopher scientist was the founder of critical thinking -- Adam Rutherford * Start the Week, BBC Radio 4 *This is seriously astounding. So lucid, so imaginative, so subtle, and so large in scope. It's like the best primer you can imagine for the non-scientist on why what you think you know about Ptolemy and Copernicus, or Popper and Kuhn, is not quite right -- Sam Leith * Twitter *

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Book SynopsisActive student engagement is key to this classroom-tested combinatorics text, boasting 1200+ carefully designed problems, ten mini-projects, section warm-up problems, and chapter opening problems. The author an award-winning teacher writes in a conversational style, keeping the reader in mind on every page. Students will stay motivated through glimpses into current research trends and open problems as well as the history and global origins of the subject. All essential topics are covered, including Ramsey theory, enumerative combinatorics including Stirling numbers, partitions of integers, the inclusion-exclusion principle, generating functions, introductory graph theory, and partially ordered sets. Some significant results are presented as sets of guided problems, leading readers to discover them on their own. More than 140 problems have complete solutions and over 250 have hints in the back, making this book ideal for self-study. Ideal for a one semester upper undergraduate course, prerequisites include the calculus sequence and familiarity with proofs.Trade Review'I would certainly accept this 'invitation.' The text covers essentially all of the basic combinatorial subjects in a both gentle and intense way. The extensive problems, examples, and 'projects,' especially the collaborative projects, exemplify current pedagogical research on effective teaching methods. I would expect it to remain as a reference on many shelves.' Bruce Rothschild, University of California, Los Angeles'Shahriari's voice as an experienced classroom teacher shines through in this brilliantly crafted student-friendly text. Each mini-project provides a guided exploration of an interesting topic in combinatorics. These, together with the plethora of interesting exercises, help the student to build problem-solving muscle and to experience the joy of mathematical discovery.' Jamie Pommersheim, Reed College'From well-chosen motivating problems in the introduction to deeper material near the book's conclusion, Shahriari invites students encountering combinatorics systematically for the first time to think, to build, and to play. His warm writing style and cross-cultural approach to core topics of the field are sure to engage readers from many backgrounds and levels of preparation.' Joshua Cooper, University of South Carolina'This book is a mathematically rigorous introductory textbook on combinatorics. It contains an excellent range of problems and exercises that will help students practice and learn the material. It also lists open questions in combinatorics so students can see that the field continues to develop. The really special feature of this book is a lovely collection of mini-projects that let students explore a variety of topics and deepen their understanding.' David Auckly, Kansas State University'I highly recommend this text. Among its most interesting, unusual, and valuable features, one finds a long list of collaborative mini-projects for students to work on in groups, together with other problems to work on individually; nice historical asides, including references to the work of non-Western mathematicians; and a very accessible conversational style. It fits well with discovery-style or problem-oriented courses on the subject.' William Monty McGovern, University of Washington'One of the major attractions of this textbook is the writing style - it is designed to be very readable, as though the author were having a conversation with the reader. The result is a text which feels engaging - a quality which is sure to be of great benefit to undergraduate students.' Audie Warren, zbMATHTable of ContentsPreface; Introduction; 1. Induction and Recurrence Relations; 2. The Pigeonhole Principle and Ramsey Theory; 3. Counting, Probability, Balls and Boxes; 4. Permutations and Combinations; 5. Binomial and Multinomial Coefficients; 6. Stirling Numbers; 7. Integer Partitions; 8. The Inclusion-Exclusion Principle; 9. Generating Functions; 10. Graph Theory; 11. Posets, Matchings, and Boolean Lattices; Appendices; Bibliography; Index.

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Book SynopsisTable of ContentsIntroduction 1 Part 1: Put Your BI Thinking Caps On 7 Chapter 1: A Crash Course in Data Analytics Terms: Power BI Style 9 Chapter 2: The Who, How, and What of Power BI 23 Chapter 3: Oh, the Choices: Power BI Versions 33 Chapter 4: Power BI: The Highlights 47 Part 2: It’s Time to Have a Data Party 65 Chapter 5: Preparing Data Sources 67 Chapter 6: Getting Data from Dynamic Sources 85 Chapter 7: Cleansing, Transforming, and Loading Your Data 103 Part 3: The Art and Science of Power BI 127 Chapter 8: Crafting the Data Model 129 Chapter 9: Designing and Deploying Data Models 145 Chapter 10: Perfecting the Data Model 167 Chapter 11: Visualizing Data 183 Chapter 12: Pumping Out Reports 213 Chapter 13: Diving into Dashboarding 233 Part 4: Oh, No! There’s a Power BI Programming Language! 247 Chapter 14: Digging Into DAX 249 Chapter 15: Fun with DAX Functions 265 Chapter 16: Digging Deeper into DAX 289 Chapter 17: Sharing and the Power BI Workspace 305 Part 5: Enhancing Your Power BI Experience 325 Chapter 18: Making Your Data Shine 327 Chapter 19: Extending the Power BI Experience 343 Part 6: The Part of Tens 367 Chapter 20: Ten Ways to Optimize DAX Using Power BI 369 Chapter 21: Ten Ways to Make Compelling Reports Accessible and User-Friendly 379 Index 389

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Book SynopsisThis remarkable text by John R. Taylor has been a non-stop best-selling international hit since it was first published forty years ago. However, the two-plus decades since the second edition was released have seen two dramatic developments; the huge rise in popularity of Bayesian statistics, and the continued increase in the power and availability of computers and calculators. In response to the former, Taylor has added a full chapter dedicated to Bayesian thinking, introducing conditional probabilities and Bayes’ theorem. The several examples presented in the new third edition are intentionally very simple, designed to give readers a clear understanding of what Bayesian statistics is all about as their first step on a journey to become practicing Bayesians. In response to the second development, Taylor has added a number of chapter-ending problems that will encourage readers to learn how to solve problems using computers. While many of these can be solved using programs such as Matlab or Mathematica, almost all of them are stated to apply to commonly available spreadsheet programs like Microsoft Excel. These programs provide a convenient way to record and process data and to calculate quantities like standard deviations, correlation coefficients, and normal distributions; they also have the wonderful ability – if students construct their own spreadsheets and avoid the temptation to use built-in functions – to teach the meaning of these concepts.Trade ReviewThe new chapter on Bayesian statistics is extremely clear and well written, and is another one of John Taylor’s fabulous expositions. I enjoyed how Taylor develops the subject by using it to answer questions about the effectiveness of a vaccine. Before reading this chapter I wondered what assumptions are needed to derive a numerical value for a vaccine’s effectiveness, and I also wondered about the data needed and the methods used. Lo and behold, all my questions were answered in this chapter! I definitely will buy the new edition of Error Analysis and I look forward to delving into the Bayesian statistics. -- Mark Semon, Bates CollegeTable of ContentsPART I 1. Preliminary Description of Error Analysis 2. How to Report and Use Uncertainties 3. Propagation of Uncertainties 4. Statistical Analysis of Random Uncertainties 5. The Normal Distribution PART II 6. Rejection of Data 7. Weighted Averages 8. Least-Squares Fitting 9. Covariance and Correlation 10. The Binomial Distribution 11. The Poisson Distribution 12. The Chi-Squared Test for a Distribution 13. Bayesian Statistics APPENDICES A. Normal Error Integral, I B. Normal Error Integral, II C. Probabilities for Correlation Coefficients D. Probabilities for Chi Squared E. Two Proofs Concerning Sample Standard Deviations Answers to Quick Checks and Odd-Numbered Problems Index

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Book SynopsisExam board: Cambridge Assessment International EducationLevel: A-levelSubject: MathematicsFirst teaching: September 2018First exams: Summer 2020Endorsed by Cambridge Assessment International Education to provide full support for Paper 2 and 3 of the syllabus for examination from 2020.Take mathematical understanding to the next level with this accessible series, written by experienced authors, examiners and teachers.- Improve confidence as a mathematician with clear explanations, worked examples, diverse activities and engaging discussion points. - Advance problem-solving, interpretation and communication skills through a wealth of questions that promote higher-order thinking. - Prepare for further study or life beyond the classroom by applying mathematics to other subjects and modelling real-world situations.- Reinforce learning with opportunities for digital practice via links to the Mathematics in Education and Industry's (MEI) Integral platform in the eBooks.**To have full access to the eBooks and Integral resources you must be subscribed to both Boost and Integral. To trial our eBooks and/or subscribe to Boost, visit: www.hoddereducation.com/Boost; to view samples of the Integral resources and/or subscribe to Integral, visit integralmaths.org/internationalPlease note that the Integral resources have not been through the Cambridge International endorsement process. This book covers the syllabus content for Pure Mathematics 2 and Pure Mathematics 3, including algebra, logarithmic and exponential functions, trigonometry, differentiation, integration, numerical solution of equations, vectors, differential equations and complex numbers.

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Book SynopsisTeacher Materials include: Presentation Books include a Guide section containing information for presenting exercises, correcting mistakes, and administering the pre-skill and placement tests. There is also a Presentation section that contains detailed lessons plans. Answer Key Booklets quickly and easily compare students' work with the actual calculations and word problem results.

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Book SynopsisNearly a century before Mondrian made geometrical red, yellow, and blue lines famous, 19th-century mathematician Oliver Byrne employed the color scheme for his 1847 edition of Euclid’s mathematical and geometric treatise Elements. Byrne’s idea was to use color to make learning easier and “diffuse permanent knowledge.” The result has been described as one of the oddest and most beautiful books of the 19th century. The facsimile of Byrne’s seminal publication is now available in a beautiful new edition. A masterwork of art and science, it is as remarkable in the boldness of its red, yellow, and blue figures and diagrams as it is in the mathematical precision of its theories. In the simplicity of forms and colors, the pages anticipate the vigor of De Stijl and Bauhaus design. In making complex information at once accessible and aesthetically engaging, this work is a forerunner to the information graphics that today define much of our data consumption.Trade Review“Every graphic designer, book lover and math nerd will be awestruck.” * The New York Times *

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Book SynopsisThe idea of this book is to help build confidence with maths via a series of tests and puzzles. After a gentle ''warm-up'' section, the puzzles and tests get progressively more challenging over the course of the book. There is a hints section for readers who get stuck, as well as a complete set of answers for every test at the back of the book. After the ''warm-up'' section, there are puzzles and tests on ''lateral thinking'', ''fun with numbers'', ''logic puzzles'', ''geometrical puzzles'' and ''difficult puzzles''. Readers will soon become familiar and comfortable with a range of tricks and tests, from magic number squares to Fibonacci numbers.Table of ContentsIntroduction. Section 1: Puzzles, tricks and tests. Chapter 1: The work out. Chapter 2: Think laterally. Chapter 3: Test your numerical IQ. Chapter 4: Funumeration. Chapter 5: Think logically. Chapter 6: The logic of gambling and probability. Chapter 7: Geometrical puzzles. Chapter 8: Complexities and curiosities. Section 2: Hints, answers and explanations. Hints. Answers and explanations. Section 3: Glossary and data. Glossary. Data. Section 4: Appendices. Appendix 1: Fibonacci and nature's use of space. Appendix 2: Pi. Appendix 3: Topology and the Mobius strip.

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Book SynopsisClear undergraduate-level introduction to background math, differential calculus, differentiation, integral calculus, integration, functions of several variables, more. Numerous problems, with new "Hints and Answers" section.

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Book SynopsisNetworks of relationships help determine the careers that people choose, the jobs they obtain, the products they buy, and how they vote. This book offers a comprehensive introduction to social and economic networks, drawing on the findings in economics, sociology, computer science, physics, and mathematics.Trade ReviewHonorable Mention for the 2008 PROSE Award in Economics, Association of American Publishers "Jackson's review of diffusion models is excellent, as tight an overview of these models as I have seen anywhere... Social and Economic Networks is a must-read for all those steeped in the traditional social network analysis paradigm. Economists will find Jackson offers them a superb and accessible introduction to network questions and models. And for others from any social science background curious about social networks, I recommend a careful read of the book."--David Krackhardt, Science "This book deserves the highest recommendations for all readers interested in networks and interdependence. It is written clearly, and could be used both as a starting textbook for a journey to the world of networks and also as an expert guide for scientists studying social and economic networks."--Karoly Takacs, Journal of Artificial Societies and Social Simulation "I strongly recommend this book to any scholar or student interested in networks, not only in economics but in any connected field such as sociology, physics, and applied mathematics. Matthew Jackson's guided tour of the literature on economic and social networks is superb."--Joan de Marti Beltran, Regional Science and Urban Economics "[T]his is a valuable book that raises crucial questions for today's sociologist interested in social networks."--Paola Tubaro, SociologyTable of ContentsPreface xi PART I: BACKGROUND AND FUNDAMENTALS OF NETWORK ANALYSIS Chapter 1 Introduction 3 1.1 Why Model Networks? 3 1.2 A Set of Examples 4 1.3 Exercises 17 Chapter 2: Representing and Measuring Networks 20 2.1 Representing Networks 20 2.2 Some Summary Statistics and Characteristics of Networks 30 2.3 Appendix: Basic Graph Theory 43 2.4 Appendix: Eigenvectors and Eigenvalues 49 2.5 Exercises 51 Chapter 3: Empirical Background on Social and Economic Networks 54 3.1 The Prevalence of Social Networks 55 3.2 Observations on the Structure of Networks 56 PART II: MODELS OF NETWORK FORMATION Chapter 4: Random-Graph Models of Networks 77 4.1 Static Random-Graph Models of Random Networks 78 4.2 Properties of Random Networks 86 4.3 An Application: Contagion and Diffusion 105 4.4 Distribution of Component Sizes 107 4.5 Appendix: Useful Facts, Tools, and Theorems 110 4.6 Exercises 121 Chapter 5: Growing Random Networks 124 5.1 Uniform Randomness: An Exponential Degree Distribution 125 5.2 Preferential Attachment 130 5.3 Hybrid Models 134 5.4 Small Worlds, Clustering, and Assortativity 141 5.5 Exercises 150 Chapter 6: Strategic Network Formation 153 6.1 Pairwise Stability 154 6.2 Efficient Networks 157 6.3 Distance-Based Utility 159 6.4 A Coauthor Model and Negative Externalities 166 6.5 Small Worlds in an Islands-Connections Model 170 6.6 A General Tension between Stability and Efficiency 173 6.7 Exercises 179 PART III: IMPLICATIONS OF NETWORK STRUCTURE Chapter 7: Diffusion through Networks 185 7.1 Background: The Bass Model 187 7.2 Spread of Information and Disease 189 7.3 Search and Navigation on Networks 209 7.4 Exercises 221 Chapter 8: Learning and Networks 223 8.1 Early Theory and Opinion Leaders 224 8.2 Bayesian and Observational Learning 225 8.3 Imitation and Social Influence Models: The DeGroot Model 228 8.4 Exercises 253 Chapter 9: Decisions, Behavior, and Games on Networks 257 9.1 Decisions and Social Interaction 258 9.2 Graphical Games 269 9.3 Semi-Anonymous Graphical Games 273 9.4 Randomly Chosen Neighbors and Network Games 279 9.5 Richer Action Spaces 286 9.6 Dynamic Behavior and Contagion 293 9.7 Multiple Equilibria and Diffusion in Network Games 297 9.8 Computing Equilibria 304 9.9 Appendix: A Primer on Noncooperative Game Theory 308 9.10 Exercises 319 Chapter 10: Networked Markets 327 10.1 Social Embeddedness of Markets and Exchange 328 10.2 Networks in Labor Markets 334 10.3 Models of Networked Markets 353 10.4 Concluding Remarks 365 10.5 Exercises 366 PART IV: METHODS, TOOLS, AND EMPIRICAL ANALYSES Chapter 11: Game-Theoretic Modeling of Network Formation 371 11.1 Defining Stability and Equilibrium 372 11.2 The Existence of Stable Networks 377 11.3 Directed Networks 383 11.4 Stochastic Strategic Models of Network Formation 388 11.5 Farsighted Network Formation 395 11.6 Transfers and Network Formation 399 11.7 Weighted Network Formation 402 11.8 Agent-Based Modeling 406 11.9 Exercises 407 Chapter 12: Allocation Rules, Networks, and Cooperative Games 411 12.1 Cooperative Game Theory 412 12.2 Communication Games 416 12.3 Networks and Allocation Rules 419 12.4 Allocation Rules When Networks Are Formed 425 12.5 Concluding Remarks 430 12.6 Exercises 430 Chapter 13: Observing and Measuring Social Interaction 434 13.1 Specification and Identification 435 13.2 Community Structures, Block Models, and Latent Spaces 443 13.3 Exercises 457 Afterword 459 Bibliography 461 Index 491

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