This book presents some of the most important modeling and prediction techniques, along with relevant applications. Topics include linear regression, classification, resampling methods, shrinkage approaches, tree- based methods, support vector machines, clustering, and more. Color graphics and real-world examples are used to illustrate the methods presented. Since the goal of this textbook is to facilitate the use of these statistical learning techniques by practitioners in science, industry, and other fields, each chapter contains a tutorial on implementing the analyses and methods presented in R, an extremely popular open source statistical software platform. Two of the authors co-wrote The Elements of Statistical Learning (Hastie, Tibshirani and Friedman, 2nd edition 2009), a popular reference book for statistics and machine learning researchers. An Introduction to Statistical Learning covers many of the same topics, but at a level accessible to a much broader audience. This book is targeted at statisticians and non-statisticians alike who wish to use cutting-edge statistical learning techniques to analyze their data. The text assumes only a previous course in linear regression and no knowledge of matrix algebra.

    Non- mathematical readers will appreciate the intuitive explanations of the techniques while an emphasis on problem-solving with real data across a wide variety of applications will aid practitioners who wish to extend their expertise. Readers should have knowledge of basic statistical ideas, such as correlation and linear regression analysis. While the text is biased against complex equations, a mathematical background is needed for advanced topics. Dr. Kuhn is a Director of Non-Clinical Statistics at Pfizer Global R&D in Groton Connecticut. He has been applying predictive models in the pharmaceutical and diagnostic industries for over 15 years and is the author of a number of R packages. Dr. Johnson has more than a decade of statistical consulting and predictive modeling experience in pharmaceutical research and development. He is a co-founder of Arbor Analytics, a firm specializing in predictive modeling and is a former Director of Statistics at Pfizer Global R&D. His scholarly work centers on the application and development of statistical methodology and learning algorithms. Applied Predictive Modeling covers the overall predictive modeling process, beginning with the crucial steps of data preprocessing, data splitting and foundations of model tuning. The text then provides intuitive explanations of numerous common and modern regression and classification techniques, always with an emphasis on illustrating and solving real data problems. Addressing practical concerns extends beyond model fitting to topics such as handling class imbalance, selecting predictors, and pinpointing causes of poor model performance-all of which are problems that occur frequently in practice. The text illustrates all parts of the modeling process through many hands-on, real-life examples. And every chapter contains extensive R code f

    Politicians and marketers present shoddy evidence for dubious claims all the time. But smart people make mistakes too, and when it comes to statistics, plenty of otherwise great scientists--yes, even those published in peer-reviewed journals--are doing statistics wrong."Statistics Done Wrong" comes to the rescue with cautionary tales of all-too-common statistical fallacies. It'll help you see where and why researchers often go wrong and teach you the best practices for avoiding their mistakes.In this book, you'll learn: - Why "statistically significant" doesn't necessarily imply practical significance- Ideas behind hypothesis testing and regression analysis, and common misinterpretations of those ideas- How and how not to ask questions, design experiments, and work with data- Why many studies have too little data to detect what they're looking for-and, surprisingly, why this means published results are often overestimates- Why false positives are much more common than "significant at the 5% level" would suggestBy walking through colorful examples of statistics gone awry, the book offers approachable lessons on proper methodology, and each chapter ends with pro tips for practicing scientists and statisticians. No matter what your level of experience, "Statistics Done Wrong" will teach you how to be a better analyst, data scientist, or researcher.

    Mathematical concepts and computational problems are motivated by applications in computer science. The reader learns by "doing," writing programs to implement the mathematical concepts and using them to carry out tasks and explore the applications. Examples include: error-correcting codes, transformations in graphics, face detection, encryption and secret-sharing, integer factoring, removing perspective from an image, PageRank (Google's ranking algorithm), and cancer detection from cell features. A companion web site, codingthematrix.com provides data and support code. Most of the assignments can be auto-graded online. Over two hundred illustrations, including a selection of relevant "xkcd" comics. Chapters: "The Function," "The Field," "The Vector," "The Vector Space," "The Matrix," "The Basis," "Dimension," "Gaussian Elimination," "The Inner Product," "Special Bases," "The Singular Value Decomposition," "The Eigenvector," "The Linear Program"

    It is based on a recently discovered connection between homotopy theory and type theory. It touches on topics as seemingly distant as the homotopy groups of spheres, the algorithms for type checking, and the definition of weak ∞-groupoids. Homotopy type theory offers a new “univalent” foundation of mathematics, in which a central role is played by Voevodsky’s univalence axiom and higher inductive types. The present book is intended as a first systematic exposition of the basics of univalent foundations, and a collection of examples of this new style of reasoning — but without requiring the reader to know or learn any formal logic, or to use any computer proof assistant. We believe that univalent foundations will eventually become a viable alternative to set theory as the “implicit foundation” for the unformalized mathematics done by most mathematicians.http://homotopytypetheory.org/book/

    Specially designed for in-service teachers, each volume of the series focuses on the content relevant to a specific grade band and provides additional information on creating an effective classroom environment, engaging families, and aligning teaching to the Common Core State Standards. Additional activities and expanded lessons are also included. The series has three objectives: 1. To illustrate what it means to teach student-centered, problem-based mathematics 2. To serve as a reference for the mathematics content and research-based instructional strategies suggested for pre-kindergarten to grade two, grades three to five, and grades six to eight 3. To present a large collection of high quality tasks and activities that can engage students in the mathematics that is important for them to learn Volume II is tailored specifically to grades 3-5, allowing teachers to quickly and easily locate information to implement in their classes. The student-centered approach will result in students who are successful in learning mathematics, making these books indispensable for 3-5 classroom teachers!

    It is a core topic of study within fields as diverse as: business, economics, engineering, physics, computer science, ecology, sociology, demography and genetics. For an example of linear algebra at work, one needs to look no further than the Google search engine, which relies upon linear algebra to rank the results of a search with respect to relevance. The strength of the text is in the large number of examples and the step-by-step explanation of each topic as it is introduced. It is compiled in a way that allows distance learning, with explicit solutions to set problems freely available online. The miscellaneous exercises at the end of each chapter comprise questions from past exam papers from various universities, helping to reinforce the reader's confidence. Also included, generally at the beginning of sections, are short historicalbiographies of the leading players in the field of linear algebra to provide context for the topics covered. The dynamic and engaging style of the book includes frequent question and answer sections to test the reader's understanding of the methods introduced, rather than requiring rote learning. When first encountered, the subject can appear abstract and students will sometimes struggle to see its relevance; to counter this, the book also contains interviews with key people who use linear algebra in practice, in both professional and academic life. It will appeal to undergraduate students inmathematics, the physical sciences and engineering.

    and around the world. Just like the camp offers both introductory and advanced courses, this book also builds up the material gradually.We begin with a theoretical chapter where we familiarize the reader with basic facts and problem-solving techniques. Then we proceed to the main part of the work, the problem sections.The problems are a carefully selected and balanced mix which offers a vast variety of flavors and difficulties, ranging from AMC and AIME levels to high-end IMO problems. Out of thousands of Olympiad problems from around the globe we chose those which best illustrate the featured techniques and their applications. The problems meet our demanding taste and fully exhibit the enchanting beauty of classical geometry. For every problem we provide a detailed solution and strive to pass on the intuition and motivation lying behind. Many problems have multiple solutions.Directly experiencing Olympiad geometry both as contestants and instructors, we are convinced that a neat diagram is essential to efficiently solving a geometry problem. Our diagrams do not contain anything superfluous, yet emphasize the key elements and benefit from a good choice of orientation. Many of the proofs should be legible only from looking at the diagrams.

    Mathematically oriented, the book presents every theorem alongside a proof. The material is presented clearly and every concept is illustrated with concrete examples from a broad range of disciplines. With numerous exercises the book is a thorough and extensive guide to game theory from undergraduate through graduate courses in economics, mathematics, computer science, engineering and life sciences to being an authoritative reference for researchers.

    Once the framework is mastered, the student is introduced to new material which includes differential geometry on manifolds, shape optimization, boundary perturbation and dynamic fluid film equations.The language of tensors, originally championed by Einstein, is as fundamental as the languages of calculus and linear algebra and is one that every technical scientist ought to speak. The tensor technique, invented at the turn of the 20th century, is now considered classical. Yet, as the author shows, it remains remarkably vital and relevant. The author's skilled lecturing capabilities are evident by the inclusion of insightful examples and a plethora of exercises. A great deal of material is devoted to the geometric fundamentals, the mechanics of change of variables, the proper use of the tensor notation and the discussion of the interplay between algebra and geometry. The early chapters have many words and few equations. The definition of a tensor comes only in Chapter 6 - when the reader is ready for it. While this text maintains a consistent level of rigor, it takes great care to avoid formalizing the subject.The last part of the textbook is devoted to the Calculus of Moving Surfaces. It is the first textbook exposition of this important technique and is one of the gems of this text. A number of exciting applications of the calculus are presented including shape optimization, boundary perturbation of boundary value problems and dynamic fluid film equations developed by the author in recent years. Furthermore, the moving surfaces framework is used to offer new derivations of classical results such as the geodesic equation and the celebrated Gauss-Bonnet theorem.

    While working with students who were preparing for various mathematics competitions or exams, the author observed that fundamental algebraic techniques were not part of their mathematical repertoire. Since algebraic skills are not only critical to Algebra itself but also to numerous other mathematical fields, a lack of such knowledge can drastically hinder a student's performance. Taking the above observations into account, the author has put together this introductory book using both simple and challenging examples which shed light upon essential algebraic strategies and techniques, as well as their application in diverse meaningful problems. This work is the first volume in a series of such books.The featured topics from elementary and classical Algebra, include factorizations, algebraic identities, inequalities, algebraic equations and systems of equations. More advanced concepts such as complex numbers, exponents and logarithms, as well as other topics are generally avoided. Nevertheless, some problems are constructed using properties of complex numbers which challenge and expose the reader to a broader spectrum of mathematics. Each chapter focuses on specific methods or strategies and provides an ample collection of accompanying problems that graduate in difficulty and complexity. In order to assist the reader with verifying mastery of the theoretical component, 105 problems are included in the last sections of the book, of which 52 are introductory and 53 are advanced.All problems come together with solutions, many employing several approaches and providing the motivation behind the solutions offered.

    Roughly speaking, if a function of many independent random variables does not depend too much on any of the variables then it is concentrated in the sense that with high probability, it is close to its expected value. This book offers a host of inequalities to illustratethis rich theory in an accessible way by covering the key developments and applications in the field. The authors describe the interplay between the probabilistic structure (independence) and a variety of tools ranging from functional inequalities to transportation arguments to information theory. Applications to the study of empirical processes, random projections, random matrix theory, andthreshold phenomena are also presented.A self-contained introduction to concentration inequalities, it includes a survey of concentration of sums of independent random variables, variance bounds, the entropy method, and the transportation method. Deep connections with isoperimetric problems are revealed whilst special attention is paidto applications to the supremum of empirical processes.Written by leading experts in the field and containing extensive exercise sections this book will be an invaluable resource for researchers and graduate students in mathematics, theoretical computer science, and engineering.

    Each definition is accompanied by commentary that motivates and explains new concepts. Starting with a repetition of the familiar arguments of elementary set theory, the level of abstract thinking gradually rises for a progressive increase in complexity.A historical introduction presents a brief account of the growth of set theory, with special emphasis on problems that led to the development of the various systems of axiomatic set theory. Subsequent chapters explore classes and sets, functions, relations, partially ordered classes, and the axiom of choice. Other subjects include natural and cardinal numbers, finite and infinite sets, the arithmetic of ordinal numbers, transfinite recursion, and selected topics in the theory of ordinals and cardinals. This updated edition features new material by author Charles C. Pinter.

    The exposition serves a narrow set of goals, and necessarily takes a particular point of view on the subject.

    They do not respect the personal rights of their victims. They violate the victim's integrity, work with hidden agendas and deliberately use dishonest tricks like faulty reasoning, coercion, blackmail and lying in an attempt to control the victim's actions. Manipulation is about suiting the manipulator's advantage or purpose only, often at the expense of the victim.Yet, it is often difficult to know when you are being manipulated: manipulators do all they can to convince you that you are the one who is to benefit most from their actions and that they are acting in good faith.If we were aware that we are being manipulated, would we allow ourselves to fall victim to it - and how would we defend ourselves against it? That is where this book comes in handy: it explains the tricks manipulators use and teaches you how to best defend and protect yourself.

    Computer scientists, specifically, approach this field based on their practical experiences in managing large amounts of data, and with far fewer assumptions- the data can be of any type, structured or unstructured, and may be extremely large. Outlier Analysis is a comprehensive exposition, as understood by data mining experts, statisticians and computer scientists. The book has been organized carefully, and emphasis was placed on simplifying the content, so that students and practitioners can also benefit. Chapters will typically cover one of three areas: methods and techniques commonly used in outlier analysis, such as linear methods, proximity-based methods, subspace methods, and supervised methods; data domains, such as, text, categorical, mixed-attribute, time-series, streaming, discrete sequence, spatial and network data; and key applications of these methods as applied to diverse domains such as credit card fraud detection, intrusion detection, medical diagnosis, earth science, web log analytics, and social network analysis are covered.

    Beast Academy 4A Guide.

    Containing hundreds of exercises, examples and applications, these books will become an invaluable resource for both students and teachers. Volume I focuses on the analysis of real-valued functions of a real variable. Volume II goes on to consider metric and topological spaces. This third volume covers complex analysis and the theory of measure and integration.

    The text covers the basics of multilinear algebra, differentiation and integration on manifolds, Lie groups and Lie algebras, homotopy and de Rham cohomology, homology, vector bundles, Riemannian and pseudo-Riemannian geometry, and degree theory. It also features over 250 detailed exercises, and a variety of applications revealing fundamental connections to classical mechanics, electromagnetism (including circuit theory), general relativity and gauge theory. Solutions to the problems are available for instructors at www.cambridge.org/9781107042193.

    No graduate student of quantum theory should leave it unread"--W.C Schieve, University of Texas

    You begin with some basic arithmetic practice, move on to fractions, decimals, and percents, tackle story problems, and finish up with basic algebra. Every practice question includes not only a solution but a step-by-step explanation. From the book, go online and find:One year free subscription to all 1001 practice problems On-the-go access any way you want it--from your computer, smart phone, or tablet Multiple choice questions on all you math course topics Personalized reports that track your progress and help show you where you need to study the most Customized practice sets for self-directed study Practice problems categorized as easy, medium, or hard The practice problems in 1001 Basic Math & Pre-Algebra Practice Problems For Dummies give you a chance to practice and reinforce the skills you learn in class and help you refine your understanding of basic math & pre-algebra. Note to readers: 1,001 Basic Math & Pre-Algebra Practice Problems For Dummies, which only includes problems to solve, is a great companion to Basic Math & Pre-Algebra I For Dummies, which offers complete instruction on all topics in a typical Basic Math & Pre-Algebra course.

    The author calls it a math enrichment textbook. The idea is to make it easy for teachers or parents to supplement what kids are getting in school with with complementary lessons that are harder, deeper, and more fun.Hard Math has chapters to accompany most textbook topics: addition with carrying, multiplication, fractions, etc. It covers other important topics - prime numbers, counting, probability - that are being squeezed out of many curricula. And it has chapters on topics which may not be as important - tiling floors, solving number puzzles, making polyhedra out of marshmallows and toothpicks - but that make the book more fun and develop higher-level reasoning skills.Hard Math can be used in many different ways. Some parents will enjoy reading it together with their child. A teacher can give the book to an exceptional student who could read through it on her own whenever she's done early with the regular math lesson. Or a teacher could treat the book as a set of lesson plans for his or her top math group: each section of the book can serve as a set of lecture notes and the students could then work separately or together on the corresponding workbook page. Hard Math can similarly be a blueprint for an after school math club.Hard Math is designed to be accessible to very advanced 3rd graders. But Hard Math is very hard. Most parents will find that there's a lot in it that they don't know and most advanced kids will be better off waiting until at least 4th grade to try it.A workbook (sold separately) contains over 100 challenging worksheets to reinforce the lessons of each section. PLEASE don't buy a copy of the book without also getting a copy of the workbook. It's really hard for anyone (let alone a 3rd grader) to learn hard concepts and figure out whether they really understand them without working through applying them. For many kids the back-and-forth between the text and the workbook is the central experience of Hard Math.An answer key for the workbook is also available. You can buy it cheaply on Amazon or view it for free on Prof. Ellison's MIT website.

    

    He is a committed and recognized popularizer of mathematics. Of Elwes, Sonder Books 2011 Standouts said, "Dr. Elwes is brilliant at giving the reader the broad perspective, with enough details to fascinate, rather than confuse." Math in 100 Key Breakthroughs offers a series of short, clear-eyed essays explaining the fundamentals of the mathematical concepts everyone should know. Professor Richard Elwes profiles the most important, groundbreaking, and astonishing discoveries, which together have profoundly influenced our understanding of the universe. From the origins of counting--traced back to more than 35,000 years ago--to such contemporary breakthroughs as Wiles' Proof of Fermat's Last Theorem and Cook & Woolfram's Rule 110, this compulsively readable book tells the story of discovery, invention, and inspiration that have led to humankind's most important mathematical achievements.

    Written by a leading expert, this book will help you if you are studying for an important exam or essay, or if you simply want to improve your knowledge. The book covers all areas of calculus, including functions, gradients, rates of change, differentiation, exponential and logarithmic functions and integration. Everything you will need to know is here in one book. Each chapter includes not only an explanation of the knowledge and skills you need, but also worked examples and test questions.

    The absence of a book, explaining the techniques in a simple language, has been felt acutely for a long time. This book has been written using a step-by-step approach, and attempts to fill the existing void. It includes several solved problems in addition to 1000 practice problems with answers. It also includes a special chapter which shows the application of the techniques to problems set in competitive exams like CAT, CET etc.People from all walks of life including school and college students, teachers, parents and also those from non-mathematical areas of study will discover the joys of solving mathematical problems using the wonderful set of techniques called Vedic Maths.

    This book investigates what cannot be known. Rather than exploring the amazing facts that science, mathematics, and reason have revealed to us, this work studies what science, mathematics, and reason tell us cannot be revealed. In The Outer Limits of Reason, Noson Yanofsky considers what cannot be predicted, described, or known, and what will never be understood. He discusses the limitations of computers, physics, logic, and our own thought processes.Yanofsky describes simple tasks that would take computers trillions of centuries to complete and other problems that computers can never solve; perfectly formed English sentences that make no sense; different levels of infinity; the bizarre world of the quantum; the relevance of relativity theory; the causes of chaos theory; math problems that cannot be solved by normal means; and statements that are true but cannot be proven. He explains the limitations of our intuitions about the world -- our ideas about space, time, and motion, and the complex relationship between the knower and the known.Moving from the concrete to the abstract, from problems of everyday language to straightforward philosophical questions to the formalities of physics and mathematics, Yanofsky demonstrates a myriad of unsolvable problems and paradoxes. Exploring the various limitations of our knowledge, he shows that many of these limitations have a similar pattern and that by investigating these patterns, we can better understand the structure and limitations of reason itself. Yanofsky even attempts to look beyond the borders of reason to see what, if anything, is out there.

    Rudolf Steiner underlined the importance of projective geometry as, "a method of training the imaginative faculties of thinking, so that they become an instrument of cognition no less conscious and exact than mathematical reasoning." This seminal approach allows for precise scientific understanding of the concept of creative fields of formative (etheric) forces at work in nature--in plants, animals and in the human being.Olive Whicher's groundbreaking book presents an accessible--non-mathematician's--approach to projective geometry. Profusely illustrated, and written with fire and intuitive genius, this work will be of interest to anyone wishing to cultivate the power of inner visualization in a realm of structural beauty.

    The author illustrates the mathematics with numerous physical examples drawn from contemporary research. In addition to basic subjects such as linear algebra, Fourier analysis, complex variables, differential equations and Bessel functions, this textbook covers topics such as the singular-value decomposition, Lie algebras, the tensors and forms of general relativity, the central limit theorem and Kolmogorov test of statistics, the Monte Carlo methods of experimental and theoretical physics, the renormalization group of condensed-matter physics and the functional derivatives and Feynman path integrals of quantum field theory.

    Interest in these methods has exploded in recent years, with numerous applications emerging in fields such as navigation, aerospace engineering, telecommunications and medicine. This compact, informal introduction for graduate students and advanced undergraduates presents the current state-of-the-art filtering and smoothing methods in a unified Bayesian framework. Readers learn what non-linear Kalman filters and particle filters are, how they are related, and their relative advantages and disadvantages. They also discover how state-of-the-art Bayesian parameter estimation methods can be combined with state-of-the-art filtering and smoothing algorithms. The book's practical and algorithmic approach assumes only modest mathematical prerequisites. Examples include MATLAB computations, and the numerous end-of-chapter exercises include computational assignments. MATLAB/GNU Octave source code is available for download at www.cambridge.org/sarkka, promoting hands-on work with the methods.

    Tim Hill's distraction-free approach combines decades of tutoring experience with the methods of his old-school Russian math teachers. The result: learn in a few days what conventional schools stretch into months. Teaches general principles that can be applied to a wide variety of problems. Avoids the mindless and excessive routine computations that characterize conventional textbooks. Treats trigonometry as a logically coherent discipline, not as a disjointed collection of techniques. Restores proofs to their proper place to remove doubt, convey insight, and encourage precise logical thinking. Omits digressions, excessive formalities, and repetitive exercises. Covers all the trigonometry needed to take a calculus course. Includes detailed solutions to all problems. Contents1. A Few Basics2. Radian Measure3. The Trig Functions4. Trig Values for Special Angles5. Graphs of Trig Functions6. The Major Formulas7. Inverse Trig Functions8. The Law of Cosines (and Sines)9. Solutions10. Trig Cheat SheetAbout the AuthorTim Hill is a private math tutor and data scientist living in Boulder, Colorado. He holds degrees in mathematics and statistics from Stanford University and the University of Colorado. When he's not crunching numbers, Tim climbs rocks, hikes canyons, and avoids malls.

    

    It includes a careful review of elementary probability and detailed coverage of Poisson, Gaussian and Markov processes with richly varied queuing applications. The theory and applications of inference, hypothesis testing, estimation, random walks, large deviations, martingales and investments are developed. Written by one of the world's leading information theorists, evolving over twenty years of graduate classroom teaching and enriched by over 300 exercises, this is an exceptional resource for anyone looking to develop their understanding of stochastic processes.

    It presents the ideas behind the theoretical concepts.

    The goal in this book is to put an array of tools at the fingertips of practitioners by explaining approaches long used by survey statisticians, illustrating how existing software can be used to solve survey problems, and developing some specialized software where needed. This book serves at least three audiences: (1) Students seeking a more in-depth understanding of applied sampling either through a second semester-long course or by way of a supplementary reference; (2) Survey statisticians searching for practical guidance on how to apply concepts learned in theoretical or applied sampling courses; and (3) Social scientists and other survey practitioners who desire insight into the statistical thinking and steps taken to design, select, and weight random survey samples.Several survey data sets are used to illustrate how to design samples, to make estimates from complex surveys for use in optimizing the sample allocation, and to calculate weights. Realistic survey projects are used to demonstrate the challenges and provide a context for the solutions. The book covers several topics that either are not included or are dealt with in a limited way in other texts. These areas include: sample size computations for multistage designs; power calculations related to surveys; mathematical programming for sample allocation in a multi-criteria optimization setting; nuts and bolts of area probability sampling; multiphase designs; quality control of survey operations; and statistical software for survey sampling and estimation. An associated R package, PracTools, contains a number of specialized functions for sample size and other calculations. The data sets used in the book are also available in PracTools, so that the reader may replicate the examples or perform further analyses.

    The authors link the theory of teaching mathematics with simple reflective questions and interesting maths tasks. There is practical advice on planning, assessment and differentiations, amongst other pertinent themes' -Jacqueline Oldham, PGCE Secondary Mathematics Course Tutor, St Mary's University College'This is a very practical guide for learning to teach mathematics for student teachers on all training routes. Chapters are focused and readable but succeed in tackling issues in depth giving the reader strong academic support' -Anne Haworth, PGCE Secondary Mathematics Course Tutor, University of ManchesterThis book is an essential companion for anyone training to teach mathematics in secondary education. It offers clear and engaging coverage of all major aspects of mathematics teaching that you will need to engage with in order to successfully train for the classroom.This Second Edition includes: a new chapter exploring different teaching approaches including active learning, effective group work and creative mathematics teaching expanded coverage of assessment, using resources in the classroom and metacognition and learning updated coverage of recent developments in education policy and the 2012 Teachers' Standards This is essential reading for anyone training to teach secondary mathematics including postgraduate (PGCE, SCITT) and school-based routes into teaching.Free digital resources for extra support is available in the book's companion website. It includes: Web links and further reading for each chapterA video series of a sample classroom lesson filmed in a real-life setting Visit www.sagepub.co.uk/chamberstimlin

    In an entertaining and practical way, readers will discover that infinity is not limited to the mathematical concept as represented by the symbol nor its metaphysical concept as the indefinable concept of eternity, but in fact, it resides in a variety of disciplines, a multitude of contexts and has a far-reaching influence on human existence. Secrets of Infinity organizes the 150 articles into six subject areas: Science e.g., Henrietta Lacks -- Her death in 1951 from uterine cancer at the age 31 did not end her existence. Her doctor took a tissue sample from the tumor and developed the first continuous culture of human cells and thus the first immortal cell line in history, known as HeLa. Mathematics e.g., Googol -- Edward Kasner (1878-1955) devised the googol to show how huge infinity is through a number so large that it is unimaginable but still not even close to infinity. Technology e.g., TA-65 -- Recently, researchers at Sierra Sciences discovered the TA-65, which could be the chromosomal catalyst to stopping, slowing or even reversing the aging process, bringing us closer to the myth of eternal youth. Art e.g., The Endless Stairs of the Vatican -- Little did the Vatican Museums know in 1932, when the stairs were built, that this formation could represent life itself, with the discovery of the DNA double helix chain in 1953.Philosophy e.g., Rene Descartes, the Infinite and God -- According to Descartes, the idea of infinity has been imposed by a nature that is higher than human, and can only come from this nature being infinite, so he interprets that the existence of infinity confirms the existence of God. Symbology e.g., The Labyrinth -- A labyrinth is a route made up of streets and crossroads with an ingenious and complex structure whose design variations are endless, especially in the case of the rhizome labyrinth, which has infinite ramifications. Engaging and free of jargon, Secrets of Infinity helps to demystify the elusive infinity and bring it closer to modern concepts and understanding. Thinking readers and students will find enjoyment and insight on its pages.

    The book teaches students how to properly model, think critically, and design their own studies to avoid common errors. It leads them to think differently not only about math and statistics but also about general research and the scientific method.With a focus on statistical models as producers of data, the book enables students to more easily understand the machinery of advanced statistics. It also downplays the "population" interpretation of statistical models and presents Bayesian methods before frequentist ones. Requiring no prior calculus experience, the text employs a "just-in-time" approach that introduces mathematical topics, including calculus, where needed. Formulas throughout the text are used to explain why calculus and probability are essential in statistical modeling. The authors also intuitively explain the theory and logic behind real data analysis, incorporating a range of application examples from the social, economic, biological, medical, physical, and engineering sciences.Enabling your students to answer the why behind statistical methods, this text teaches them how to successfully draw conclusions when the premises are flawed. It empowers them to use advanced statistical methods with confidence and develop their own statistical recipes. Ancillary materials are available on the book's website.

    Containing hundreds of exercises, examples and applications, these books will become an invaluable resource for both students and teachers. Volume I focuses on the analysis of real-valued functions of a real variable. This second volume goes on to consider metric and topological spaces. Topics such as completeness, compactness and connectedness are developed, with emphasis on their applications to analysis. This leads to the theory of functions of several variables. Differential manifolds in Euclidean space are introduced in a final chapter, which includes an account of Lagrange multipliers and a detailed proof of the divergence theorem. Volume III covers complex analysis and the theory of measure and integration.

    Written by a leading expert, this book will help you if you are studying for an important exam or essay, or if you simply want to improve your knowledge. The book covers all the key areas of algebra including elementary operations, linear equations, formulae, simultaneous equations, quadratic equations, logarithms, variation, laws and sequences. Everything you will need is here in this one book. Each chapter includes not only an explanation of the knowledge and skills you need, but also worked examples and test questions.

    Written by a leading expert, this book will help you if you are studying for an important exam or essay, or if you simply want to improve your knowledge. The book covers all areas of trigonometry including the theory and equations of tangent, sine and cosine, using trigonometry in three dimensions and for angles of any magnitude, and applications of trigonometry including radians, ratio, compound angles and circles related to triangles. Everything you will need is here in this one book. Each chapter includes not only an explanation of the knowledge and skills you need, but also worked examples and test questions.

    This second course in the calculus sequence introduces you to exciting new techniques and applications of one of the most powerful mathematical tools ever invented. Equipped with the skills of Calculus II, you can solve a wide array of problems in the physical, biological, and social sciences, engineering, economics, and other areas. Success at Calculus II also gives you a solid foundation for the further study of mathematics, and it meets the math requirement for many undergraduate majors.

    Covering this emerging area of research in biostatistics and epidemiology, this book examines the use of genetic variants as instrumental variables to assess causal associations. It also discusses statistical issues with instrumental variable analysis and explores practical applications of Mendelian randomization. The methods are illustrated with a variety of detailed worked examples using real data.

    But in fact, the connections between the two go back thousands of years, such as Pythagoras's ideas about how to quantify changes of pitch for musical tones (musical intervals). Mathematics and Music: Composition, Perception, and Performance explores the many links between mathematics and different genres of music, deepening students' understanding of music through mathematics.In an accessible way, the text teaches the basics of reading music and explains how various patterns in music can be described with mathematics. The authors extensively use the powerful time-frequency method of spectrograms to analyze the sounds created in musical performance. Numerous examples of music notation assist students in understanding basic musical scores. The text also provides mathematical explanations for musical scales, harmony, and rhythm and includes a concise introduction to digital audio synthesis.Along with helping students master some fundamental mathematics, this book gives them a deeper appreciation of music by showing how music is informed by both its mathematical and aesthetic structures.Web ResourceOn the book's CRC Press web page, students can access videos of many of the spectrograms discussed in the text as well as musical scores playable with the free music software MuseScore. An online bibliography offers many links to free downloadable articles on math and music. The web page also provides links to other websites related to math and music, including all the sites mentioned in the book.

    The lambda calculus forms a prototype universal programming language, which in its untyped version is related to Lisp, and was treated in the first author's classic The Lambda Calculus (1984). The formalism has since been extended with types and used in functional programming (Haskell, Clean) and proof assistants (Coq, Isabelle, HOL), used in designing and verifying IT products and mathematical proofs. In this book, the authors focus on three classes of typing for lambda terms: simple types, recursive types and intersection types. It is in these three formalisms of terms and types that the unexpected mathematical beauty is revealed. The treatment is authoritative and comprehensive, complemented by an exhaustive bibliography, and numerous exercises are provided to deepen the readers' understanding and increase their confidence using types.

    Behind the computing devices and applications that have transformed our lives are clever algorithms, and for every worthwhile algorithm there is a problem that it solves and a proof that it works. Before this proof there was an open problem: can one create an efficient algorithm to solve the computational problem? And, finally, behind these questions are the people who are excited about these fundamental issues in our computational world. In this book the authors draw on their outstanding research and teaching experience to showcase some key people and ideas in the domain of theoretical computer science, particularly in computational complexity and algorithms, and related mathematical topics. They show evidence of the considerable scholarship that supports this young field, and they balance an impressive breadth of topics with the depth necessary to reveal the power and the relevance of the work described. Beyond this, the authors discuss the sustained effort of their community, revealing much about the culture of their field. A career in theoretical computer science at the top level is a vocation: the work is hard, and in addition to the obvious requirements such as intellect and training, the vignettes in this book demonstrate the importance of human factors such as personality, instinct, creativity, ambition, tenacity, and luck.The authors' style is characterized by personal observations, enthusiasm, and humor, and this book will be a source of inspiration and guidance for graduate students and researchers engaged with or planning careers in theoretical computer science.

    "Provides a straightforward, bottom-up approach that assists the reader in obtaining a clear (but theoretically rigorous) understanding of Evolutionary Algorithms, with an emphasis on implementation rather than models"--

    He must walk to the bar and then walk to her. What's the shortest path that he can take?Your iPod seems to be playing the same songs over again. Is there something wrong with the shuffle feature, or might the songs be playing randomly?You have 100 dimes, and I have 99 pennies. At the same time, we will toss our coins in the air and let them fall on the floor. Then we meticulously count the outcomes of our tosses. You win if you show more heads than I do. What’s the probability that you will win?And of course, the puzzle that provides the title. What do an infinite tower, a classic physics puzzle, and coin flipping have in common?

    Appropriate for self-study, the book will also be useful for AMIE and IETE students. Written in a student-friendly readable manner, the book explains the basic fundamentals and concepts of control systems in a clearly understandable form. It is a balanced survey of theory aimed to provide the students with an in-depth insight into system behaviour and control of continuous-time control systems. All the solved and unsolved problems in this book are classroom tested, designed to illustrate the topics in a clear and thorough way.

    This book provides a thorough and self-contained introduction to the basic aspects of both linear and nonlinear functional analysis. Most of the major results are accompanied by complete proofs, and illustrated with a variety of applications to numerical analysis, optimisation theory, and partial differential equations. As well as covering a vast amount of foundational material, historical notes and many original references are included to help the reader explore the genesis of some important results. This book is intended for advanced undergraduates, graduate students, and researchers. With illustrations and over 400 problems, it is ideal for both teaching and self-study.

    

    This subject is now taught not only in departments of economics but also in professional schools and programs oriented toward business, government and administration, and public policy. This book attempts to unify the subject matter in a simple, accessible manner. Part I of the book focuses on the economics of uncertainty; Part II examines the economics of information. This revised and updated second edition places a greater focus on game theory. New topics include posted-price markets, mechanism design, common-value auctions, and the one-shot deviation principle for repeated games.

    

    Understanding these objects requires extensive knowledge in many different areas: accretion disks, the physics of dust and ionized gas, astronomical spectroscopy, star formation, and the cosmological evolution of galaxies and black holes. This new text by Hagai Netzer, a renowned astronomer and leader in the field, provides a comprehensive introduction to the theory underpinning our study of AGN and the ways that we observe them. It emphasizes the basic physics underlying AGN, the different types of active galaxies and their various components, and the complex interplay between them and other astronomical objects. Recent developments regarding the evolutionary connections between active galaxies and star-forming galaxies are explained in detail. Both graduate students and researchers will benefit from Netzer's authoritative contributions to this exciting field of research.

    Campe begs to differ. Mathematical probability, he argues, took over the role of the old probability of poets, orators, and logicians, albeit in scientific terms. Indeed, mathematical probability would not even have been possible without the other probability, whose roots lay in classical antiquity.The Game of Probability revisits the seventeenth and eighteenth-century "probabilistic revolution," providing a history of the relations between mathematical and rhetorical techniques, between the scientific and the aesthetic. This was a revolution that overthrew the "order of things," notably the way that science and art positioned themselves with respect to reality, and its participants included a wide variety of people from as many walks of life. Campe devotes chapters to them in turn. Focusing on the interpretation of games of chance as the model for probability and on the reinterpretation of aesthetic form as verisimilitude (a critical question for theoreticians of that new literary genre, the novel), the scope alone of Campe's book argues for probability's crucial role in the constitution of modernity.

    Discusses frequentist likelihood-based inference from a Fisherian viewpoint, Bayesian inference techniques including point and interval estimates, model choice and prediction and more.

    Explores how the work of audio engineers combines the science of sound with the engineering design process, including how these engineers find solutions to audio challenges.

    

    Readers are also introduced to the tool engineers use to solve problems: The Engineering Design Process.

    By looking carefully at what mathematicians really do when they are doing mathematics, Reuben Hersh offers an escape from this trap. This book of selected articles and essays provides an honest, coherent, and clearly understandable account of mathematicians' proof as it really is, and of the existence and reality of mathematical entities. It follows in the footsteps of Poincare, Hadamard, and Polya. The pragmatism of John Dewey is a better fit for mathematical practice than the dominant analytic philosophy. Dialogue, satire, and fantasy enliven the philosophical and methodological analysis. Reuben Hersh has written extensively on mathematics, often from the point of view of a philosopher of science. His book with Philip Davis, The Mathematical Experience, won the National Book Award in science.

    Historically, axiomatic geometry marks the origin of formalized mathematical activity. It is in this discipline that most historically famous problems can be found, the solutions of which have led to various presently very active domains of research, especially in algebra. The recognition of the coherence of two-by-two contradictory axiomatic systems for geometry (like one single parallel, no parallel at all, several parallels) has led to the emergence of mathematical theories based on an arbitrary system of axioms, an essential feature of contemporary mathematics.This is a fascinating book for all those who teach or study axiomatic geometry, and who are interested in the history of geometry or who want to see a complete proof of one of the famous problems encountered, but not solved, during their studies: circle squaring, duplication of the cube, trisection of the angle, construction of regular polygons, construction of models of non-Euclidean geometries, etc. It also provides hundreds of figures that support intuition.Through 35 centuries of the history of geometry, discover the birth and follow the evolution of those innovative ideas that allowed humankind to develop so many aspects of contemporary mathematics. Understand the various levels of rigor which successively established themselves through the centuries. Be amazed, as mathematicians of the 19th century were, when observing that both an axiom and its contradiction can be chosen as a valid basis for developing a mathematical theory. Pass through the door of this incredible world of axiomatic mathematical theories!

    

    

    Inventive, humorous, and very, very smart, this is a book truly like no other—and a sheer delight."—Cole SwensenLiat Berdugo, mathematician and artist, collects and reinterprets mathematical diagrams. Funny, dark, surprising, and revelatory, this book shows us what we often overlook: that meaning is everywhere what we make of it. Her making is a delight.

    Open Tennis Championship, and solve other amusing and challenging puzzles — including a mathematical brainteaser involving a couple of holes of golf on the surface of the moon.In addition to logical puzzles and mathematical paradoxes, this original collection features a variety of word problems and sports-related riddles. The puzzles, which vary in complexity from playful propositions to tough mathematical conundrums, are suitable for ages 12 and up. Detailed solutions appear at the end.

    

    In many (but not all) cases, these constraints have a mathematical nature, for example, the geometric transformations governing the canons of J. S. Bach, the various projection systems used in classical painting, the catalog of symmetries found in Islamic art, or the rules concerning poetic structure. This fascinating book describes geometric frameworks underlying this constraint-based creation. The author provides both a development in geometry and a description of how these frameworks fit the creative process within several art practices. He furthermore discusses the perceptual effects derived from the presence of particular geometric characteristics. The book began life as a liberal arts course and it is certainly suitable as a textbook. However, anyone interested in the power and ubiquity of mathematics will enjoy this revealing insight into the relationship between mathematics and the arts.

    Math Girls has something for everyone, from advanced high school students to math majors and educators.

    It features a distinctive, detailed treatment of the real numbers system, and combines an introduction to set theory with exposition of the essence of analysis.

    With this special bundle, you'll get the complete text of the following two titles:Statistics For Dummies, 2nd Edition "Statistics For Dummies" shows you how to interpret and critique graphs and charts, determine the odds with probability, guesstimate with confidence using confidence intervals, set up and carry out a hypothesis test, compute statistical formulas, and more.Tracks to a typical first semester statistics courseUpdated examples resonate with today's studentsExplanations mirror teaching methods and classroom protocolPacked with practical advice and real-world problems, "Statistics For Dummies" gives you everything you need to analyze and interpret data for improved classroom or on-the-job performance.Statistics II For Dummies The ideal supplement and study guide for students preparing for advanced statistics. Packed with fresh and practical examples appropriate for a range of degree-seeking students, "Statistics II For Dummies" helps any reader succeed in an upper-level statistics course. It picks up with data analysis where "Statistics For Dummies" left off, featuring new and updated examples, real-world applications, and test-taking strategies for success. This easy-to-understand guide covers such key topics as sorting and testing models, using regression to make predictions, performing variance analysis (ANOVA), drawing test conclusions with chi-squares, and making comparisons with the Rank Sum Test.About the AuthorDeborah Rumsey has a PhD in Statistics from The Ohio State University. Upon graduating, she joined the faculty in the Department of Statistics at Kansas State University, where she won the distinguished Presidential Teaching Award and earned tenure and promotion. She returned to Ohio State and is now a Statistics Education Specialist/Auxiliary Faculty Member for the Department of Statistics. Dr. Rumsey has served on the American Statistical Associations Statistics Education Executive Committee and is the Editor of the Teaching Bits section of the Journal of Statistics Education. She is the author of the both books in this bundle. Additionally, she has published many papers and given many professional presentations on the subject of Statistics Education. Her particular research interests are curriculum materials development, teacher training and support, and immersive learning environments.

    Although humans have tried to forecast weather for millennia, mathematical principles were used in meteorology only after the turn of the twentieth century. From the first proposal for using mathematics to predict weather, to the supercomputers that now process meteorological information gathered from satellites and weather stations, Ian Roulstone and John Norbury narrate the groundbreaking evolution of modern forecasting.The authors begin with Vilhelm Bjerknes, a Norwegian physicist and meteorologist who in 1904 came up with a method now known as numerical weather prediction. Although his proposed calculations could not be implemented without computers, his early attempts, along with those of Lewis Fry Richardson, marked a turning point in atmospheric science. Roulstone and Norbury describe the discovery of chaos theory's butterfly effect, in which tiny variations in initial conditions produce large variations in the long-term behavior of a system--dashing the hopes of perfect predictability for weather patterns. They explore how weather forecasters today formulate their ideas through state-of-the-art mathematics, taking into account limitations to predictability. Millions of variables--known, unknown, and approximate--as well as billions of calculations, are involved in every forecast, producing informative and fascinating modern computer simulations of the Earth system.Accessible and timely, Invisible in the Storm explains the crucial role of mathematics in understanding the ever-changing weather.

    Kids will also learn about money around the world from a National Geographic expert, featured in "Explorer's Corners" throughout the book. Packed with fun facts and amazing photographs, this book gives kids an in-depth look at this fascinating and important topic.National Geographic supports K-12 educators with ELA Common Core Resources.Visit www.natgeoed.org/commoncore for more information.

    Harvard's mathematics department was at the center of these developments. A History in Sum is an inviting account of the pioneers who trailblazed a distinctly American tradition of mathematics--in algebraic geometry and topology, complex analysis, number theory, and a host of esoteric subdisciplines that have rarely been written about outside of journal articles or advanced textbooks. The heady mathematical concepts that emerged, and the men and women who shaped them, are described here in lively, accessible prose.The story begins in 1825, when a precocious sixteen-year-old freshman, Benjamin Peirce, arrived at the College. He would become the first American to produce original mathematics--an ambition frowned upon in an era when professors largely limited themselves to teaching. Peirce's successors--William Fogg Osgood and Maxime B cher--undertook the task of transforming the math department into a world-class research center, attracting to the faculty such luminaries as George David Birkhoff. Birkhoff produced a dazzling body of work, while training a generation of innovators--students like Marston Morse and Hassler Whitney, who forged novel pathways in topology and other areas. Influential figures from around the world soon flocked to Harvard, some overcoming great challenges to pursue their elected calling.A History in Sum elucidates the contributions of these extraordinary minds and makes clear why the history of the Harvard mathematics department is an essential part of the history of mathematics in America and beyond.

    The book provides a unified presentation of the mathematical properties and statistical applications of matrices in order to define and manipulate data.Written for theoretical and applied statisticians, the book utilizes multiple numerical examples to illustrate key ideas, methods, and techniques crucial to understanding matrix algebra's application in linear models. Matrix Algebra for Linear Models expertly balances concepts and methods allowing for a side-by-side presentation of matrix theory and its linear model applications. Including concise summaries on each topic, the book also features:Methods of deriving results from the properties of eigenvalues and the singular value decomposition Solutions to matrix optimization problems for obtaining more efficient biased estimators for parameters in linear regression models A section on the generalized singular value decomposition Multiple chapter exercises with selected answers to enhance understanding of the presented material Matrix Algebra for Linear Models is an ideal textbook for advanced undergraduate and graduate-level courses on statistics, matrices, and linear algebra. The book is also an excellent reference for statisticians, engineers, economists, and readers interested in the linear statistical model.