Reflecting the need for even minor programming in today's model-based statistics, the book pushes readers to perform step-by-step calculations that are usually automated. This unique computational approach ensures that readers understand enough of the details to make reasonable choices and interpretations in their own modeling work.The text presents generalized linear multilevel models from a Bayesian perspective, relying on a simple logical interpretation of Bayesian probability and maximum entropy. It covers from the basics of regression to multilevel models. The author also discusses measurement error, missing data, and Gaussian process models for spatial and network autocorrelation.By using complete R code examples throughout, this book provides a practical foundation for performing statistical inference. Designed for both PhD students and seasoned professionals in the natural and social sciences, it prepares them for more advanced or specialized statistical modeling.Web ResourceThe book is accompanied by an R package (rethinking) that is available on the author's website and GitHub. The two core functions (map and map2stan) of this package allow a variety of statistical models to be constructed from standard model formulas.

    Featuring numerous entries by leading experts and organized thematically, it introduces readers to applied mathematics and its uses; explains key concepts; describes important equations, laws, and functions; looks at exciting areas of research; covers modeling and simulation; explores areas of application; and more.Modeled on the popular Princeton Companion to Mathematics, this volume is an indispensable resource for undergraduate and graduate students, researchers, and practitioners in other disciplines seeking a user-friendly reference book on applied mathematics.Features nearly 200 entries organized thematically and written by an international team of distinguished contributorsPresents the major ideas and branches of applied mathematics in a clear and accessible wayExplains important mathematical concepts, methods, equations, and applicationsIntroduces the language of applied mathematics and the goals of applied mathematical researchGives a wide range of examples of mathematical modelingCovers continuum mechanics, dynamical systems, numerical analysis, discrete and combinatorial mathematics, mathematical physics, and much moreExplores the connections between applied mathematics and other disciplinesIncludes suggestions for further reading, cross-references, and a comprehensive index

    As a small-town girl in Nova Scotia bullied for liking numbers more than boys, and lacking the encouragement of her unsupportive single mother who frowns at her daughter’s unrealistic ambition, Bethany MacDonald's road to the International Math Olympiad has been marked by numerous challenges.Through persistence, perseverance, and the support of innovative mentors who inspire her with a love of learning, Bethany confronts these challenges and develops the creativity and confidence to reach her potential.In training to become a world-champion "mathlete", Bethany discovers the heart of mathematics – a subject that’s not about memorizing formulas, but rather about problem-solving and detecting patterns to uncover truth, as well as learning how to apply the deep and unexpected connections of mathematics to every aspect of her life, including athletics, spirituality, and environmental sustainability.As Bethany reflects on her long journey and envisions her exciting future, she realizes that she has shattered the misguided stereotype that only boys can excel in math, and discovers a sense of purpose that through mathematics, she can and she will make an extraordinary contribution to society.

    Unlike most other test prep books, this one is truly geared towards the student aiming for the perfect score. It leaves no stones unturned.Inside, You'll Find:Clear explanations of the tested math concepts, from the simplest to the most obscureHundreds of examples to illustrate all the question types and the different ways they can show upOver 500 practice questions and explanations to help you master each topicThe most common mistakes students make (so you don't)This is the most thorough SAT prep out there. For more sample chapters and information, check out http: //thecollegepanda.com/books

     Learn the essential concepts using concrete analogies and vivid diagrams, not mechanical definitions. Calculus isn't a set of rules, it's a specific, practical viewpoint we can apply to everyday thinking. Frustrated With Abstract, Mechanical Lessons? I was too. Despite years of classes, I didn't have a strong understanding of calculus concepts. Sure, I could follow mechanical steps, but I had no lasting intuition. The classes I've seen are too long, taught in the wrong order, and without solid visualizations. Here's how this course is different: 1) It gets to the point. A typical class plods along, saving concepts like Integrals until Week 8. I want to see what calculus can offer by Minute 8. Each compact, tightly-written lesson can be read in 15 minutes. 2) Concepts are taught in their natural order. Most classes begin with the theory of limits, a technical concept discovered 150 years after calculus was invented. That's like putting a new driver into a Formula-1 racecar on day 1. We can begin with the easy-to-grasp concepts discovered 2000 years ago. 3) It has vivid analogies and visualizations. Calculus is usually defined as the "study of change"... which sounds like history or geology. Instead of an abstract definition, we'll see calculus a step-by-step viewpoint to explore patterns. 4) It's written by a human, for humans. I'm not a haughty professor or strict schoolmarm. I'm a friend who saw a fun way to internalize some difficult ideas. This course is a chat over coffee, not a keep-your-butt-in-your-seat lecture. The goal is to help you grasp the Aha! moments behind calculus in hours, not a painful semester (or a decade, in my case). Join Thousands Of Happy Readers Here's a few samples of anonymous feedback as people went through the course. The material covers a variety of levels, whether you're looking for intuitive appreciation or the specifics of the rules. "I've done all of this stuff before, and I do understand calculus intuitively, but this was the most fun I've had going through this kind of thing. The informal writing and multitude of great analogies really helps this become an enjoyable read and the rest is simple after that - you make this seem easy, but at the same time, you aren't doing it for us…This is what math education is supposed to be like :)" "I have psychology and medicine background so I relate your ideas to my world. To me the most useful idea was what each circle production feels like. Rings are natural growth…Slices are automatable chunks and automation cheapens production… Boards in the shape on an Arch are psychologically most palatable for work (wind up, hard part, home stretch). Brilliant and kudos, from one INTP to another." "I like how you're introducing both derivatives and integrals at the same time - it's really helps with understanding the relationship between them. Also, I appreciate how you're coming from such a different angle than is traditionally taken - it's always interesting to see where you decide to go next." "That was breathtaking. Seriously, mail my air back please, I've grown used to it. Beautiful work, thank you. Lesson 15 was masterful. I am starting to feel calculus. "d/dx is good" (sorry, couldn't resist!)."

    Learn incredible maths facts as you draw the beautiful designs. From simple geometric patterns to fascinating fractal art, to awesome anamorphic art, and cool celtic knots, discover the beauty in maths, and the maths in beauty. Left-brain and right-brain come together to create fantastic maths art!

    The mathematician Bernhard Riemann made a celebrated conjecture about primes in 1859, the so-called Riemann Hypothesis, which remains to be one of the most important unsolved problems in mathematics. Through the deep insights of the authors, this book introduces primes and explains the Riemann Hypothesis. Students with minimal mathematical background and scholars alike will enjoy this comprehensive discussion of primes. The first part of the book will inspire the curiosity of a general reader with an accessible explanation of the key ideas. The exposition of these ideas is generously illuminated by computational graphics that exhibit the key concepts and phenomena in enticing detail. Readers with more mathematical experience will then go deeper into the structure of primes and see how the Riemann Hypothesis relates to Fourier analysis using the vocabulary of spectra. Readers with a strong mathematical background will be able to connect these ideas to historical formulations of the Riemann Hypothesis.

    

    A tour de force of imagination and exposition, he guides us through uncompromisingly challenging territory that expands our minds and encourages a playful and exploratory approach to study. "The puzzles," he says, "are like toys. We should pick up the one we most enjoy, and play with it."Whether you are an aspiring scientist or an old-hand, pitting yourself against these problems will test your ability to think, and inspire you with curiosity and enthusiasm for physics. Presented with charm and wit, the questions span the gap between high-school and university-entrance standard material. Detailed answers are lightened with a fascinating and refreshing blend of scientific history, application and personal anecdote.On this delightful and idiosyncratic romp through pre-university maths and physics, the author shows us that behind every single one of these questions lies a new way of thinking about subjects we thought we had understood. He argues that engaging with the unfamiliar is key to forming deeper insights and developing intellectual independence. Professor Povey's Perplexing Problems is a manifesto that science should be playful, and a celebration of the curious.

    This concise, original text for a one-semester course on the subject is derived from courses that author Emily Riehl taught at Harvard and Johns Hopkins Universities. The treatment introduces the essential concepts of category theory: categories, functors, natural transformations, the Yoneda lemma, limits and colimits, adjunctions, monads, and other topics. Suitable for advanced undergraduates and graduate students in mathematics, the text provides tools for understanding and attacking difficult problems in algebra, number theory, algebraic geometry, and algebraic topology. Drawing upon a broad range of mathematical examples from the categorical perspective, the author illustrates how the concepts and constructions of category theory arise from and illuminate more basic mathematical ideas. Prerequisites are limited to familiarity with some basic set theory and logic.

    

    This book explains how the entire universe can be created using just two ingredients: nothing at all and the principle of sufficient reason.This is the final book in The God Series.

    In doing so, first the common approach is shown, and then a more elegant strategy is provided. Elementary mathematics is used so that the reader can focus on the strategy and not be distracted by some more sophisticated mathematics.

    Many important problems involve decision making under uncertainty--that is, choosing actions based on often imperfect observations, with unknown outcomes. Designers of automated decision support systems must take into account the various sources of uncertainty while balancing the multiple objectives of the system. This book provides an introduction to the challenges of decision making under uncertainty from a computational perspective. It presents both the theory behind decision making models and algorithms and a collection of example applications that range from speech recognition to aircraft collision avoidance.Focusing on two methods for designing decision agents, planning and reinforcement learning, the book covers probabilistic models, introducing Bayesian networks as a graphical model that captures probabilistic relationships between variables; utility theory as a framework for understanding optimal decision making under uncertainty; Markov decision processes as a method for modeling sequential problems; model uncertainty; state uncertainty; and cooperative decision making involving multiple interacting agents. A series of applications shows how the theoretical concepts can be applied to systems for attribute-based person search, speech applications, collision avoidance, and unmanned aircraft persistent surveillance.Decision Making Under Uncertainty unifies research from different communities using consistent notation, and is accessible to students and researchers across engineering disciplines who have some prior exposure to probability theory and calculus. It can be used as a text for advanced undergraduate and graduate students in fields including computer science, aerospace and electrical engineering, and management science. It will also be a valuable professional reference for researchers in a variety of disciplines.

    Without philosophy we cannot penetrate deeply into mathematics. Without both we cannot penetrate deeply into anything.” – LeibnizIn intellectual history, perhaps nothing has been more misinterpreted than Gödel’s incompleteness theorems. Stephen Hawking, adopting the popular misconception, said, “Thus mathematics is either inconsistent, or incomplete. The smart money is on incomplete.”This book is about the titanic struggle for the soul of mathematics, and reflects two immense battles in which mathematics is immersed to this day.Firstly, if mathematics is tautology, as Wittgenstein said, mathematics cannot be inconsistent and/or incomplete, and so Gödel’s work cannot be about mathematics. If mathematics is not tautological, mathematics is necessarily mired in inconsistency and/or incompleteness, just as Stephen Hawking said, hence is wholly unreliable.Secondly, if mathematics is non-ontological, it cannot say anything about reality. If mathematics is ontological, it’s the only thing that can say anything true about reality.There can’t be a world where math is a bit true and a bit false. Either the world is wholly mathematical – in which case math and not science is how we must study the world – or the world isn’t mathematical at all, in which case it’s absurd for science to use math in its attempts to account for, or model, reality.Math presents a deadly challenge to science. If math is real, we don’t need science. If math isn’t real, then science, which is so heavily reliant on math, is nonsense! The greatest challenge facing science isn’t to define and understand the universe, but to define and understand math.Of course, it turns out that math and the universe are one and the same. Only if the universe is mathematical can it be rational and intelligible. It must be entirely mathematical since a universe that is partly mathematical and partly something else would be irrational and unintelligible given that mathematical things cannot interact with non-mathematical things (this would constitute a version of Cartesian dualism where two incompatible substances cannot interact since they have no common ground).To understand what math actually is, you must strip all non-mathematical considerations from it. Are you ready to ponder existence in itself - bare existence - shorn of all subjective experiences, feelings, desires, sensations, perceptions, mystical intuitions, beliefs, opinions, and interpretations?What is naked existence? What is existence in its rawest, oldest, most primitive and primordial state? Until you understand that, you will have no idea what it is when you impose an appearance on it.

    Using examples from a broad base of computational tasks, including data processing, computational photography, and animation, the textbook introduces numerical modeling and algorithmic design from a practical standpoint and provides insight into the theoretical tools needed to support these skills.The book covers a wide range of topics--from numerical linear algebra to optimization and differential equations--focusing on real-world motivation and unifying themes. It incorporates cases from computer science research and practice, accompanied by highlights from in-depth literature on each subtopic. Comprehensive end-of-chapter exercises encourage critical thinking and build students' intuition while introducing extensions of the basic material.The text is designed for advanced undergraduate and beginning graduate students in computer science and related fields with experience in calculus and linear algebra. For students with a background in discrete mathematics, the book includes some reminders of relevant continuous mathematical background.

    This is an ideal approach for students who would like to understand the basics, but are unsatisfied with the common textbook format. The book contains three lessons. The function, as well as related concepts such as the domain and the graph, are introduced in lesson one. Lesson two consists of a detailed look at linear functions. The final lesson deals with all aspects of quadratic functions. Whether you've been struggling or you just want to know what's going on - this book is for you.From the author of "Great Formulas Explained", "Statistical Snacks" and the "Math Shorts" series.

    Physics examples serve to introduce the fundamental partial differential equations and “special functions” of mathematical physics. A thorough analysis of Green’s functions leads to a discussion of integral equations. Supplementary topics include dispersion relations and rational function approximation.

    Topics include the basic trig functions, special angles, the reference angle, the unit circle, going beyond Quadrant I, inverse trig functions, and radians. A few chapters are intended to help students memorize the trig functions of common angles like 30, 150, or 315 degrees, which will be especially useful for students who may take exams without a calculator (that’s the case with the MCAT and many math and science courses). Each chapter works out examples with step-by-step solutions and explanations. Problems at the end of each chapter offer practice carrying out the techniques. The answer to every exercise can be found at the back of the book.

    The book’s organization makes it easy to adapt to a variety of course syllabi. The text introduces the fundamental concepts of algebra while addressing the needs of students with diverse backgrounds and learning styles. Each topic builds upon previously developed material to demonstrate the cohesiveness and structure of mathematics.

    Readers can join the cast of crazy characters on a tour of the Murderous Maths building to discover the darkest and deadliest mathematical secrets, including: a sure-fire way how to make birthdays last twice as long, how the number 1 starts fights, how triangles lead to murder, and much more. Maths has never been so much fun!

    Numerous rigorously tested examples and coherent to-the-point explanations, presented in an easy-to-follow format, provide valuable tools for conquering this challenging subject. The treatment is organized in a way that permits readers to advance sequentially or skip around between chapters. An essential companion volume to the author's Attacking Trigonometry Problems, this book will equip students with the skills they will need to successfully approach the problems in logarithms and exponential functions that they will encounter on exams.

    This book is an introduction to Mathematica. The goal is to provide a hands-on experience introducing the breadth of Mathematica, with a focus on ease of use. Readers get detailed instruction with examples for interactive learning and end-of-chapter exercises. Each chapter also contains authors tips from their combined 50+ years of Mathematica use.

    In this richly illustrated book, accessible examples are used to show how information theory can be understood in terms of everyday games like '20 Questions', and the simple MatLab programs provided give hands-on experience of information theory in action. Written in a tutorial style, with a comprehensive glossary, this text represents an ideal primer for novices who wish to become familiar with the basic principles of information theory.Download chapter 1 from http://jim-stone.staff.shef.ac.uk/Boo...

    

    Along with her skis and poles, she takes her love for math to the slopes. Throughout the day, Addie showcases her math skills adding everything she sees. Spend a day with Addie on Snowdrift Mountain adding the things she encounters. Join in for twice the fun.

    Implementation of the algorithms takes a lot of time. With the help of Mathematica, you can quickly get a result from the use of a particular method, because this system contains almost all the known algorithms for data analysis.If you are not a programmer but you need to analyze data, this book will show you the capabilities of Mathematica when just few strings of intelligible code help to solve huge tasks from statistical issues to pattern recognition. If you're a programmer, with the help of this book, you will learn how to use the library of algorithms implemented in Mathematica in your programs, as well as how to write algorithm testing procedure.With each chapter, you'll be more immersed in the special world of Mathematica. Along with intuitive queries for data processing, we will highlight the nuances and features of this system, allowing you to build effective analysis systems.With the help of this book, you will learn how to optimize the computations by combining your libraries with the Mathematica kernel.

    It is about the latent beauty of mathematics, its history, and the puzzles that have advanced and emerged from the science of numbers. It is full of challenging historical facts, thinking puzzles, paradoxes, illusions, and problem solving.There are 315 puzzles in this book. Extended captions explain in easy terms the value of the puzzles for mathematical and educational purposes, particularly in light of the findings of recent research. This historical and pedagogical dimension sets The Puzzle Universe apart from similar books.The puzzles appear in a dynamic layout for a visual experience that is Ivan Moscovich's trademark. There are ten chapters complete with answers. Icons show the challenge rating and the tools needed (pencil, scissors, ruler, and of course, brain) to solve the puzzle.

    Python is easy to learn, and it's perfect for exploring topics like statistics, geometry, probability, and calculus. You’ll learn to write programs to find derivatives, solve equations graphically, manipulate algebraic expressions, even examine projectile motion.Rather than crank through tedious calculations by hand, you'll learn how to use Python functions and modules to handle the number crunching while you focus on the principles behind the math. Exercises throughout teach fundamental programming concepts, like using functions, handling user input, and reading and manipulating data. As you learn to think computationally, you'll discover new ways to explore and think about math, and gain valuable programming skills that you can use to continue your study of math and computer science.If you’re interested in math but have yet to dip into programming, you’ll find that Python makes it easy to go deeper into the subject—let Python handle the tedious work while you spend more time on the math.

    Your children can develop mental flexibility by playing with numbers, from basic math facts to the hundreds and beyond. Logic games build strategic thinking skills, and dice games give students hands-on experience with probability.Chapters include: Tens and Teens: Master the concept of number bonds—the relationship between a whole number and the parts that combine to make it—and build a logical foundation for future math. Numbers to One Hundred: Develop mental math skills for working with larger numbers. Practice using place value, addition, and subtraction. Mixed Operations: Give mental muscles a workout with games that require number skills and logical thinking. Logic and Probability: Logic games sharpen inductive and deductive thinking skills, while games of chance build an intuition for probability. Math games pump up mental muscle, reduce the fear of failure, and generate a positive attitude toward mathematics. Through playful interaction, games strengthen a child’s intuitive understanding of numbers and build problem-solving strategies. Mastering a math game can be hard work, but kids do it willingly because it is fun.If you are a parent, these games provide opportunities to enjoy quality time with your children. If you are a classroom teacher, use the games as warm-ups and learning center activities or for a relaxing review day at the end of a term. If you are a tutor or homeschooler, make games a regular feature in your lesson plans to build your students’ mental math skills.So what are you waiting for? Clear off a table, grab a deck of cards, and let's play some math!

    AS & A Level Maths For Dummies offers detailed, simple steps for all of the main types of problems you'll face in your exams, offering explanations of how the topics link together, advice on how to remember the key facts and methods, and ways to structure revision. Even if your head is spinning and you don't know where to begin, this fun and friendly guide gives in-depth support on exactly what you need to know.In the big data and digital age, maths skills have never been more important to career success. AS & A Level Maths For Dummies guides you through the skills needed to pass the exams taken at the end of the first and second year of the course. It begins with the knowledge needed to get a top grade at GCSE, followed by sections on Algebra (functions, graph-sketching, and logarithms), Geometry (coordinate geometry, trigonometry, and working with shapes) and Calculus (differentiation, integration, and differential equations).Helps you build the confidence you need to pass your exams Serves as an excellent supplement to classroom learning Makes difficult maths concepts easy to understand Offers in-depth support in a fun and friendly style If you're an AS & A level student looking to do your very best at exam time, AS & A Level Maths For Dummies makes it easier.

    It covers all types of Triangles, Squares, Rectangle, Paralellogram, Circle and important formulaes on Mensuration.

    It is intended for quantitative researchers and students in the medical and social sciences who wish to learn how to perform meta-analysis with R. As such, the book introduces the key concepts and models used in meta-analysis. It also includes chapters on the following advanced topics: publication bias and small study effects; missing data; multivariate meta-analysis, network meta-analysis; and meta-analysis of diagnostic studies.

    There are large academic textbooks that cover the subject with great depth and rigor. Probably the best known of these is the book by Cover and Thomas. At the other extreme are the popular books such as the ones by Pierceand Gleick. They provide a very superficial introduction to the subject, enough to engage in cocktail party conversation but little else. This book attempts to bridge these two extremes.This book is written for someone who is at least semi-mathematically literate and wants a concise introduction to some of the major concepts in information theory. The level of mathematics needed is very elementary. A rudimentary grasp of logarithms, probability, and basic algebra is all that is required. Two chapters at the end of the book provide a review of everything the reader needs to know aboutlogarithms and discrete probability to get the most out of the book. Very little attention is given to mathematical proof. Instead the results are presented in a way that makes them almost obvious or at least plausible.The book will appeal to anyone looking for a fast introduction to most of the major topics in information theory. An introduction that is concise but not superficial.

    In Galois Theory, Fourth Edition, mathematician and popular science author Ian Stewart updates this well-established textbook for today’s algebra students. New to the Fourth Edition The replacement of the topological proof of the fundamental theorem of algebra with a simple and plausible result from point-set topology and estimates that will be familiar to anyone who has taken a first course in analysis Revised chapter on ruler-and-compass constructions that results in a more elegant theory and simpler proofs A section on constructions using an angle-trisector since it is an intriguing and direct application of the methods developed A new chapter that takes a retrospective look at what Galois actually did compared to what many assume he did Updated references This bestseller continues to deliver a rigorous yet engaging treatment of the subject while keeping pace with current educational requirements. More than 200 exercises and a wealth of historical notes augment the proofs, formulas, and theorems.

    Emphasis was on programming languages, compilers, operating systems, and the mathematical theory that supported these areas. Courses in theoretical computer science covered finite automata, regular expressions, context-free languages, and computability. In the 1970’s, the study of algorithms was added as an important component of theory. The emphasis was on making computers useful. Today, a fundamental change is taking place and the focus is more on a wealth of applications. There are many reasons for this change. The merging of computing and communications has played an important role. The enhanced ability to observe, collect, and store data in the natural sciences, in commerce, and in other fields calls for a change in our understanding of data and how to handle it in the modern setting. The emergence of the web and social networks as central aspects of daily life presents both opportunities and challenges for theory.While traditional areas of computer science remain highly important, increasingly researchers of the future will be involved with using computers to understand and extract usable information from massive data arising in applications, not just how to make computers useful on specific well-defined problems. With this in mind we have written this book to cover the theory we expect to be useful in the next 40 years, just as an understanding of automata theory, algorithms, and related topics gave students an advantage in the last 40 years. One of the major changes is an increase in emphasis on probability, statistics, and numerical methods.Early drafts of the book have been used for both undergraduate and graduate courses. Background material needed for an undergraduate course has been put in the appendix. For this reason, the appendix has homework problems.

    He describes his experiences as a long-term substitute teacher at a high school and middle school. He teaches math as he best knows how while schools throughout California make the transition to the Common Core standards. It is the 50th anniversary of key historical events including the JFK assassination and the Beatles’ arrival in the U.S. It is also the 50th anniversary of his first algebra course, the technical and personal memories of which he uses to guide him through the 21st century educational belief system that surrounds him.Includes a forward by Ze'ev Wurman.Available at Amazon: http://www.amazon.com/Teaching-Math-C... .

    It deals with the Trigonometry rules and processes that are commonly used in GCSE and A'level and dissects the rules to explain how and why they work. This book is part of a series so please look out for new books to follow.

    When complete, Beast Academy will provide a full, rigorous, and entertaining curriculum for aspiring math beasts in grades 2-5. The series consists of four two-book sets for each grade. The Guide book of each set presents the lessons and the Practice book provides exercises and problems to reinforce the lessons.Beast Academy 4D is the fourth set in the four-set series for Grade 4. Guide 4D delivers complete lessons to the students of Beast Academy in an engaging comic-book style. The companion book, Practice 4D, provides nearly 500 problems ranging from introductory level exercises to very challenging puzzles and word problems, to reinforce the lessons in the Guide.

    

    Problems of interest to gamblers led to the modern theory of probability, for example, and surreal numbers were inspired by the game of Go. Yet even with such groundbreaking findings and a wealth of popular-level books exploring puzzles and brainteasers, research in recreational mathematics has often been neglected. The Mathematics of Various Entertaining Subjects brings together authors from a variety of specialties to present fascinating problems and solutions in recreational mathematics.Contributors to the book show how sophisticated mathematics can help construct mazes that look like famous people, how the analysis of crossword puzzles has much in common with understanding epidemics, and how the theory of electrical circuits is useful in understanding the classic Towers of Hanoi puzzle. The card game SET is related to the theory of error-correcting codes, and simple tic-tac-toe takes on a new life when played on an affine plane. Inspirations for the book's wealth of problems include board games, card tricks, fake coins, flexagons, pencil puzzles, poker, and so much more.Looking at a plethora of eclectic games and puzzles, The Mathematics of Various Entertaining Subjects is sure to entertain, challenge, and inspire academic mathematicians and avid math enthusiasts alike.

    Without assuming anything beyond an introductory course in quantum field theory, it begins by guiding the reader through the basic concepts of field theory and gauge theory, general relativity, supersymmetry, supergravity, string theory and conformal field theory, before moving on to give a clear and rigorous account of AdS/CFT correspondence. The final section discusses the more specialised applications, including QCD, quark-gluon plasma and condensed matter. This book is self-contained and learner-focused, featuring numerous exercises and examples. It is essential reading for both students and researchers across the fields of particle, nuclear and condensed matter physics.

    A tasty dish for gourmets of popular math, The Proof and the Pudding offers a witty and flavorful blend of mathematical treats and gastronomic delights that reveal how life in the mathematical world is tantalizingly similar to life in the kitchen.Take a tricky Sudoku puzzle and a cake that fell. Henle shows you that the best way to deal with cooking disasters is also the best way to solve math problems. Or take an L-shaped billiard table and a sudden desire for Italian potstickers. He explains how preferring geometry over algebra (or algebra over geometry) is just like preferring a California roll to chicken tikka masala. Do you want to know why playfulness is rampant in math and cooking? Or how to turn stinky cheese into an awesome ice cream treat? It's all here: original math and original recipes plus the mathematical equivalents of vegetarianism, Asian fusion, and celebrity chefs.Pleasurable and lighthearted, The Proof and the Pudding is a feast for the intellect as well as the palate.

    These equations led to the prediction of radio waves, the realization that light is a type of electromagnetic wave, and the discovery of the special theory of relativity. In fact, almost all current descriptions of the fundamental laws of the universe can be viewed as deep generalizations of Maxwell's equations. Even more surprising is that these equations and their generalizations have led to some of the most important mathematical discoveries of the past thirty years. It seems that the mathematics behind Maxwell's equations is endless. The goal of this book is to explain to mathematicians the underlying physics behind electricity and magnetism and to show their connections to mathematics. Starting with Maxwell's equations, the reader is led to such topics as the special theory of relativity, differential forms, quantum mechanics, manifolds, tangent bundles, connections, and curvature.

    Devised by an expert on brain training, these mental challenges will fire up your powers of imagination and logic. There are handy tips if you need help, plus an answer key at the back!

    This book contains everything you need to know to get up and running quickly with this industry-leading software, with clear, helpful guidance on working with both the software and your data. Every chapter of this new edition has been updated with screenshots and steps that align with SPSS 23.0. You'll learn how to set up the software and organize your workflow, then delve deep into analysis to discover the power of SPSS capabilities. You'll discover the mechanics behind the calculations, perform predictive analysis, produce informative graphs, and maximize your data, even if it's been awhile since your last statistics class. SPSS is the leading statistical software for social sciences, marketing, health care, demography, government, education, data mining, and more. This powerful package gives you the tools you need to get more out of your data, and this book is your beginner-friendly guide to getting the most out of the software. Install and configure SPSS and learn the basics of how it works Master the process of getting data into SPSS and manipulating it to produce results See how to display data in dozens of different graphic formats to fit specific needs Make SPSS manufacture the numbers you want and take advantage of the many analysis options Discover ways to customize the SPSS interface and the look of your results, edit graphics and pivot tables, and program SPSS with Command Syntax Statistical analysis is crucial to so many industries, and accuracy and efficiency are crucial. SPSS offers you the capability to deliver, but you still must know how to take utmost advantage of the tools at your fingertips. SPSS Statistics For Dummies shows you how to handle data like a pro, with step-by-step instruction and expert advice.

    The style used is simple, yet thorough and rigorous. Each chapter ends with a broad set of exercises that range from the routine to the more challenging and thought-provoking. Solutions to selected exercises can be found at the end of the book. The book contains many interesting examples on topics such as electric circuits, the pendulum equation, the logistic equation, the Lotka-Volterra system, the Laplace Transform, etc., which introduce students to a number of interesting aspects of the theory and applications. The work is mainly intended for students of Mathematics, Physics, Engineering, Computer Science and other areas of the natural and social sciences that use ordinary differential equations, and who have a firm grasp of Calculus and a minimal understanding of the basic concepts used in Linear Algebra. It also studies a few more advanced topics, such as Stability Theory and Boundary Value Problems, which may be suitable for more advanced undergraduate or first-year graduate students. The second edition has been revised to correct minor errata, and features a number of carefully selected new exercises, together with more detailed explanations of some of the topics.

    Specifically the authors develop a unified mathematical framework in which a Bayesian formulation of the problem provides the bedrock for the derivation, development and analysis of algorithms; the many examples used in the text, together with the algorithms which are introduced and discussed, are all illustrated by the MATLAB software detailed in the book and made freely available online.The book is organized into nine chapters: the first contains a brief introduction to the mathematical tools around which the material is organized; the next four are concerned with discrete time dynamical systems and discrete time data; the last four are concerned with continuous time dynamical systems and continuous time data and are organized analogously to the corresponding discrete time chapters.This book is aimed at mathematical researchers interested in a systematic development of this interdisciplinary field, and at researchers from the geosciences, and a variety of other scientific fields, who use tools from data assimilation to combine data with time-dependent models. The numerous examples and illustrations make understanding of the theoretical underpinnings of data assimilation accessible. Furthermore, the examples, exercises and MATLAB software, make the book suitable for students in applied mathematics, either through a lecture course, or through self-study.

    The book first deals with basic counting principles, compositions and partitions, and generating functions. It then focuses on the structure of permutations, graph enumeration, and extremal combinatorics. Lastly, the text discusses supplemental topics, including error-correcting codes, properties of sequences, and magic squares.Strengthening the analytic flavor of the book, this Second Edition:Features a new chapter on analytic combinatorics and new sections on advanced applications of generating functions Demonstrates powerful techniques that do not require the residue theorem or complex integration Adds new exercises to all chapters, significantly extending coverage of the given topicsIntroduction to Enumerative and Analytic Combinatorics, Second Edition makes combinatorics more accessible, increasing interest in this rapidly expanding field.Outstanding Academic Title of the Year, Choice magazine, American Library Association.

    With chapters written by leading scientists across a variety of subdisciplines, it examines the field's influence on related research areas such as cognitive psychology, developmental psychology, clinical psychology, and neuroscience. The Handbook emphasizes examples and applications of the latest research, and will appeal to readers possessing various levels of modeling experience.The Oxford Handbook of Computational and mathematical Psychology covers the key developments in elementary cognitive mechanisms (signal detection, information processing, reinforcement learning), basic cognitive skills (perceptual judgment, categorization, episodic memory), higher-level cognition (Bayesian cognition, decision making, semantic memory, shape perception), modeling tools (Bayesian estimation and other new model comparison methods), and emerging new directions in computation and mathematical psychology (neurocognitive modeling, applications to clinical psychology, quantum cognition).The Handbook would make an ideal graduate-level textbook for courses in computational and mathematical psychology. Readers ranging from advanced undergraduates to experienced faculty members and researchers in virtually any area of psychology--including cognitive science and related social and behavioral sciences such as consumer behavior and communication--will find the text useful.

    It provides accessible self-contained explanations of mathematical principles, avoiding intimidating formal proofs. Worked examples and targeted exercises enable the student to master the realities of using numerical techniques for common needs such as solution of ordinary and partial differential equations, fitting experimental data, and simulation using particle and Monte Carlo methods. Topics are carefully selected and structured to build understanding, and illustrate key principles such as: accuracy, stability, order of convergence, iterative refinement, and computational effort estimation. Enrichment sections and in-depth footnotes form a springboard to more advanced material and provide additional background. Whether used for self-study, or as the basis of an accelerated introductory class, this compact textbook provides a thorough grounding in computational physics and engineering.

    Written by highly-qualified experts in the fields of computer science and mathematics, the book features accessible coverage for readers with various levels of experience and explores number theory in the context of programming without relying on advanced prerequisite knowledge and concepts in either area.Elementary Number Theory with Programming features comprehensive coverage of the methodology and applications of the most well-known theorems, problems, and concepts in number theory. Using standard mathematical applications within the programming field, the book presents modular arithmetic and prime decomposition, which are the basis of the public-private key system of cryptography. In addition, the book includes:Numerous examples, exercises, and research challenges in each chapter to encourage readers to work through the discussed concepts and ideas Select solutions to the chapter exercises in an appendix Plentiful sample computer programs to aid comprehension of the presented material for readers who have either never done any programming or need to improve their existing skill set A related website with links to select exercises An Instructor's Solutions Manual available on a companion website Elementary Number Theory with Programming is a useful textbook for undergraduate and graduate-level students majoring in mathematics or computer science, as well as an excellent supplement for teachers and students who would like to better understand and appreciate number theory and computer programming. The book is also an ideal reference for computer scientists, programmers, and researchers interested in the mathematical applications of programming.

    This powerful methodology can be used to analyze data from various fields, including medical and health outcomes research, business analytics and data science, ecology, fisheries, astronomy, transportation, insurance, economics, recreation, and sports. By harnessing the capabilities of the logistic model, analysts can better understand their data, make appropriate predictions and classifications, and determine the odds of one value of a predictor compared to another. Drawing on his many years of teaching logistic regression, using logistic-based models in research, and writing about the subject, Professor Hilbe focuses on the most important features of the logistic model. Serving as a guide between the author and readers, the book explains how to construct a logistic model, interpret coefficients and odds ratios, predict probabilities and their standard errors based on the model, and evaluate the model as to its fit. Using a variety of real data examples, mostly from health outcomes, the author offers a basic step-by-step guide to developing and interpreting observation and grouped logistic models as well as penalized and exact logistic regression. He also gives a step-by-step guide to modeling Bayesian logistic regression.R statistical software is used throughout the book to display the statistical models while SAS and Stata codes for all examples are included at the end of each chapter. The example code can be adapted to readers’ own analyses. All the code is available on the author’s website.

    This book introduces readers to state-of-the-art computational techniques used in the Bayesian analysis of DSGE models. The book covers Markov chain Monte Carlo techniques for linearized DSGE models, novel sequential Monte Carlo methods that can be used for parameter inference, and the estimation of nonlinear DSGE models based on particle filter approximations of the likelihood function. The theoretical foundations of the algorithms are discussed in depth, and detailed empirical applications and numerical illustrations are provided. The book also gives invaluable advice on how to tailor these algorithms to specific applications and assess the accuracy and reliability of the computations.Bayesian Estimation of DSGE Models is essential reading for graduate students, academic researchers, and practitioners at policy institutions.

    It walks you through the "how" and "why" to help you master the crucial operations that underpin every math class you'll ever take. With no-nonsense lessons, step-by-step instructions, practical examples, and plenty of practice, you'll learn how to manipulate non-whole numbers, tackle pesky fractions, deal with weights and measures, simplify algebraic expressions, and so much more. The "learn it - do it" style helps you move at your own pace, with lesson-sized explanations, examples, and practice. You also get access to 1,001 more practice problems online, where you can create customized quizzes and study the topics where you need the most help.Math can be hard -- and the basics in "U Can: Basic Math & Pre-Algebra For Dummies" lay the foundation for classes down the line. Consider this resource as your guide to math mastery, with step-by-step help for learning to: Put numbers in their place Make sense of fractions, decimals, and percents Get a grasp of basic geometry Simplify basic algebraic equationsBelieve it or not, math can be fun! And the better you understand it now, the more likely you are to do well in school, earn a degree, and get a good job. "U Can: Basic Math & Pre-Algebra For Dummies" gives you the skills, understanding, and confidence you need to conquer math once and for all.

    Studying these breakthroughs, transitions, and revolutions, their stumbling-blocks and their triumphs, can help illuminate the importance of the history of mathematics for its teaching, learning, and appreciation.Some of the turning points considered are the rise of the axiomatic method (most famously in Euclid), and the subsequent major changes in it (for example, by David Hilbert); the "wedding," via analytic geometry, of algebra and geometry; the "taming" of the infinitely small and the infinitely large; the passages from algebra to algebras, from geometry to geometries, and from arithmetic to arithmetics; and the revolutions in the late nineteenth and early twentieth centuries that resulted from Georg Cantor's creation of transfinite set theory. The origin of each turning point is discussed, along with the mathematicians involved and some of the mathematics that resulted. Problems and projects are included in each chapter to extend and increase understanding of the material. Substantial reference lists are also provided.Turning Points in the History of Mathematics will be a valuable resource for teachers of, and students in, courses in mathematics or its history. The book should also be of interest to anyone with a background in mathematics who wishes tolearn more about the important moments in its development.

    The modular approach and richness of content ensure that the book meets the needs of a variety of courses. College Algebra offers a wealth of examples with detailed, conceptual explanations, building a strong foundation in the material before asking students to apply what they’ve learned.

    The book’s main features include:Four practice exams in Calculus AB and four more in Calculus BCAll test questions answered with solutions explainedA detailed subject review covering topics for both examsAdvice to students on efficient use of their graphing calculatorsThe manual can be purchased alone or with an optional CD-ROM presenting two more practice tests with answers. One test is in Calculus AB, and the other in Calculus BC.BONUS ONLINE PRACTICE TEST: Students who purchase this book or package will also get FREE access to one additional full-length online AP Calculus test with all questions answered and explained.

    This book is an introduction to Mathematica. The goal is to provide a hands-on experience introducing the breadth of Mathematica, with a focus on ease of use. Readers get detailed instruction with examples for interactive learning and end-of-chapter exercises. Each chapter also contains authors tips from their combined 50+ years of Mathematica use.

    This treatment raises deep questions about the nature of human reason and its relation to the world. Dana Densmore's Questions for Discussion are intended as examples, to urge readers to think more carefully about what they are watching unfold, and to help them find their own questions in a genuine and exhilarating inquiry.

    He also offers a concise overview of algebra’s history and its many practical applications in modern life.Combining Gonick’s unique ability to make difficult topics fun, interesting, and easy-to-understand—while still relaying the essential information in a clear, organized and accurate format—The Cartoon Guide to Algebra is an essential supplement for students of all levels, in high school, college, and beyond.

    

    Mathematical Sciences Research Institute, Berkeley, California.

    This book gives a coherent account of the statistical theory in infinite-dimensional parameter spaces. The mathematical foundations include self-contained 'mini-courses' on the theory of Gaussian and empirical processes, on approximation and wavelet theory, and on the basic theory of function spaces. The theory of statistical inference in such models - hypothesis testing, estimation and confidence sets - is then presented within the minimax paradigm of decision theory. This includes the basic theory of convolution kernel and projection estimation, but also Bayesian nonparametrics and nonparametric maximum likelihood estimation. In a final chapter the theory of adaptive inference in nonparametric models is developed, including Lepski's method, wavelet thresholding, and adaptive inference for self-similar functions.