The aim of a course in real analysis should be to challenge and improve mathematical intuition rather than to verify it. The philosophy of this book is to focus attention on questions which give analysis its inherent fascination.

    Connecting games to math, science, and psychology, GameTek has grown to be one of the most popular parts of the show.This volume commemorates the anniversary with a collection of over seventy of the best segments, many with annotations and illustrations.With chapters on everything from Rock, Paper, Scissors to the Prisoner’s Dilemma to Player Engagement to Quasicrystals to Buddha’s Forbidden Games, GameTek is sure to delight not just game designers and players, but anyone who wants to learn about the world from a new perspective.Sections:• Game Theory• Math• Psychology• Science• Game Mechanics• Psychology Games• HistoryFrom the first time I heard it, the GameTek segment in The Dice Tower podcast became my favorite part of the show. Listening to Geoff is like going to your favorite lesson with your favorite teacher. He teaches about games (yay!) and does it in a very interesting way with lots of examples. He does amazing stuff. He knows about the construction of games, he knows the theory, he knows all that stuff behind the scenes that we gamers do not see when just playing a game and having fun.Ignacy Trzewiczek, Portal GamesThere are many hobby game 'experts' out there, dying to give you their opinion on how the industry works, how games work, what types of games are best, and so on. Geoff Engelstein is the expert that requires your attention. He is a scholar of games, and his research on games and other principles that apply to gaming is matched by none.Stephen Buonocore, Stronghold GamesOver the years, I’ve listened to a lot of people talk about board games, yet the short snippets that Geoff puts out are the ones that I find myself thinking about in the quiet of the night. His are the segments that you laugh at and say, “I have NO idea what you are talking about” — but later on use to show people just how intellectual you are.Tom Vasel, The Dice Tower

    Even the simplest numbers can become powerful forces when manipulated by politicians or the media, but in the case of the law, your liberty -- and your life -- can depend on the right calculation. In Math on Trial, mathematicians Leila Schneps and Coralie Colmez describe ten trials spanning from the nineteenth century to today, in which mathematical arguments were used -- and disastrously misused -- as evidence. They tell the stories of Sally Clark, who was accused of murdering her children by a doctor with a faulty sense of calculation; of nineteenth-century tycoon Hetty Green, whose dispute over her aunt's will became a signal case in the forensic use of mathematics; and of the case of Amanda Knox, in which a judge's misunderstanding of probability led him to discount critical evidence -- which might have kept her in jail. Offering a fresh angle on cases from the nineteenth-century Dreyfus affair to the murder trial of Dutch nurse Lucia de Berk, Schneps and Colmez show how the improper application of mathematical concepts can mean the difference between walking free and life in prison. A colorful narrative of mathematical abuse, Math on Trial blends courtroom drama, history, and math to show that legal expertise isn't't always enough to prove a person innocent.

    It can be freely downloaded and it works on multiple computer platforms. This book provides an elementary introduction to R. In each chapter, brief introductory sections are followed by code examples and comments from the computational and statistical viewpoint. A supplementary R package containing the datasets can be downloaded from the web.

    The book begins with an introduction to the language of statistics and then covers descriptive statistics and inferential statistics. Throughout, the author offers readers:- Difficulty Rating Index for each chapter′s material- Tips for doing and thinking about a statistical technique- Top tens for everything from the best ways to create a graph to the most effective techniques for data collection- Steps that break techniques down into a clear sequence of procedures- SPSS tips for executing each major statistical technique- Practice exercises at the end of each chapter, followed by worked out solutions.The book concludes with a statistical software sampler and a description of the best Internet sites for statistical information and data resources. Readers also have access to a website for downloading data that they can use to practice additional exercises from the book. Students and researchers will appreciate the book′s unhurried pace and thorough, friendly presentation.

    The first chapter describes basic features of the program and shows how to use it in simple arithmetic operations with scalars. The next two chapters focus on the topic of arrays (the basis of MATLAB), while the remaining text covers a wide range of other applications. Computer screens, tutorials, samples, and homework questions in math, science, and engineering, provide the student with the practical hands-on experience needed for total proficiency.

    The applications and computations in operations research are emphasized. Significantly revised, this text streamlines the coverage of the theory, applications, and computations of operations research. Numerical examples are effectively used to explain complex mathematical concepts. A separate chapter of fully analyzed applications aptly demonstrates the diverse use of OR. The popular commercial and tutorial software AMPL, Excel, Excel Solver, and Tora are used throughout the book to solve practical problems and to test theoretical concepts. New materials include Markov chains, TSP heuristics, new LP models, and a totally new simplex-based approach to LP sensitivity analysis.

    Data Science For Dummies is the perfect starting point for IT professionals and students interested in making sense of their organization’s massive data sets and applying their findings to real-world business scenarios. From uncovering rich data sources to managing large amounts of data within hardware and software limitations, ensuring consistency in reporting, merging various data sources, and beyond, you’ll develop the know-how you need to effectively interpret data and tell a story that can be understood by anyone in your organization. Provides a background in data science fundamentals before moving on to working with relational databases and unstructured data and preparing your data for analysis Details different data visualization techniques that can be used to showcase and summarize your data Explains both supervised and unsupervised machine learning, including regression, model validation, and clustering techniques Includes coverage of big data processing tools like MapReduce, Hadoop, Dremel, Storm, and Spark It’s a big, big data world out there – let Data Science For Dummies help you harness its power and gain a competitive edge for your organization.

    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...

    It provides a transition from elementary calculus to advanced courses in real and complex function theory and introduces the reader to some of the abstract thinking that pervades modern analysis.

    Gigabytes, exabytes (that’s one quintillion bytes) of data are sitting on servers across the world. So how can we start to access this explosion of information, this “big data,” and what can it tell us?   Erez Aiden and Jean-Baptiste Michel are two young scientists at Harvard who started to ask those questions. They teamed up with Google to create the Ngram Viewer, a Web-based tool that can chart words throughout the massive Google Books archive, sifting through billions of words to find fascinating cultural trends. On the day that the Ngram Viewer debuted in 2010, more than one million queries were run through it.   On the front lines of Big Data, Aiden and Michel realized that this big dataset—the Google Books archive that contains remarkable information on the human experience—had huge implications for looking at our shared human history. The tool they developed to delve into the data has enabled researchers to track how our language has evolved over time, how art has been censored, how fame can grow and fade, how nations trend toward war. How we remember and how we forget. And ultimately, how Big Data is changing the game for the sciences, humanities, politics, business, and our culture.

    It is the basis for a new approach to artificial intelligence that aims to program computers to use example data or past experience to solve a given problem. In this volume in the MIT Press Essential Knowledge series, Ethem Alpayd�n offers a concise and accessible overview of the new AI. This expanded edition offers new material on such challenges facing machine learning as privacy, security, accountability, and bias. Alpayd�n, author of a popular textbook on machine learning, explains that as Big Data has gotten bigger, the theory of machine learning--the foundation of efforts to process that data into knowledge--has also advanced. He describes the evolution of the field, explains important learning algorithms, and presents example applications. He discusses the use of machine learning algorithms for pattern recognition; artificial neural networks inspired by the human brain; algorithms that learn associations between instances; and reinforcement learning, when an autonomous agent learns to take actions to maximize reward. In a new chapter, he considers transparency, explainability, and fairness, and the ethical and legal implications of making decisions based on data.

    In studying number theory from such a perspective, mathematics majors are spared repetition and provided with new insights, while other students benefit from the consequent simplicity of the proofs for many theorems.Among the topics covered in this accessible, carefully designed introduction are multiplicativity-divisibility, including the fundamental theorem of arithmetic, combinatorial and computational number theory, congruences, arithmetic functions, primitive roots and prime numbers. Later chapters offer lucid treatments of quadratic congruences, additivity (including partition theory) and geometric number theory.Of particular importance in this text is the author's emphasis on the value of numerical examples in number theory and the role of computers in obtaining such examples. Exercises provide opportunities for constructing numerical tables with or without a computer. Students can then derive conjectures from such numerical tables, after which relevant theorems will seem natural and well-motivated..

    G. Wells predicted that statistical thinking would be as necessary for citizenship in a technological world as the ability to read and write. But in the twenty-first century, we are often overwhelmed by a baffling array of percentages and probabilities as we try to navigate in a world dominated by statistics. Cognitive scientist Gerd Gigerenzer says that because we haven't learned statistical thinking, we don't understand risk and uncertainty. In order to assess risk -- everything from the risk of an automobile accident to the certainty or uncertainty of some common medical screening tests -- we need a basic understanding of statistics.Astonishingly, doctors and lawyers don't understand risk any better than anyone else. Gigerenzer reports a study in which doctors were told the results of breast cancer screenings and then were asked to explain the risks of contracting breast cancer to a woman who received a positive result from a screening. The actual risk was small because the test gives many false positives. But nearly every physician in the study overstated the risk. Yet many people will have to make important health decisions based on such information and the interpretation of that information by their doctors.Gigerenzer explains that a major obstacle to our understanding of numbers is that we live with an illusion of certainty. Many of us believe that HIV tests, DNA fingerprinting, and the growing number of genetic tests are absolutely certain. But even DNA evidence can produce spurious matches. We cling to our illusion of certainty because the medical industry, insurance companies, investment advisers, and election campaigns have become purveyors of certainty, marketing it like a commodity.To avoid confusion, says Gigerenzer, we should rely on more understandable representations of risk, such as absolute risks. For example, it is said that a mammography screening reduces the risk of breast cancer by 25 percent. But in absolute risks, that means that out of every 1,000 women who do not participate in screening, 4 will die; while out of 1,000 women who do, 3 will die. A 25 percent risk reduction sounds much more significant than a benefit that 1 out of 1,000 women will reap.This eye-opening book explains how we can overcome our ignorance of numbers and better understand the risks we may be taking with our money, our health, and our lives.

    Its big-picture, calculus-based approach makes it an especially authoriatative reference for engineering and science majors. Now thoroughly update, this second edition includes vital new coverage of order statistics, best critical regions, likelihood ratio tests, and other key topics.