"A gem…An unforgettable account of one of the great moments in the history of human thought." —Steven PinkerProbing the life and work of Kurt Gödel, Incompleteness indelibly portrays the tortured genius whose vision rocked the stability of mathematical reasoning—and brought him to the edge of madness.

    In this heartfelt and passionate book, Frenkel shows that mathematics, far from occupying a specialist niche, goes to the heart of all matter, uniting us across cultures, time, and space.Love and Math tells two intertwined stories: of the wonders of mathematics and of one young man’s journey learning and living it. Having braved a discriminatory educational system to become one of the twenty-first century’s leading mathematicians, Frenkel now works on one of the biggest ideas to come out of math in the last 50 years: the Langlands Program. Considered by many to be a Grand Unified Theory of mathematics, the Langlands Program enables researchers to translate findings from one field to another so that they can solve problems, such as Fermat’s last theorem, that had seemed intractable before.At its core, Love and Math is a story about accessing a new way of thinking, which can enrich our lives and empower us to better understand the world and our place in it. It is an invitation to discover the magic hidden universe of mathematics.

    Admittedly real life wasn’t like that. But only, they argued, because we didn’t have enough data to be certain.Then the cracks began to appear. It proved impossible to predict exactly how three planets orbiting each other would move. Meteorologists discovered that the weather was truly chaotic – so dependent on small variations that it could never be predicted for more than a few days out. And the final nail in the coffin was quantum theory, showing that everything in the universe has probability at its heart.That gives human beings a problem. We understand the world through patterns. Randomness and probability will always be alien to us. But it’s time to plunge into this fascinating, shadowy world, because randomness crops up everywhere. Probability and statistics are the only way to get a grip on nature’s workings. They may even seal the fate of free will and predict how the universe will end.Forget Newton’s clockwork universe. Welcome to Dice World.

    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.

    The most fundamental differences are philosophical, and readers of this book will emerge with a clearer understandingof paradoxical-sounding concepts such as infinity, curved space, and imaginary numbers. The first few chapters are about general aspects of mathematical thought. These are followed by discussions of more specific topics, and the book closes with a chapter answering common sociological questionsabout the mathematical community (such as Is it true that mathematicians burn out at the age of 25?) It is the ideal introduction for anyone who wishes to deepen their understanding of mathematics.About the Series: Combining authority with wit, accessibility, and style, Very Short Introductions offer an introduction to some of life's most interesting topics. Written by experts for the newcomer, they demonstrate the finest contemporary thinking about the central problems and issues in hundredsof key topics, from philosophy to Freud, quantum theory to Islam.

    It features a visual presentation, designed to encourage learning; revised exercises to ensure clarity, balance and relevance; and clear commentary on the difficult subject of critical multivariable calculus topics.

    Covering every disorder routinely encountered in clinical practice, Frances provides the appropriate ICD-9-CM code for each one (the same code utilized in the DSM), a useful screening question, a colorful descriptive prototype, lucid diagnostic tips, and a discussion of other disorders that must be ruled out. The book closes with an index of the most common presenting symptoms, listing possible diagnoses that must be considered for each. Frances was instrumental in the development of past editions of the DSM and provides helpful cautions on questionable aspects of DSM-5.

    Major retailers are predicting everything from when their customers are pregnant to when they want a new pair of Chuck Taylors. It's a brave new world where seemingly meaningless data can be transformed into valuable insight to drive smart business decisions.But how does one exactly do data science? Do you have to hire one of these priests of the dark arts, the "data scientist," to extract this gold from your data? Nope.Data science is little more than using straight-forward steps to process raw data into actionable insight. And in Data Smart, author and data scientist John Foreman will show you how that's done within the familiar environment of a spreadsheet. Why a spreadsheet? It's comfortable! You get to look at the data every step of the way, building confidence as you learn the tricks of the trade. Plus, spreadsheets are a vendor-neutral place to learn data science without the hype. But don't let the Excel sheets fool you. This is a book for those serious about learning the analytic techniques, the math and the magic, behind big data.Each chapter will cover a different technique in a spreadsheet so you can follow along: - Mathematical optimization, including non-linear programming and genetic algorithms- Clustering via k-means, spherical k-means, and graph modularity- Data mining in graphs, such as outlier detection- Supervised AI through logistic regression, ensemble models, and bag-of-words models- Forecasting, seasonal adjustments, and prediction intervals through monte carlo simulation- Moving from spreadsheets into the R programming languageYou get your hands dirty as you work alongside John through each technique. But never fear, the topics are readily applicable and the author laces humor throughout. You'll even learn what a dead squirrel has to do with optimization modeling, which you no doubt are dying to know.

    Now in it's tenth edition, this text makes chemistry exciting to students by showing them why important concepts are relevant to their lives and future careers.

    The algorithms you'll use most often as a programmer have already been discovered, tested, and proven. If you want to take a hard pass on Knuth's brilliant but impenetrable theories and the dense multi-page proofs you'll find in most textbooks, this is the book for you. This fully-illustrated and engaging guide makes it easy for you to learn how to use algorithms effectively in your own programs.Grokking Algorithms is a disarming take on a core computer science topic. In it, you'll learn how to apply common algorithms to the practical problems you face in day-to-day life as a programmer. You'll start with problems like sorting and searching. As you build up your skills in thinking algorithmically, you'll tackle more complex concerns such as data compression or artificial intelligence. Whether you're writing business software, video games, mobile apps, or system utilities, you'll learn algorithmic techniques for solving problems that you thought were out of your grasp. For example, you'll be able to:Write a spell checker using graph algorithmsUnderstand how data compression works using Huffman codingIdentify problems that take too long to solve with naive algorithms, and attack them with algorithms that give you an approximate answer insteadEach carefully-presented example includes helpful diagrams and fully-annotated code samples in Python. By the end of this book, you will know some of the most widely applicable algorithms as well as how and when to use them.

    As he did so masterfully in Prime Obsession, Derbyshire brings the evolution of mathematical thinking to dramatic life by focusing on the key historical players. Unknown Quantity begins in the time of Abraham and Isaac and moves from Abel's proof to the higher levels of abstraction developed by Galois through modern-day advances. Derbyshire explains how a simple turn of thought from this plus this equals this to this plus what equals this? gave birth to a whole new way of perceiving the world. With a historian's narrative authority and a beloved teacher's clarity and passion, Derbyshire leads readers on an intellectually satisfying and pleasantly challenging historical and mathematical journey.

    This text has invited more than 4 million students into the study of this dynamic and essential discipline.The authors have restructured each chapter around a conceptual framework of five or six big ideas. An Overview draws students in and sets the stage for the rest of the chapter, each numbered Concept Head announces the beginning of a new concept, and Concept Check questions at the end of each chapter encourage students to assess their mastery of a given concept. New Inquiry Figures focus students on the experimental process, and new Research Method Figures illustrate important techniques in biology. Each chapter ends with a Scientific Inquiry Question that asks students to apply scientific investigation skills to the content of the chapter.

    Problems are designed to progressively enhance MATLAB-use proficiency, so students need not be familiar with MATLAB at the start of your course. Program scripts that are answers to exercises in the text are available at no charge in electronic form (see Teaching Resources below). *Supplement and Review Mini-Chapters after each of the text's three parts contain an extensive review list of terms, test-like problem sets with answers, and detailed suggestions on supplemental reading to reinforce students' learning and help them prepare for exams. *Read-Only Chapters, strategically placed to provide a change of pace during the course, provide informative, yet enjoyable reading for students. *Measurement Details and Results samples offer students a realistic perspective on the seldom-perfect nature of device characteristics, contrary to the way they are often represented in introductory texts. Content Highlig

    To its adherents, it is an elegant statement about learning from experience. To its opponents, it is subjectivity run amok.In the first-ever account of Bayes' rule for general readers, Sharon Bertsch McGrayne explores this controversial theorem and the human obsessions surrounding it. She traces its discovery by an amateur mathematician in the 1740s through its development into roughly its modern form by French scientist Pierre Simon Laplace. She reveals why respected statisticians rendered it professionally taboo for 150 years—at the same time that practitioners relied on it to solve crises involving great uncertainty and scanty information (Alan Turing's role in breaking Germany's Enigma code during World War II), and explains how the advent of off-the-shelf computer technology in the 1980s proved to be a game-changer. Today, Bayes' rule is used everywhere from DNA de-coding to Homeland Security.Drawing on primary source material and interviews with statisticians and other scientists, The Theory That Would Not Die is the riveting account of how a seemingly simple theorem ignited one of the greatest controversies of all time.

    This teaching guide is a must-have for new and experienced teachers alike. Over 1.3 million teachers around the world already know how the techniques in this book turn educators into classroom champions. With ideas for everything from boosting academic rigor, to improving classroom management, and inspiring student engagement, you will be able to strengthen your teaching practice right away.The first edition of Teach Like a Champion influenced thousands of educators because author Doug Lemov's teaching strategies are simple and powerful. Now, updated techniques and tools make it even easier to put students on the path to college readiness. Here are just a few of the brand new resources available in the 2.0 edition:Over 70 new video clips of real teachers modeling the techniques in the classroom (note: for online access of this content, please visit my.teachlikeachampion.com) A selection of never before seen techniques inspired by top teachers around the world Brand new structure emphasizing the most important techniques and step by step teaching guidelines Updated content reflecting the latest best practices from outstanding educators Organized by category and technique, the book's structure enables you to read start to finish, or dip in anywhere for the specific challenge you're seeking to address. With examples from outstanding teachers, videos, and additional, continuously updated resources at teachlikeachampion.com, you will soon be teaching like a champion. The classroom techniques you'll learn in this book can be adapted to suit any context. Find out why Teach Like a Champion is a "teaching Bible" for so many educators worldwide.