Working through the book you will develop an arsenal of techniques to help you unlock the meaning of definitions, theorems and proofs, solve problems, and write mathematics effectively. All the major methods of proof - direct method, cases, induction, contradiction and contrapositive - are featured. Concrete examples are used throughout, and you'll get plenty of practice on topics common to many courses such as divisors, Euclidean algorithms, modular arithmetic, equivalence relations, and injectivity and surjectivity of functions. The material has been tested by real students over many years so all the essentials are covered. With over 300 exercises to help you test your progress, you'll soon learn how to think like a mathematician.

    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.

    It proceeds from familiar concepts to the unfamiliar, from the concrete to the abstract. Readers consistently praise this outstanding text for its expository style and clarity of presentation. The applications version features a wide variety of interesting, contemporary applications. Clear, accessible, step-by-step explanations make the material crystal clear. Established the intricate thread of relationships between systems of equations, matrices, determinants, vectors, linear transformations and eigenvalues.

    'Big data', 'data science', and 'machine learning' have become familiar terms in the news, as statistical methods are brought to bear upon the enormous data sets of modern science and commerce. How did we get here? And where are we going? This book takes us on an exhilarating journey through the revolution in data analysis following the introduction of electronic computation in the 1950s. Beginning with classical inferential theories - Bayesian, frequentist, Fisherian - individual chapters take up a series of influential topics: survival analysis, logistic regression, empirical Bayes, the jackknife and bootstrap, random forests, neural networks, Markov chain Monte Carlo, inference after model selection, and dozens more. The distinctly modern approach integrates methodology and algorithms with statistical inference. The book ends with speculation on the future direction of statistics and data science.

    An effective testing strategy will deliver new functionality more aggressively, accelerate user feedback, and improve quality. However, for many developers, creating effective automated tests is a unique and unfamiliar challenge. xUnit Test Patterns is the definitive guide to writing automated tests using xUnit, the most popular unit testing framework in use today. Agile coach and test automation expert Gerard Meszaros describes 68 proven patterns for making tests easier to write, understand, and maintain. He then shows you how to make them more robust and repeatable--and far more cost-effective. Loaded with information, this book feels like three books in one. The first part is a detailed tutorial on test automation that covers everything from test strategy to in-depth test coding. The second part, a catalog of 18 frequently encountered "test smells," provides trouble-shooting guidelines to help you determine the root cause of problems and the most applicable patterns. The third part contains detailed descriptions of each pattern, including refactoring instructions illustrated by extensive code samples in multiple programming languages. Topics covered includeWriting better tests--and writing them faster The four phases of automated tests: fixture setup, exercising the system under test, result verification, and fixture teardown Improving test coverage by isolating software from its environment using Test Stubs and Mock Objects Designing software for greater testability Using test "smells" (including code smells, behavior smells, and project smells) to spot problems and know when and how to eliminate them Refactoring tests for greater simplicity, robustness, and execution speed This book will benefit developers, managers, and testers working with any agile or conventional development process, whether doing test-driven development or writing the tests last. While the patterns and smells are especially applicable to all members of the xUnit family, they also apply to next-generation behavior-driven development frameworks such as RSpec and JBehave and to other kinds of test automation tools, including recorded test tools and data-driven test tools such as Fit and FitNesse.Visual Summary of the Pattern Language Foreword Preface Acknowledgments Introduction Refactoring a Test PART I: The Narratives Chapter 1 A Brief Tour Chapter 2 Test Smells Chapter 3 Goals of Test Automation Chapter 4 Philosophy of Test Automation Chapter 5 Principles of Test Automation Chapter 6 Test Automation Strategy Chapter 7 xUnit Basics Chapter 8 Transient Fixture Management Chapter 9 Persistent Fixture Management Chapter 10 Result Verification Chapter 11 Using Test Doubles Chapter 12 Organizing Our Tests Chapter 13 Testing with Databases Chapter 14 A Roadmap to Effective Test Automation PART II: The Test Smells Chapter 15 Code Smells Chapter 16 Behavior Smells Chapter 17 Project Smells PART III: The Patterns Chapter 18 Test Strategy Patterns Chapter 19 xUnit Basics Patterns Chapter 20 Fixture Setup Patterns Chapter 21 Result Verification Patterns Chapter 22 Fixture Teardown Patterns Chapter 23 Test Double Patterns Chapter 24 Test Organization Patterns Chapter 25 Database Patterns Chapter 26 Design-for-Testability Patterns Chapter 27 Value Patterns PART IV: Appendixes Appendix A Test Refactorings Appendix B xUnit Terminology Appendix C xUnit Family Members Appendix D Tools Appendix E Goals and Principles Appendix F Smells, Aliases, and Causes Appendix G Patterns, Aliases, and Variations Glossary References Index "

    Hundreds of thousands of Python developers around the world rely on Python for general-purpose tasks, Internet scripting, systems programming, user interfaces, and product customization. Available on all major computing platforms, including commercial versions of Unix, Linux, Windows, and Mac OS X, Python is portable, powerful and remarkable easy to use.With its convenient, quick-reference format, "Python Pocket Reference," 3rd Edition is the perfect on-the-job reference. More importantly, it's now been refreshed to cover the language's latest release, Python 2.4. For experienced Python developers, this book is a compact toolbox that delivers need-to-know information at the flip of a page. This third edition also includes an easy-lookup index to help developers find answers fast!Python 2.4 is more than just optimization and library enhancements; it's also chock full of bug fixes and upgrades. And these changes are addressed in the "Python Pocket Reference," 3rd Edition. New language features, new and upgraded built-ins, and new and upgraded modules and packages--they're all clarified in detail.The "Python Pocket Reference," 3rd Edition serves as the perfect companion to "Learning Python" and "Programming Python."

    A remarkable pictorial discussion of the curved space-time we call home, it achieves even greater impact through the use of 141 excellent illustrations. This is the first sustained visual account of many important topics in relativity theory that up till now have only been treated separately.Finding a perfect analogy in the situation of the geometrical characters in Flatland, Professor Rucker continues the adventures of the two-dimensional world visited by a three-dimensional being to explain our three-dimensional world in terms of the fourth dimension. Following this adventure into the fourth dimension, the author discusses non-Euclidean geometry, curved space, time as a higher dimension, special relativity, time travel, and the shape of space-time. The mathematics is sound throughout, but the casual reader may skip those few sections that seem too purely mathematical and still follow the line of argument. Readable and interesting in itself, the annotated bibliography is a valuable guide to further study.Professor Rucker teaches mathematics at the State University of New York in Geneseo. Students and laymen will find his discussion to be unusually stimulating. Experienced mathematicians and physicists will find a great deal of original material here and many unexpected novelties. Annotated bibliography. 44 problems.

    We are living in an age where data comes in abundance, and thanks to the self-learning algorithms from the field of machine learning, we can turn this data into knowledge. Automated speech recognition on our smart phones, web search engines, e-mail spam filters, the recommendation systems of our favorite movie streaming services – machine learning makes it all possible.Thanks to the many powerful open-source libraries that have been developed in recent years, machine learning is now right at our fingertips. Python provides the perfect environment to build machine learning systems productively.This book will teach you the fundamentals of machine learning and how to utilize these in real-world applications using Python. Step-by-step, you will expand your skill set with the best practices for transforming raw data into useful information, developing learning algorithms efficiently, and evaluating results.You will discover the different problem categories that machine learning can solve and explore how to classify objects, predict continuous outcomes with regression analysis, and find hidden structures in data via clustering. You will build your own machine learning system for sentiment analysis and finally, learn how to embed your model into a web app to share with the world

    The Art of Problem Solving, Volume 1, is the classic problem solving textbook used by many successful MATHCOUNTS programs, and have been an important building block for students who, like the authors, performed well enough on the American Mathematics Contest series to qualify for the Math Olympiad Summer Program which trains students for the United States International Math Olympiad team.Volume 1 is appropriate for students just beginning in math contests. MATHCOUNTS and novice high school students particularly have found it invaluable. Although the Art of Problem Solving is widely used by students preparing for mathematics competitions, the book is not just a collection of tricks. The emphasis on learning and understanding methods rather than memorizing formulas enables students to solve large classes of problems beyond those presented in the book.Speaking of problems, the Art of Problem Solving, Volume 1, contains over 500 examples and exercises culled from such contests as MATHCOUNTS, the Mandelbrot Competition, the AMC tests, and ARML. Full solutions (not just answers!) are available for all the problems in the solution manual.

    But as anyone who has ever opened up a spreadsheet packed with seemingly infinite lines of data knows, numbers aren't enough: we need to know how to make those numbers talk. In The Model Thinker, social scientist Scott E. Page shows us the mathematical, statistical, and computational models—from linear regression to random walks and far beyond—that can turn anyone into a genius. At the core of the book is Page's "many-model paradigm," which shows the reader how to apply multiple models to organize the data, leading to wiser choices, more accurate predictions, and more robust designs. The Model Thinker provides a toolkit for business people, students, scientists, pollsters, and bloggers to make them better, clearer thinkers, able to leverage data and information to their advantage.

    Until now. This practical guide provides the first comprehensive overview of software architecture's many aspects. You'll examine architectural characteristics, architectural patterns, component determination, diagramming and presenting architecture, evolutionary architecture, and many other topics.Authors Neal Ford and Mark Richards help you learn through examples in a variety of popular programming languages, such as Java, C#, JavaScript, and others. You'll focus on architecture principles with examples that apply across all technology stacks.

    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.

    Intuition and computational abilities are stressed. Original material on DE and multiple integrals has been expanded.

    This guide also helps you understand the many data-mining techniques in use today.Based on an MBA course Provost has taught at New York University over the past ten years, Data Science for Business provides examples of real-world business problems to illustrate these principles. You’ll not only learn how to improve communication between business stakeholders and data scientists, but also how participate intelligently in your company’s data science projects. You’ll also discover how to think data-analytically, and fully appreciate how data science methods can support business decision-making.Understand how data science fits in your organization—and how you can use it for competitive advantageTreat data as a business asset that requires careful investment if you’re to gain real valueApproach business problems data-analytically, using the data-mining process to gather good data in the most appropriate wayLearn general concepts for actually extracting knowledge from dataApply data science principles when interviewing data science job candidates

    Written by one of the foremost experts on mathematical magic, it employs considerable historical data to summarize all previous work in this field. It is also a creative examination of laws and their exemplification, with scores of new tricks, insights, and demonstrations. Dozens of topological tricks are explained, and dozens of manipulation tricks are aligned with mathematical law.Nontechnical, detailed, and clear, this volume contains 115 sections discussing tricks with cards, dice, coins, etc.; topological tricks with handkerchiefs, cards, etc.; geometrical vanishing effects; demonstrations with pure numbers; and dozens of other topics. You will learn how a Moebius strip works and how a Curry square can "prove" that the whole is not equal to the sum of its parts.No skill at sleight of hand is needed to perform the more than 500 tricks described because mathematics guarantees their success. Detailed examination of laws and their application permits you to create your own problems and effects.