Today, unfortunately, the traditional place of mathematics in education is in grave danger. The teaching and learning of mathematics has degenerated into the realm of rote memorization, the outcome of which leads to satisfactory formal ability but does not lead to real understanding or to greater intellectual independence. This new edition of Richard Courant's and Herbert Robbins's classic work seeks to address this problem. Its goal is to put the meaning back into mathematics.Written for beginners and scholars, for students and teachers, for philosophers and engineers, What is Mathematics? Second Edition is a sparkling collection of mathematical gems that offers an entertaining and accessible portrait of the mathematical world. Covering everything from natural numbers and the number system to geometrical constructions and projective geometry, from topology and calculus to matters of principle and the Continuum Hypothesis, this fascinating survey allows readers to delve into mathematics as an organic whole rather than an empty drill in problem solving. With chapters largely independent of one another and sections that lead upward from basic to more advanced discussions, readers can easily pick and choose areas of particular interest without impairing their understanding of subsequent parts.Brought up to date with a new chapter by Ian Stewart, What is Mathematics? Second Edition offers new insights into recent mathematical developments and describes proofs of the Four-Color Theorem and Fermat's Last Theorem, problems that were still open when Courant and Robbins wrote this masterpiece, but ones that have since been solved.Formal mathematics is like spelling and grammar - a matter of the correct application of local rules. Meaningful mathematics is like journalism - it tells an interesting story. But unlike some journalism, the story has to be true. The best mathematics is like literature - it brings a story to life before your eyes and involves you in it, intellectually and emotionally. What is Mathematics is like a fine piece of literature - it opens a window onto the world of mathematics for anyone interested to view.

    In 2000, Chertavian dedicated his life to closing that divide and Year Up was born.Year Up is an intensive program that offers low income young adults training, mentorship, internships, and ultimately real jobs—often with Fortune 500 companies. 85 percent of program graduates are employed or in full-time college within four months of graduation. Today, Year Up serves more than 1,300 students in nine cities across the nation.Following a Year Up class from admissions through graduation, A Year Up lets students share—in their own words—the challenges, failures, and personal successes they’ve experienced during their program year. This deeply moving and inspirational story also explains Chertavian’s philosophy and the program’s genesis, offering a road map for real change in our country and a beacon for young adults who want the opportunity to enter the economic mainstream.

    And then we wonder why software is notorious for being delivered late and full of bugs, while other engineers routinely deliver finished bridges, automobiles, electrical appliances, etc., on time and with only minor defects. This book sets out to redress this imbalance. Members of my advanced development team at Adobe who took the course based on the same material all benefited greatly from the time invested. It may appear as a highly technical text intended only for computer scientists, but it should be required reading for all practicing software engineers." --Martin Newell, Adobe Fellow"The book contains some of the most beautiful code I have ever seen." --Bjarne Stroustrup, Designer of C++"I am happy to see the content of Alex's course, the development and teaching of which I strongly supported as the CTO of Silicon Graphics, now available to all programmers in this elegant little book." --Forest Baskett, General Partner, New Enterprise Associates"Paul's patience and architectural experience helped to organize Alex's mathematical approach into a tightly-structured edifice--an impressive feat!" --Robert W. Taylor, Founder of Xerox PARC CSL and DEC Systems Research Center Elements of Programming provides a different understanding of programming than is presented elsewhere. Its major premise is that practical programming, like other areas of science and engineering, must be based on a solid mathematical foundation. The book shows that algorithms implemented in a real programming language, such as C++, can operate in the most general mathematical setting. For example, the fast exponentiation algorithm is defined to work with any associative operation. Using abstract algorithms leads to efficient, reliable, secure, and economical software.This is not an easy book. Nor is it a compilation of tips and tricks for incremental improvements in your programming skills. The book's value is more fundamental and, ultimately, more critical for insight into programming. To benefit fully, you will need to work through it from beginning to end, reading the code, proving the lemmas, and doing the exercises. When finished, you will see how the application of the deductive method to your programs assures that your system's software components will work together and behave as they must.The book presents a number of algorithms and requirements for types on which they are defined. The code for these descriptions--also available on the Web--is written in a small subset of C++ meant to be accessible to any experienced programmer. This subset is defined in a special language appendix coauthored by Sean Parent and Bjarne Stroustrup.Whether you are a software developer, or any other professional for whom programming is an important activity, or a committed student, you will come to understand what the book's experienced authors have been teaching and demonstrating for years--that mathematics is good for programming, and that theory is good for practice.

    With an accessible and lively writing style, it introduces modern techniques to what can often be a formal and intimidating subject. Readers are led from the physics of flat spacetime (special relativity), through the intricacies of differential geometry and Einstein's equations, and on to exciting applications such as black holes, gravitational radiation, and cosmology.

    It is designed as a reference for students in the physical sciences and engineering.

    This foundational text is the first comprehensive introduction to statistical natural language processing (NLP) to appear. The book contains all the theory and algorithms needed for building NLP tools. It provides broad but rigorous coverage of mathematical and linguistic foundations, as well as detailed discussion of statistical methods, allowing students and researchers to construct their own implementations. The book covers collocation finding, word sense disambiguation, probabilistic parsing, information retrieval, and other applications.

    With SQL and this task-based guide to it, you can do it too—no programming experience required!After going over the relational database model and SQL syntax in the first few chapters, veteran author Chris Fehily launches into the tasks that will get you comfortable with SQL fast. In addition to explaining SQL basics, this updated reference covers the ANSI SQL:2003 standard and contains a wealth of brand-new information, including a new chapter on set operations and common tasks, well-placed optimization tips to make your queries run fast, sidebars on advanced topics, and added IBM DB2 coverage.Best of all, the book's examples were tested on the latest versions of Microsoft Access, Microsoft SQL Server, Oracle, IBM DB2, MySQL, and PostgreSQL. On the companion Web site, you can download the SQL scripts and sample database for all these systems and put your knowledge to work immediately on a real database..

    Employing a methodology that is primarily learning by example and “thinking with our eyes,” this manual features graphs and practical analytical techniques that can be applied to a broad range of data analysis tools—including the most commonly used Microsoft Excel. This approach is particularly valuable to those who need to make sense of quantitative business data by discerning meaningful patterns, trends, relationships, and exceptions that reveal business performance, potential problems and opportunities, and hints about the future. It provides practical skills that are useful to managers at all levels and to those interested in keeping a keen eye on their business.

    Like earlier editions of the book, physical concepts are highlighted while also giving necessary attention to math-ematical techniques. Both theory and modeling are developed from simple beginnings so that they can be readily extended to new and complex situations. Beginning in Ch. 3, students are introduced to new concepts critical to analyzing power systems, including coverage of both balanced and unbalanced operating conditions. The authors incorporate new tools and material to aid students with design issues and reflect recent trends in the field. Each book now contains a CD with Power World software. This package is commonly used in industry and will enable students to analyze and simulate power systems. The authors use the software to extend, rather than replace, the fully worked examples provided in previous editions. In the new edition, each Power World Simulator example includes a fully worked hand solution of the problem along with a Power World Simulator case (except when the problem size makes it impractical). The new edition also contains updated case studies on recent trends in the Power Systems field, including coverage of deregulation, increased power demand, economics, and alternative sources of energy. These case studies are derived from real life situations.

    In Turing’s Cathedral, George Dyson focuses on a small group of men and women, led by John von Neumann at the Institute for Advanced Study in Princeton, New Jersey, who built one of the first computers to realize Alan Turing’s vision of a Universal Machine. Their work would break the distinction between numbers that mean things and numbers that do things—and our universe would never be the same. Using five kilobytes of memory (the amount allocated to displaying the cursor on a computer desktop of today), they achieved unprecedented success in both weather prediction and nuclear weapons design, while tackling, in their spare time, problems ranging from the evolution of viruses to the evolution of stars. Dyson’s account, both historic and prophetic, sheds important new light on how the digital universe exploded in the aftermath of World War II. The proliferation of both codes and machines was paralleled by two historic developments: the decoding of self-replicating sequences in biology and the invention of the hydrogen bomb. It’s no coincidence that the most destructive and the most constructive of human inventions appeared at exactly the same time.  How did code take over the world? In retracing how Alan Turing’s one-dimensional model became John von Neumann’s two-dimensional implementation, Turing’s Cathedral offers a series of provocative suggestions as to where the digital universe, now fully three-dimensional, may be heading next.

    Aimed at accountants or readers of other career paths, this book helps them build their decision making skills and understand how to use accounting information to make quality business decisions.

    But in spirit, the title is apt, as the book does cover a much broader range of topics than a typical introductory book on mathematical statistics. This book is for people who want to learn probability and statistics quickly. It is suitable for graduate or advanced undergraduate students in computer science, mathematics, statistics, and related disciplines. The book includes modern topics like nonparametric curve estimation, bootstrapping, and clas- sification, topics that are usually relegated to follow-up courses. The reader is presumed to know calculus and a little linear algebra. No previous knowledge of probability and statistics is required. Statistics, data mining, and machine learning are all concerned with collecting and analyzing data. For some time, statistics research was con- ducted in statistics departments while data mining and machine learning re- search was conducted in computer science departments. Statisticians thought that computer scientists were reinventing the wheel. Computer scientists thought that statistical theory didn't apply to their problems. Things are changing. Statisticians now recognize that computer scientists are making novel contributions while computer scientists now recognize the generality of statistical theory and methodology. Clever data mining algo- rithms are more scalable than statisticians ever thought possible. Formal sta- tistical theory is more pervasive than computer scientists had realized.

    This supplement will cater to the requirements of students by covering all important topics of Laplace transformation, Matrices, Numerical Methods. Further enhanced is its usability by inclusion of chapter end questions in sync with student needs. Table of contents: 1. Basic Concepts 2. An Introduction to Modeling and Qualitative Methods 3. Classification of First-Order Differential Equations 4. Separable First-Order Differential Equations 5. Exact First-order Differential Equations 6. Linear First-Order Differential Equations 7. Applications of First-Order Differential Equations 8. Linear Differential Equations: Theory of Solutions 9. Second-Order Linear Homogeneous Differential Equations with Constant Coefficients 10. nth-Order Linear Homogeneous Differential Equations with Constant Coefficients 11. The Method of Undetermined Coefficients 12. Variation of Parameters 13. Initial-Value Problems for Linear Differential Equations 14. Applications of Second-Order Linear Differential Equations 15. Matrices 16. eAt 17. Reduction of Linear Differential Equations to a System of First-Order Equations 18. Existence and Uniqueness of Solutions 19. Graphical and Numerical Methods for Solving First-Order Differential Equations 20. Further Numerical Methods for Solving First-Order Differential Equations 21. Numerical Methods for Solving Second-Order Differential Equations Via Systems 22. The Laplace Transform 23. Inverse Laplace Transforms 24. Convolutions and the Unit Step Function 25. Solutions of Linear Differential Equations with Constant Coefficients by Laplace Transforms 26. Solutions of Linear?Systems by Laplace Transforms 27. Solutions of Linear Differential Equations with Constant Coefficients by Matrix Methods 28. Power Series Solutions of Linear Differential Equations with Variable Coefficients 29. Special Functions 30. Series Solutions N

    This simple way to manage your household income and expenses includes a stylish cover, coin purse, places for your checkbook and check register, memo pad, debit card holders, and extra cash-management envelopes.

    Tony goes beyond teaching you how to use Lightroom. Tony shows you why and when to use each feature to create stunning, natural photos. When Lightroom isn t the best tool, Tony suggests better alternatives. Combining the benefits of video training and book learning, this video book gives you over 14 hours of video and dozens of free presets and raw images to practice with. If you learn better with video, watch the video training and refer to the book for quick reference. If you prefer reading, the book is concise and practical, and each chapter links to relevant videos when you want to understand a topic more deeply or see it used in the real world. Tony covers every aspect of Lightroom in-depth, but structures his teaching so that both beginner and advanced photographers can learn as efficiently as possible. If you just want a quick start, you can watch the first video or read the first chapter and you'll be organizing and editing your pictures in less than an hour. If you want to know more about a specific feature, switch to that video or jump to that chapter in the ebook. If you want to know everything about Lightroom, watch the videos and read the book from start to finish.