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.

    This book leads the reader from simple graphs through planar graphs, Euler's formula, Platonic graphs, coloring, the genus of a graph, Euler walks, Hamilton walks, more. Includes exercises. 1976 edition.

    However, Python’s unique strengths, charms, and expressiveness can be hard to grasp, and there are hidden pitfalls that can easily trip you up. This second edition of Effective Python will help you master a truly “Pythonic” approach to programming, harnessing Python’s full power to write exceptionally robust and well-performing code. Using the concise, scenario-driven style pioneered in Scott Meyers’ best-selling Effective C++, Brett Slatkin brings together 90 Python best practices, tips, and shortcuts, and explains them with realistic code examples so that you can embrace Python with confidence. Drawing on years of experience building Python infrastructure at Google, Slatkin uncovers little-known quirks and idioms that powerfully impact code behavior and performance. You’ll understand the best way to accomplish key tasks so you can write code that’s easier to understand, maintain, and improve. In addition to even more advice, this new edition substantially revises all items from the first edition to reflect how best practices have evolved. Key features include 30 new actionable guidelines for all major areas of Python Detailed explanations and examples of statements, expressions, and built-in types Best practices for writing functions that clarify intention, promote reuse, and avoid bugs Better techniques and idioms for using comprehensions and generator functions Coverage of how to accurately express behaviors with classes and interfaces Guidance on how to avoid pitfalls with metaclasses and dynamic attributes More efficient and clear approaches to concurrency and parallelism Solutions for optimizing and hardening to maximize performance and quality Techniques and built-in modules that aid in debugging and testing Tools and best practices for collaborative development   Effective Python will prepare growing programmers to make a big impact using Python.

    From Mary, Queen of Scots, trapped by her own code, to the Navajo Code Talkers who helped the Allies win World War II, to the incredible (and incredibly simple) logisitical breakthrough that made Internet commerce secure, The Code Book tells the story of the most powerful intellectual weapon ever known: secrecy.Throughout the text are clear technical and mathematical explanations, and portraits of the remarkable personalities who wrote and broke the world’s most difficult codes. Accessible, compelling, and remarkably far-reaching, this book will forever alter your view of history and what drives it. It will also make you wonder how private that e-mail you just sent really is.

    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.

    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.

    

    Written by two of the best-known names in categorical logic, Conceptual Mathematics is the first book to apply categories to the most elementary mathematics. It thus serves two purposes: first, to provide a key to mathematics for the general reader or beginning student; and second, to furnish an easy introduction to categories for computer scientists, logicians, physicists, and linguists who want to gain some familiarity with the categorical method without initially committing themselves to extended study.

    . . Nothing less than a major contribution to the scientific culture of this world." — The New York Times Book ReviewThis major survey of mathematics, featuring the work of 18 outstanding Russian mathematicians and including material on both elementary and advanced levels, encompasses 20 prime subject areas in mathematics in terms of their simple origins and their subsequent sophisticated developement. As Professor Morris Kline of New York University noted, "This unique work presents the amazing panorama of mathematics proper. It is the best answer in print to what mathematics contains both on the elementary and advanced levels."Beginning with an overview and analysis of mathematics, the first of three major divisions of the book progresses to an exploration of analytic geometry, algebra, and ordinary differential equations. The second part introduces partial differential equations, along with theories of curves and surfaces, the calculus of variations, and functions of a complex variable. It furthur examines prime numbers, the theory of probability, approximations, and the role of computers in mathematics. The theory of functions of a real variable opens the final section, followed by discussions of linear algebra and nonEuclidian geometry, topology, functional analysis, and groups and other algebraic systems.Thorough, coherent explanations of each topic are further augumented by numerous illustrative figures, and every chapter concludes with a suggested reading list. Formerly issued as a three-volume set, this mathematical masterpiece is now available in a convenient and modestly priced one-volume edition, perfect for study or reference."This is a masterful English translation of a stupendous and formidable mathematical masterpiece . . ." — Social Science

    By presenting actual experiences and analyzing them as they are described, the author conveys the developmental thought processes employed and shows a style of thinking that leads to successful results is something that can be learned. Along with spectacular successes, the author also conveys how failures contributed to shaping the thought processes. Provides the reader with a style of thinking that will enhance a person's ability to function as a problem-solver of complex technical issues. Consists of a collection of stories about the author's participation in significant discoveries, relating how those discoveries came about and, most importantly, provides analysis about the thought processes and reasoning that took place as the author and his associates progressed through engineering problems.

    Kai-Fu Lee—one of the world’s most respected experts on AI and China—reveals that China has suddenly caught up to the US at an astonishingly rapid and unexpected pace.In AI Superpowers, Kai-Fu Lee argues powerfully that because of these unprecedented developments in AI, dramatic changes will be happening much sooner than many of us expected. Indeed, as the US-Sino AI competition begins to heat up, Lee urges the US and China to both accept and to embrace the great responsibilities that come with significant technological power.Most experts already say that AI will have a devastating impact on blue-collar jobs. But Lee predicts that Chinese and American AI will have a strong impact on white-collar jobs as well. Is universal basic income the solution? In Lee’s opinion, probably not.  But he provides a clear description of which jobs will be affected and how soon, which jobs can be enhanced with AI, and most importantly, how we can provide solutions to some of the most profound changes in human history that are coming soon.

    Sold in over 85 countries and translated into more than 5 languages.---------------Want to get started on data science?Our promise: no math added.This book has been written in layman's terms as a gentle introduction to data science and its algorithms. Each algorithm has its own dedicated chapter that explains how it works, and shows an example of a real-world application. To help you grasp key concepts, we stick to intuitive explanations and visuals.Popular concepts covered include:- A/B Testing- Anomaly Detection- Association Rules- Clustering- Decision Trees and Random Forests- Regression Analysis- Social Network Analysis- Neural NetworksFeatures:- Intuitive explanations and visuals- Real-world applications to illustrate each algorithm- Point summaries at the end of each chapter- Reference sheets comparing the pros and cons of algorithms- Glossary list of commonly-used termsWith this book, we hope to give you a practical understanding of data science, so that you, too, can leverage its strengths in making better decisions.

    Jon has done a wonderful job of updating the material. I am very impressed at how fresh the new examples seem." - Steve McConnell, author, Code CompleteWhen programmers list their favorite books, Jon Bentley's collection of programming pearls is commonly included among the classics. Just as natural pearls grow from grains of sand that irritate oysters, programming pearls have grown from real problems that have irritated real programmers. With origins beyond solid engineering, in the realm of insight and creativity, Bentley's pearls offer unique and clever solutions to those nagging problems. Illustrated by programs designed as much for fun as for instruction, the book is filled with lucid and witty descriptions of practical programming techniques and fundamental design principles. It is not at all surprising that Programming Pearls has been so highly valued by programmers at every level of experience. In this revision, the first in 14 years, Bentley has substantially updated his essays to reflect current programming methods and environments. In addition, there are three new essays on (1) testing, debugging, and timing; (2) set representations; and (3) string problems. All the original programs have been rewritten, and an equal amount of new code has been generated. Implementations of all the programs, in C or C++, are now available on the Web.What remains the same in this new edition is Bentley's focus on the hard core of programming problems and his delivery of workable solutions to those problems. Whether you are new to Bentley's classic or are revisiting his work for some fresh insight, this book is sure to make your own list of favorites.

    It’s time we stand face-to-digital-face with the true powers and limitations of the algorithms that already automate important decisions in healthcare, transportation, crime, and commerce. Hello World is indispensable preparation for the moral quandaries of a world run by code, and with the unfailingly entertaining Hannah Fry as our guide, we’ll be discussing these issues long after the last page is turned.

    Python is considered easy to learn, but there's no quicker way to mastery of the language than learning from an expert teacher. This edition of "Learning Python" puts you in the hands of two expert teachers, Mark Lutz and David Ascher, whose friendly, well-structured prose has guided many a programmer to proficiency with the language. "Learning Python," Second Edition, offers programmers a comprehensive learning tool for Python and object-oriented programming. Thoroughly updated for the numerous language and class presentation changes that have taken place since the release of the first edition in 1999, this guide introduces the basic elements of the latest release of Python 2.3 and covers new features, such as list comprehensions, nested scopes, and iterators/generators. Beyond language features, this edition of "Learning Python" also includes new context for less-experienced programmers, including fresh overviews of object-oriented programming and dynamic typing, new discussions of program launch and configuration options, new coverage of documentation sources, and more. There are also new use cases throughout to make the application of language features more concrete. The first part of "Learning Python" gives programmers all the information they'll need to understand and construct programs in the Python language, including types, operators, statements, classes, functions, modules and exceptions. The authors then present more advanced material, showing how Python performs common tasks by offering real applications and the libraries available for those applications. Each chapter ends with a series of exercises that will test your Python skills and measure your understanding."Learning Python," Second Edition is a self-paced book that allows readers to focus on the core Python language in depth. As you work through the book, you'll gain a deep and complete understanding of the Python language that will help you to understand the larger application-level examples that you'll encounter on your own. If you're interested in learning Python--and want to do so quickly and efficiently--then "Learning Python," Second Edition is your best choice.