It provides a simple, thorough survey of elementary topics, starting with set theory and advancing to metric and topological spaces, connectedness, and compactness. 1975 edition.

    Aczel turns his sights on probability theory -- the branch of mathematics that measures the likelihood of a random event. He explains probability in clear, layman's terms, and shows its practical applications. What is commonly called luck has mathematical roots and in Chance, you'll learn to increase your odds of success in everything from true love to the stock market. For thousands of years, the twin forces of chance and mischance have beguiled humanity like none other. Why does fortune smile on some people, and smirk on others? What is luck, and why does it so often visit the undeserving? How can we predict the random events happening around us? Even better, how can we manipulate them? In this delightful and lucid voyage through the realm of the random, Dr. Aczel once again makes higher mathematics intelligible to us.

    Subjects ranging from the philosophical to the practical--what mathematics is and why it's worth doing, the relationship between logic and proof, the role of beauty in mathematical thinking, the future of mathematics, how to deal with the peculiarities of the mathematical community, and many others--are dealt with in Stewart's much-admired style, which combines subtle, easygoing humor with a talent for cutting to the heart of the matter. In the tradition of G.H. Hardy's classic A Mathematician's Apology, this book is sure to be a perennial favorite with students at all levels, as well as with other readers who are curious about the frequently incomprehensible world of mathematics.

    It is also a practical, modern introduction to scientific computing in Python, tailored for data-intensive applications. This is a book about the parts of the Python language and libraries you'll need to effectively solve a broad set of data analysis problems. This book is not an exposition on analytical methods using Python as the implementation language.Written by Wes McKinney, the main author of the pandas library, this hands-on book is packed with practical cases studies. It's ideal for analysts new to Python and for Python programmers new to scientific computing.Use the IPython interactive shell as your primary development environmentLearn basic and advanced NumPy (Numerical Python) featuresGet started with data analysis tools in the pandas libraryUse high-performance tools to load, clean, transform, merge, and reshape dataCreate scatter plots and static or interactive visualizations with matplotlibApply the pandas groupby facility to slice, dice, and summarize datasetsMeasure data by points in time, whether it's specific instances, fixed periods, or intervalsLearn how to solve problems in web analytics, social sciences, finance, and economics, through detailed examples

    Turing Mathematician Alan Turing invented an imaginary computer known as the Turing Machine; in an age before computers, he explored the concept of what it meant to be "computable," creating the field of computability theory in the process, a foundation of present-day computer programming.The book expands Turing's original 36-page paper with additional background chapters and extensive annotations; the author elaborates on and clarifies many of Turing's statements, making the original difficult-to-read document accessible to present day programmers, computer science majors, math geeks, and others.Interwoven into the narrative are the highlights of Turing's own life: his years at Cambridge and Princeton, his secret work in cryptanalysis during World War II, his involvement in seminal computer projects, his speculations about artificial intelligence, his arrest and prosecution for the crime of "gross indecency," and his early death by apparent suicide at the age of 41.

    Not anymore. The best-selling author of The Complete Idiot's Guide® to Calculus has taken what appears to be a typical calculus workbook, chock full of solved calculus problems, and made legible notes in the margins, adding missing steps and simplifying solutions. Finally, everything is made perfectly clear. Students will be prepared to solve those obscure problems that were never discussed in class but always seem to find their way onto exams.--Includes 1,000 problems with comprehensive solutions--Annotated notes throughout the text clarify what's being asked in each problem and fill in missing steps--Kelley is a former award-winning calculus teacher

    I also hope that it will serve as a useful reference too for the many workers engaged in one type of solid state research activity or another, who may be without formal training in the subject.

    As the recent collapse on Wall Street shows, we are often ill-equipped to deal with uncertainty and risk. Yet every day we base our personal and business plans on uncertainties, whether they be next month's sales, next year's costs, or tomorrow's stock price. In The Flaw of Averages, Sam Savage-known for his creative exposition of difficult subjects- describes common avoidable mistakes in assessing risk in the face of uncertainty. Along the way, he shows why plans based on average assumptions are wrong, on average, in areas as diverse as healthcare, accounting, the War on Terror, and climate change. In his chapter on Sex and the Central Limit Theorem, he bravely grasps the literary third rail of gender differences.Instead of statistical jargon, Savage presents complex concepts in plain English. In addition, a tightly integrated web site contains numerous animations and simulations to further connect the seat of the reader's intellect to the seat of their pants.The Flaw of Averages typically results when someone plugs a single number into a spreadsheet to represent an uncertain future quantity. Savage finishes the book with a discussion of the emerging field of Probability Management, which cures this problem though a new technology that can pack thousands of numbers into a single spreadsheet cell.Praise for The Flaw of Averages"Statistical uncertainties are pervasive in decisions we make every day in business, government, and our personal lives. Sam Savage's lively and engaging book gives any interested reader the insight and the tools to deal effectively with those uncertainties. I highly recommend The Flaw of Averages." --William J. Perry, Former U.S. Secretary of Defense"Enterprise analysis under uncertainty has long been an academic ideal. . . . In this profound and entertaining book, Professor Savage shows how to make all this practical, practicable, and comprehensible." ---Harry Markowitz, Nobel Laureate in Economics

    It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity. Topics include sets, logic, counting, methods of conditional and non-conditional proof, disproof, induction, relations, functions and infinite cardinality.

    The R language provides everything you need to do statistical work, but its structure can be difficult to master. This collection of concise, task-oriented recipes makes you productive with R immediately, with solutions ranging from basic tasks to input and output, general statistics, graphics, and linear regression.Each recipe addresses a specific problem, with a discussion that explains the solution and offers insight into how it works. If you're a beginner, R Cookbook will help get you started. If you're an experienced data programmer, it will jog your memory and expand your horizons. You'll get the job done faster and learn more about R in the process.Create vectors, handle variables, and perform other basic functionsInput and output dataTackle data structures such as matrices, lists, factors, and data framesWork with probability, probability distributions, and random variablesCalculate statistics and confidence intervals, and perform statistical testsCreate a variety of graphic displaysBuild statistical models with linear regressions and analysis of variance (ANOVA)Explore advanced statistical techniques, such as finding clusters in your dataWonderfully readable, R Cookbook serves not only as a solutions manual of sorts, but as a truly enjoyable way to explore the R language--one practical example at a time.--Jeffrey Ryan, software consultant and R package author

    But how can you get started working in a wide-ranging, interdisciplinary field that’s so clouded in hype? This insightful book, based on Columbia University’s Introduction to Data Science class, tells you what you need to know.In many of these chapter-long lectures, data scientists from companies such as Google, Microsoft, and eBay share new algorithms, methods, and models by presenting case studies and the code they use. If you’re familiar with linear algebra, probability, and statistics, and have programming experience, this book is an ideal introduction to data science.Topics include:Statistical inference, exploratory data analysis, and the data science processAlgorithmsSpam filters, Naive Bayes, and data wranglingLogistic regressionFinancial modelingRecommendation engines and causalityData visualizationSocial networks and data journalismData engineering, MapReduce, Pregel, and HadoopDoing Data Science is collaboration between course instructor Rachel Schutt, Senior VP of Data Science at News Corp, and data science consultant Cathy O’Neil, a senior data scientist at Johnson Research Labs, who attended and blogged about the course.

    Heath's translation of the thirteen books of Euclid's Elements. In keeping with Green Lion's design commitment, diagrams have been placed on every spread for convenient reference while working through the proofs; running heads on every page indicate both Euclid's book number and proposition numbers for that page; and adequate space for notes is allowed between propositions and around diagrams. The all-new index has built into it a glossary of Euclid's Greek terms.Heath's translation has stood the test of time, and, as one done by a renowned scholar of ancient mathematics, it can be relied upon not to have inadvertantly introduced modern concepts or nomenclature. We have excised the voluminous historical and scholarly commentary that swells the Dover edition to three volumes and impedes classroom use of the original text. The single volume is not only more convenient, but less expensive as well.

    Selected for originality, general interest, or because they demonstrate valuable techniques, the problems are ideal as a supplement to courses in probability or statistics, or as stimulating recreation for the mathematically minded. Detailed solutions. Illustrated.

    Wood and Bruce F. Wollenberg presented their comprehensive introduction to the engineering and economic factors involved in operating and controlling power generation systems in electric utilities, the electric power industry has undergone unprecedented change. Deregulation, open access to transmission systems, and the birth of independent power producers have altered the structure of the industry, while technological advances have created a host of new opportunities and challenges. In Power Generation, Operation, and Control, Second Edition, Wood and Wollenberg bring professionals and students alike up to date on the nuts and bolts of the field. Continuing in the tradition of the first edition, they offer a practical, hands-on guide to theoretical developments and to the application of advanced operations research methods to realistic electric power engineering problems. This one-of-a-kind text also addresses the interaction between human and economic factors to prepare readers to make real-world decisions that go beyond the limits of mere technical calculations. The Second Edition features vital new material, including: * A computer disk developed by the authors to help readers solve complicated problems * Examination of Optimal Power Flow (OPF) * Treatment of unit commitment expanded to incorporate the Lagrange relaxation technique * Introduction to the use of bounding techniques and other contingency selection methods * Applications suited to the new, deregulated systems as well as to the traditional, vertically organized utilities company Wood and Wollenberg draw upon nearly 30 years of classroom testing to provide valuable data on operations research, state estimation methods, fuel scheduling techniques, and more. Designed for clarity and ease of use, this invaluable reference prepares industry professionals and students to meet the future challenges of power generation, operation, and control.

    In this Very Short Introduction, Kenneth Falconer explains the basic concepts of fractal geometry, which produced a revolution in our mathematical understanding of patterns in the twentieth century, and explores the wide range of applications in science, and in aspects of economics.About the Series: Oxford's Very Short Introductions series offers concise and original introductions to a wide range of subjects--from Islam to Sociology, Politics to Classics, Literary Theory to History, and Archaeology to the Bible. Not simply a textbook of definitions, each volume in this series provides trenchant and provocative--yet always balanced and complete--discussions of the central issues in a given discipline or field. Every Very Short Introduction gives a readable evolution of the subject in question, demonstrating how the subject has developed and how it has influenced society. Eventually, the series will encompass every major academic discipline, offering all students an accessible and abundant reference library. Whatever the area of study that one deems important or appealing, whatever the topic that fascinates the general reader, the Very Short Introductions series has a handy and affordable guide that will likely prove indispensable.