It is highly recommended for anyone planning to study advanced analysis, e.g., complex variables, differential equations, Fourier analysis, numerical analysis, several variable calculus, and statistics. It is also recommended for future secondary school teachers. A limited number of concepts involving the real line and functions on the real line are studied. Many abstract ideas, such as metric spaces and ordered systems, are avoided. The least upper bound property is taken as an axiom and the order properties of the real line are exploited throughout. A thorough treatment of sequences of numbers is used as a basis for studying standard calculus topics. Optional sections invite students to study such topics as metric spaces and Riemann-Stieltjes integrals.

    Whether you are a student, software developer, tech entrepreneur, or researcher in computer science, this authoritative and self-contained book tells you everything you need to know about the new global money for the Internet age.How do Bitcoin and its block chain actually work? How secure are your bitcoins? How anonymous are their users? Can cryptocurrencies be regulated? These are some of the many questions this book answers. It begins by tracing the history and development of Bitcoin and cryptocurrencies, and then gives the conceptual and practical foundations you need to engineer secure software that interacts with the Bitcoin network as well as to integrate ideas from Bitcoin into your own projects. Topics include decentralization, mining, the politics of Bitcoin, altcoins and the cryptocurrency ecosystem, the future of Bitcoin, and more.An essential introduction to the new technologies of digital currencyCovers the history and mechanics of Bitcoin and the block chain, security, decentralization, anonymity, politics and regulation, altcoins, and much moreFeatures an accompanying website that includes instructional videos for each chapter, homework problems, programming assignments, and lecture slidesAlso suitable for use with the authors' Coursera online courseElectronic solutions manual (available only to professors)

    Even the simplest numbers can become powerful forces when manipulated by politicians or the media, but in the case of the law, your liberty -- and your life -- can depend on the right calculation. In Math on Trial, mathematicians Leila Schneps and Coralie Colmez describe ten trials spanning from the nineteenth century to today, in which mathematical arguments were used -- and disastrously misused -- as evidence. They tell the stories of Sally Clark, who was accused of murdering her children by a doctor with a faulty sense of calculation; of nineteenth-century tycoon Hetty Green, whose dispute over her aunt's will became a signal case in the forensic use of mathematics; and of the case of Amanda Knox, in which a judge's misunderstanding of probability led him to discount critical evidence -- which might have kept her in jail. Offering a fresh angle on cases from the nineteenth-century Dreyfus affair to the murder trial of Dutch nurse Lucia de Berk, Schneps and Colmez show how the improper application of mathematical concepts can mean the difference between walking free and life in prison. A colorful narrative of mathematical abuse, Math on Trial blends courtroom drama, history, and math to show that legal expertise isn't't always enough to prove a person innocent.

    While many of the mathematicians and software engineers on Wall Street failed when their abstractions turned ugly in practice, a special breed of physicists has a much deeper history of revolutionizing finance. Taking us from fin-de-siècle Paris to Rat Pack-era Las Vegas, from wartime government labs to Yippie communes on the Pacific coast, Weatherall shows how physicists successfully brought their science to bear on some of the thorniest problems in economics, from options pricing to bubbles.The crisis was partly a failure of mathematical modeling. But even more, it was a failure of some very sophisticated financial institutions to think like physicists. Models—whether in science or finance—have limitations; they break down under certain conditions. And in 2008, sophisticated models fell into the hands of people who didn’t understand their purpose, and didn’t care. It was a catastrophic misuse of science.The solution, however, is not to give up on models; it's to make them better. Weatherall reveals the people and ideas on the cusp of a new era in finance. We see a geophysicist use a model designed for earthquakes to predict a massive stock market crash. We discover a physicist-run hedge fund that earned 2,478.6% over the course of the 1990s. And we see how an obscure idea from quantum theory might soon be used to create a far more accurate Consumer Price Index.Both persuasive and accessible, The Physics of Wall Street is riveting history that will change how we think about our economic future.

    Clear, comprehensive coverage of utility theory, 2-person zero-sum games, 2-person non-zero-sum games, n-person games, individual and group decision-making, more. Bibliography.

    economy and economies around the world. In this trenchant book, best-selling economist Robert Shiller reveals the origins of this crisis and puts forward bold measures to solve it. He calls for an aggressive response--a restructuring of the institutional foundations of the financial system that will not only allow people once again to buy and sell homes with confidence, but will create the conditions for greater prosperity in America and throughout the deeply interconnected world economy.Shiller blames the subprime crisis on the irrational exuberance that drove the economy's two most recent bubbles--in stocks in the 1990s and in housing between 2000 and 2007. He shows how these bubbles led to the dangerous overextension of credit now resulting in foreclosures, bankruptcies, and write-offs, as well as a global credit crunch. To restore confidence in the markets, Shiller argues, bailouts are needed in the short run. But he insists that these bailouts must be targeted at low-income victims of subprime deals. In the longer term, the subprime solution will require leaders to revamp the financial framework by deploying an ambitious package of initiatives to inhibit the formation of bubbles and limit risks, including better financial information; simplified legal contracts and regulations; expanded markets for managing risks; home equity insurance policies; income-linked home loans; and new measures to protect consumers against hidden inflationary effects.This powerful book is essential reading for anyone who wants to understand how we got into the subprime mess--and how we can get out.

    Author Steven Drobny demystifies how these star traders make billions for well-heeled investors, revealing their theories, strategies and approaches to markets. Drobny, cofounder of Drobny Global Advisors, an international macroeconomic research and advisory firm, has tapped into his network and beyond in order assemble this collection of thirteen interviews with the industry's best minds. Along the way, you'll get an inside look at firsthand trading experiences through some of the major world financial crises of the last few decades. Whether Russian bonds, Pakistani stocks, Southeast Asian currencies or stakes in African brewing companies, no market or instrument is out of bounds for these elite global macro hedge fund managers. Highly accessible and filled with in-depth expert opinion, Inside the House of Money is a must-read for financial professionals and anyone else interested in understanding the complexities at stake in world financial markets. "The ruminations of supposedly hush-hush hedge fund operators are richly illuminating." --New York Times

    This book helps you even the odds. Using easy-to-understand explanations and examples, it demystifies probability -- and even offers savvy tips to boost your chances of gambling success Discover how to* Conquer combinations and permutations* Understand probability models from binomial to exponential* Make good decisions using probability* Play the odds in poker, roulette, and other games

    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.

    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.

    Now, America finds itself cash poor, and to a great extent power follows money. In The End of Influence, renowned economic analysts Stephen S. Cohen and J. Bradford DeLong explore the grave consequences this loss will have for America's place in the world. America, Cohen and DeLong argue, will no longer be the world's hyperpower. It will no longer wield soft cultural power or dictate a monolithic foreign policy. More damaging, though, is the blow to the world's ability to innovate economically, financially, and politically. Cohen and DeLong also explore American's complicated relationship with China, the misunderstood role of sovereign wealth funds, and the return of state-led capitalism. An essential read for anyone interested in how global economics and finance interact with national policy, The End of Influence explains the far-reaching and potentially long-lasting but little-noted consequences of our great fiscal crisis.

    This book starts from the ground up to provide detailed explanations of both these techniques: - An introduction to the different types of execution is followed by a review of market microstructure theory. Throughout the book examples from empirical studies bridge the gap between the theory and practice of trading. - Orders are the fundamental building blocks for any strategy. Market, limit, stop, hidden, iceberg, peg, routed and immediate-or-cancel orders are all described with illustrated examples. - Trading algorithms are explained and compared using charts to show potential trading patterns. TWAP, VWAP, Percent of Volume, Minimal Impact, Implementation Shortfall, Adaptive Shortfall, Market On Close and Pairs trading algorithms are all covered, together with common variations. - Transaction costs can have a significant effect on investment returns. An in-depth example shows how these may be broken down into constituents such as market impact, timing risk, spread and opportunity cost and other fees. - Coverage includes all the major asset classes, from equities to fixed income, foreign exchange and derivatives. Detailed overviews for each of the world's major markets are provided in the appendices. - Order placement and execution tactics are covered in more detail, as well as potential enhancements (such as short-term forecasts), for those interested in the specifics of implementing these strategies. - Cutting edge applications such as portfolio and multi-asset trading are also considered, as are handling news and data mining/artificial intelligence.

    This introductory text is suitable for use in a course on the subject or for self-study, featuring broad coverage and a readable exposition, with many examples and exercises. The four main chapters present the basics: fundamental group and covering spaces, homology and cohomology, higher homotopy groups, and homotopy theory generally. The author emphasizes the geometric aspects of the subject, which helps students gain intuition. A unique feature is the inclusion of many optional topics not usually part of a first course due to time constraints: Bockstein and transfer homomorphisms, direct and inverse limits, H-spaces and Hopf algebras, the Brown representability theorem, the James reduced product, the Dold-Thom theorem, and Steenrod squares and powers.

    Wade have on violent crime? Freakonomics will literally redefine the way we view the modern world.These may not sound like typical questions for an economist to ask. But Steven D. Levitt is not a typical economist. He is a much heralded scholar who studies the stuff and riddles of everyday life -- from cheating and crime to sports and child rearing -- and whose conclusions regularly turn the conventional wisdom on its head. He usually begins with a mountain of data and a simple, unasked question. Some of these questions concern life-and-death issues; others have an admittedly freakish quality. Thus the new field of study contained in this book: freakonomics.Through forceful storytelling and wry insight, Levitt and co-author Stephen J. Dubner show that economics is, at root, the study of incentives -- how people get what they want, or need, especially when other people want or need the same thing. In Freakonomics, they set out to explore the hidden side of ... well, everything. The inner workings of a crack gang. The truth about real-estate agents. The myths of campaign finance. The telltale marks of a cheating schoolteacher. The secrets of the Ku Klux Klan.What unites all these stories is a belief that the modern world, despite a surfeit of obfuscation, complication, and downright deceit, is not impenetrable, is not unknowable, and -- if the right questions are asked -- is even more intriguing than we think. All it takes is a new way of looking. Steven Levitt, through devilishly clever and clear-eyed thinking, shows how to see through all the clutter.Freakonomics establishes this unconventional premise: If morality represents how we would like the world to work, then economics represents how it actually does work. It is true that readers of this book will be armed with enough riddles and stories to last a thousand cocktail parties. But Freakonomics can provide more than that. It will literally redefine the way we view the modern world.(front flap)

    Its world-class authors provide guidance on all aspects of Bayesian data analysis and include examples of real statistical analyses, based on their own research, that demonstrate how to solve complicated problems. Changes in the new edition include:Stronger focus on MCMC Revision of the computational advice in Part III New chapters on nonlinear models and decision analysis Several additional applied examples from the authors' recent research Additional chapters on current models for Bayesian data analysis such as nonlinear models, generalized linear mixed models, and more Reorganization of chapters 6 and 7 on model checking and data collectionBayesian computation is currently at a stage where there are many reasonable ways to compute any given posterior distribution. However, the best approach is not always clear ahead of time. Reflecting this, the new edition offers a more pluralistic presentation, giving advice on performing computations from many perspectives while making clear the importance of being aware that there are different ways to implement any given iterative simulation computation. The new approach, additional examples, and updated information make Bayesian Data Analysis an excellent introductory text and a reference that working scientists will use throughout their professional life.