From the bestselling author of "The Theoretical Minimum," a DIY introduction to the math and science of quantum physics. First he taught you classical mechanics. Now, physicist Leonard Susskind has teamed up with data engineer Art Friedman to present the theory and associated mathematics of the strange world of quantum mechanics. In this follow-up to "The Theoretical Minimum," Susskind and Friedman provide a lively introduction to this famously difficult field, which attempts to understand the behavior of sub-atomic objects through mathematical abstractions. Unlike other popularizations that shy away from quantum mechanics' weirdness, "Quantum Mechanics" embraces the utter strangeness of quantum logic. The authors offer crystal-clear explanations of the principles of quantum states, uncertainty and time dependence, entanglement, and particle and wave states, among other topics, and each chapter includes exercises to ensure mastery of each area. Like "The Theoretical Minimum," this volume runs parallel to Susskind's eponymous Stanford University-hosted continuing education course. An approachable yet rigorous introduction to a famously difficult topic, "Quantum Mechanics" provides a tool kit for amateur scientists to learn physics at their own pace.

"The Volatility Smile: An Introduction for Students and Practitioners The Black-Scholes-Merton options model was the greatest innovation of 20th Century finance, and remains the most widely applied theory in all of finance. Despite this success, the model is fundamentally at odds with the observed behavior of option markets: a graph of implied volatilities against strike will typically display a curve or skew, which practitioners refer to as the smile, and which the model cannot explain. Option valuation is not a solved problem, and the past forty years have witnessed an abundance of new models that try to reconcile theory with markets. The Volatility Smile presents a unified treatment of the Black-Scholes-Merton model and the more advanced models that have replaced it. It is also a book about the principles of financial valuation and how to apply them. Celebrated author and quant Emanuel Derman and Michael B. Miller explain not just the mathematics but the ideas behind the models. By examining the foundations, the implementation, and the pros and cons of various models, and by carefully exploring their derivations and their assumptions, readers will learn not only how to handle the volatility smile but how to evaluate and build their own financial models. Topics covered include: The principles of valuation Static and dynamic replication The Black-Scholes-Merton model Hedging strategies Transaction costs The behavior of the volatility smile Implied distributions Local volatility models Stochastic volatility models Jump-diffusion models"--

A funny, insightful, and self-contained guide to Einstein's relativity theory and classical field theories--including electromagnetism Physicist Leonard Susskind and data engineer Art Friedman are back. This time, they introduce readers to Einstein's special relativity and Maxwell's classical field theory. Using their typical brand of real math, enlightening drawings, and humor, Susskind and Friedman walk us through the complexities of waves, forces, and particles by exploring special relativity and electromagnetism. It's a must-read for both devotees of the series and any armchair physicist who wants to improve their knowledge of physics' deepest truths.

In the late 19th century, a brilliant mathematician languished in an asylum. His greatest accomplishment, the result of a series of leaps of insight, was his pioneering understanding of the nature of infinity. This is the story of Georg Cantor: how he came to his theories and the reverberations of his work, the consequences of which shape our world. Cantor's theory of the infinite is famous for its many seeming contradictions: for example, we can prove there are as many points on a line one inch long as on a line one mile long; we can also prove that in all time there are as many years as there are days. According to Cantor, infinite sets are equal. The mind-twisting, deeply philosophical work of Cantor has its roots in ancient Greek mathematics and Jewish numerology as found in the mystical work known as the Kabbalah. Cantor used the term aleph-the first letter of the Hebrew alphabet, with all its attendant divine associations-to refer to the mysterious number which is the sum of positive integers. It is not the last positive number, because . . . there is no last. It is the ultimate number that is always being approached: just as, for example, there is no last fraction before the number 1.

This book is the result of a unique experience: a research mathematician teaching in an elementary school. It tells about a fascinating discovery made by the author -- that elementary mathematics has a lot of depth and beauty, and that the secret to its teaching is in understanding its deep points.The first part of the book discusses the nature of mathematics and its beauty. The second part tells about the teaching principles the author distilled from his experience. The third part is an excursion through the arithmetic studied in elementary school, accompanied by personal stories, historical anecdotes and teaching suggestions. The appendix relates the fascinating story of modern day politics of mathematical education.The book was a bestseller in Israel, and has been translated into many languages. The extraordinary combination of mathematical and didactic insights makes it an essential guide for parents and teachers alike.

With his ability to make abstract ideas concrete and approachable, Berlinski tells an engrossing tale and introduces us to one of the greatest of all human endeavours.

"An engaging, accessible introduction into how numbers work and why we shouldn't be afraid of them, from maths expert Rachel Riley. Do you know your fractions from your percentages? Your adjacent to your hypotenuse? And who really knows how to do long division, anyway? Puzzled already? Don't blame you... But fret not! You won't be At Sixes and Sevens for long. In this brilliant, well-rounded guide, Countdown's Rachel Riley will take you back to the very basics, allow you to revisit what you learnt at school (and may have promptly forgotten, *ahem*), build your understanding of maths from the get-go and provide you with the essential toolkit to gain confidence in your numerical abilities. Discover how to divide and conquer, make your decimal debut, become a pythagoras professional and so much more with these easy-to-learn tips and tricks. Packed full of working examples, fool-proof methods, quirky trivia and brainteasers to try from puzzle-pro Dr Gareth Moore, this book is an absolute must-read for anyone and everyone who ever thought maths was 'above' them. Because the truth is: you can do it. What's more, it can be pretty fun too!"--

Master expositor Paul Halmos presents Linear Algebra in the pure axiomatic spirit. He writes "My purpose in this book is to treat linear transformations on finite dimensional vector spaces by the methods of more general theories. The idea is to emphasize the simple geometric notions common to many parts of mathematics and its applications, and to do so in a language that gives away the trade secrets ...". This text is an ideal supplement to modern treatments of Linear Algebra. "The theory is systematically developed by the axiomatic method that has, since von Neumann, dominated the general approach to linear functional analysis and that achieves here a high degree of lucidity and clarity....The book contains about 350 well placed and instructive problems, which cover a considerable part of the subject. All in all this is an excellent work, of equally high value for both student and teacher." --Zentralblatt für Mathematik.

This fascinating exploration of the great discoveries of history's most important mathematicians seeks an answer to the eternal question: Does mathematics hold the key to understanding the mysteries of the physical world?

Are people ever rational? Consider this: You auction off a one-dollar bill to the highest bidder, but you set the rules so that the second highest bidder also has to pay the amount of his last bid, even though he gets nothing. Would people ever enter such an auction? Not only do they, but according to Martin Shubik, the game's inventor, the average winning bid (for a dollar, remember) is $3.40. Many winners report that they bid so high only because their opponent "went completely crazy." This game lies at the intersection of three subjects of eternal fascination: human psychology, morality, and John von Neumann's game theory. Hungarian game-theorist Laszlo Mero introduces us to the basics of game theory, including such concepts as zero-sum games, Prisoner's Dilemma and the origins of altruism; shows how game theory is applicable to fields ranging from physics to politics; and explores the role of rational thinking in the context of many different kinds of thinking. This fascinating, urbane book will interest everyone who wonders what mathematics can tell us about the human condition.

Nicolas Bourbaki, whose mathematical publications began to appear in the late 1930s and continued to be published through most of the twentieth century, was a direct product as well as a major force behind an important revolution that took place in the early decades of the twentieth century that completely changed Western culture. Pure mathematics, the area of Bourbaki's work, seems on the surface to be an abstract field of human study with no direct connection with the real world. In reality, however, it is closely intertwined with the general culture that surrounds it. Major developments in mathematics have often followed important trends in popular culture; developments in mathematics have acted as harbingers of change in the surrounding human culture. The seeds of change, the beginnings of the revolution that swept the Western world in the early decades of the twentieth century — both in mathematics and in other areas — were sown late in the previous century. This is the story both of Bourbaki and the world that created him in that time. It is the story of an elaborate intellectual joke — because Bourbaki, one of the foremost mathematicians of his day — never existed.

"Will delight and inform anyone who enjoys rigorous thinking and the unexpected conclusions it delivers." -- Jamie Whyte, author of Crimes Against Logic "This ingenious gallop through the mind of Steven Landsburg enables you to think like an economist without incurring a Keynesian headache or a huge student loan. You may even end up 'smarter than Google.' But you will not readily put down this exhilarating adventure in ideas." -- George Gilder, author of Knowledge and Power and Life After Google Can you outsmart an economist? Steven Landsburg, acclaimed author and professor of economics, dares you to try. In this whip-smart, entertaining, and entirely unconventional economics primer, he brings together over one hundred puzzles and brain teasers that illustrate the subject's key concepts and pitfalls. From warm-up exercises to get your brain working, to logic and probability problems, to puzzles covering more complex topics like inferences, strategy, and irrationality, Can You Outsmart an Economist? will show you how to do just that by expanding the way you think about decision making and problem solving. Let the games begin "Entertaining as well as edifying. Read it, expand your mind, and have fun "-- N. Gregory Mankiw, Robert M. Beren Professor of Economics, Harvard University

The book is overflowing with mathematical ideas, which are always explained clearly and elegantly, and above all, with penetrating insight. It is a joy to read, both for beginners and experienced mathematicians.

Everything is interesting if you go into it deeply enough says Richard P. Feynman in The Smartest Men in the World, one of the many pieces in this collection of Feynman's best short works.

Recent statistical techniques, including nonlinear programming, have been added to a basic survey of equilibrium systems, comparative statistics, consumer behavior theory, and cost and production theory.

An entertaining look at the origins of mathematical symbols While all of us regularly use basic math symbols such as those for plus, minus, and equals, few of us know that many of these symbols weren't available before the sixteenth century. What did mathematicians rely on for their work before then? And how did mathematical notations evolve into what we know today? In Enlightening Symbols , popular math writer Joseph Mazur explains the fascinating history behind the development of our mathematical notation system. He shows how symbols were used initially, how one symbol replaced another over time, and how written math was conveyed before and after symbols became widely adopted. Traversing mathematical history and the foundations of numerals in different cultures, Mazur looks at how historians have disagreed over the origins of the numerical system for the past two centuries. He follows the transfigurations of algebra from a rhetorical style to a symbolic one, demonstrating that most algebra before the sixteenth century was written in prose or in verse employing the written names of numerals. Mazur also investigates the subconscious and psychological effects that mathematical symbols have had on mathematical thought, moods, meaning, communication, and comprehension. He considers how these symbols influence us (through similarity, association, identity, resemblance, and repeated imagery), how they lead to new ideas by subconscious associations, how they make connections between experience and the unknown, and how they contribute to the communication of basic mathematics. From words to abbreviations to symbols, this book shows how math evolved to the familiar forms we use today.

The present English edition is not a mere translation of the German original. Many new problems have been added and there are also other changes, mostly minor. Yet all the alterations amount to less than ten percent of the text. We intended to keep intact the general plan and the original flavor of the work. Thus we have not introduced any essentially new subject matter, although the mathematical fashion has greatly changed since 1924. We have restricted ourselves to supplementing the topics originally chosen. Some of our problems first published in this work have given rise to extensive research. To include all such developments would have changed the character of the work, and even an incomplete account, which would be unsatisfactory in itself, would have cost too much labor and taken up too much space. We have to thank many readers who, since the publication of this work almost fifty years ago, communicated to us various remarks on it, some of which have been incorporated into this edition. We have not listed their names; we have forgotten the origin of some contributions, and an incomplete list would have been even less desirable than no list. The first volume has been translated by Mrs. Dorothee Aeppli, the second volume by Professor Claude Billigheimer. We wish to express our warmest thanks to both for the unselfish devotion and scrupulous conscientiousness with which they attacked their far from easy task.

Mathematical probability theory is especially interesting to scientists and engineers. It introduces probability theory, showing how probability problems can be formulated mathematically to systematically attack routine methods. Topics include independence and dependence, probability laws and random variables. Over 500 exercises, an appendix of useful tables and answers to odd-numbered questions are also included.