Best Mathematics Reference

In Fermat's Enigma --based on the author's award-winning documentary film, which aired on PBS's "Nova"--Simon Singh tells the astonishingly entertaining story of the pursuit of that grail, and the lives that were devoted to, sacrificed for, and saved by it. Fermat's Enigma contains some problems that offer a taste of the math, but it also includes limericks to give a feeling for the goofy side of mathematicians. In the 17th century, a French judicial assistant and amateur mathematician, Pierre De Fermat, produced many brilliant ideas in the field of number theory. Finally, after working in isolation for eight years, Andrew Wiles, a young British mathematician at Princeton University, published a proof in 1995.

Features nearly 200 entries, organized thematically and written by an international team of distinguished contributors Presents major ideas and branches of pure mathematics in a clear, accessible style Defines and explains important mathematical concepts, methods, theorems, and open problems Introduces the language of mathematics and the goals of mathematical research Covers number theory, algebra, analysis, geometry, logic, probability, and more Traces the history and development of modern mathematics Profiles more than ninety-five mathematicians who influenced those working today Explores the influence of mathematics on other disciplines Includes bibliographies, cross-references, and a comprehensive index Contributors incude: Graham Allan, Noga Alon, George Andrews, Tom Archibald, Sir Michael Atiyah, David Aubin, Joan Bagaria, Keith Ball, June Barrow-Green, Alan Beardon, David D. Ben-Zvi, Vitaly Bergelson, Nicholas Bingham, Béla Bollobás, Henk Bos, Bodil Branner, Martin R. Bridson, John P. Burgess, Kevin Buzzard, Peter J. Cameron, Jean-Luc Chabert, Eugenia Cheng, Clifford C. Cocks, Alain Connes, Leo Corry, Wolfgang Coy, Tony Crilly, Serafina Cuomo, Mihalis Dafermos, Partha Dasgupta, Ingrid Daubechies, Joseph W. Dauben, John W. Dawson Jr., Francois de Gandt, Persi Diaconis, Jordan S. Ellenberg, Lawrence C. Evans, Florence Fasanelli, Anita Burdman Feferman, Solomon Feferman, Charles Fefferman, Della Fenster, José Ferreirós, David Fisher, Terry Gannon, A. Gardiner, Charles C. Gillispie, Oded Goldreich, Catherine Goldstein, Fernando Q. Gouvêa, Timothy Gowers, Andrew Granville, Ivor Grattan-Guinness, Jeremy Gray, Ben Green, Ian Grojnowski, Niccolò Guicciardini, Michael Harris, Ulf Hashagen, Nigel Higson, Andrew Hodges, F. E. A. Johnson, Mark Joshi, Kiran S. Kedlaya, Frank Kelly, Sergiu Klainerman, Jon Kleinberg, Israel Kleiner, Jacek Klinowski, Eberhard Knobloch, János Kollár, T. W. Körner, Michael Krivelevich, Peter D. Lax, Imre Leader, Jean-François Le Gall, W. B. R. Lickorish, Martin W. Liebeck, Jesper Lützen, Des MacHale, Alan L. Mackay, Shahn Majid, Lech Maligranda, David Marker, Jean Mawhin, Barry Mazur, Dusa McDuff, Colin McLarty, Bojan Mohar, Peter M. Neumann, Catherine Nolan, James Norris, Brian Osserman, Richard S. Palais, Marco Panza, Karen Hunger Parshall, Gabriel P. Paternain, Jeanne Peiffer, Carl Pomerance, Helmut Pulte, Bruce Reed, Michael C. Reed, Adrian Rice, Eleanor Robson, Igor Rodnianski, John Roe, Mark Ronan, Edward Sandifer, Tilman Sauer, Norbert Schappacher, Andrzej Schinzel, Erhard Scholz, Reinhard Siegmund-Schultze, Gordon Slade, David J. Spiegelhalter, Jacqueline Stedall, Arild Stubhaug, Madhu Sudan, Terence Tao, Jamie Tappenden, C. H. Taubes, Rüdiger Thiele, Burt Totaro, Lloyd N. Trefethen, Dirk van Dalen, Richard Weber, Dominic Welsh, Avi Wigderson, Herbert Wilf, David Wilkins, B. Yandell, Eric Zaslow, Doron Zeilberger. " The Princeton Companion to Mathematics makes a heroic attempt to keep [abstract concepts] to a minimum . "Although the editors' original goal of text that could be understood by anyone with a good background in high school mathematics provided short-lived, this wide-ranging account should reward undergraduate and graduate students and anyone curious about math as well as help research mathematicians understand the work of their colleagues in other specialties. The editors note some advantages a carefully organized printed reference may enjoy over a collection of Web pages, and this impressive volume supports their claim." "This impressive book represents an extremely ambitious and, I might add, highly successful attempt by Timothy Gowers and his coeditors, June Barrow-Green and Imre Leader, to give a current account of the subject of mathematics. It has something for nearly everyone, from beginning students of mathematics who would like to get some sense of what the subject is all about, all the way to professional mathematicians who would like to get a better idea of what their colleagues are doing. If I had to choose just one book in the world to give an interested reader some idea of the scope, goals and achievements of modern mathematics, without a doubt this would be the one. Described as a 'companion', this 1000-page tome is an authoritative and informative reference work that is also highly pleasurable to dip into. That is what Timothy Gowers, the 1998 Fields Medal laureate, has successfully accomplished in compiling and editing The Princeton Companion to Mathematics . At more than 1,000 pages and with nearly 200 entries written by some of the leading mathematicians of our time and specialists in their fields, this book is a one-of-a-kind reference for all things mathematics." "Overall [ The Princeton Companion to Mathematics ] is an enormous achievement for which the authors deserve to be thanked. It contains a wealth of material, much of a kind one would not find elsewhere, and can be enjoyed by readers with man different backgrounds." "This is an enormously ambitious book, full of beautiful things; I would wish to keep it on my bedside table, but that could only be possible relays, since of course it is far too large. "My advice to you, reader is to buy the book, open it to a random page, read, enjoy, and be enlightened." "This volume is an enormous, far-reaching effort to survey the current landscape of (pure) mathematics. Chief editor Gowers and associate editors Barrow-Green and Leader have enlisted scores of leading mathematicians worldwide to produce a gorgeous volume of longer essays and short, specific articles that convey some of the dense fabric of ideas and techniques of modern mathematics. This volume should be on the shelf of every university and public library, and of every mathematician--professional and amateur alike." Any reader from a curious high school student to an experienced mathematician seeking information on a particular mathematical subject outside his or her field will find this book useful. Even an academic sourpuss should be pleased with the attention to detail of The Companion 's publishers, editors, and authors and with many judicious decisions about the level of exposition, level of detail, what to include and what to omit, and much more--which have led to a well-integrated and highly readable volume." "Edited by Gowers, a recipient of the Fields Medal, this volume contains almost 200 entries, commissioned especially for this book from the world's leading mathematicians. Packed with information presented in an accessible style, this is an indispensable resource for undergraduate and graduate students in mathematics as well as for researchers and scholars seeking to understand areas outside their specialties." If you are in an absolute rush, the short version of my post today is, buy this book. You don't have to click on the link with my referral if you don't want to, seriously just pick up a copy of this book, I can guarantee you that it will be love at first sight. The Princeton Companion to Mathematics is not only a beautiful book from an aesthetic standpoint, with its heavy, high quality pages and sturdy binding, but above all it's a monumental piece of work. After many years of slogging through textbooks that presented too many proofs and demonstrations that were left to the student or lacking numerous intermediate steps, after encountering numerous 'introductions' that were obtuse and highly theoretical and after digesting far too many explanations with maximal equations and minimal verbiage, we arrive at the happy medium. Many in the sugar industry with a fairly good grasp of mathematics will probably not struggle with it, and will invariably marvel at its richness and diversity. "The book contains some valuable surveys of the main branches of mathematics that are written in an accessible style.

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Secrets of Mental Math will have you thinking like a math genius in no time. “A great introduction to the wonder of numbers, from two superb teachers.” —Brian Greene, author of The Elegant Universe “A magical mystery tour of mental mathematics! Michael Shermer is host of the Caltech public lecture series, a contributing editor to and monthly columnist of Scientific American , the publisher of Skeptic magazine, and the author of several science books.

It tells the human story of numerous phi-fixated individuals, including the followers of Pythagoras who believed that this proportion revealed the hand of God; astronomer Johannes Kepler, who saw phi as the greatest treasure of geometry; such Renaissance thinkers as mathematician Leonardo Fibonacci of Pisa; and such masters of the modern world as Goethe, Cezanne, Bartok, and physicist Roger Penrose. Theoretical astrophysicist Livio gives pi's overlooked cousin phi its due with this lively account, the first on the subject written for the layperson. Livio (The Accelerating Universe) carefully investigates these and other claims and does not hesitate to debunk myths perpetuated by overzealous enthusiasts he calls "Golden Numberists." Livio is gifted with an accessible, entertaining style: one typical chapter bounds within five pages from an extended discourse on prime numbers to a clever Oscar Wilde quote about beauty to an amusing anecdote about Samuel Beckett and finally to an eminently clear explanation of G"del's incompleteness theorem. On the way, he debunks a number of popular myths (e.g., the notion that Mondrian used it in his abstract paintings) and does a wonderful job explaining the Fibonacci sequence and its relationship to phi.

In The Indisputable Existence of Santa Claus , distinguished mathematicians Hannah Fry and Thomas Oléron Evans demonstrate, with eminently readable clarity, how applied mathematics are so thoroughly interwoven throughout our everyday lives by explaining mathematical concepts through one very merry motif: Christmas. Thomas Oléron Evans, PhD is a Teaching Fellow for the Smart Cities and Spatial Data Courses at the University College London.

Included are step-by-step instructions on how to carry out Bayesian data analyses in the popular and free software R and WinBugs, as well as new programs in JAGS and Stan. Accessible, including the basics of essential concepts of probability and random sampling Examples with R programming language and JAGS software Comprehensive coverage of all scenarios addressed by non-Bayesian textbooks: t-tests, analysis of variance (ANOVA) and comparisons in ANOVA, multiple regression, and chi-square (contingency table analysis) Coverage of experiment planning R and JAGS computer programming code on website Exercises have explicit purposes and guidelines for accomplishment Provides step-by-step instructions on how to conduct Bayesian data analyses in the popular and free software R and WinBugs. "Both textbook and practical guide, this work is an accessible account of Bayesian data analysis starting from the basics…This edition is truly an expanded work and includes all new programs in JAGS and Stan designed to be easier to use than the scripts of the first edition, including when running the programs on your own data sets." “has the potential to change the way most cognitive scientists and experimental psychologists approach the planning and analysis of their experiments" Prof. Geoffrey Iverson, U. of Cal., Irvine; past pres. The book begins with the basics, including essential concepts of probability and random sampling, and gradually progresses to advanced hierarchical modeling methods for realistic data. It provides a bridge between undergraduate training and modern Bayesian methods for data analysis, which is becoming the accepted research standard.

Jason speaks in simple English and uses the metaphor of The Seven Steps to SEO Fitness to explain to you how to 'get SEO fit.'. Goals : Define Your SEO Goals Keywords : Identify Winnable, High Value SEO Keywords On Page SEO : Optimize Your Website to 'Speak Google' via Page Tabs, your home page, and structural elements Content Marketing : Learn to produce content that pleases Google and your customers Off Page SEO : Build links, leverage social media, and go local. Check out the other 2018 SEO Books on Amazon - SEO For Dummies , SEO for Growth , SEO Book , SEO Like I'm 5 etc., - they're great, they're good, but they don't include powerful step-by-step worksheets, links to online videos, and the free SEO Toolbook with hundreds of free tools for search engine optimization 2018. Listed on many SEO book lists as one of the best books SEO books of 2018 as well as a best SEO book for beginners. ~ Alexandra Hager. In Sept. and Oct. 2016, I took Jason's SEO (Search Engine Optimization), Ad Words, and Social Media Marketing online class series. However, since SEO, Ad Words, and Social Media live on the internet, watching Jason walk through everything in an online format works really well. He demonstrates this through his exhaustive list of resources that he shares in his classes as well as his expert, insider tips about internet marketing that you cannot get from Google. The book grew out of my class at Stanford University's Continuing Studies Program, "Marketing without Money."

Freakonomics is a groundbreaking collaboration between Levitt and Stephen J. Dubner, an award-winning author and journalist. Thus the new field of study contained in this book: freakonomics.Through forceful storytelling and wry insight, Levitt and 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. What unites all these stories is a belief that the modern world, despite a great deal of complexity and downright deceit, is not impenetrable, is not unknowable, and—if the right questions are asked—is even more intriguing than we think. 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 will literally redefine the way we view the modern world.Bonus material added to the revised and expanded 2006 edition.The original New York Times Magazine article about Steven D. Levitt by Stephen J. Dubner, which led to the creation of this book.Seven “Freakonomics” columns written for the New York Times Magazine, published between August 2005 and April 2006. “Levitt dissects complex real-world phenomena, e.g. baby-naming patterns and Sumo wrestling, with an economist’s laser.” (San Diego Union-Tribune). This is bracing fun of the highest order.” (Kurt Andersen, host of public radio's Studio 360 and author of Turn of the Century). “Freakonomics challenges conventional wisdom and makes for fun reading.” (Book Sense Picks and Notables). Steven D. Levitt, a professor of economics at the University of Chicago, was awarded the John Bates Clark Medal, given to the most influential American economist under forty. Stephen J. Dubner, an award-winning journalist and radio and TV personality, has worked for the New York Times and published three non- Freakonomics books.

David Foster Wallace brings his intellectual ambition and characteristic bravura style to the story of how mathematicians have struggled to understand the infinite, from the ancient Greeks to the nineteenth-century mathematical genius Georg Cantor's counterintuitive discovery that there was more than one kind of infinity. The task Wallace (author of the bestseller Infinite Jest and other fiction) has set himself is enormously challenging: without radically compromising the complexity of the philosophy, metaphysics, or mathematics that underlies the evolving concept of infinity, present the material to a lay audience in a manner that is entertaining. --Patrick O’Kelley The subject of infinity would probably strike most readers familiar with Wallace as perfectly suited to his recursive style, and this book is as weird and wonderful as you'd expect. There are footnotes galore, frequently prefaced by the acronym IYI ("If You're Interested"), which can signal either pure digression or the first hint of an idea more fully developed in later chapters. Had he not pursued a career in literary fiction, it's not difficult to imagine Wallace as a historian of science, producing quirky and challenging volumes such as this every few years.

The reader learns by doing, writing programs to implement the mathematical concepts and using them to carry out tasks and explore the applications. He has been a Visiting Scientist at Princeton’s Computer Science Department, at MIT’s Mathematics Department, and at MIT’s Computer Science and Artificial Intelligence Laboratory (CSAIL), where he is currently a Research Affiliate. His love for computer science has never abated, but in a chance encounter with E. W. Dijkstra in 1979, he was told that, if he wanted to do computer science, he had better learn some math.

Secrets of Mental Math will have you thinking like a math genius in no time. “A great introduction to the wonder of numbers, from two superb teachers.” —Brian Greene, author of The Elegant Universe “A magical mystery tour of mental mathematics! Michael Shermer is host of the Caltech public lecture series, a contributing editor to and monthly columnist of Scientific American , the publisher of Skeptic magazine, and the author of several science books.

Lockhart’s Mathematician’s Lament outlined how we introduce math to students in the wrong way. (Steven Strogatz, New York Times contributor and author of The Joy of X (forthcoming)). No matter what mathematical education you had, or didn't have, you will be delighted by this enticing book if you take up Paul Lockhart's invitation to engage in the mathematical sensibility that radiates from its pages, and try your own hand―not only at answering, but even more fruitfully, at formulating questions as you explore the world of mathematics. Lockhart presents math as an art and argues that just as there is no systematic way to create beautiful and meaningful art, there is also no method for producing beautiful and meaningful mathematical arguments. Measurement is only one of the many rivers in the "vast, ever-expanding jungle" of mathematics, which for Lockhart satisfies our need to find patterns as well as our curiosity...His playful and ingenious approach not only takes the fear out of math but also elegantly illustrates that universe and the joy he finds in it. Lockhart is famous in the math world for a 2002 essay about the state of mathematics teaching. Measurement is his attempt to change the equation: a conversational book about mathematics as an art that invites the reader to join in the fun. Prospective readers should rest assured that while aimed at the nonexpert, Lockhart 's writing is sophisticated and mathematically modern...In place of the usual boxed and high-lighted formulas and tricks, Measurement offers questions to be pondered. Lockhart invites readers to trade tutorial fake problems about actual objects, which lead students to abhor school mathematics, for real problems about fantastical objects, which lead mathematicians to love math.

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In the years following her role as the lead author of the international bestseller, Limits to Growth —the first book to show the consequences of unchecked growth on a finite planet— Donella Meadows remained a pioneer of environmental and social analysis until her untimely death in 2001. Just before her death, scientist, farmer and leading environmentalist Meadows (1941-2001) completed an updated, 30th anniversary edition of her influential 1972 environmental call to action, Limits to Growth, as well as a draft of this book, in which she explains the methodology-systems analysis-she used in her ground-breaking work, and how it can be implemented for large-scale and individual problem solving. An invaluable companion piece to Limits to Growth, this is also a useful standalone overview of systems-based problem solving, "a simple book about a complex world" graced by the wisdom of a profound thinker committed to "shaping a better future." Just before her death, scientist, farmer and leading environmentalist Meadows (1941-2001) completed an updated, 30th anniversary edition of her influential 1972 environmental call to action, Limits to Growth , as well as a draft of this book, in which she explains the methodology-systems analysis-she used in her ground-breaking work, and how it can be implemented for large-scale and individual problem solving. An invaluable companion piece to Limits to Growth , this is also a useful standalone overview of systems-based problem solving, "a simple book about a complex world" graced by the wisdom of a profound thinker committed to "shaping a better future. This is modestly called a primer, and indeed it is, but unlike most books with that title, this one quickly takes one from the elementary into deep systems thinking about issues as critical today as they were when Dana wrote these words. As the book moves from the 'mechanics' of systems dynamics to Dana's more philosophical perspective, we are treated to her inherent belief in human values that consider the good of all, and how much more effective considering the needs of others is likely to be in solving larger, complex problems. The universe and our society may be very complex and operate in counterintuitive, non-liner fashion, but following the insights of this book and applying them will provide for far more effective solutions to the challenges of a 7 billion person planet than current incremental, linear responses by governments, corporations and individuals." For her systems thinking included the expected things like recognizing patterns, connections, leverage points, feedback loops and also the human qualities of judgment, foresight, and kindness. To live sustainably on our planet, we must learn to understand human-environment interactions as complex systems marked by the impact of human actions, the prominence of nonlinear change, the importance of initial conditions, and the significance of emergent properties. "An inspiring sequel to Dana Meadows' lifetime of seminal contributions to systems thinking, this highly accessible book should be read by everyone concerned with the world's future and how we can make it as good as it possibly can be."

Organized according to level and subject area of mathematics, it first covers the basics of high school algebra and graphing, continues with calculus and differential equations then moves on to more advanced topics, such as linear algebra, vector calculus, complex analysis, special functions, group theory, number theory and combinatorics.

Steadfast Support for your Evolving Course The College Algebra series, by Lial, Hornsby, Schneider, and Daniels, combines the experience of master teachers to help students develop both the conceptual understanding and the analytical skills necessary for success in mathematics. Students, if interested in purchasing this title with MyMathLab, ask your instructor for the correct package ISBN and Course ID. When John Hornsby enrolled as an undergraduate at Louisiana State University, he was uncertain whether he wanted to study mathematics education or journalism. His specific professional interests are recreational mathematics, mathematics history, and incorporating graphing calculators into the curriculum. He has an undergraduate degree in mathematics from Oberlin College and a PhD in mathematics from MIT. She has two Master’s degrees: one in Applied Mathematics and Statistics from the University of Missouri—Rolla, the second in Adult Education from the University of Missouri—St. Her professional interests include improving success in the community college mathematics sequence, using technology to enhance students’ understanding of mathematics, and creating materials that support classroom teaching and student understanding.

Generations of readers have relished Polya's deft—indeed, brilliant—instructions on stripping away irrelevancies and going straight to the heart of the problem. The traditional mathematics professor who reads a paper before one of the Mathematical Societies might also learn something from the book: 'He writes a, he says b, he means c; but it should be d.' " --E. T. Bell, Mathematical Monthly "[This] elementary textbook on heuristic reasoning, shows anew how keen its author is on questions of method and the formulation of methodological principles. "Every mathematics student should experience and live this book" -- Mathematics Magazine. "In an age that all solutions should be provided with the least possible effort, this book brings a very important message: mathematics and problem solving in general needs a lot of practice and experience obtained by challenging creative thinking, and certainly not by copying predefined recipes provided by others. John H. Conway is professor emeritus of mathematics at Princeton University.