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An introduction to the use of the axiom of choice is followed by explorations of consistency, permutation models, and independence. Subsequent chapters examine embedding theorems, models with finite supports, weaker versions of the axiom, and nontransferable statements. The final sections consider mathematics without choice, cardinal numbers in set theory without choice, and properties that contradict the axiom of choice, including the axiom of determinacy and related topics

Many people take math in high school and promptly forget much of it. But math plays a part in all of our lives all of the time, whether we know it or not. In The Joy of x, Steven Strogatz expands on his hit New York Times series to explain the big ideas of math gently and clearly, with wit, insight, and brilliant illustrations.

Whether he is illuminating how often you should flip your mattress to get the maximum lifespan from it, explaining just how Google searches the internet, or determining how many people you should date before settling down, Strogatz shows how math connects to every aspect of life. Discussing pop culture, medicine, law, philosophy, art, and business, Strogatz is the math teacher you wish you’d had. Whether you aced integral calculus or aren’t sure what an integer is, you’ll find profound wisdom and persistent delight in The Joy of x.

Whether you are a student or teacher preparing and need to grown up on basic math, this book of Basics of Math easily learn numbers system, HCF and LCF, surds and indices, fractions, linear and quadratic equations decimals, average and percents. This Math book covers large number of problems with example and its solution for the purpose of practice on the range of topics covered under the basics of math.

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Logic For Dummies tracks an introductory logic course at the college level. Concrete, real-world examples help you understand each concept you encounter, while fully worked out proofs and fun logic problems encourage you students to apply what you’ve learned.

Navigate fractions, decimals, and percents in business and real estate transactions, and take fancy math skills to work. You’ll be able to read graphs and tables and apply statistics and data analysis. You’ll discover ways you can use math in finance and payroll investments, banking and payroll, goods and services, and business facilities and operations. You’ll learn how to calculate discounts and markup, use loans and credit, and understand the ins and outs of math for business facilities and operations. You’ll be the company math whiz in no time at all! Find out how to:

Read graphs and tables Invest in the future Use loans and credit Navigate bank accounts, insurance, budgets, and payroll Calculate discounts and markup Measure properties and handle mortgages and loans Manage rental and commercial propertiesComplete with lists of ten math shortcuts to do in meetings and drive your coworkers nuts and ten tips for reading annual reports, Business MathFor Dummies is your one-stop guide to solving math problems in business situations.

Unparalleled in its depth of coverage, The Princeton Companion to Mathematics surveys the most active and exciting branches of pure mathematics. Accessible in 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.

Features nearly 200 entries, organized thematically and written by an international team of distinguished contributorsPresents major ideas and branches of pure mathematics in a clear, accessible styleDefines and explains important mathematical concepts, methods, theorems, and open problemsIntroduces the language of mathematics and the goals of mathematical researchCovers number theory, algebra, analysis, geometry, logic, probability, and moreTraces the history and development of modern mathematicsProfiles more than ninety-five mathematicians who influenced those working todayExplores the influence of mathematics on other disciplinesIncludes bibliographies, cross-references, and a comprehensive indexContributors 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

While recounting memorable episodes such as "Bart the Genius†? and "Homer3,†? Singh weaves in mathematical stories that explore everything from p to Mersenne primes, Euler's equation to the unsolved riddle of P v. NP; from perfect numbers to narcissistic numbers, infinity to even bigger infinities, and much more. Along the way, Singh meets members of The Simpsons' brilliant writing team-among them David X. Cohen, Al Jean, Jeff Westbrook, and Mike Reiss-whose love of arcane mathematics becomes clear as they reveal the stories behind the episodes.

With wit and clarity, displaying a true fan's zeal, and replete with images from the shows, photographs of the writers, and diagrams and proofs, The Simpsons and Their Mathematical Secrets offers an entirely new insight into the most successful show in television history.

An Introduction to Numerical Methods and Analysis, Second Edition reflects the latest trends in the field, includes new material and revised exercises, and offers a unique emphasis on applications. The author clearly explains how to both construct and evaluate approximations for accuracy and performance, which are key skills in a variety of fields. A wide range of higher-level methods and solutions, including new topics such as the roots of polynomials, spectral collocation, finite element ideas, and Clenshaw-Curtis quadrature, are presented from an introductory perspective, and theSecond Edition also features: Chapters and sections that begin with basic, elementary material followed by gradual coverage of more advanced material Exercises ranging from simple hand computations to challenging derivations and minor proofs to programming exercises Widespread exposure and utilization of MATLAB® An appendix that contains proofs of various theorems and other material

In Pursuit of the Traveling Salesman travels to the very threshold of our understanding about the nature of complexity, and challenges you yourself to discover the solution to this captivating mathematical problem.

Some images inside the book are unavailable due to digital copyright restrictions.

Riemann's basic inquiry, the primary topic of his paper, concerned a straightforward but nevertheless important matter of arithmetic â€" defining a precise formula to track and identify the occurrence of prime numbers. But it is that incidental remark â€" the Riemann Hypothesis â€" that is the truly astonishing legacy of his 1859 paper. Because Riemann was able to see beyond the pattern of the primes to discern traces of something mysterious and mathematically elegant shrouded in the shadows â€" subtle variations in the distribution of those prime numbers. Brilliant for its clarity, astounding for its potential consequences, the Hypothesis took on enormous importance in mathematics. Indeed, the successful solution to this puzzle would herald a revolution in prime number theory. Proving or disproving it became the greatest challenge of the age.

It has become clear that the Riemann Hypothesis, whose resolution seems to hang tantalizingly just beyond our grasp, holds the key to a variety of scientific and mathematical investigations. The making and breaking of modern codes, which depend on the properties of the prime numbers, have roots in the Hypothesis. In a series of extraordinary developments during the 1970s, it emerged that even the physics of the atomic nucleus is connected in ways not yet fully understood to this strange conundrum. Hunting down the solution to the Riemann Hypothesis has become an obsession for many â€" the veritable "great white whale" of mathematical research. Yet despite determined efforts by generations of mathematicians, the Riemann Hypothesis defies resolution.

Alternating passages of extraordinarily lucid mathematical exposition with chapters of elegantly composed biography and history, Prime Obsession is a fascinating and fluent account of an epic mathematical mystery that continues to challenge and excite the world. Posited a century and a half ago, the Riemann Hypothesis is an intellectual feast for the cognoscenti and the curious alike. Not just a story of numbers and calculations, Prime Obsession is the engrossing tale of a relentless hunt for an elusive proof â€" and those who have been consumed by it.

"This is quite a well-done book: very tightly organized, better-than-average exposition, and numerous examples, illustrations, and applications."

—Mathematical Reviews of the American Mathematical Society

An Introduction to Linear Programming and Game Theory, Third Edition presents a rigorous, yet accessible, introduction to the theoretical concepts and computational techniques of linear programming and game theory. Now with more extensive modeling exercises and detailed integer programming examples, this book uniquely illustrates how mathematics can be used in real-world applications in the social, life, and managerial sciences, providing readers with the opportunity to develop and apply their analytical abilities when solving realistic problems.

This Third Edition addresses various new topics and improvements in the field of mathematical programming, and it also presents two software programs, LP Assistant and the Solver add-in for Microsoft Office Excel, for solving linear programming problems. LP Assistant, developed by coauthor Gerard Keough, allows readers to perform the basic steps of the algorithms provided in the book and is freely available via the book's related Web site. The use of the sensitivity analysis report and integer programming algorithm from the Solver add-in for Microsoft Office Excel is introduced so readers can solve the book's linear and integer programming problems. A detailed appendix contains instructions for the use of both applications.

Additional features of the Third Edition include:

A discussion of sensitivity analysis for the two-variable problem, along with new examples demonstrating integer programming, non-linear programming, and make vs. buy modelsRevised proofs and a discussion on the relevance and solution of the dual problem

A section on developing an example in Data Envelopment Analysis

An outline of the proof of John Nash's theorem on the existence of equilibrium strategy pairs for non-cooperative, non-zero-sum games

Providing a complete mathematical development of all presented concepts and examples, Introduction to Linear Programming and Game Theory, Third Edition is an ideal text for linear programming and mathematical modeling courses at the upper-undergraduate and graduate levels. It also serves as a valuable reference for professionals who use game theory in business, economics, and management science.

This revision is a cover-to-cover expansion and renovation of the third edition. It now includes an introduction to tensor computations and brand new sections on • fast transforms• parallel LU• discrete Poisson solvers• pseudospectra• structured linear equation problems• structured eigenvalue problems• large-scale SVD methods• polynomial eigenvalue problems

Matrix Computations is packed with challenging problems, insightful derivations, and pointers to the literature—everything needed to become a matrix-savvy developer of numerical methods and software.

Fortunately, there's Schaum's.

More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. You also get hundreds of examples, solved problems, and practice exercises to test your skills.

This Schaum's Outline gives you

More than 2,400 formulas and tables Covers elementary to advanced math topics Arranged by topics for easy referenceFully compatible with your classroom text, Schaum's highlights all the important facts you need to know. Use Schaum's to shorten your study time--and get your best test scores!

Widely lauded for avoiding the typical black box approach found in other operating system textbooks, the first edition of this bestselling book taught readers how an operating system works and explained how to build it from the ground up.

Continuing to follow a logical pattern for system design, Operating System Design: The Xinu Approach, Second Edition removes the mystery from operating system design and consolidates the body of material into a systematic discipline. It presents a hierarchical design paradigm that organizes major operating system components in an orderly, understandable manner.

The book guides readers through the construction of a conventional process-based operating system using practical, straightforward primitives. It gives the implementation details of one set of primitives, usually the most popular set. Once readers understand how primitives can be implemented on conventional hardware, they can then easily implement alternative versions.

The text begins with a bare machine and proceeds step-by-step through the design and implementation of Xinu, which is a small, elegant operating system that supports dynamic process creation, dynamic memory allocation, network communication, local and remote file systems, a shell, and device-independent I/O functions. The Xinu code runs on many hardware platforms. This second edition has been completely rewritten to contrast operating systems for RISC and CISC processors. Encouraging hands-on experimentation, the book provides updated code throughout and examples for two low-cost experimenter boards: BeagleBone Black from ARM and Galileo from Intel.

Got a grasp on the terms and concepts you need to know, but get lost halfway through a problem or worse yet, not know where to begin? No fear - this hands-on-guide focuses on helping you solve the many types of trigonometry equations you encounter in a focused, step-by-step manner. With just enough refresher explanations before each set of problems, you'll sharpen your skills and improve your performance. You'll see how to work with angles, circles, triangles, graphs, functions, the laws of sines and cosines, and more!

100s of Problems!

* Step-by-step answer sets clearly identify where you went wrong (or right) with a problem

* Get the inside scoop on graphing trig functions

* Know where to begin and how to solve the most common equations

* Use trig in practical applications with confidence

The book serves two very different audiences: the curious science reader and the technical computational reader. The chapters build in mathematical sophistication, so that the first five are accessible to the general academic reader. While other chapters are much more mathematical in nature, each one contains something for both audiences. For example, the authors include entertaining asides such as how search engines make money and how the Great Firewall of China influences research.

The book includes an extensive background chapter designed to help readers learn more about the mathematics of search engines, and it contains several MATLAB codes and links to sample web data sets. The philosophy throughout is to encourage readers to experiment with the ideas and algorithms in the text.

Any business seriously interested in improving its rankings in the major search engines can benefit from the clear examples, sample code, and list of resources provided.

Many illustrative examples and entertaining asides MATLAB code Accessible and informal style Complete and self-contained section for mathematics reviewStorytelling with Data teaches you the fundamentals of data visualization and how to communicate effectively with data. You'll discover the power of storytelling and the way to make data a pivotal point in your story. The lessons in this illuminative text are grounded in theory, but made accessible through numerous real-world examples—ready for immediate application to your next graph or presentation.

Storytelling is not an inherent skill, especially when it comes to data visualization, and the tools at our disposal don't make it any easier. This book demonstrates how to go beyond conventional tools to reach the root of your data, and how to use your data to create an engaging, informative, compelling story. Specifically, you'll learn how to:

Understand the importance of context and audience Determine the appropriate type of graph for your situation Recognize and eliminate the clutter clouding your information Direct your audience's attention to the most important parts of your data Think like a designer and utilize concepts of design in data visualization Leverage the power of storytelling to help your message resonate with your audienceTogether, the lessons in this book will help you turn your data into high impact visual stories that stick with your audience. Rid your world of ineffective graphs, one exploding 3D pie chart at a time. There is a story in your data—Storytelling with Data will give you the skills and power to tell it!

The Second Edition maintained the accessibility of the first, while providing an introduction to the use of computers and expanding discussion on certain topics. Further emphasis was placed on topological properties, properties of geodesics, singularities of vector fields, and the theorems of Bonnet and Hadamard.

This revision of the Second Edition provides a thorough update of commands for the symbolic computation programs Mathematica or Maple, as well as additional computer exercises. As with the Second Edition, this material supplements the content but no computer skill is necessary to take full advantage of this comprehensive text.

Over 36,000 copies sold worldwideAccessible, practical yet rigorous approach to a complex topic--also suitable for self-studyExtensive update of appendices on Mathematica and Maple software packagesThorough streamlining of second edition's numbering systemFuller information on solutions to odd-numbered problemsAdditional exercises and hints guide students in using the latest computer modeling toolsThe Essentials For Dummies Series

Dummies is proud to present our new series, The Essentials For Dummies. Now students who are prepping for exams, preparing to study new material, or who just need a refresher can have a concise, easy-to-understand review guide that covers an entire course by concentrating solely on the most important concepts. From algebra and chemistry to grammar and Spanish, our expert authors focus on the skills students most need to succeed in a subject.

The book starts at an elementary level of mathematical modeling, assuming that the reader has had high school mathematics and first-year calculus. Otto and Day then gradually build in depth and complexity, from classic models in ecology and evolution to more intricate class-structured and probabilistic models. The authors provide primers with instructive exercises to introduce readers to the more advanced subjects of linear algebra and probability theory. Through examples, they describe how models have been used to understand such topics as the spread of HIV, chaos, the age structure of a country, speciation, and extinction.

Ecologists and evolutionary biologists today need enough mathematical training to be able to assess the power and limits of biological models and to develop theories and models themselves. This innovative book will be an indispensable guide to the world of mathematical models for the next generation of biologists.

A how-to guide for developing new mathematical models in biology Provides step-by-step recipes for constructing and analyzing models Interesting biological applications Explores classical models in ecology and evolution Questions at the end of every chapter Primers cover important mathematical topics Exercises with answers Appendixes summarize useful rules Labs and advanced material availableThe ability to guesstimate on your feet is an essential skill to have in today's world, whether you're trying to distinguish between a billion-dollar subsidy and a trillion-dollar stimulus, a megawatt wind turbine and a gigawatt nuclear plant, or parts-per-million and parts-per-billion contaminants. Lawrence Weinstein begins with a concise tutorial on how to solve these kinds of order of magnitude problems, and then invites readers to have a go themselves. The book features dozens of problems along with helpful hints and easy-to-understand solutions. It also includes appendixes containing useful formulas and more.

Guesstimation 2.0 shows how to estimate everything from how closely you can orbit a neutron star without being pulled apart by gravity, to the fuel used to transport your food from the farm to the store, to the total length of all toilet paper used in the United States. It also enables readers to answer, once and for all, the most asked environmental question of our day: paper or plastic?

Dr. Michael Guillen, known to millions as the science editor of ABC's Good Morning America, tells the fascinating stories behind five mathematical equations.

As a regular contributor to daytime's most popular morning news show and an instructor at Harvard University, Dr. Michael Guillen has earned the respect of millions as a clear and entertaining guide to the exhilarating world of science and mathematics.

Now Dr. Guillen unravels the equations that have led to the inventions and events that characterize the modern world, one of which -- Albert Einstein's famous energy equation, E=mc2 -- enabled the creation of the nuclear bomb. Also revealed are the mathematical foundations for the moon landing, airplane travel, the electric generator -- and even life itself.

Praised by Publishers Weekly as "a wholly accessible, beautifully written exploration of the potent mathematical imagination," and named a Best Nonfiction Book of 1995, the stories behind The Five Equations That Changed the World, as told by Dr. Guillen, are not only chronicles of science, but also gripping dramas of jealousy, fame, war, and discovery.

For the philosopher, scientist, poet, art historian, music listener, artist, as well as the general reader who wants to understand more about the fascinating properties of numbers, this is a beautifully written, exciting account of the search for a naturally manifested aesthetic that has occupied man since he first asked the question "why?"

"This is a delightful book to read. . . . It wanders here and there through some of the most attractive byways of simple mathematics, returning always to the oddities and pleasures of the golden section. This is a browser's book — a happy, untidy traveling or bedside book for those who know how to enjoy the charm of numbers and shapes." — Dr. J. Bronowski, The Salk Institute.

Like the original, Ian Stewart's commentary takes readers on a strange and wonderful journey. With clarity and wit, Stewart illuminates Abbott's numerous Victorian references and touches on such diverse topics as ancient Babylon, Karl Marx, Mary Shelley's Frankenstein, Mt. Everest, H.G. Wells, and phrenology. The Annotated Flatland makes fascinating connections between Flatland and Abbott's era, resulting in a classic to rival Abbott's own, and a book that will inspire and delight curious readers for generations to come.

For more than forty years, A History of Mathematics has been the reference of choice for those looking to learn about the fascinating history of humankind’s relationship with numbers, shapes, and patterns. This revised edition features up-to-date coverage of topics such as Fermat’s Last Theorem and the Poincaré Conjecture, in addition to recent advances in areas such as finite group theory and computer-aided proofs.

Distills thousands of years of mathematics into a single, approachable volume Covers mathematical discoveries, concepts, and thinkers, from Ancient Egypt to the present Includes up-to-date references and an extensive chronological table of mathematical and general historical developments.Whether you're interested in the age of Plato and Aristotle or Poincaré and Hilbert, whether you want to know more about the Pythagorean theorem or the golden mean, A History of Mathematics is an essential reference that will help you explore the incredible history of mathematics and the men and women who created it.

Along the way, you'll go beyond solving hundreds of repetitive problems, and actually use what you learn to make real-life decisions. Does it make sense to buy two years of insurance on a car that depreciates as soon as you drive it off the lot? Can you really afford an XBox 360 and a new iPhone? Learn how to put algebra to work for you, and nail your class exams along the way.

Your time is way too valuable to waste struggling with new concepts. Using the latest research in cognitive science and learning theory to craft a multi-sensory learning experience, Head First Algebra uses a visually rich format specifically designed to take advantage of the way your brain really works.

- An introduction to positive and negative numbers and place values

- A solid review of the four basic math operations: addition, subtraction, multiplication, and division

- Step-by-step guidance on how to understand and solve word problems

- An explanation of the concepts of factors and multiples

- Help in working with fractions, decimals, and percents

- The basics of geometry

- Weights, measures, and other practical applications of mathematics

- How to create and interpret mathematical graphs

- A grounding in statistics and probability

- An introduction to algebraic concepts and problems, including expressions and equations

This book is intended for both students and teachers who love mathematics and want to study its various branches beyond the limits of school curriculum.

SHE’LL TRY TO SOLVE FIVE QUESTIONS IN THREE HOURS, FOR ONE IMPROBABLE DREAM.

THE DREAM OF REPRESENTING HER COUNTRY, AND BECOMING A MATH OLYMPIAN.

As a small-town girl in Nova Scotia bullied for liking numbers more than boys, and lacking the encouragement of her unsupportive single mother who frowns at her daughter’s unrealistic ambition, Bethany's road to the International Math Olympiad has been marked by numerous challenges.

Through persistence, perseverance, and the support of innovative mentors who inspire her with a love of learning, Bethany confronts these challenges and develops the creativity and confidence to reach her potential.

In training to become a world-champion "mathlete", Bethany discovers the heart of mathematics – a subject that’s not about memorizing formulas, but rather about problem-solving and detecting patterns to uncover truth, as well as learning how to apply the deep and unexpected connections of mathematics to every aspect of her life, including athletics, spirituality, and environmental sustainability.

As Bethany reflects on her long journey and envisions her exciting future, she realizes that she has shattered the misguided stereotype that only boys can excel in math, and discovers a sense of purpose that through mathematics, she can and she will make an extraordinary contribution to society.