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This third edition is completed by a number of additional figures, examples and exercises. The text and formulae have been revised and improved where necessary.

“Artfully envisions a breathtakingly better world.” —Los Angeles Times

“Elaborate, smart and persuasive.” —The Boston Globe

“A pleasure to read.” —The Wall Street Journal

One of CBS News’s Best Fall Books of 2005 • Among St Louis Post-Dispatch’s Best Nonfiction Books of 2005 • One of Amazon.com’s Best Science Books of 2005

A radical and optimistic view of the future course of human development from the bestselling author of How to Create a Mind and The Age of Spiritual Machines who Bill Gates calls “the best person I know at predicting the future of artificial intelligence”

For over three decades, Ray Kurzweil has been one of the most respected and provocative advocates of the role of technology in our future. In his classic The Age of Spiritual Machines, he argued that computers would soon rival the full range of human intelligence at its best. Now he examines the next step in this inexorable evolutionary process: the union of human and machine, in which the knowledge and skills embedded in our brains will be combined with the vastly greater capacity, speed, and knowledge-sharing ability of our creations.

From the Trade Paperback edition.

Artificial Intelligence helps choose what books you buy, what movies you see, and even who you date. It puts the "smart" in your smartphone and soon it will drive your car. It makes most of the trades on Wall Street, and controls vital energy, water, and transportation infrastructure. But Artificial Intelligence can also threaten our existence.

In as little as a decade, AI could match and then surpass human intelligence. Corporations and government agencies are pouring billions into achieving AI's Holy Grail—human-level intelligence. Once AI has attained it, scientists argue, it will have survival drives much like our own. We may be forced to compete with a rival more cunning, more powerful, and more alien than we can imagine.

Through profiles of tech visionaries, industry watchdogs, and groundbreaking AI systems, Our Final Invention explores the perils of the heedless pursuit of advanced AI. Until now, human intelligence has had no rival. Can we coexist with beings whose intelligence dwarfs our own? And will they allow us to?

Ray Kurzweil is arguably today’s most influential—and often controversial—futurist. In How to Create a Mind, Kurzweil presents a provocative exploration of the most important project in human-machine civilization—reverse engineering the brain to understand precisely how it works and using that knowledge to create even more intelligent machines.

Kurzweil discusses how the brain functions, how the mind emerges from the brain, and the implications of vastly increasing the powers of our intelligence in addressing the world’s problems. He thoughtfully examines emotional and moral intelligence and the origins of consciousness and envisions the radical possibilities of our merging with the intelligent technology we are creating.

Certain to be one of the most widely discussed and debated science books of the year, How to Create a Mind is sure to take its place alongside Kurzweil’s previous classics which include Fantastic Voyage: Live Long Enough to Live Forever and The Age of Spiritual Machines.

From the Hardcover edition.

Jeff Hawkins, the man who created the PalmPilot, Treo smart phone, and other handheld devices, has reshaped our relationship to computers. Now he stands ready to revolutionize both neuroscience and computing in one stroke, with a new understanding of intelligence itself.

Hawkins develops a powerful theory of how the human brain works, explaining why computers are not intelligent and how, based on this new theory, we can finally build intelligent machines.

The brain is not a computer, but a memory system that stores experiences in a way that reflects the true structure of the world, remembering sequences of events and their nested relationships and making predictions based on those memories. It is this memory-prediction system that forms the basis of intelligence, perception, creativity, and even consciousness.

In an engaging style that will captivate audiences from the merely curious to the professional scientist, Hawkins shows how a clear understanding of how the brain works will make it possible for us to build intelligent machines, in silicon, that will exceed our human ability in surprising ways.

Written with acclaimed science writer Sandra Blakeslee, On Intelligence promises to completely transfigure the possibilities of the technology age. It is a landmark book in its scope and clarity.

Whether you are a student struggling to fulfill a math or science requirement, or you are embarking on a career change that requires a new skill set, A Mind for Numbers offers the tools you need to get a better grasp of that intimidating material. Engineering professor Barbara Oakley knows firsthand how it feels to struggle with math. She flunked her way through high school math and science courses, before enlisting in the army immediately after graduation. When she saw how her lack of mathematical and technical savvy severely limited her options—both to rise in the military and to explore other careers—she returned to school with a newfound determination to re-tool her brain to master the very subjects that had given her so much trouble throughout her entire life.

In A Mind for Numbers, Dr. Oakley lets us in on the secrets to learning effectively—secrets that even dedicated and successful students wish they’d known earlier. Contrary to popular belief, math requires creative, as well as analytical, thinking. Most people think that there’s only one way to do a problem, when in actuality, there are often a number of different solutions—you just need the creativity to see them. For example, there are more than three hundred different known proofs of the Pythagorean Theorem. In short, studying a problem in a laser-focused way until you reach a solution is not an effective way to learn. Rather, it involves taking the time to step away from a problem and allow the more relaxed and creative part of the brain to take over. The learning strategies in this book apply not only to math and science, but to any subject in which we struggle. We all have what it takes to excel in areas that don't seem to come naturally to us at first, and learning them does not have to be as painful as we might think!

From the Trade Paperback edition.

In Love and Math, renowned mathematician Edward Frenkel reveals a side of math we’ve never seen, suffused with all the beauty and elegance of a work of art. In this heartfelt and passionate book, Frenkel shows that mathematics, far from occupying a specialist niche, goes to the heart of all matter, uniting us across cultures, time, and space.

Love and Math tells two intertwined stories: of the wonders of mathematics and of one young man’s journey learning and living it. Having braved a discriminatory educational system to become one of the twenty-first century’s leading mathematicians, Frenkel now works on one of the biggest ideas to come out of math in the last 50 years: the Langlands Program. Considered by many to be a Grand Unified Theory of mathematics, the Langlands Program enables researchers to translate findings from one field to another so that they can solve problems, such as Fermat’s last theorem, that had seemed intractable before.

At its core, Love and Math is a story about accessing a new way of thinking, which can enrich our lives and empower us to better understand the world and our place in it. It is an invitation to discover the magic hidden universe of mathematics.

The math we learn in school can seem like a dull set of rules, laid down by the ancients and not to be questioned. In How Not to Be Wrong, Jordan Ellenberg shows us how terribly limiting this view is: Math isn’t confined to abstract incidents that never occur in real life, but rather touches everything we do—the whole world is shot through with it.

Math allows us to see the hidden structures underneath the messy and chaotic surface of our world. It’s a science of not being wrong, hammered out by centuries of hard work and argument. Armed with the tools of mathematics, we can see through to the true meaning of information we take for granted: How early should you get to the airport? What does “public opinion” really represent? Why do tall parents have shorter children? Who really won Florida in 2000? And how likely are you, really, to develop cancer?

How Not to Be Wrong presents the surprising revelations behind all of these questions and many more, using the mathematician’s method of analyzing life and exposing the hard-won insights of the academic community to the layman—minus the jargon. Ellenberg chases mathematical threads through a vast range of time and space, from the everyday to the cosmic, encountering, among other things, baseball, Reaganomics, daring lottery schemes, Voltaire, the replicability crisis in psychology, Italian Renaissance painting, artificial languages, the development of non-Euclidean geometry, the coming obesity apocalypse, Antonin Scalia’s views on crime and punishment, the psychology of slime molds, what Facebook can and can’t figure out about you, and the existence of God.

Ellenberg pulls from history as well as from the latest theoretical developments to provide those not trained in math with the knowledge they need. Math, as Ellenberg says, is “an atomic-powered prosthesis that you attach to your common sense, vastly multiplying its reach and strength.” With the tools of mathematics in hand, you can understand the world in a deeper, more meaningful way. How Not to Be Wrong will show you how.

Everything you need to pass the exam and get the college credit you deserve.

CLEP* is the most popular credit-by-examination program in the country, accepted by more than 2,900 colleges and universities. For over 15 years, REA has helped students pass the CLEP* exam and earn college credit while reducing their tuition costs.

Our CLEP* test preps are perfect for adults returning to college (or attending for the first time), military service members, high-school graduates looking to earn college credit, or home-schooled students with knowledge that can translate into college credit.

There are many different ways to prepare for the CLEP*. What's best for you depends on how much time you have to study and how comfortable you are with the subject matter. Our test prep for CLEP* College Algebra and the free online tools that come with it, will allow you to create a personalized CLEP* study plan that can be customized to fit you: your schedule, your learning style, and your current level of knowledge.

Here's how it works:

Diagnostic exam at the REA Study Center focuses your study

Our online diagnostic exam pinpoints your strengths and shows you exactly where you need to focus your study. Armed with this information, you can personalize your prep and review where you need it the most.

Most complete subject review for CLEP* College Algebra

Our targeted review covers all the material you'll be expected to know for the exam and includes a glossary of must-know terms.

Two full-length practice exams

The online REA Study Center gives you two full-length practice tests and the most powerful scoring analysis and diagnostic tools available today. Instant score reports help you zero in on the CLEP* College Algebra topics that give you trouble now and show you how to arrive at the correct answer-so you'll be prepared on test day.

Alpha Teach Yourself Algebra I in 24 Hours provides readers with a structured, self-paced, straight-forward tutorial on algebra. It's the perfect textbook companion for students struggling with algebra, a solid primer for those looking to get a head start on an upcoming class, and a welcome refresher for parents tasked with helping out with homework. The book provides 24 one-hour lessons, with each chapter designed to build on the previous one.

? Covers classifying number sets, expressions, polynomials, factoring, radicals, exponents and logarithms, and much more

? Each chapter ends with a quiz so readers can identify where they may need more help

From the Trade Paperback edition.

Factor fearlessly, conquer the quadratic formula, and solve linear equations

There's no doubt that algebra can be easy to some while extremely challenging to others. If you're vexed by variables, Algebra I For Dummies, 2nd Edition provides the plain-English, easy-to-follow guidance you need to get the right solution every time!

Now with 25% new and revised content, this easy-to-understand reference not only explains algebra in terms you can understand, but it also gives you the necessary tools to solve complex problems with confidence. You'll understand how to factor fearlessly, conquer the quadratic formula, and solve linear equations.

Includes revised and updated examples and practice problems Provides explanations and practical examples that mirror today's teaching methods Other titles by Sterling: Algebra II For Dummies and Algebra Workbook For DummiesWhether you're currently enrolled in a high school or college algebra course or are just looking to brush-up your skills, Algebra I For Dummies, 2nd Edition gives you friendly and comprehensible guidance on this often difficult-to-grasp subject.

For those who slept through Stats 101, this book is a lifesaver. Wheelan strips away the arcane and technical details and focuses on the underlying intuition that drives statistical analysis. He clarifies key concepts such as inference, correlation, and regression analysis, reveals how biased or careless parties can manipulate or misrepresent data, and shows us how brilliant and creative researchers are exploiting the valuable data from natural experiments to tackle thorny questions.

And in Wheelan’s trademark style, there’s not a dull page in sight. You’ll encounter clever Schlitz Beer marketers leveraging basic probability, an International Sausage Festival illuminating the tenets of the central limit theorem, and a head-scratching choice from the famous game show Let’s Make a Deal—and you’ll come away with insights each time. With the wit, accessibility, and sheer fun that turned Naked Economics into a bestseller, Wheelan defies the odds yet again by bringing another essential, formerly unglamorous discipline to life.

Tips for simplifying tricky basic math and pre-algebra operations

Whether you're a student preparing to take algebra or a parent who wants or needs to brush up on basic math, this fun, friendly guide has the tools you need to get in gear. From positive, negative, and whole numbers to fractions, decimals, and percents, you'll build necessary math skills to tackle more advanced topics, such as imaginary numbers, variables, and algebraic equations.

Explanations and practical examples that mirror today's teaching methods Relevant cultural vernacular and references Standard For Dummiesmaterials that match the current standard and designBasic Math & Pre-Algebra For Dummies takes the intimidation out of tricky operations and helps you get ready for algebra!

Written by two pioneers of the concept of math anxiety and how to overcome it, Arithmetic and Algebra Again has helped tens of thousands of people conquer their irrational fear of math.

This revised and expanded second edition of the perennial bestseller:

Features the latest techniques for breaking through common anxieties about numbers Takes a real-world approach that lets mathphobes learn the math they need as they need it Covers all key math areas--from whole numbers and fractions to basic algebra Features a section on practical math for banking, mortgages, interest, and statistics and probability Includes a new section on the graphing calculator, a chapter on the metric system, a section on word problems, and all updated exercisesThis authoritative, modern translation by I. Bernard Cohen and Anne Whitman, the first in more than 285 years, is based on the 1726 edition, the final revised version approved by Newton; it includes extracts from the earlier editions, corrects errors found in earlier versions, and replaces archaic English with contemporary prose and up-to-date mathematical forms.

Newton's principles describe acceleration, deceleration, and inertial movement; fluid dynamics; and the motions of the earth, moon, planets, and comets. A great work in itself, the Principia also revolutionized the methods of scientific investigation. It set forth the fundamental three laws of motion and the law of universal gravity, the physical principles that account for the Copernican system of the world as emended by Kepler, thus effectively ending controversy concerning the Copernican planetary system.

The translation-only edition of this preeminent work is truly accessible for today's scientists, scholars, and students.

This well-known and highly regarded text makes the subject accessible to undergraduates with little mathematical experience. Written mainly for students in physics, engineering, economics, and other fields outside mathematics, the book gives the theory of matrices and applications to systems of linear equations, as well as many related topics such as determinants, eigenvalues, and differential equations.

Table of Contents:

l. The Algebra of Matrices

2. Linear Equations

3. Vector Spaces

4. Determinants

5. Linear Transformations

6. Eigenvalues and Eigenvectors

7. Inner Product Spaces

8. Applications to Differential Equations

For the second edition, the authors added several exercises in each chapter and a brand new section in Chapter 7. The exercises, which are both true-false and multiple-choice, will enable the student to test his grasp of the definitions and theorems in the chapter. The new section in Chapter 7 illustrates the geometric content of Sylvester's Theorem by means of conic sections and quadric surfaces. 6 line drawings. lndex. Two prefaces. Answer section.

Trying to tackle algebra but nothing's adding up? No problem! Factor in Algebra Demystified, Second Edition and multiply your chances of learning this important branch of mathematics.

Written in a step-by-step format, this practical guide covers fractions, variables, decimals, negative numbers, exponents, roots, and factoring. Techniques for solving linear and quadratic equations and applications are discussed in detail. Clear examples, concise explanations, and worked problems with complete solutions make it easy to understand the material, and end-of-chapter quizzes and a final exam help reinforce learning.

It's a no-brainer! You'll learn how to:

Translate English sentences into mathematical symbols Write the negative of numbers and variables Factor expressions Use the distributive property to expand expressions Solve applied problemsSimple enough for a beginner, but challenging enough for an advanced student, Algebra Demystified, Second Edition helps you master this essential math subject. It's also the perfect resource for preparing you for higher level math classes and college placement tests.

Linear Sentences in One Variable

Segments, Lines, and Inequalities

Linear Sentences in Two Variables

Linear Equations in Three Variables

Polynomial Arithmetic

Factoring Polynomials

Rational Expressions

Relations and Functions

Polynomial Functions

Radicals and Complex Numbers

Quadratics in One Variable

Conic Sections

Quadratic Systems

Exponential and Logarithmic Functions

Sequences and Series

Additional Topics

Word Problems

Review Questions

Resource Center

Glossary

This popular study guide shows students easy ways to solve what they struggle with most in algebra: word problems. How to Solve Word Problems in Algebra, Second Edition, is ideal for anyone who wants to master these skills. Completely updated, with contemporary language and examples, features solution methods that are easy to learn and remember, plus a self-test.

Now updated with 30% new material, Roark Formulas for Stress and Strain, Seventh Edition, is the ultimate resource for designers, engineers, and analysts who need to calculate loads and stress. This landmark reference from Warren Young and Richard Budynas provides you with equations and diagrams of structural properties in an easy-to-use, thumb-through format. Updated, with a user-friendly page layout, this new edition includes expanded coverage of joints, bearing and shear stress, experimental stress analysis, and stress concentrations, as well as material behavior coverage and stress and strain measurement. You’ll also find expanded tables and cases; improved notations and figures in the tables; consistent table and equation numbering; and verification of correction factors.

Practice makes perfect—and helps deepen your understanding of algebra by solving problems

1,001 Algebra I Practice Problems For Dummies, with free access to online practice problems, takes you beyond the instruction and guidance offered in Algebra I For Dummies, giving you 1,001 opportunities to practice solving problems from the major topics in algebra. You start with some basic operations, move on to algebraic properties, polynomials, and quadratic equations, and finish up with graphing. Every practice question includes not only a solution but a step-by-step explanation. From the book, go online and find:

One year free subscription to all 1,001 practice problems On-the-go access any way you want it—from your computer, smart phone, or tablet Multiple choice questions on all you math course topics Personalized reports that track your progress and help show you where you need to study the most Customized practice sets for self-directed study Practice problems categorized as easy, medium, or hardWhether you're studying algebra at the high school or college level, the practice problems in 1,001 Algebra I Practice Problems For Dummies give you a chance to practice and reinforce the skill s you learn in the classroom and help you refine your understanding of algebra.

Note to readers: 1,001 Algebra I Practice Problems For Dummies, which only includes problems to solve, is a great companion to Algebra I For Dummies, 2nd Edition which offers complete instruction on all topics in a typical Algebra I course.

Fortunately, there's Schaum's. This all-in-one-package includes more than 1,900 fully solved problems, examples, and practice exercises to sharpen your problem-solving skills. Plus, you will have access to 30 detailed videos featuring Math instructors who explain how to solve the most commonly tested problems--it's just like having your own virtual tutor! You'll find everything you need to build confidence, skills, and knowledge for the highest score possible.

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. Helpful tables and illustrations increase your understanding of the subject at hand.

This Schaum's Outline gives you

1,940 fully solved problems Hundreds of additional practice problems with answers Coverage of all course conceptsFully 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!

Schaum's Outlines--Problem Solved.

Ready to learn math fundamentals but can't seem to get your brain to function? No problem! Add Pre-Algebra Demystified, Second Edition, to the equation and you'll solve your dilemma in no time.

Written in a step-by-step format, this practical guide begins by covering whole numbers, integers, fractions, decimals, and percents. You'll move on to expressions, equations, measurement, and graphing. Operations with monomials and polynomials are also discussed. Detailed examples, concise explanations, and worked problems make it easy to understand the material, and end-of-chapter quizzes and a final exam help reinforce learning.

It's a no-brainer! You'll learn:

Addition, subtraction, multiplication, and division of whole numbers, integers, fractions, decimals, and algebraic expressions Techniques for solving equations and problems Measures of length, weight, capacity, and time Methods for plotting points and graphing linesSimple enough for a beginner, but challenging enough for an advanced student, Pre-Algebra Demystified, Second Edition, helps you master this essential mathematics subject. It's also the perfect way to review the topic if all you need is a quick refresh.

Assuming no knowledge of programming, this book guides the reader both programming and built-in functions to easily exploit MATLAB's extensive capabilities for tackling engineering problems. The book starts with programming concepts, such as variables, assignments, and selection statements, moves on to loops, and then solves problems using both the programming concept and the power of MATLAB. In-depth coverage is given to input/output, a topic fundamental to many engineering applications.

Winner of a 2017 Textbook Excellence Award (Texty) from the Textbook and Academic Authors AssociationPresents programming concepts and MATLAB built-in functions side-by-sideOffers a systematic, step-by-step approach, building on concepts throughout the book and facilitating easier learningIncludes sections on common pitfalls and programming guidelines to direct students toward best practicesCombines basic programming concepts, built-in functions, and advanced topics for problem solving with MATLAB to make this book uniquely suitable for a wide range of courses teaching or using MATLAB across the curriculumThis authoritative, modern translation by I. Bernard Cohen and Anne Whitman, the first in more than 285 years, is based on the 1726 edition, the final revised version approved by Newton; it includes extracts from the earlier editions, corrects errors found in earlier versions, and replaces archaic English with contemporary prose and up-to-date mathematical forms.

Newton's principles describe acceleration, deceleration, and inertial movement; fluid dynamics; and the motions of the earth, moon, planets, and comets. A great work in itself, the Principia also revolutionized the methods of scientific investigation. It set forth the fundamental three laws of motion and the law of universal gravity, the physical principles that account for the Copernican system of the world as emended by Kepler, thus effectively ending controversy concerning the Copernican planetary system.

The illuminating Guide to Newton's Principia by I. Bernard Cohen makes this preeminent work truly accessible for today's scientists, scholars, and students.

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.

Physicist Dave Goldberg speeds across space, time and everything in between showing that our elegant universe—from the Higgs boson to antimatter to the most massive group of galaxies—is shaped by hidden symmetries that have driven all our recent discoveries about the universe and all the ones to come.

Why is the sky dark at night? If there is anti-matter, can there be anti-people? Why are past, present, and future our only options? Saluting the brilliant but unsung female mathematician Emmy Noether as well as other giants of physics, Goldberg answers these questions and more, exuberantly demonstrating that symmetry is the big idea—and the key to what lies ahead.

From the Trade Paperback edition.

Practice Makes Perfect: Algebra II presents thorough coverage of skills, such as handling decimals and fractions, functions, and linear and quadratic equations, as well as an introducing you to probability and trigonometry. Inside you will find the help you need for boosting your skills, preparing for an exam or re-introducing yourself to the subject. More than 500 exercises and answers covering all aspects of algebra will get you on your way to mastering algebra!

"The main object of this book is to dispel the fear of mathematics," declares author W. W. Sawyer, adding that "Many people regard mathematicians as a race apart, possessed of almost supernatural powers. While this is very flattering for successful mathematicians, it is very bad for those who, for one reason or another, are attempting to learn the subject." Now retired, Sawyer won international renown for his innovative teaching methods, which he used at colleges in England and Scotland as well as Africa, New Zealand, and North America. His insights into the pleasures and practicalities of mathematics will appeal to readers of all backgrounds.

In this charming volume, a noted English mathematician uses humor and anecdote to illuminate the concepts underlying "new math": groups, sets, subsets, topology, Boolean algebra, and more. According to Professor Stewart, an understanding of these concepts offers the best route to grasping the true nature of mathematics, in particular the power, beauty, and utility of pure mathematics. No advanced mathematical background is needed (a smattering of algebra, geometry, and trigonometry is helpful) to follow the author's lucid and thought-provoking discussions of such topics as functions, symmetry, axiomatics, counting, topology, hyperspace, linear algebra, real analysis, probability, computers, applications of modern mathematics, and much more.

By the time readers have finished this book, they'll have a much clearer grasp of how modern mathematicians look at figures, functions, and formulas and how a firm grasp of the ideas underlying "new math" leads toward a genuine comprehension of the nature of mathematics itself.

With eight books and more than 30 years of hard-core classroom experience, Bob Miller is the frustrated student's best friend. He breaks down the complexities of every problem into easy-to-understand pieces that any math-phobe can understand-and this fully updated second edition of Bob Miller's Algebra for the Clueless covers everything a you need to know to excel in Algebra I and II.

Algebra II builds on your Algebra I skills to prepare you for trigonometry, calculus, and a of myriad STEM topics. Working through practice problems helps students better ingest and retain lesson content, creating a solid foundation to build on for future success.

Algebra II Workbook For Dummies, 2nd Edition helps you learn Algebra II by doing Algebra II. Author and math professor Mary Jane Sterling walks you through the entire course, showing you how to approach and solve the problems you encounter in class. You'll begin by refreshing your Algebra I skills, because you'll need a strong foundation to build upon. From there, you'll work through practice problems to clarify concepts and improve understanding and retention.

Revisit quadratic equations, inequalities, radicals, and basic graphs Master quadratic, exponential, and logarithmic functions Tackle conic sections, as well as linear and nonlinear systems Grasp the concepts of matrices, sequences, and imaginary numbersAlgebra II Workbook For Dummies, 2nd Edition includes sections on graphing and special sequences to familiarize you with the key concepts that will follow you to trigonometry and beyond. Don't waste any time getting started. Algebra II Workbook For Dummies, 2nd Edition is your complete guide to success.

"Such a richness of topics and amazing splendor of illustrations!" — Mathematics Magazine

"An inviting exposition for a literate but not highly scientific audience." — American Mathematical Monthly

This fascinating book explores the connections between chaos theory, physics, biology, and mathematics. Its award-winning computer graphics, optical illusions, and games illustrate the concept of self-similarity, a typical property of fractals. Author Manfred Schroeder — hailed by Publishers Weekly as a modern Lewis Carroll — conveys memorable insights in the form of puns and puzzles that relate abstract mathematics to everyday experience.

Excellent entertainment for readers with a grasp of algebra and some calculus, this book forms a fine university-level introduction to fractal math. Eight pages of color images clarify the text, along with numerous black-and-white illustrations.

Two of the authors co-wrote The Elements of Statistical Learning (Hastie, Tibshirani and Friedman, 2nd edition 2009), a popular reference book for statistics and machine learning researchers. An Introduction to Statistical Learning covers many of the same topics, but at a level accessible to a much broader audience. This book is targeted at statisticians and non-statisticians alike who wish to use cutting-edge statistical learning techniques to analyze their data. The text assumes only a previous course in linear regression and no knowledge of matrix algebra.

-- A natural transition from basic math to algebra, with a review of relevant concepts and operations.

-- An introduction to linear equations and functions, including graphing and inequalities.

-- Explanations of how to solve absolute-value equations and radical equations.

-- Instructions on how to perform operations on polynomials, and factoring.

-- An exploration of how to work with quadratic equations and quadratic functions; and rational expressions, equations, and functions.

-- Special sidebars pointing out the reasoning behind the techniques, which is an essential part of Common Core instruction.

-- Separate workbook section of extra Algebra practice problems-like getting two books in one!

Programming Collective Intelligence takes you into the world of machine learning and statistics, and explains how to draw conclusions about user experience, marketing, personal tastes, and human behavior in general -- all from information that you and others collect every day. Each algorithm is described clearly and concisely with code that can immediately be used on your web site, blog, Wiki, or specialized application. This book explains:Collaborative filtering techniques that enable online retailers to recommend products or mediaMethods of clustering to detect groups of similar items in a large datasetSearch engine features -- crawlers, indexers, query engines, and the PageRank algorithmOptimization algorithms that search millions of possible solutions to a problem and choose the best oneBayesian filtering, used in spam filters for classifying documents based on word types and other featuresUsing decision trees not only to make predictions, but to model the way decisions are madePredicting numerical values rather than classifications to build price modelsSupport vector machines to match people in online dating sitesNon-negative matrix factorization to find the independent features in a datasetEvolving intelligence for problem solving -- how a computer develops its skill by improving its own code the more it plays a gameEach chapter includes exercises for extending the algorithms to make them more powerful. Go beyond simple database-backed applications and put the wealth of Internet data to work for you.

"Bravo! I cannot think of a better way for a developer to first learn these algorithms and methods, nor can I think of a better way for me (an old AI dog) to reinvigorate my knowledge of the details."

-- Dan Russell, Google

"Toby's book does a great job of breaking down the complex subject matter of machine-learning algorithms into practical, easy-to-understand examples that can be directly applied to analysis of social interaction across the Web today. If I had this book two years ago, it would have saved precious time going down some fruitless paths."

-- Tim Wolters, CTO, Collective Intellect

After a brief overview, the approach begins with elementary toposes and advances to internal category theory, topologies and sheaves, geometric morphisms, and logical aspects of topos theory. Additional topics include natural number objects, theorems of Deligne and Barr, cohomology, and set theory. Each chapter concludes with a series of exercises, and an appendix and indexes supplement the text.