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A general methodology for solving functional equations is provided in Chapter 2. The different types of functional equations are described and solved in Chapters 3 to 8. Many examples, coming from different fields, as geometry, science, engineering, economics, probability, statistics, etc, help the reader to change his/her mind in order to state problems as functional equations as an alternative to differential equations, and to state new problems in terms of functional equations or systems.

An interesting feature of the book is that it deals with functional networks, a powerful generalization of neural networks that allows solving many practical problems. The second part of the book, Chapters 9 to 13, is devoted to the applications of this important paradigm.

The book contains many examples and end of chapter exercises, that facilitates the understanding of the concepts and applications.

· A general methodology for solving functional equations is provided in Chapter 2.

· It deals with functional networks, a powerful generalization of neural networks.

· Many examples, coming from different fields, as geometry, science, engineering, economics, probability, statistics, etc, illustrate the concept of functional equation.

· Functional equations are presented as a powerful alternative to differential equations.

· The book contains end of chapter exercises.

Modeling is one of the most effective, commonly used tools in engineering and the applied sciences. In this book, the authors deal with mathematical programming models both linear and nonlinear and across a wide range of practical applications.

Whereas other books concentrate on standard methods of analysis, the authors focus on the power of modeling methods for solving practical problems-clearly showing the connection between physical and mathematical realities-while also describing and exploring the main concepts and tools at work. This highly computational coverage includes:

* Discussion and implementation of the GAMS programming system

* Unique coverage of compatibility

* Illustrative examples that showcase the connection between model and reality

* Practical problems covering a wide range of scientific disciplines, as well as hundreds of examples and end-of-chapter exercises

* Real-world applications to probability and statistics, electrical engineering, transportation systems, and more

Building and Solving Mathematical Programming Models in Engineering and Science is practically suited for use as a professional reference for mathematicians, engineers, and applied or industrial scientists, while also tutorial and illustrative enough for advanced students in mathematics or engineering.

Several distinguished and active researchers highlight some of the recent developments in statistical distribution theory, order statistics and their properties, as well as inferential methods associated with them. Applications to survival analysis, reliability, quality control, and environmental problems are emphasized. The volume is classified into the following five parts, according to the focus of the articles:

* Discrete distributions and applications

* Continuous distributions and applications

* Order statistics and applications

* Reliability and applications

* Inference

This comprehensive reference work will serve the statistical and applied mathematics communities, as well as practitioners, researchers, and graduate students in applied probability and statistics, reliability engineering, and biostatistics.

Departing from the standard methods of analysis, this unique book presents methodologies and algorithms based on the concept of orthogonality and demonstrates their application to both standard and novel problems in linear algebra. Covering basic theory of linear systems, linear inequalities, and linear programming, it focuses on elegant, computationally simple solutions to real-world physical, economic, and engineering problems. The authors clearly explain the reasons behind the analysis of different structures and concepts and use numerous illustrative examples to correlate the mathematical models to the reality they represent. Readers are given precise guidelines for:

* Checking the equivalence of two systems

* Solving a system in certain selected variables

* Modifying systems of equations

* Solving linear systems of inequalities

* Using the new exterior point method

* Modifying a linear programming problem

With few prerequisites, but with plenty of figures and tables, end-of-chapter exercises as well as Java and Mathematica programs available from the authors' Web site, this is an invaluable text/reference for mathematicians, engineers, applied scientists, and graduate students in mathematics.

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.

Barron's popular "Painless Series " of study guides for middle school and high school students offer a lighthearted, often humorous approach to their subjects, transforming details that might once have seemed boring or difficult into a series of interesting and mentally challenging ideas. Most titles in the series feature many fun-to-solve "Brain Tickler" problems with answers at the end of each chapter.

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.

If you are absolutely confused by absolute value equations, or you think parabolas are short moral stories, College Algebra DeMYSTiFied, Second Edition is your solution to mastering the topic's concepts and theories at your own pace. This thoroughly revised and updated guide eases you into the subject, beginning with the math fundamentals then introducing you to this advanced form of algebra. As you progress, you will learn how to simplify rational expressions, divide complex numbers, and solve quadratic equations. You will understand the difference between odd and even functions and no longer be confused by the multiplicity of zeros. Detailed examples make it easy to understand the material, and end-of-chapter quizzes and a final exam help reinforce key ideas.

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

The x-y coordinate plane Lines and intercepts The FOIL method Functions Nonlinear equations Graphs of functions Exponents and logarithmsSimple enough for a beginner, but challenging enough for an advanced student, College Algebra DeMYSTiFieD, Second Edition is your shortcut to a working knowledge of this engaging subject.

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

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The Future of the Mind brings a topic that once belonged solely to the province of science fiction into a startling new reality. This scientific tour de force unveils the astonishing research being done in top laboratories around the world—all based on the latest advancements in neuroscience and physics—including recent experiments in telepathy, mind control, avatars, telekinesis, and recording memories and dreams. The Future of the Mind is an extraordinary, mind-boggling exploration of the frontiers of neuroscience. Dr. Kaku looks toward the day when we may achieve the ability to upload the human brain to a computer, neuron for neuron; project thoughts and emotions around the world on a brain-net; take a “smart pill” to enhance cognition; send our consciousness across the universe; and push the very limits of immortality.

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

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Glossary

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 exercisesTrying 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.

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.

Space and time form the very fabric of the cosmos. Yet they remain among the most mysterious of concepts. Is space an entity? Why does time have a direction? Could the universe exist without space and time? Can we travel to the past? Greene has set himself a daunting task: to explain non-intuitive, mathematical concepts like String Theory, the Heisenberg Uncertainty Principle, and Inflationary Cosmology with analogies drawn from common experience. From Newton’s unchanging realm in which space and time are absolute, to Einstein’s fluid conception of spacetime, to quantum mechanics’ entangled arena where vastly distant objects can instantaneously coordinate their behavior, Greene takes us all, regardless of our scientific backgrounds, on an irresistible and revelatory journey to the new layers of reality that modern physics has discovered lying just beneath the surface of our everyday world.

The 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.

“Where did the universe come from? What was there before it? What will the future bring? And finally, why is there something rather than nothing?”

One of the few prominent scientists today to have crossed the chasm between science and popular culture, Krauss describes the staggeringly beautiful experimental observations and mind-bending new theories that demonstrate not only can something arise from nothing, something will always arise from nothing. With a new preface about the significance of the discovery of the Higgs particle, A Universe from Nothing uses Krauss’s characteristic wry humor and wonderfully clear explanations to take us back to the beginning of the beginning, presenting the most recent evidence for how our universe evolved—and the implications for how it’s going to end.

Provocative, challenging, and delightfully readable, this is a game-changing look at the most basic underpinning of existence and a powerful antidote to outmoded philosophical, religious, and scientific thinking.

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.

The third edition contains major improvements and revisions throughout the book. More than 300 new exercises have been added since the previous edition. Many new examples have been added to illustrate the key ideas of linear algebra. New topics covered in the book include product spaces, quotient spaces, and dual spaces. Beautiful new formatting creates pages with an unusually pleasant appearance in both print and electronic versions.

No prerequisites are assumed other than the usual demand for suitable mathematical maturity. Thus the text starts by discussing vector spaces, linear independence, span, basis, and dimension. The book then deals with linear maps, eigenvalues, and eigenvectors. Inner-product spaces are introduced, leading to the finite-dimensional spectral theorem and its consequences. Generalized eigenvectors are then used to provide insight into the structure of a linear operator.

The crisis was partly a failure of mathematical modeling. But even more, it was a failure of some very sophisticated financial institutions to think like physicists. Models—whether in science or finance—have limitations; they break down under certain conditions. And in 2008, sophisticated models fell into the hands of people who didn’t understand their purpose, and didn’t care. It was a catastrophic misuse of science.

The solution, however, is not to give up on models; it's to make them better. Weatherall reveals the people and ideas on the cusp of a new era in finance. We see a geophysicist use a model designed for earthquakes to predict a massive stock market crash. We discover a physicist-run hedge fund that earned 2,478.6% over the course of the 1990s. And we see how an obscure idea from quantum theory might soon be used to create a far more accurate Consumer Price Index.

Both persuasive and accessible, The Physics of Wall Street is riveting history that will change how we think about our economic future.

Fortunately for you, 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

885 fully solved problems Complete review of all course fundamentalsFully 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!

Topics include: Fundamental Concepts; Polynomials; Rational Expressions; First-Degree Equations and Inequalities; Exponents, Roots, and Radicals; Second-Degree Equations and Inequalities; Systems of Equations and Inequalities; Relations and Functions; Exponential and Logarithmic Functions; and Sequences, Series, and the Binomial Theorem

Schaum's Outlines--Problem Solved.

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!

Google is one of the 5 most popular sites on the internet with more than 380 million unique users per month (Nielsen/NetRatings 8/05). But, Google’s search capabilities are so powerful, they sometimes discover content that no one ever intended to be publicly available on the Web including: social security numbers, credit card numbers, trade secrets, and federally classified documents. Google Hacking for Penetration Testers Volume 2 shows the art of manipulating Google used by security professionals and system administrators to find this sensitive information and “self-police their own organizations.

Readers will learn how Google Maps and Google Earth provide pinpoint military accuracy, see how bad guys can manipulate Google to create super worms, and see how they can "mash up" Google with MySpace, LinkedIn, and more for passive reconaissance.

• Learn Google Searching Basics

Explore Google’s Web-based Interface, build Google queries, and work with Google URLs.

• Use Advanced Operators to Perform Advanced Queries

Combine advanced operators and learn about colliding operators and bad search-fu.

• Learn the Ways of the Google Hacker

See how to use caches for anonymity and review directory listings and traversal techniques.

• Review Document Grinding and Database Digging

See the ways to use Google to locate documents and then search within the documents to locate information.

• Understand Google’s Part in an Information Collection Framework

Learn the principles of automating searches and the applications of data mining.

• Locate Exploits and Finding Targets

Locate exploit code and then vulnerable targets.

• See Ten Simple Security Searches

Learn a few searches that give good results just about every time and are good for a security assessment.

• Track Down Web Servers

Locate and profile web servers, login portals, network hardware and utilities.

• See How Bad Guys Troll for Data

Find ways to search for usernames, passwords, credit card numbers, social security numbers, and other juicy information.

• Hack Google Services

Learn more about the AJAX Search API, Calendar, Blogger, Blog Search, and more.

-- 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!

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.

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.

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.

A comprehensive and comprehensible introduction to the subject, this book is ideal for undergraduates in computer science, physicists, communications engineers, workers involved in artificial intelligence, biologists, psychologists, and physiologists.

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.

In the first three chapters the authors briefly review the great explosions that will form the subject matter of the book--namely, supernovae and gamma-ray bursters. They describe the very early universe, after the Big Bang, and then how "the lights came on all over the universe as the very first stars began to shine." The importance of stellar mass in governing not only the lifetime of a star (the most massive stars live relatively short lives) but also the way in which a star ends its days is also explained.

Chapter 4 describes the explosion of certain massive stars, outlining the various stages at the end of these stars' lives, which result in the cataclysmic explosions known as supernovae. In Chapter 5 the authors introduce the more exotic and spectacular forms of stellar explosion known as gamma-ray bursters. Chapter 6 studies the markers used for cosmic surveys and Hubble's contributions to the field. The penultimate chapter looks at the very distant, highly luminous sources known as quasars and the evolution of our universe from the earliest times. The final chapter shows how observations of distant supernovae have revealed that the expansion of the universe is in fact accelerating--one of the most exciting and remarkable discoveries in recent years. It was this discovery that lead to the idea that 70% of the universe is made up of mysterious dark energy.

"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.

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Richard Feynman, winner of the Nobel Prize in physics, thrived on outrageous adventures. Here he recounts in his inimitable voice his experience trading ideas on atomic physics with Einstein and Bohr and ideas on gambling with Nick the Greek; cracking the uncrackable safes guarding the most deeply held nuclear secrets; accompanying a ballet on his bongo drums; painting a naked female toreador. In short, here is Feynman's life in all its eccentric—a combustible mixture of high intelligence, unlimited curiosity, and raging chutzpah.

And if this e-book leaves you wanting even more! more! more! there's The Math Dude's Quick and Dirty Guide to Algebra, with even more math number games, explanations, and—dare we say it—fun.

"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 a series of brief and largely self-contained chapters, Nahin discusses a wide range of topics in which math and physics are mutually dependent and mutually illuminating, from Newtonian gravity and Newton's laws of mechanics to ballistics, air drag, and electricity. The mathematical subjects range from algebra, trigonometry, geometry, and calculus to differential equations, Fourier series, and theoretical and Monte Carlo probability. Each chapter includes problems--some three dozen in all--that challenge readers to try their hand at applying what they have learned. Just as in his other books of mathematical puzzles, Nahin discusses the historical background of each problem, gives many examples, includes MATLAB codes, and provides complete and detailed solutions at the end.

Mrs. Perkins's Electric Quilt will appeal to students interested in new math and physics applications, teachers looking for unusual examples to use in class--and anyone who enjoys popular math books.