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© 2014,The book is a primer of the theory of Ordinary Differential Equations. Each chapter is completed by a broad set of exercises; the reader will also find a set of solutions of selected exercises. The book contains many interesting examples as well (like the equations for the electric circuits, the pendulum equation, the logistic equation, the LotkaVolterra system, and many other) which introduce the reader to some interesting aspects of the theory and its applications. The work is mainly addressed to students of Mathematics, Physics, Engineering, Statistics, Computer Sciences, with knowledge of Calculus and Linear Algebra, and contains more advanced topics for further developments, such as Laplace transform; Stability theory and existence of solutions to Boundary Value problems. A complete Solutions Manual, containing solutions to all the exercises published in the book, is available. Instructors who wish to adopt the book may request the manual by writing directly to one of the authors.

© 2014,Convex optimization has an increasing impact on many areas of mathematics, applied sciences, and practical applications. It is now being taught at many universities and being used by researchers of different fields. As convex analysis is the mathematical foundation for convex optimization, having a deep knowledge of convex analysis helps students and researchers apply these tools more effectively. The main goal of this book is to provide an easy access to the most fundamental parts of convex analysis and its applications to optimization. Modern techniques of variational analysis are employed to clarify and simplify some basic proofs in convex analysis and build a theory of generalized differentiation for convex functions and sets in finite dimensions. We also present new applications of convex analysis to location problems in connection with many interesting geometric problems such as the FermatTorricelli problem, the Heron problem, the Sylvester problem, and their generalizations. Of course, we do not expect to touch every aspect of convex analysis, but the book consists of sufficient material for a first course on this subject. It can also serve as supplemental reading material for a course on convex optimization and applications.

© 2014,This undergraduate textbook introduces students to the basics of real analysis, provides an introduction to more advanced topics including measure theory and Lebesgue integration, and offers an invitation to functional analysis. While these advanced topics are not typically encountered until graduate study, the text is designed for the beginner. The author's engaging style makes advanced topics approachable without sacrificing rigor. The text also consistently encourages the reader to pick up a pencil and take an active part in the learning process. Key features include:  examples to reinforce theory;  thorough explanations preceding definitions, theorems and formal proofs;  illustrations to support intuition;  over 450 exercises designed to develop connections between the concrete and abstract. This text takes students on a journey through the basics of real analysis and provides those who wish to delve deeper the opportunity to experience mathematical ideas that are beyond the standard undergraduate curriculum.

© 2014,Few mathematical results capture the imagination like Georg Cantor's groundbreaking work on infinity in the late nineteenth century. This opened the door to an intricate axiomatic theory of sets which was born in the decades that followed. Written for the motivated novice, this book provides an overview of key ideas in set theory, bridging the gap between technical accounts of mathematical foundations and popular accounts of logic. Readers will learn of the formal construction of the classical number systems, from the natural numbers to the real numbers and beyond, and see how set theory has evolved to analyse such deep questions as the status of the continuum hypothesis and the axiom of choice. Remarks and digressions introduce the reader to some of the philosophical aspects of the subject and to adjacent mathematical topics. The rich, annotated bibliography encourages the dedicated reader to delve into what is now a vast literature.

© 2014,"...I know of no better book of its kind..." (Journal of the Royal Statistical Society, Vol 169 (1), January 2006) A revised and updated edition of this bestselling introductory textbook to statistical analysis using the leading free software package R This new edition of a bestselling title offers a concise introduction to a broad array of statistical methods, at a level that is elementary enough to appeal to a wide range of disciplines. Stepbystep instructions help the nonstatistician to fully understand the methodology. The book covers the full range of statistical techniques likely to be needed to analyse the data from research projects, including elementary material like ttests and chisquared tests, intermediate methods like regression and analysis of variance, and more advanced techniques like generalized linear modelling. Includes numerous worked examples and exercises within each chapter.

© 2014,An authoritative and quantitative approach tonbsp;modern game theory with applications from diverse areas including economics, political science, military science, and finance. Explores areas which are not covered in current game theory texts, including a thorough examination of zerosum game. Provides introductory material to game theory, including bargaining, parlour games, sport, networking games and dynamic games. Explores Bargaining models, discussing new result such as resource distributions, buyerseller instructions and reputation in bargaining models. Theoretical results are presented alongnbsp;with numerous examples and detailed solutionsnbsp;at the end of each chapter. Presents a good balancenbsp;of both theoretical foundations and complex applications of game theory.

© 2013,This book is about the theory and practice of integer factorization presented in a historic perspective. It describes about twenty algorithms for factoring and a dozen other number theory algorithms that support the factoring algorithms. Most algorithms are described both in words and in pseudocode to satisfy both number theorists and computer scientists. Each of the ten chapters begins with a concise summary of its contents. The book starts with a general explanation of why factoring integers is important. The next two chapters present number theory results that are relevant to factoring. Further on there is a chapter discussing, in particular, mechanical and electronic devices for factoring, as well as factoring using quantum physics and DNA molecules. Another chapter applies factoring to breaking certain cryptographic algorithms. Yet another chapter is devoted to practical vs. theoretical aspects of factoring. The book contains more than 100 examples illustrating various algorithms and theorems. It also contains more than 100 interesting exercises to test the reader's understanding. Hints or answers are given for about a third of the exercises. The book concludes with a dozen suggestions of possible new methods for factoring integers. This book is written for readers who want to learn more about the best methods of factoring integers, many reasons for factoring, and some history of this fascinating subject. It can be read by anyone who has taken a first course in number theory.

© 2014,Calculus. For some of us, the word conjures up memories of tenpound textbooks and visions of tedious abstract equations. And yet, in reality, calculus is fun, accessible, and surrounds us everywhere we go. In Everyday Calculus , Oscar Fernandez shows us how to see the math in our coffee, on the highway, and even in the night sky. Fernandez uses our everyday experiences to skillfully reveal the hidden calculus behind a typical day's events. He guides us through how math naturally emerges from simple observationshow hot coffee cools down, for exampleand in discussions of over fifty familiar events and activities. Fernandez demonstrates that calculus can be used to explore practically any aspect of our lives, including the most effective number of hours to sleep and the fastest route to get to work. He also shows that calculus can be both usefuldetermining which seat at the theater leads to the best viewing experience, for instanceand fascinatingexploring topics such as time travel and the age of the universe. Throughout, Fernandez presents straightforward concepts, and no prior mathematical knowledge is required. For advanced math fans, the mathematical derivations are included in the appendixes. Whether you're new to mathematics or already a curious math enthusiast, Everyday Calculus invites you to spend a day discovering the calculus all around you. The book will convince even diehard skeptics to view this area of math in a whole new way.

© 2014,This book provides a fun, handson approach to learning how mathematics and computing relate to the world around us and help us to better understand it. How can reposting on Twitter kill a movie's opening weekend? How can you use mathematics to find your celebrity lookalike? What is Homer Simpson's method for disproving Fermat's Last Theorem? Each topic in this refreshingly inviting book illustrates a famous mathematical algorithm or resultsuch as Google's PageRank and the traveling salesman problemand the applications grow more challenging as you progress through the chapters. But don't worry, helpful solutions are provided each step of the way. Math Bytes shows you how to do calculus using a bag of chocolate chips, and how to prove the Euler characteristic simply by doodling. Generously illustrated in color throughout, this lively and entertaining book also explains how to create fractal landscapes with a roll of the dice, pick a competitive bracket for March Madness, decipher the math that makes it possible to resize a computer font or launch an Angry Birdand much, much more. All of the applications are presented in an accessible and engaging way, enabling beginners and advanced readers alike to learn and explore at their own pacea bit and a byte at a time.

© 2014,In An Equation for Every Occasion , John M. Henshaw tells fiftytwo entertaining true stories, each inspired by a different mathematical equation. His succinct, easytoread narratives come from the spheres of sports, business, history, the arts, science, and technology. Anecdotes about famous equations, like E=mc2, appear alongside tales of notsofamousbut equally fascinatingequations, such as the one that's used to determine the SPF number on a bottle of sunscreen. Drawn from the breadth of human endeavor, Henshaw's stories demonstrate the power and utility of math. He entertains us by exploring the ways that equations can be used to explain, among other things, Ponzi schemes, the placebo effect, "dog years," IQ, the wave mechanics of tsunamis, the troubled modern beekeeping industry, and the Challenger disaster. Smartly conceived and fast paced, his book offers something for anyone curious about math and its impacts. Yet readers will find themselves learning more than just math; they'll learn about the workings of the universe. Once immersed in this book you'll find yourself thirsting for the next equation in this original pageturner.

© 2014,This book draws on ideas from philosophical logic, computational logic, multiagent systems, and game theory to offer a comprehensive account of logic and games viewed in two complementary ways. It examines the logic of games: the development of sophisticated modern dynamic logics that model information flow, communication, and interactive structures in games. It also examines logic as games: the idea that logical activities of reasoning and many related tasks can be viewed in the form of games. In doing so, the book takes up the "intelligent interaction" of agents engaging in competitive or cooperative activities and examines the patterns of strategic behavior that arise. It develops modern logical systems that can analyze informationdriven changes in players' knowledge and beliefs, and introduces the "Theory of Play" that emerges from the combination of logic and game theory. This results in a new view of logic itself as an interactive rational activity based on reasoning, perception, and communication that has particular relevance for games. Logic in Games , based on a course taught by the author at Stanford University, the University of Amsterdam, and elsewhere, can be used in advanced seminars and as a resource for researchers.

© 2014,If you've ever thought that mathematics and art don't mix, this stunning visual history of geometry will change your mind. As much a work of art as a book about mathematics, Beautiful Geometry presents more than sixty exquisite color plates illustrating a wide range of geometric patterns and theorems, accompanied by brief accounts of the fascinating history and people behind each. With artwork by Swiss artist Eugen Jost and text by acclaimed math historian Eli Maor, this unique celebration of geometry covers numerous subjects, from straightedgeandcompass constructions to intriguing configurations involving infinity. The result is a delightful and informative illustrated tour through the 2,500yearold history of one of the most important and beautiful branches of mathematics.

© 2014,What are the chances of a gameshow contestant finding a chicken in a box? Is the Hanukkah dreidel a fair game? Will you be alive ten years from now? These are just some of the oneofakind probability puzzles that acclaimed popular math writer Paul Nahin offers in this lively and informative book. Nahin brings probability to life with colorful and amusing historical anecdotes as well as an electrifying approach to solving puzzles that illustrates many of the techniques that mathematicians and scientists use to grapple with probability. He looks at classic puzzles from the pastfrom Galileo's dicetossing problem to a disarming dice puzzle that would have astonished even Newtonand also includes a dozen challenge problems for you to tackle yourself, with complete solutions provided in the back of the book. Nahin then presents twentyfive unusual probability puzzlers that you aren't likely to find anywhere else, and which range in difficulty from ones that are easy but clever to others that are technically intricate. Each problem is accompanied by an entertaining discussion of its background and solution, and is backed up by theory and computer simulations whenever possible in order to show how theory and computer experimentation can often work together on probability questions. All the MATLAB® Monte Carlo simulation codes needed to solve the problems computationally are included in the book.With his characteristic wit, audacity, and insight, Nahin demonstrates why seemingly simple probability problems can stump even the experts.

© 2014,The Freakonomics of math #151; a mathworld superstar unveils the hidden beauty and logic of the world and puts its power in our hands 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#151;the whole world is shot through with it. nbsp; 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 #147;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? nbsp; 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 hardwon insights of the academic community to the layman#151;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 nonEuclidean 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. nbsp; 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 #147;an atomicpowered 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.

© 2013,The book beginsnbsp;at the level ofnbsp;an undergraduate student assuming only basic knowledge of calculus in one variable. It rigorously treats topics such as multivariable differential calculus, Lebesgue integral, vector calculus and differential equations. After having built on a solid foundation of topology and linear algebra, the text later expands into more advanced topics such as complex analysis, differential forms, calculus of variations, differential geometry and even functional analysis. Overall, this text provides a unique and wellrounded introduction to the highly developed and multifaceted subject of mathematical analysis, as understood by a mathematician today. nbsp;

© 2013,This book is a unique collection of challenging geometry problems and detailed solutions that will build students' confidence in mathematics. By proposing several methods to approach each problem and emphasizing geometry's connections with different fields of mathematics, Methods of Solving Complex Geometry Problems serves as a bridge to more advanced problem solving. nbsp;Written by an accomplished female mathematician who struggled with geometry as a child, it does not intimidate, but instead fosters the reader's ability to solve math problems through the direct application of theorems. nbsp; Containing over 160 complex problems with hints and detailed solutions, Methods of Solving Complex Geometry Problems can be used as a selfstudy guide for mathematics competitions and for improving problemsolving skills in courses on plane geometry or the history of mathematics. It contains important and sometimes overlooked topics on triangles, quadrilaterals, and circles such as the MenelausCeva theorem, Simson's line, Heron's formula, and the theorems of the three altitudes and medians. It can also be used by professors as a resource to stimulate the abstract thinking required to transcend the tedious and routine, bringing forth the original thought of which their students are capable. nbsp; Methods of Solving Complex Geometry Problems will interest high school and college students needing to prepare for exams and competitions, as well as anyone who enjoys an intellectual challenge and has a special love of geometry. It will also appeal to instructors of geometry, history of mathematics, and math education courses.

© 2013,By focusing on quadratic numbers, this advanced undergraduate or master's level textbook on algebraic number theory is accessible even to students who have yet to learn Galois theory. The techniques of elementary arithmetic, ring theory and linear algebra are shown working together to prove important theorems, such as the unique factorization of ideals and the finiteness of the ideal class group.nbsp; The book concludes with two topics particular to quadratic fields: continued fractions and quadratic forms.nbsp; The treatment of quadratic forms is somewhat more advancednbsp; than usual, with an emphasis on their connection with ideal classes and a discussion of Bhargava cubes. The numerous exercises in the text offer the reader handson computational experience with elements and ideals in quadratic number fields.nbsp; The reader is also asked to fill in the details of proofs and develop extra topics, like the theory of orders.nbsp; Prerequisites include elementary number theory and a basic familiarity with ring theory.

© 2013,For over three decades, this bestselling classic has been used by thousands of students in the United States and abroad as a musthave textbook for a transitional course from calculus to analysis. It has proven to be very useful for mathematics majors who have no previous experience with rigorous proofs. Its friendly style unlocks the mystery of writing proofs, while carefully examining the theoretical basis for calculus. Proofs are given in full, and the large number of wellchosen examples and exercises range from routine to challenging. The second edition preserves the book's clear and concise style, illuminating discussions, and simple, wellmotivated proofs. New topics include material on the irrationality of pi, the Baire category theorem, Newton's method and the secant method, and continuous nowheredifferentiable functions. Review from the first edition: "This book is intended for the student who has a good, but naïve, understanding of elementary calculus and now wishes to gain a thorough understanding of a few basic concepts in analysis.... The author has tried to write in an informal but precise style, stressing motivation and methods of proof, and ... has succeeded admirably." MATHEMATICAL REVIEWS

© 2013,This book is concerned with one of the most fundamental questions of mathematics: the relationship between algebraic formulas and geometric images. At one of the first international mathematical congresses (in Paris in 1900), Hilbert stated a special case of this question in the form of his 16th problem (from his list of 23 problems left over from the nineteenth century as a legacy for the twentieth century). In spite of the simplicity and importance of this problem (including its numerous applications), it remains unsolved to this day (although, as you will now see, many remarkable results have been discovered).

© 2014,The subject of mathematics is not something distant, strange, and abstract that you can only learn aboutand often dislikein school. It is in everyday situations, such as housekeeping, communications, traffic, and weather reports. Taking you on a trip into the world of mathematics, Do I Count? Stories from Mathematics describes in a clear and captivating way the people behind the numbers and the places where mathematics is made. Written by top scientist and engaging storyteller Günter M. Ziegler and translated by Thomas von Foerster, the book presents mathematics and mathematicians in a manner that you have not previously encountered. It guides you on a scenic tour through the field, pointing out which beds were useful in constructing which theorems and which notebooks list the prizes for solving particular problems. Forgoing esoteric areas, the text relates mathematics to celebrities, history, travel, politics, science and technology, weather, clever puzzles, and the future. Can bees count? Is 13 bad luck? Are there equations for everything? What's the real practical value of the Pythagorean Theorem? Are there Sudoku puzzles with fewer than 17 entries and just one solution? Where and how do mathematicians work? Who invented proofs and why do we need them? Why is there no Nobel Prize for mathematics? What kind of life did Paul Erds lead? Find out the answers to these and other questions in this entertaining book of stories. You'll see that everyone counts, but no computation is needed.

© 2014,This book traces the history of the concept of work from its earliest stages and shows that its further formalization leads to equilibrium principle and to the principle of virtual works, and so pointing the way ahead for future research and applications. The idea that something remains constant in a machine operation is very old and has been expressed by many mathematicians and philosophers such as, for instance, Aristotle. Thus, a concept of energy developed. Another important idea in machine operation is Archimedes' lever principle. In modern times the concept of work is analyzed in the context of applied mechanics mainly in Lazare Carnot mechanics and the mechanics of the new generation of polytechnical engineers like Navier, Coriolis and Poncelet. In this context the word "work" is finally adopted. These engineers are also responsible for the incorporation of the concept of work into the discipline of economics when they endeavoured to combine the study of the work of machines and men together.

© 2012,With many examples and numerous photos, this book explains important geometrical terms and concepts such as multiview projection and 3D projection, curve bends and surface cambering, the geometry of movement and nonEuclidian space.

© 2013,Each year tens of thousands of professors confront over a million students required to take statistics courses in almost every discipline, from anthropology to zoology. Because they did not choose to take "stat" courses, most students lack the motivation to learn and use statistics and, therefore, experience statistics as a "grunt" subject to pass at all costs. Professors try to overcome this problem by giving interesting lectures and assigning good textbooks and websites, but these literary and electronic resources are not meant to inspire students to want to learn and use statistics. This important gap is filled by Dancing on the Tails of the Bell Curvea unique anthology designed to supplement the technical resources professors assign in their classroomswhich has one goal: to inspire or motivate students to want to learn and use statistics. Through carefully selected readings, this book provides role models for students to identify with who have experienced joy from their use of statistics and concrete examples of how statistics shape almost every decision in society that involves our laws, medications, food supply, interest rates, educational programs, sporting events, mass media, and entitlement programs, to name only a few. In addition to professors, this reader is ideal for parents of children underachieving in their statistics courses and students who want to gain motivation to learn and use statistics.