From Mary, Queen of Scots, trapped by her own code, to the Navajo Code Talkers who helped the Allies win World War II, to the incredible (and incredibly simple) logisitical breakthrough that made Internet commerce secure, The Code Book tells the story of the most powerful intellectual weapon ever known: secrecy.Throughout the text are clear technical and mathematical explanations, and portraits of the remarkable personalities who wrote and broke the world’s most difficult codes. Accessible, compelling, and remarkably far-reaching, this book will forever alter your view of history and what drives it. It will also make you wonder how private that e-mail you just sent really is.

    It discusses new results, along with applications of probability theory to a variety of problems. The book contains many exercises and is suitable for use as a textbook on graduate-level courses involving data analysis. Aimed at readers already familiar with applied mathematics at an advanced undergraduate level or higher, it is of interest to scientists concerned with inference from incomplete information.

    Readers are encouraged to do math rather than just study it. The author draws upon his experience as a coach for the International Mathematics Olympiad to give students an enhanced sense of mathematics and the ability to investigate and solve problems.

    This book examines the huge scope of mathematical areas explored and developed by Euler, which includes number theory, combinatorics, geometry, complex variables and many more. The information known to Euler over 300 years ago is discussed, and many of his advances are reconstructed. Readers will be left in no doubt about the brilliance and pervasive influence of Euler's work.

    students on international comparisons of mathematics competency. Paradoxically, Chinese teachers receive far less education than U.S. teachers--11 to 12 years of schooling versus 16 to 18 years of schooling.Studies of U.S. teacher knowledge often document insufficient subject matter knowledge in mathematics. But, they give few examples of the knowledge teachers need to support teaching, particularly the kind of teaching demanded by recent reforms in mathematics education.This book describes the nature and development of the "profound understanding of fundamental mathematics" that elementary teachers need to become accomplished mathematics teachers, and suggests why such teaching knowledge is much more common in China than the United States, despite the fact that Chinese teachers have less formal education than their U.S. counterparts.The studies described in this book suggest that Chinese teachers begin their teaching careers with a better understanding of elementary mathematics than that of most U.S. elementary teachers. Their understanding of the mathematics they teach and--equally important--of the ways that elementary mathematics can be presented to students, continues to grow throughout their professional lives.Teaching conditions in the United States, unlike those in China, militate against the development of elementary teachers' mathematical knowledge and its organization for teaching. The concluding chapter of the book suggests changes in teacher preparation, teacher support, and mathematics education research that might allow teachers in the United States to attain profound understanding of fundamental mathematics.

    Fractal geometry has emerged as one of the most exciting frontiers on the border between mathematics and information technology and can be seen in many of the swirling patterns produced by computer graphics. It has become a new tool for modeling in biology, geology, and other natural sciences. Anthropologists have observed that the patterns produced in different cultures can be characterized by specific design themes. In Europe and America, we often see cities laid out in a grid pattern of straight streets and right-angle corners. In contrast, traditional African settlements tend to use fractal structures-circles of circles of circular dwellings, rectangular walls enclosing ever-smaller rectangles, and streets in which broad avenues branch down to tiny footpaths with striking geometric repetition. These indigenous fractals are not limited to architecture; their recursive patterns echo throughout many disparate African designs and knowledge systems. Drawing on interviews with African designers, artists, and scientists, Ron Eglash investigates fractals in African architecture, traditional hairstyling, textiles, sculpture, painting, carving, metalwork, religion, games, practical craft, quantitative techniques, and symbolic systems. He also examines the political and social implications of the existence of African fractal geometry. His book makes a unique contribution to the study of mathematics, African culture, anthropology, and computer simulations.

    Self-contained chapters allow researchers to locate the commands and an example program for each category of mathematical equatio

    This book covers everythig from First Order PDE's, everything in between then ending with the Valedictory.

    In Essays on Life Itself, Rosen takes to task the central objective of the natural sciences, calling into question the attempt to create objectivity in a subjective world and forcing us to reconsider where science can lead us in the years to come.

    Although not primarily research texts, they point out the direction which research is currently taking and where it is expected to lead.

    Concentrating on the probabilistics theory of continuous arbitrage pricing of financial derivatives, including stochastic optimal control theory and Merton's fund separation theory, the book is designed for graduate students and combines necessary mathematical background with a solid economic focus. It includes a solved example for every new technique presented, contains numerous exercises and suggests further reading in each chapter. In this substantially extended new edition, Bjork has added separate and complete chapters on measure theory, probability theory, Girsanov transformations, LIBOR and swap market models, and martingale representations, providing two full treatments of arbitrage pricing: the classical delta-hedging and the modern martingales. More advanced areas of study are clearly marked to help students and teachers use the book as it suits their needs.

    This book uses problems, puzzles, and games to teach students how to think critically. It emphasizes active participation in problem solving, with emphasis on logic, number and graph theory, games of strategy, and much more. Includes answers to selected problems. Index. 1980 edition.

    

    The result is a unique book written for engineering students, which takes a starting point below GCSE level. Basic Engineering Mathematics is therefore ideal for students of a wide range of abilities, and especially for those who find the theoretical side of mathematics difficult. All students taking vocational engineering courses who require fundamental knowledge of mathematics for engineering and do not have prior knowledge beyond basic school mathematics, will find this book essential reading. The content has been designed primarily to meet the needs of students studying Level 2 courses, including GCSE Engineering and Intermediate GNVQ, and is matched to BTEC First specifications. However Level 3 students will also find this text to be a useful resource for getting to grips with the essential mathematics concepts needed for their study, as the compulsory topics required in BTEC National and AVCE / A Level courses are also addressed. logarithmic scales, and inequalities key topics needed for GCSE and Level 2 study. John Birds approach is based on numerous worked examples, supported by 600 worked problems, followed by 1050 further problems within exercises included throughout the text. In addition, 15 Assignments are included at regular intervals. Ideal for use as tests or homework, full solutions to the Assignments are supplied in the accompanying Instructors Manual, available as a free download for lecturers from the Newnes website at http: //books.elsevier.com

    

    The contributors cover all the fundamental symmetries of modern physics, such as CPT and permutation symmetry, as well as discussing symmetry-breaking and general interpretational issues. Classic texts are followed by new review articles and shorter commentaries for each topic. Suitable for courses on the foundations of physics, philosophy of physics and philosophy of science, the volume is a valuable reference for students and researchers.

    The first part of the text overviews the concept of a wave, describes one-dimensional waves using functions of two variables, provides an introduction to partial differential equations, and discusses computer-aided visualization techniques. The second part of the book discusses travelling waves, leading to a description of solitary waves and soliton solutions of the Klein-Gordon and Korteweg-deVries equations. The wave equation is derived to model the small vibrations of a taut string, and solutions are constructed via d'Alembert's formula and Fourier series.

    Substructural logics have independently led to significant developments in philosophy, computing and linguistics. An Introduction to Substrucural Logics is the first book to systematically survey the new results and the significant impact that this class of logics has had on a wide range of fields.The following topics are covered: * Proof Theory* Propositional Structures* Frames* Decidability* CodaBoth students and professors of philosophy, computing, linguistics, and mathematics will find this to be an important addition to their reading.

    Advances in many different areas have been inspired by insights from physics. In 1996-97 the Institute for Advanced Study (Princeton, New Jersey) organized a special year-long programme designed to teach mathematicians the basic physical ideas which underlie the mathematical applications. The purpose was to create and convey an understanding, in terms useful to mathematicians, of some fundamental notions of physics and develop the sort of intuition common among physicists for those who are used to thought processes stemming from geometry and algebra.

    It gives a simple but rigorous treatment of the subject including a range of advanced topics, it is useful for practitioners who use advanced theoretical results. It covers advanced applications, such as models in mathematical finance, biology and engineering.Self-contained and unified in presentation, the book contains many solved examples and exercises. It may be used as a textbook by advanced undergraduates and graduate students in stochastic calculus and financial mathematics. It is also suitable for practitioners who wish to gain an understanding or working knowledge of the subject. For mathematicians, this book could be a first text on stochastic calculus; it is good companion to more advanced texts by a way of examples and exercises. For people from other fields, it provides a way to gain a working knowledge of stochastic calculus. It shows all readers the applications of stochastic calculus methods and takes readers to the technical level required in research and sophisticated modelling.This second edition contains a new chapter on bonds, interest rates and their options. New materials include more worked out examples in all chapters, best estimators, more results on change of time, change of measure, random measures, new results on exotic options, FX options, stochastic and implied volatility, models of the age-dependent branching process and the stochastic Lotka-Volterra model in biology, non-linear filtering in engineering and five new figures.Instructors can obtain slides of the text from the author.

    The topics range from seventeenth-century medicine and the circulation of blood, to the cause of the Great Depression and the effect of the California gold discoveries of 1848 upon price levels, to the determinations of the shape of the Earth and the speed of light, to the meter of Virgil's poetry and the prediction of the Second Coming of Christ. The title essay tells how the statistician Karl Pearson came to issue the challenge to put "statistics on the table" to the economists Marshall, Keynes, and Pigou in 1911. The 1911 dispute involved the effect of parental alcoholism upon children, but the challenge is general and timeless: important arguments require evidence, and quantitative evidence requires statistical evaluation. Some essays examine deep and subtle statistical ideas such as the aggregation and regression paradoxes; others tell of the origin of the Average Man and the evaluation of fingerprints as a forerunner of the use of DNA in forensic science. Several of the essays are entirely nontechnical; all examine statistical ideas with an ironic eye for their essence and what their history can tell us about current disputes.

    African games such as mankala and elaborate versions of tic-tac-toe show how complex this thinking can be. An invaluable resource for students, teachers, and others interested in African cultures and multiculturalism, this third edition is updated with an introduction covering two decades of new research in the ethnomathematics of Africa.

    The comprehensive treatment allows you to explore the venerable but somewhat obscure principles of kinematic design (widely practiced in the design of precision instruments for well over 100 years). You get a unique and powerful set of rules and techniques to facilitate the design of any machine-of every type and size. A central technique is constraint pattern analysis, which enables you to visualize the constraints and degrees of freedom of mechanical connection as patterns of lines in space. Understanding these principles, collectively called exact constraint design principles, can lead you to unobvious solutions to design problems, as well as designing for lower cost and higher performance. The book is supplemented with many hardware examples, which allow you to: acquire a greatly enhanced understanding of how machines work, improve your ability to create innovative machines, and maximize your ability to analyze and understand complex machinery.

    He has authored hundreds of technical articles, as well as textbooks, popular accounts of science, science fiction, and two autobiograqphies. His honors and accomplishments include Plumian professor of astronomy and experimental philosophy,Cambridge University, 1958 Founded and became first Director of the Cambridge Institute of Theretical Astronomy, 1967 Knighted, 1972 Awarded the Crafoord prize for basic science, 1997.

    His study ranges from an exploration of whether computers producing mathematical proofs or conjectures are doing real mathematics to the use of analogy; the prospects for a Bayesian confirmation theory; the notion of a mathematical research program; and the ways in which new concepts are justified. This highly original book will challenge philosophers as well as mathematicians to develop the broadest and most complete philosophical resources for research in their disciplines.

    Stimulating and thought-provoking, this collection is sure to interest students, mathematicians, and any math buff with its lucid treatment of geometry and the crucial role geometry plays in a wide range of mathematical applications.

    Drawing on his experiences with three professional development programs, author Mark Driscoll outlines key habits of thinking that characterize the successful learning and use of algebra. He offers strategies teachers can use to cultivate these habits of thinking and guidelines for assessing students' development.Fostering Algebraic Thinking is organized according to the critical challenges algebra teachers face. Excerpts from discussions among the classroom teachers who participated in the professional development projects help place these issues in context. Each chapter also includes activities to encourage teachers to reflect on how they think about algebra and how that thinking informs their practice. There are also samples and analyses of student work to help teachers identify patterns of algebraic thinking along with questions and strategies that can be used to guide and extend students' thinking.

    

    Abhinay Muthoo provides a masterful synthesis of the fundamental results and insights obtained from the wide-ranging and diverse (game-theoretic) bargaining theory literature. Furthermore, he develops new analyses and results, especially on the relative impacts of two or more forces on the bargaining outcome. Many topics - such as inside options, commitment tactics and repeated bargaining situations - receive their most extensive treatment to date. In the concluding chapter, he offers pointers towards future research. Bargaining Theory with Applications is a textbook for graduate students in economic theory and other social sciences and a research resource for scholars interested in bargaining situations.A major new upper level textbook with global adoption potential on a central economic and social scientific topicAn easy to follow, up-to-date exposition including numerous examples, case studies and pathways designed to allow rigorous and intuitive studyOriginal research--cambridge.org

    It provides extensive coverage of conditional probability and expectation, strong laws of large numbers, martingale theory, the central limit theorem, ergodic theory, and Brownian motion.* Clear, readable style* Solutions to many problems presented in text* Solutions manual for instructors* Material new to the second edition on ergodic theory, Brownian motion, and convergence theorems used in statistics* No knowledge of general topology required, just basic analysis and metric spaces* Efficient organization

    However, few people are familiar with the actual accomplishments upon which his enduring reputation rests, and it is the aim of this book to shed light upon this matter. Archimedes' ability to achieve so much with the few mathematical tools at his disposal was astonishing. He made fundamental advances in the fields of geometry, mechanics, and hydrostatics. No great mathematical expertise is required of the reader, and the book is well illustrated with over 100 diagrams. It will prove fascinating to students and professional mathematicians alike.

    To do so intelligently requires a good working knowledge of numerical analysis. This book equips students to craft their own software and to understand the advantages and disadvantages of different numerical methods. Issues of numerical stability, accurate approximation, computational complexity, and mathematical modeling share the limelight in a broad yet rigorous overview of those parts of numerical analysis most relevant to statisticians. In this second edition, the material on optimization has been completely rewritten. There is now an entire chapter on the MM algorithm in addition to more comprehensive treatments of constrained optimization, penalty and barrier methods, and model selection via the lasso. There is also new material on the Cholesky decomposition, Gram-Schmidt orthogonalization, the QR decomposition, the singular value decomposition, and reproducing kernel Hilbert spaces. The discussions of the bootstrap, permutation testing, independent Monte Carlo, and hidden Markov chains are updated, and a new chapter on advanced MCMC topics introduces students to Markov random fields, reversible jump MCMC, and convergence analysis in Gibbs sampling. Numerical Analysis for Statisticians can serve as a graduate text for a course surveying computational statistics. With a careful selection of topics and appropriate supplementation, it can be used at the undergraduate level. It contains enough material for a graduate course on optimization theory. Because many chapters are nearly self-contained, professional statisticians will also find the book useful as a reference.

    This series is the work of a distinguished mathematician who taught at the University of Chicago for 4 decades and is celebrated for his many contributions to number theory and group theory. 1919 edition.

    Next, Dr. Stahl develops the basic tools of advanced calculus, introducing the various aspects of the completeness of the real number system, sequential continuity and differentiability, as well as uniform convergence. Finally, he presents applications and examples to reinforce concepts and demonstrate the validity of many of the historical methods and results.

    It introduces the reader to the main concepts, notions and results of stochastic financial mathematics, and develops applications of these results to various kinds of calculations required in financial engineering. It also answers the requests of teachers of financial mathematics and engineering by making a bias towards probabilistic and stastical ideas and the methods of stochastic calculus in the analysis of market risks.

    The book has been extensively revised to bring the subject up-to-date, and features two new chapters: "Building and Using Fuzzy Cognitive Map Models" and "Building ME-OWA Models." The multiplatform CD-ROM contains all the C++ source code from the book's examples - but its real value is the robust package of fuzzy system related tools and utilities, featuring two notable components. First: Metus Systems' basic fuzzy modeling software, which includes complete C/C++ source code for creating and executing fuzzy models, a Visual Basic shell that can be used to create fuzzy sets and generate the C/C++ include files, and code for models for pricing, project management, risk assessment, and more. Second: The ME-OWA (Minimum-Entropy, Ordered Weighted Aggregation) decision modeling software from Fuzzy Logic, Inc. This software is used to focus on a single objective function from a set of alternatives given a fuzzy ranking among various alternatives. It is not only an important technique as a stand-alone tool, but is an important methodology in parameter selection (and parameterization ordering) for genetic algorithms and various data mining techniques. It is also an important technique used to establish rule and policy level peer weights in fuzzy models. Key Features* Tutorial style, requiring no background in fuzzy logic* Case studies illustrate real-world fuzzy applications* Mathematically straightforward exposition, with emphasis on practicaluse* CD-ROM features all the C++ source code from the book and a robust package of fuzzy system related tools and utilities

    For many students the tools of matrix and linear algebra will be as fundamental in their professional work as the tools of calculus; thus it is important to ensure that students appreciate the utility and beauty of these subjects as well as the mechanics. To this end, applied mathematics and mathematical modeling ought to have an important role in an introductory treatment of linear algebra. In this way students see that concepts of matrix and linear algebra make concrete problems workable. In this book we weave signi?cant motivating examples into the fabric of the text. I hope that instructors will not omit this material; that would be a missed opportunity for linear algebra! The text has a strong orientation toward numerical computation and applied mathematics, which means that matrix analysis plays a central role. All three of the basic components of l- ear algebra -- theory, computation, and applications -- receive their due. The proper balance of these components gives students the tools they need as well as the motivation to acquire these tools. Another feature of this text is an emphasis on linear algebra as an experimental science; this emphasis is found in certain examples, computer exercises, and projects. Contemporary mathematical software make ideal "labs" for mathematical experimentation. Nonetheless, this text is independent of speci?c hardware and software pl- forms. Applications and ideas should take center stage, not software.

    The approach is that of Klein in his Erlangen program: a geometry is a space together with a set of transformations of that space. The authors explore various geometries: affine, projective, inversive, non-Euclidean and spherical. In each case they carefully explain key results and discuss the relationship among geometries. This richly illustrated and clearly written text includes full solutions to over 200 problems and is suitable both for undergraduate courses on geometry and as a resource for self study.

    Following on the success of the award-winning First Edition book and written by teacher/tutor Josh Rappaport, the Second Edition Guide offers time-tested advice for understanding the key areas of this gateway math subject. The new Algebra Survival Guide features a unique Q&A format so students hear their own questions echoed in the text. The book’s answers, written in the voice of a friendly tutor, provide conversational responses, along with step-by-step instructions in English right next to the math steps. Each page is a one-page mini-lesson so students can focus without feeling overwhelmed. Following each lesson is a short set of practice problems, offering students instant feedback. At the end of each section, chapter tests provide comprehensive checks on understanding. Since word problems are often the highest “hurdle” of algebra, the Second Edition contains a new 62-page chapter on advanced word problems. This chapter provides detailed strategies for setting up and solving word problems on such dastardly areas as rate, time and distance, work performed, mixture formulas, and even those crazy problems about Joe being three years older than four times Jane’s age 10 years in the future.In its twelve content chapters the 352-page Second Edition covers all key areas of PreAlgebra and Algebra 1: Algebraic Properties, Sets of Numbers, Positive and Negative Numbers, Order of Operations, Absolute Value, Exponents, Radicals, Factoring, Cancelling, Solving Equations, the Coordinate Plane, and Word Problems. As a major bonus, the Guide buzzes with lively illustrations by award-winning artist Sally Blakemore. Ms. Blakemore’s cartoons not only provide comic relief, they also offer a visual way to grasp algebra’s challenging abstractions. (Example:  to illustrate the Reflexive Property of x = x, a cartoon shows a sad ‘x’ gazing at itself in the mirror while suffering a ‘bad hair day.’) With all of these features, the Second Edition Algebra Survival Guide appeals equally to homeschoolers, students, parents, teachers, tutors and adult students striving to recall the math they learned a decade or so ago.The Second Edition aligns with the Common Core State Standards for Math, so it’s up-to-date for today’s teachers. Loaded with thorough explanations, practice problems and answers, the new Algebra Survival Guide gives anyone and everyone the needed boost for learning or teaching the timeless and critical subject of algebra.

    This book provides readers with a self-contained introduction to the classical theory as well as modern developments and applications. The text concentrates on the study of binary forms (polynomials) in characteristic zero, and uses analytical as well as algebraic tools to study and classify invariants, symmetry, equivalence and canonical forms. A variety of innovations make this text of interest even to veterans of the subject; these include the use of differential operators and the transform approach to the symbolic method, extension of results to arbitrary functions, graphical methods for computing identities and Hilbert bases, complete systems of rationally and functionally independent covariants, introduction of Lie group and Lie algebra methods, as well as a new geometrical theory of moving frames and applications. Aimed at advanced undergraduate and graduate students the book includes many exercises and historical details, complete proofs of the fundamental theorems, and a lively and provocative exposition.

    It starts with a general probabilistic description of physics, which encompasses both classical and quantum physics. The basic key physical notions are clarified at this point. It then introduces operator algebraic methods for quantum theory, and goes on to discuss the theory of special relativity, scattering theory, and sector theory in this context.

    Children learn about fractions at school but fractions are also an important part of everyday life outside the classroom.In this riotous book, Stuart J. Murphy and G. Brian Karas introduce the simplest of fractions, 1/2. Book Details: Format: Paperback Publication Date: 3/27/1996 Pages: 40 Reading Level: Age 6 and Up

    In his relatively short lifetime, this great mathematician made outstanding contributions to nearly all branches of mathematics; today Riemanna (TM)s name appears prominently throughout the literature."The book is highly recommendablea "for students and scientific workersa "not only for the valuable information in it, but also for its spirit: history and higher mathematics are not dry here; they become alive and motivate further studies."a "ZAA"This is a new translation of a book first published in English in 1987... Translated from Russian...it consists of two separate but related works. The first is an account of the life and work of Riemann, the second an account of several different topics in physics which are illuminated by the introduction of topological ideas. The discussion of Riemann is even better in the new edition. The mathematical account is richer and various errors have been corrected... The second half has been revised in a similar fashion... It has also been enriched by a new chapter which starts with von Neumann algebras and the work of Vaughn Jones... The book does three things very well: it reminds us of the range and depth of Riemanna (TM)s interests, which are emblematic of what the author values in mathematical physics; describes some of the many successes of Russian mathematicians and physicists; and it provides a lucid account of some modern work in which topology is genuinely applied. Books like this are vital for the health of mathematics and it is to be hoped that more will be written."---Mathematical Reviews

    The authors' comprehensive yet accessible presentation for one- or two-term courses offers a balanced depth of topic coverage and mathematical rigor.

    The Nine Chapters quickly acquired a distinguished reputation, and was the standard mathematics textbook in China and the surrounding regions until Western science was introduced in about 1600. This volume contains the first complete English translation of the Nine Chapters, together with the illuminating commentary of Liu Hui written in the 3rd century AD and other early century commentaries and further insights provided by the translators. The Nine Chapters contains 246 problems and their solutions, which fall into nine categories that are firmly based on practical needs. There are methods for solving problems in areas such as land measurement, construction, agriculture, commerce, and taxation, while the Chinese commentators provide the algorithms needed to solve the problems, and explanations of how the algorithms work. The translators' commentary provides clear and accessible background material for the Western reader, explanations of technicalities, and notes on the treatment of similar or identical mathematical problems in other countries. This first, full-English translation gives us an idea of the distinctive style and important contributions that have been made by traditional Chinese mathematics.

    The chapter on symmetric functions provides the only available treatment of this subject suitable for an introductory graduate course on combinatorics, and includes the important Robinson-Schensted-Knuth algorithm. Also covered are connections between symmetric functions and representation theory. An appendix by Sergey Fomin covers some deeper aspects of symmetric function theory, including jeu de taquin and the Littlewood-Richardson rule. As in Volume 1, the exercises play a vital role in developing the material. There are over 250 exercises, all with solutions or references to solutions, many of which concern previously unpublished results. Graduate students and research mathematicians who wish to apply combinatorics to their work will find this an authoritative reference.

    This art form lends itself wonderfully to teaching mathematicsbut it's been up to you to find ways to do it. Now comes Unfolding Mathematics with Unit Origami, designed especially for algebra and geometry students in high school or middle school. Its elegant illustrations and detailed folding and assembly instructions enable you and your students to create beautiful and intriguing three-dimensional origami models. Its 16 absorbing activitiesall in blackline master formhave been carefully prepared in order of increasing difficulty of both folds and mathematical concepts. Through origami folding sequences, basic mathematical ideas reveal themselves: algebraic and angle relationships and different types of symmetry in two and three dimensions will engage your students'interest in new ways. You can choose activities from anywhere in the book, but if you move from front to back you'll cover an amazingly broad range of mathematical topics. And while the book's purpose is to teach mathematics, it also introduces students to the art of origami and contributions made to that art by noted origami experts, such as Tomoko Fus, Kunihiko Kasahara, David Masunaga, and Robert Neale. Most activities can be done in one class period and offer opportunities for group work, journal writing, and projects. Autobiographical vignettes by origami artists introduce students to origami culture and prompt students to discuss their own experiences with origami. The overview explains how you can best use this book in your classroom, including methods for assessing student work. Every activity gives you teaching ideas and strategies, as well as suggestions for extensions of the activity. There's also a glossary of terms and a list of recommended readings.

    A must-read for mathematicians, scientists and engineers who want to understand difference equations and discrete dynamicsContains the most complete and comprehenive analysis of the stability of one-dimensional maps or first order difference equations.Has an extensive number of applications in a variety of fields from neural network to host-parasitoid systems.Includes chapters on continued fractions, orthogonal polynomials and asymptotics.Lucid and transparent writing style

    This book provides a detailed treatment of algebraic topology both for teachers of the subject and for advanced graduate students in mathematics either specializing in this area or continuing on to other fields.J. Peter May's approach reflects the enormous internal developments within algebraic topology over the past several decades, most of which are largely unknown to mathematicians in other fields. But he also retains the classical presentations of various topics where appropriate. Most chapters end with problems that further explore and refine the concepts presented. The final four chapters provide sketches of substantial areas of algebraic topology that are normally omitted from introductory texts, and the book concludes with a list of suggested readings for those interested in delving further into the field.

    The sun is shining, the Nile River is almost flooding, and everywhere you look, humongous pyramids are being erected. You have a strong hunch that it's going to be a truly amazing day. You'll spend the day with a family in the land of Giza during the Fourth Dynasty and learn all about Egyptian culture with loads of exotic and fun-filled activities. Join ten-year-old Meryt as she practices playing the harp for the festival of Bastet, and make your own music with a string of menat rhythm beads. Be an apprentice scribe to the pyramid builders with Meryt's twelve-year-old brother, lpy, as you learn to count with hieroglyphs. Join the family for a round of Senet, a traditional Egyptian board game, using a board and game pieces you've made yourself. Then, before your day in Egypt is through, make a delicious feast fit for a pharaoh!Ages 8 to 12 Collect the whole Spend the Day series! Spend the Day in Ancient Greece Spend the Day in Ancient Rome

    It includes methods for both equilibrium and out of equilibrium systems, and discusses in detail such common algorithms as the Metropolis and heat-bath algorithms, as well as more sophisticated ones such as continuous time Monte Carlo, cluster algorithms, multigrid methods, entropic sampling and simulated tempering. Data analysis techniques are also explained starting with straightforward measurement and error-estimation techniques and progressing to topics such as the single and multiple histogram methods and finite size scaling. The last few chapters of the book are devoted to implementation issues, including lattice representations, efficient implementation of data structures, multispin coding, parallelization of Monte Carlo algorithms, and random number generation. The book also includes example programs which show how to apply these techniques to a variety of well-known models.

    It becomes important, then, that engineers and scientists have a working understanding of wavelets. Until now, however, the study of wavelets has been beyond the mathematical grasp of many who need this understanding. Most treatments of the subject involve ideas from functional analysis, harmonic analysis, and other difficult mathematical techniques.Wavelets and their Scientific Applications offers an introduction to wavelet analysis without mathematical rigor, requiring only algebra and some very basic calculus. The author stresses applications, and explains, using elementary algebra, how wavelet methods are typically applied in analyzing digital data.Software is available for download through CRC's Website that will enable recording, playing, and modifying sound files, and includes a facility for displaying, printing and modifying IEEE gray field images. Unlike other software packages for wavelet analysis, the author developed this attractive, easy-to-use software without the need for a C++ compiler or MATLAB�. Throughout the book the author provides numerous suggestions for computer experiments designed to challenge and enhance the reader's comprehension and provide practice in applying the concepts learned.Wavelets and their Scientific Applications thus provides the perfect vehicle for understanding wavelets and their uses. It provides a fast-track learning opportunity for scientists and mathematicians unfamiliar with wavelet concepts and applications, and it is ideal for anyone without an extensive mathematical background.

    Soon afterwards, Hermann Minkowski recast special relativity essentially as a new geometric structure for spacetime. These ideas are the subject of the first part of the book. The second part develops the main implications of Einstein's general relativity as a theory of gravity rooted in the differential geometry of surfaces. The author explores the way an individual observer views the world and how a pair of observers collaborate to gain objective knowledge of the world. To encompass both the general and special theory, he uses the geometry of spacetime as the unifying theme of the book. To read it, one needs only a first course in linear algebra and multivariable calculus and familiarity with the physical applications of calculus.

    Readers will enjoy 366 days' worth of stimulating math.

    It will also be useful for students and teachers in related areas such as finance theory, electrical engineering, and operations research. The text covers the essentials in a directed and lean way with 28 short chapters, and assumes only an undergraduate background in mathematics. Readers are taken right up to a knowledge of the basics of Martingale Theory, and the interested student will be ready to continue with the study of more advanced topics, such as Brownian Motion and Ito Calculus, or Statistical Inference.