Lang, one of the worlds foremost origami artists and scientists, presents the never-before-described mathematical and geometric principles that allow anyone to design original origami, something once restricted to an elite few. From the theoretical underpinnings to detailed step-by-step folding sequences, this book takes a modern look at the centuries-old art of origami.

    Alternating passages of extraordinarily lucid mathematical exposition with chapters of elegantly composed biography and history, Prime Obsession is a fascinating and fluent account of an epic mathematical mystery that continues to challenge and excite the world.

    The subject was the mystery of prime numbers. At the heart of the presentation was an idea that Riemann had not yet proved but one that baffles mathematicians to this day.Solving the Riemann Hypothesis could change the way we do business, since prime numbers are the lynchpin for security in banking and e-commerce. It would also have a profound impact on the cutting-edge of science, affecting quantum mechanics, chaos theory, and the future of computing. Leaders in math and science are trying to crack the elusive code, and a prize of $1 million has been offered to the winner. In this engaging book, Marcus du Sautoy reveals the extraordinary history behind the holy grail of mathematics and the ongoing quest to capture it.

    The Art of Problem Solving, Volume 2, is the classic problem solving textbook used by many successful high school math teams and enrichment programs and have been an important building block for students who, like the authors, performed well enough on the American Mathematics Contest series to qualify for the Math Olympiad Summer Program which trains students for the United States International Math Olympiad team.Volume 2 is appropriate for students who have mastered the problem solving fundamentals presented in Volume 1 and are ready for a greater challenge. Although the Art of Problem Solving is widely used by students preparing for mathematics competitions, the book is not just a collection of tricks. The emphasis on learning and understanding methods rather than memorizing formulas enables students to solve large classes of problems beyond those presented in the book.Speaking of problems, the Art of Problem Solving, Volume 2, contains over 500 examples and exercises culled from such contests as the Mandelbrot Competition, the AMC tests, and ARML. Full solutions (not just answers!) are available for all the problems in the solution manual.

    But in spirit, the title is apt, as the book does cover a much broader range of topics than a typical introductory book on mathematical statistics. This book is for people who want to learn probability and statistics quickly. It is suitable for graduate or advanced undergraduate students in computer science, mathematics, statistics, and related disciplines. The book includes modern topics like nonparametric curve estimation, bootstrapping, and clas- sification, topics that are usually relegated to follow-up courses. The reader is presumed to know calculus and a little linear algebra. No previous knowledge of probability and statistics is required. Statistics, data mining, and machine learning are all concerned with collecting and analyzing data. For some time, statistics research was con- ducted in statistics departments while data mining and machine learning re- search was conducted in computer science departments. Statisticians thought that computer scientists were reinventing the wheel. Computer scientists thought that statistical theory didn't apply to their problems. Things are changing. Statisticians now recognize that computer scientists are making novel contributions while computer scientists now recognize the generality of statistical theory and methodology. Clever data mining algo- rithms are more scalable than statisticians ever thought possible. Formal sta- tistical theory is more pervasive than computer scientists had realized.

    You proceed at your own rate and any difficulties you may encounter are resolved before you move on to the next topic. With a step-by-step programmed approach that is complemented by hundreds of worked examples and exercises, Advanced Engineering Mathematics is ideal as an on-the-job reference for professionals or as a self-study guide for students.Uses a unique technique-oriented approach that takes the reader through each topic step-by-step.Features a wealth of worked examples and progressively more challenging exercises.Contains Test Exercises, Learning Outcomes, Further Problems, and Can You? Checklists to guide and enhance learning and comprehension.Expanded coverage includes new chapters on Z Transforms, Fourier Transforms, Numerical Solutions of Partial Differential Equations, and more Complex Numbers.Includes a new chapter, Introduction to Invariant Linear Systems, and new material on difference equations integrated into the Z transforms chapter.

    Along the tidal rivers of Malaysia, thousands of fireflies congregate and flash in unison; the moon spins in perfect resonance with its orbit around the earth; our hearts depend on the synchronous firing of ten thousand pacemaker cells. While the forces that synchronize the flashing of fireflies may seem to have nothing to do with our heart cells, there is in fact a deep connection. Synchrony is a science in its infancy, and Strogatz is a pioneer in this new frontier in which mathematicians and physicists attempt to pinpoint just how spontaneous order emerges from chaos. From underground caves in Texas where a French scientist spent six months alone tracking his sleep-wake cycle, to the home of a Dutch physicist who in 1665 discovered two of his pendulum clocks swinging in perfect time, this fascinating book spans disciplines, continents, and centuries. Engagingly written for readers of books such as Chaos and The Elegant Universe, Sync is a tour-de-force of nonfiction writing.

    Following closely behind is y, or gamma, a constant that arises in many mathematical areas yet maintains a profound sense of mystery. In a tantalizing blend of history and mathematics, Julian Havil takes the reader on a journey through logarithms and the harmonic series, the two defining elements of gamma, toward the first account of gamma's place in mathematics. Introduced by the Swiss mathematician Leonhard Euler (1707-1783), who figures prominently in this book, gamma is defined as the limit of the sum of 1 + 1/2 + 1/3 + . . . Up to 1/n, minus the natural logarithm of n--the numerical value being 0.5772156. . . . But unlike its more celebrated colleagues π and e, the exact nature of gamma remains a mystery--we don't even know if gamma can be expressed as a fraction. Among the numerous topics that arise during this historical odyssey into fundamental mathematical ideas are the Prime Number Theorem and the most important open problem in mathematics today--the Riemann Hypothesis (though no proof of either is offered!). Sure to be popular with not only students and instructors but all math aficionados, Gamma takes us through countries, centuries, lives, and works, unfolding along the way the stories of some remarkable mathematics from some remarkable mathematicians.-- "Notices of the American Mathematical Society"

    The answers are easy to explain, but without this book, devilishly hard to find. Creative reasoning is the key to these puzzles. No involved computation or higher mathematics is necessary, but your ability to construct a mathematical proof will be severly tested--even if you are a professional mathematician. For the truly adventurous, there is even a chapter on unsolved puzzles.

    It begins with the simple conviction that Fourier arrived at in the early nineteenth century when studying problems in the physical sciences--that an arbitrary function can be written as an infinite sum of the most basic trigonometric functions.The first part implements this idea in terms of notions of convergence and summability of Fourier series, while highlighting applications such as the isoperimetric inequality and equidistribution. The second part deals with the Fourier transform and its applications to classical partial differential equations and the Radon transform; a clear introduction to the subject serves to avoid technical difficulties. The book closes with Fourier theory for finite abelian groups, which is applied to prime numbers in arithmetic progression.In organizing their exposition, the authors have carefully balanced an emphasis on key conceptual insights against the need to provide the technical underpinnings of rigorous analysis. Students of mathematics, physics, engineering and other sciences will find the theory and applications covered in this volume to be of real interest.The Princeton Lectures in Analysis represents a sustained effort to introduce the core areas of mathematical analysis while also illustrating the organic unity between them. Numerous examples and applications throughout its four planned volumes, of which Fourier Analysis is the first, highlight the far-reaching consequences of certain ideas in analysis to other fields of mathematics and a variety of sciences. Stein and Shakarchi move from an introduction addressing Fourier series and integrals to in-depth considerations of complex analysis; measure and integration theory, and Hilbert spaces; and, finally, further topics such as functional analysis, distributions and elements of probability theory.

    It encourages readers to think creatively about techniques and strategies for problem solving in the real world.The problems are clustered by topic into self-contained chapters. The book begins with elementary facts, followed by carefully selected problems and detailed, step-by-step solutions, which then lead to more complicated, challenging problems and their solutions. Reflecting the experience of two professors and coaches of Mathematical Olympiads, the text will be valuable to teachers, students, and puzzle enthusiasts.

    Topics include Pythagorean arithmetic, Plato's use and philosophy of mathematics, an in-depth analysis of Euclid's "Elements," the beginnings of Greek algebra and trigonometry, and other mathematical milestones. 1931 edition.

    Yet this esoteric knowledge quickly became accessible in the nineteenth and early twentieth centuries when Britain produced many leading mathematical physicists. In this book, Andrew Warwick shows how the education of these "masters of theory" led them to transform our understanding of everything from the flight of a boomerang to the structure of the universe. Warwick focuses on Cambridge University, where many of the best physicists trained. He begins by tracing the dramatic changes in undergraduate education there since the eighteenth century, especially the gradual emergence of the private tutor as the most important teacher of mathematics. Next he explores the material culture of mathematics instruction, showing how the humble pen and paper so crucial to this study transformed everything from classroom teaching to final examinations. Balancing their intense intellectual work with strenuous physical exercise, the students themselves—known as the "Wranglers"—helped foster the competitive spirit that drove them in the classroom and informed the Victorian ideal of a manly student. Finally, by investigating several historical "cases," such as the reception of Albert Einstein's special and general theories of relativity, Warwick shows how the production, transmission, and reception of new knowledge was profoundly shaped by the skills taught to Cambridge undergraduates.Drawing on a wealth of new archival evidence and illustrations, Masters of Theory examines the origins of a cultural tradition within which the complex world of theoretical physics was made commonplace.

    This book allows parents and teachers to instill a deeper level of mathematical understanding and thinking skills in young children while nurturing a love of mathematics. (Grades 1st - 4th) Each chapter's questions are broken down into four levels: Level 1 (easy) Level 2 (somewhat challenging) Level 3 (challenging) Einstein (very challenging)Includes chapters on: Sequences, Problem-solving, Money, Percents, Algebraic Thinking, Negative Numbers, Logic, Ratios, Probability, Measurements, Fractions, Division.

    Covers a range of topics including sets, real numbers, real functions, infinite series and limit points of a set.

    This book also explains topics, such as the connections between knot theory and surgery.

    Key elements of differential equations and linear algebra are introduced early and are consistently referenced, all theorems are proved using elementary methods, and numerous worked-out examples appear throughout. The highly readable text approaches calculus from the student's viewpoint and points out potential stumbling blocks before they develop. A collection of more than 1,600 problems ranges from exercise material to exploration of new points of theory — many of the answers are found at the end of the book; some of them worked out fully so that the entire process can be followed. This well-organized, unified text is copiously illustrated, amply cross-referenced, and fully indexed.

    Now, more than ever, it provides an outstanding text for upper-level and graduate courses in survival analysis, biostatistics, and time-to-event analysis.The treatment begins with an introduction to survival analysis and a description of four studies that lead to survival data. Subsequent chapters then use those data sets and others to illustrate the various analytical techniques applicable to such data, including the Cox regression model, the Weibull proportional hazards model, and others. This edition features a more detailed treatment of topics such as parametric models, accelerated failure time models, and analysis of interval-censored data. The author also focuses the software section on the use of SAS, summarising the methods used by the software to generate its output and examining that output in detail. Profusely illustrated with examples and written in the author's trademark, easy-to-follow style, Modelling Survival Data in Medical Research, Second Edition is a thorough, practical guide to survival analysis that reflects current statistical practices.

    Drawing on areas of mathematics from probability theory, number theory, and geometry, he explores a wide range of concepts, some more light-hearted, others central to the development of the field and used daily by mathematicians, physicists, and engineers.Each of the book's ten chapters begins by outlining key concepts and goes on to discuss, with the minimum of technical detail, the principles that underlie them. Each includes puzzles and problems of varying difficulty. While the chapters are self-contained, they also reveal the links between seemingly unrelated topics. For example, the problem of how to design codes for satellite communication gives rise to the same idea of uncertainty as the problem of screening blood samples for disease.Accessible to anyone familiar with basic calculus, this book is a treasure trove of ideas that will entertain, amuse, and bemuse students, teachers, and math lovers of all ages.

    The Challenger explosion, the failure of the Mars Orbiter, and the Kansas City Hyatt Regency walkway collapse all involved thinking errors. This book presents the ten things our future mathematicians and scientists must know to prevent these kinds of tragedies from occurring. Because science and mathematics instruction is often dominated by facts and calculation, children are rarely exposed to these important concepts. Over 50 stories are included that show children the strong connections between mathematics and science and the real world.

    M. Joshi covers the strengths and weaknesses of such models as stochastic volatility, jump diffusion, and variance gamma, as well as the Black-Scholes. Examples and exercises, with answers, as well as computer projects, challenge the mind and encourage learning how to become a good quantitative analyst.

    As the title suggests, the author's technique relies on visual elements, and his approach employs the most graphic and least "forbidding" aspects of mathematics. Most people, he observes, possess a direct vision that permits them to "see" only the smaller numbers; with the larger numbers, however, vision fails and mental chaos ensues.Sawyer addresses this difficulty, speaking both for those who like recreational mathematics and for those who teach, suggesting a variety of methods used by many effective teachers — techniques of visualizing, dramatizing, and analyzing numbers that attract and retain the attention and understanding of students. His topics, ranging from basic multiplication and division to algebra, encompass word problems, graphs, negative numbers, fractions, and many other practical applications of elementary mathematics.A valuable resource for parents and teachers, this book will captivate any reader seeking an improved understanding of mathematics.

    The book is self-contained and does not require that readers have previous training in econometrics. The focus is on models used by applied economists and the computational techniques necessary to implement Bayesian methods when doing empirical work. The book includes numerous empirical examples and the website associated with it contains data sets and computer programs to help the student develop the computational skills of modern Bayesian econometrics.

    With an emphasis on clarity and brevity, it features a streamlined and updated format and the absolute essence of the subject, presented in a concise and readily understandable form. Graphic elements such as sidebars, reader-alert icons, and boxed highlights stress selected points from the text, illuminate keys to learning, and give you quick pointers to the essentials.Expert tips for mastering applied physicsLast-minute essentials to pass the courseAppropriate for the following courses: Beginning Physics, Technical Physics, Basic Physics, Introduction to Physics, Physics for Engineers, Atomic PhysicsEasy-to-follow review of applied physicsSupports all the major textbooks for applied physics

    Examining such readily observable phenomena, this book introduces readers to the beauty of nature as revealed by mathematics and the beauty of mathematics as revealed in nature.Generously illustrated, written in an informal style, and replete with examples from everyday life, Mathematics in Nature is an excellent and undaunting introduction to the ideas and methods of mathematical modeling. It illustrates how mathematics can be used to formulate and solve puzzles observed in nature and to interpret the solutions. In the process, it teaches such topics as the art of estimation and the effects of scale, particularly what happens as things get bigger. Readers will develop an understanding of the symbiosis that exists between basic scientific principles and their mathematical expressions as well as a deeper appreciation for such natural phenomena as cloud formations, halos and glories, tree heights and leaf patterns, butterfly and moth wings, and even puddles and mud cracks.Developed out of a university course, this book makes an ideal supplemental text for courses in applied mathematics and mathematical modeling. It will also appeal to mathematics educators and enthusiasts at all levels, and is designed so that it can be dipped into at leisure.

    For each theory, the authors discuss the main conceptual points, detail many practical calculations of physical quantities from first principles, and compare these quantitative predictions with experimental results. The text emphasizes the development of both calculation skills and physical insight.

    This book includes such topics as affine and projective spaces, tensor algebra, Galois theory, Lie groups, and associative algebras and their representations. It is suitable for independent study for advanced undergraduates and graduate students.

    He looks at science historically, emphasizing not only the achievements of scientists from Galileo onwards, but also their mistakes. He rejects the claim that all scientific knowledge is provisional, by citing examples from chemistry, biology and geology. A major feature of the book is its defense of the view that mathematics was invented rather than discovered. A large number of examples are used to illustrate these points, and many of the deep issues in today's world discussed-from psychology and evolution to quantum theory, consciousness and even religious belief. Disentangling knowledge from opinion and aspiration is a hard task, but this book provided a clear guide to the difficulties.

    Delivering valuation theory, the consensus view on application, and the tools to make it happen, James Hitchners all-star cast of contributors offer numerous examples, checklists, and models to assist in navigating a valuation project. The book contains hundreds of short, easily understandable "Valuation Tips," and covers best practices from the view of these twenty-five experts.

    Suitable for either classroom use or self-paced study, it uses innovative discussions, cartoons, anecdotes, examples, and exercises that unfailingly capture and hold student interest..

    It begins with the simple conviction that Fourier arrived at in the early nineteenth century when studying problems in the physical sciences--that an arbitrary function can be written as an infinite sum of the most basic trigonometric functions.The first part implements this idea in terms of notions of convergence and summability of Fourier series, while highlighting applications such as the isoperimetric inequality and equidistribution. The second part deals with the Fourier transform and its applications to classical partial differential equations and the Radon transform; a clear introduction to the subject serves to avoid technical difficulties. The book closes with Fourier theory for finite abelian groups, which is applied to prime numbers in arithmetic progression.In organizing their exposition, the authors have carefully balanced an emphasis on key conceptual insights against the need to provide the technical underpinnings of rigorous analysis. Students of mathematics, physics, engineering and other sciences will find the theory and applications covered in this volume to be of real interest.The Princeton Lectures in Analysis represents a sustained effort to introduce the core areas of mathematical analysis while also illustrating the organic unity between them. Numerous examples and applications throughout its four planned volumes, of which Fourier Analysis is the first, highlight the far-reaching consequences of certain ideas in analysis to other fields of mathematics and a variety of sciences. Stein and Shakarchi move from an introduction addressing Fourier series and integrals to in-depth considerations of complex analysis; measure and integration theory, and Hilbert spaces; and, finally, further topics such as functional analysis, distributions and elements of probability theory.

    A large number of problems are sprinkled throughout the book, and a full set of problems from examinations given in Moscow are included at the end. Some of these problems are quite challenging! What makes the book unique is Arnold's particular talent at holding a topic up for examination from a new and fresh perspective. He likes to blow away the fog of generality that obscures so much mathematical writing and reveal the essentially simple intuitive ideas underlying the subject. No other mathematical writer does this quite so well as Arnold.

    The book provides a firm foundation for advanced work in any of these directions.

    Dazzle your students with Peculiar number patterns and properties Clever shortcuts and tricks for avoiding cumbersome mathematic processes Curious problems that reveal problem-solving strategies Algebra problems that shed light on patterns in mathematics and the behavior of numbers Activities and demonstrations that uncover timeless geometric principles Used as attention-getters, motivators, or enrichment activities, these math wonders leave students questioning and exploring further, regardless of their grade level or ability.

    REVIEWERS SAY: "Examples are excellent. They cover a wide range of physics problems." - Bing Zhou, University of Michigan "The ideas are communicated very well and it is easy to understand...It has a more modern treatment than most, has a very complete range of topics and each is treated in sufficient detail....I'm not aware of another better book at this level..." -Gary Wysin, Kansas State University * This is a more accessible version of Arken/Weber's blockbuster reference, which already has more than 13,000 sales worldwide * Many more detailed, worked-out examples illustrate how to use and apply mathematical techniques to solve physics problems * More frequent and thorough explanations help readers understand, recall, and apply the theory * New introductions and review material provide context and extra support for key ideas * Many more routine problems reinforce basic, foundational concepts and computations

    The University's Lucasian Professorship of Mathematics is one of the world's most celebrated academic positions. Since its foundation in 1663, the chair has been held by seventeen men who represent some of the most influential minds in science and technology. This informative work offers new perspectives on such world-famous scientists as Isaac Newton, Charles Babbage, Paul Dirac, and Stephen Hawking.

    Covering concepts, theorems and notable mathematicians, this comprehensive calculus primer covers such topics as absolute value; binomial theorem; implicit differentiation; polynomial functions; and the second derivative.

    Explores tensor algebra, the line element, covariant differentiation, geodesics and parallelism, and curvature tensor. Also covers Euclidean 3-dimensional differential geometry, Cartesian tensors and elasticity, and the theory of relativity. 1960 edition.

    Building on very simple principles, it develops these mathematical highlights, known to every well-rounded mathematician, in an intuitive and entertaining way. The aim of the book is to motivate and inspire the reader to discover and understand some of these truly amazing mathematical structures and ideas which are frequently not fully grasped, pass unnoticed or simply swamped in an undergraduate mathematics course. For the experienced mathematician the book offers refreshing, often enlightening, hindsight. For the novice it is an exciting intellectual journey.

    We could even go as far as to say that we ourselves shape the space around us according to how our perceptions of the universe alter and develop, and mathematics plays a pivotal role. In this book, the "virtual" protagonist of the journey through the concept of space is the square. Michele Emmer, born in 1945, is Professor of Mathematics at the University La Sapienza in Rome and has authored many books and films on the subject of mathematics and art and culture. He was also responsible for exhibitions at the Venetian Biennale and the CitA(c) des Sciences La Villette in Paris.

    Each chapter highlights a particular aspect of the subject and casts combinatorial concepts in the guise of questions, illustrations, and exercises that are designed to encourage creativity, improve problem-solving techniques, and widen the reader's mathematical horizons.Topics encompass permutations and combinations, binomial coefficients and their applications, recursion, bijections, inclusions and exclusions, and generating functions. The work is replete with a broad range of useful methods and results, such as Sperner's Theorem, Catalan paths, integer partitions and Young's diagrams, and Lucas' and Kummer's Theorems on divisibility. Strong emphasis is placed on connections between combinatorial and graph-theoretic reasoning and on links between algebra and geometry.The authors' previous text, 102 Combinatorial Problems, makes a fine companion volume to the present work, which is ideal for Olympiad participants and coaches, advanced high school students, undergraduates, and

    This book also contains a description of the basic elements of a mathematical education, as well as a glossary and appendices on the structure of a typical department.

    It presents a unique blend of theory and applications, with special emphasis on mathematical modelling, computational techniques and examples from the biological sciences. It is appropriate for students in applied mathematics, biostatistics, computational biology, computer science, physics, and statistics.

    It offers serious mathematics in a lively, reader-friendly style. Included are exercises and many figures that illustrate the main concepts. The first chapter presents the geometry and topology of surfaces. Among other topics, the authors discuss the Poincare-Hopf theorem on critical points of vector fields on surfaces and the Gauss-Bonnet theorem on the relation between curvature and topology (the Euler characteristics). The second chapter addresses various aspects of the concept of dimension, including the Peano curve and the Poincare approach. Also addressed are the structure of three-dimensional manifolds, in particular, provided that the three-dimensional sphere is the union of two doughnuts. This is the first of three volumes originating from a series of lectures given by the authors at Kyoto University (Japan). It is suitable for classroom use for high school mathematics teachers and undergraduate courses in science and liberal arts.

    This classic text, written by a distinguished mathematician and teacher, focuses on a fundamental cornerstone of elementary geometry, the theorem of Pythagoras, and its applications. Translated by Dr. Ambikeshwar Sharma.

    It introduces children of 5 upwards to the vocabulary they need to describe their early maths work and promotes confidence in discussing the role that maths plays in their everyday lives.

    Throughout the text emphasis is on the interplay between algebra and topology, with graphical interpretation of algebraic operations, and topological structures described algebraically in terms of generators and relations. Includes numerous exercises and examples.

    The authors both explore and extend Husserl’s thought, addressing the issues which led to the development of analytic philosophy early in the twentieth century. This collection of essays offers a fresh and provocative alternative to contemporary mainstream philosophy of mathematics and covers key areas of disagreements between Husserl, the father of phenomenology, and Frege, the founder of analytic philosophy.

    It reflects the dramatic progress of mathematical music theory and its operationalization by information technology since the publication of Geometrie der T ne in 1990. The conceptual basis has been vastly generalized to topos-theoretic foundations, including a corresponding thoroughly geometric musical logic. The theoretical models and results now include topologies for rhythm, melody, and harmony, as well as a classification theory of musical objects that comprises the topos-theoretic concept framework. Classification also implies techniques of algebraic moduli theory. The classical models of modulation and counterpoint have been extended to exotic scales and counterpoint interval dichotomies. The probably most exciting new field of research deals with musical performance and its implementation on advanced object-oriented software environments. This subject not only uses extensively the existing mathematical music theory, it also opens the language to differential equations and tools of differential geometry, such as Lie derivatives. Mathematical performance theory is the key to inverse performance theory, an advanced new research field which deals with the calculation of varieties of parameters which give rise to a determined performance. This field uses techniques of algebraic geometry and statistics, approaches which have already produced significant results in the understanding of highest-ranked human performances. The book's formal language and models are currently being used by leading researchers in Europe and Northern America and have become a foundation of music software design. This is also testified by the book's nineteen collaborators and the included CD-ROM containing software and music examples.

    So when Mrs. Brandt asks her students to write a report on any subject that fascinates them, Bill chooses money, of course! Filled with tons of cool facts, wonderful illustrations, and photographs of coins and money from all over the world, Money: A Rich History is worth every penny! Illustrated by Thor Wickstrom.

    This title moves from Newton's definitions and axioms through the essential propositions, as Newton himself identified them, to the establishment of universal gravitation and elliptical orbits.

    With additional exercises, this edition offers more comprehensive coverage of the fundamental theory, techniques, and applications of elliptic curves. New to the Second EditionChapters on isogenies and hyperelliptic curves A discussion of alternative coordinate systems, such as projective, Jacobian, and Edwards coordinates, along with related computational issues A more complete treatment of the Weil and Tate-Lichtenbaum pairings Doud's analytic method for computing torsion on elliptic curves over Q An explanation of how to perform calculations with elliptic curves in several popular computer algebra systems Taking a basic approach to elliptic curves, this accessible book prepares readers to tackle more advanced problems in the field. It introduces elliptic curves over finite fields early in the text, before moving on to interesting applications, such as cryptography, factoring, and primality testing. The book also discusses the use of elliptic curves in Fermat's Last Theorem. Relevant abstract algebra material on group theory and fields can be found in the appendices.

    This fully revised second edition continues to offer a carefully crafted blend of numerical applications and theoretical grounding in economics, finance, and mathematics, and provides plenty of opportunities for students to practice applied mathematics and cutting-edge finance. Ales Cern� mixes tools from calculus, linear algebra, probability theory, numerical mathematics, and programming to analyze in an accessible way some of the most intriguing problems in financial economics. The textbook is the perfect hands-on introduction to asset pricing, optimal portfolio selection, risk measurement, and investment evaluation.The new edition includes the most recent research in the area of incomplete markets and unhedgeable risks, adds a chapter on finite difference methods, and thoroughly updates all bibliographic references. Eighty figures, over seventy examples, twenty-five simple ready-to-run computer programs, and several spreadsheets enhance the learning experience. All computer codes have been rewritten using MATLAB and online supplementary materials have been completely updated. A standard textbook for graduate finance courses Introduction to asset pricing, portfolio selection, risk measurement, and investment evaluation Detailed examples and MATLAB codes integrated throughout the text Exercises and summaries of main points conclude each chapter

    Now available in this two volume set, it contains all the important informationboth volumes provides. Considered to be a complete benefit for all researchers and academics in theoretical computer science, logicians and philosophers who study the foundations of mathematics, and those working in differential geometry and continuum physics.

    Written for high school students, this book aims to show a younger audience why math should matter and to make the problems found in math intriguing. Klein presents for his readers an investigation of the possibility or impossibility of finding solutions for the following problems in light of mathematics available to him: duplication of the cube trisection of an angle quadrature of the circle Mathematicians and students of the history of math will find this an intriguing work. German mathematician FELIX KLEIN (1849 1925), a great teacher and scientific thinker, significantly advanced the field of mathematical physics and made a number of profound discoveries in the field of geometry. His published works include Elementary Mathematics from an Advanced Standpoint: Arithmetic, Algebra, Analysis and Elementary Mathematics from an Advanced Standpoint: Geometry.

    Suitable for those wishing to advance their understanding by exploring mirror symmetry at the interface of mathematics and physics, and for graduate students and research mathematicians interested in mathematical and theoretical physics.

    The first 10 chapters discuss theoretical methods in Measure Theory and Functional Analysis and contain over 120 end of chapter exercises. the final two chapters apply theory to applications in Probability Theory and Partial Differential Equations.

    In his scholarly supplement to Riemann's complex mathematical theory, rather than offer proofs in support of the theorem, Klein chose to offer this exposition and annotation, first published in 1893, in an effort to broaden and deepen understanding. This approach makes Klein's commentary an essential element of any mathematics scholar's library.

    Among the topics covered are smooth manifolds and maps, the structure of the tangent bundle and its associates, the calculation of real cohomology groups using differential forms (de Rham theory), and applications such as the Poincaré-Hopf theorem relating the Euler number of a manifold and the index of a vector field. Each chapter contains exercises of varying difficulty for which solutions are provided. Special features include examples drawn from geometric manifolds in dimension 3 and Brieskorn varieties in dimensions 5 and 7, as well as detailed calculations for the cohomology groups of spheres and tori.

    Written for engineers and students alike, the aim of the book is to provide the necessary theories and techniques of the FEM for readers to be able to use a commercial FEM package to solve primarily linear problems in mechanical and civil engineering with the main focus on structural mechanics and heat transfer. Fundamental theories are introduced in a straightforward way, and state-of-the-art techniques for designing and analysing engineering systems, including microstructural systems are explained in detail. Case studies are used to demonstrate these theories, methods, techniques and practical applications, and numerous diagrams and tables are used throughout. The case studies and examples use the commercial software package ABAQUS, but the techniques explained are equally applicable for readers using other applications including NASTRAN, ANSYS, MARC, and more. Full sets of PowerPoint slides developed by the authors for their course on FEM are available as a free download from a companion website.

    Van der Vorst demonstrates how these methods can be derived from basic iteration formulas and how they are related. Focusing on the ideas behind the methods rather than a complete presentation of the theory, the volume includes a substantial amount of references for further reading as well as exercises to help students initially encountering the material.

    This book presents an introduction to the development of algebraic geometry during the years 1955-1965. It is suitable for specialists in algebraic geometry, and mathematical historians.

    Organized in thematic sections that cover topics as diverse as science and technology, sports and culture, and religion and mythology, it is a gold mine of facts, figures, and statistics. Backed by maps, diagrams, and a full index and now fully revised and updated, The Penguin Factfinder explores facts and figures on every conceivable topic of current interest, from world climates to musical notation. Whether you are seeking to establish the precise population of Guatemala, the chemical symbol for radium, or a list of Olympic Games medalists, this is the essential source of information.

    This edition contains new chapters on generation methods and their application, classification of metrics by invariants, and treatments of homothetic motions and methods from dynamical systems theory. It also includes colliding waves, inhomogeneous cosmological solutions, and spacetimes containing special subspaces.

    It also presents historical background on their ancient origins and describes the reflective properties and roles of curves in design applications. Only a basic knowledge of plane geometry needed. 1993 edition. Includes 98 figures.

    Phase Change builds on and deepens his assessment of the role of the computer as a tool driving profound change by examining the role of computers in changing the face of the sciences and mathematics. He shows that paradigm shifts in understanding in science have generally been triggered by the availability of new tools, allowing the investigator a new way of seeing into questions that had not earlier been amenable to scientific probing.

    Carefully structured, coherent and comprehensive, each chapter contains tailored exercises and solutions to selected questions, and miscellaneous exercises are presented throughout. This is an invaluable text for students seeking a clear introduction to discrete mathematics, graph theory, combinatorics, number theory and abstract algebra.

    Numerous problems, examples, and diagrams--some with solutions--plus clear-cut, highlighted summaries of results. Advanced undergraduate to graduate level. Contents: 1. Introduction. 2. Probability Model. 3. Probability Distributions. 4. Introduction to Statistical Inference. 5. More on Mathematical Expectation. 6. Some Discrete Models. 7. Some Continuous Models. 8. Functions of Random Variables and Random Vectors. 9. Large-Sample Theory. 10. General Methods of Point and Interval Estimation. 11. Testing Hypotheses. 12. Analysis of Categorical Data. 13. Analysis of Variance: k-Sample Problems. Appendix-Tables. Answers to Odd-Numbered Problems. Index. Unabridged republication of the edition published by John Wiley & Sons, New York, 1984. 144 Figures. 35 Tables. Errata list prepared by the author

    Application problems drawn from the literature of many different fields prepares readers to use the techniques covered to solve a wide variety of practical problems. KEY TOPICS: Rootfinding. Systems of Equations. Eigenvalues and Eigenvectors. Interpolation and Curve Fitting. Numerical Differentiation and Integration. Numerical Methods for Initial Value Problems of Ordinary Differential Equations. Second-Order One-Dimensional Two-Point Boundary Value Problems. Finite Difference Method for Elliptic Partial Differential Equations. Finite Difference Method for Parabolic Partial Differential Equations. Finite Difference Method for Hyperbolic Partial Differential Equations and the Convection-Diffusion Equation. MARKET: For anyone interested in numerical analysis/methods and their applications in many fields