Best of
Mathematics

1996

Introduction to the Theory of Computation


Michael Sipser - 1996
    Sipser's candid, crystal-clear style allows students at every level to understand and enjoy this field. His innovative "proof idea" sections explain profound concepts in plain English. The new edition incorporates many improvements students and professors have suggested over the years, and offers updated, classroom-tested problem sets at the end of each chapter.

Mathematical Circles: Russian Experience (Mathematical World, Vol. 7)


Dmitri Fomin - 1996
    The work is predicated on the idea that studying mathematics can generate the same enthusiasm as playing a team sport - without necessarily being competitive.

Understanding Digital Signal Processing


Richard G. Lyons - 1996
    This second edition is appropriate as a supplementary (companion) text for any college-level course covering digital signal processing.

Indiscrete Thoughts


Gian-Carlo Rota - 1996
    The era covered by this book, 1950 to 1990, was surely one of the golden ages of science as well as the American university.Cherished myths are debunked along the way as Gian-Carlo Rota takes pleasure in portraying, warts and all, some of the great scientific personalities of the period Stanislav Ulam (who, together with Edward Teller, signed the patent application for the hydrogen bomb), Solomon Lefschetz (Chairman in the 50s of the Princeton mathematics department), William Feller (one of the founders of modern probability theory), Jack Schwartz (one of the founders of computer science), and many others.Rota is not afraid of controversy. Some readers may even consider these essays indiscreet. After the publication of the essay "The Pernicious Influence of Mathematics upon Philosophy" (reprinted six times in five languages) the author was blacklisted in analytical philosophy circles. Indiscrete Thoughts should become an instant classic and the subject of debate for decades to come."Read Indiscrete Thoughts for its account of the way we were and what we have become; for its sensible advice and its exuberant rhetoric."--The Mathematical Intelligencer"Learned, thought-provoking, politically incorrect, delighting in paradox, and likely to offend but everywhere readable and entertaining."--The American Mathematical Monthly"It is about mathematicians, the way they think, and the world in which the live. It is 260 pages of Rota calling it like he sees it... Readers are bound to find his observations amusing if not insightful. Gian-Carlo Rota has written the sort of book that few mathematicians could write. What will appeal immediately to anyone with an interest in research mathematics are the stories he tells about the practice of modern mathematics."--MAA Reviews"

Math Olympiad Contest Problems for Elementary and Middle Schools


George Lenchner - 1996
    Product Condition: No Defects.

Mathematical Mysteries: The Beauty and Magic of Numbers


Calvin C. Clawson - 1996
    This recreational math book takes the reader on a fantastic voyage into the world of natural numbers. From the earliest discoveries of the ancient Greeks to various fundamental characteristics of the natural number sequence, Clawson explains fascinating mathematical mysteries in clear and easy prose. He delves into the heart of number theory to see and understand the exquisite relationships among natural numbers, and ends by exploring the ultimate mystery of mathematics: the Riemann hypothesis, which says that through a point in a plane, no line can be drawn parallel to a given line.While a professional mathematician's treatment of number theory involves the most sophisticated analytical tools, its basic ideas are surprisingly easy to comprehend. By concentrating on the meaning behind various equations and proofs and avoiding technical refinements, Mathematical Mysteries lets the common reader catch a glimpse of this wonderful and exotic world.

The Pleasures of Counting


T.W. Körner - 1996
    K�rner describes a variety of lively topics that continue to intrigue professional mathematicians. The topics range from the design of anchors and the Battle of the Atlantic to the outbreak of cholera in Victorian Soho. The author uses relatively simple terms and ideas, yet explains difficulties and avoids condescension. If you are a mathematician who wants to explain to others how you spend your working days, then seek inspiration here. This book will appeal to everyone interested in the uses of mathematics.

Student's Solution Manual, An Outline for the Study of Calculus TC7 Louis Leithold (Vol. 1, Chapters 1-4)


Leon Gerber - 1996
    

Data Analysis: A Bayesian Tutorial


Devinderjit Singh Sivia - 1996
    This book attempts to remedy the situation by expounding a logical and unified approach to the whole subject of data analysis.This text is intended as a tutorial guide for senior undergraduates and research students in science and engineering. After explaining the basic principles of Bayesian probability theory, their use is illustrated with a variety of examples ranging from elementary parameter estimation to imageprocessing. Other topics covered include reliability analysis, multivariate optimization, least-squares and maximum likelihood, error-propagation, hypothesis testing, maximum entropy and experimental design.The Second Edition of this successful tutorial book contains a new chapter on extensions to the ubiquitous least-squares procedure, allowing for the straightforward handling of outliers and unknown correlated noise, and a cutting-edge contribution from John Skilling on a novel numerical techniquefor Bayesian computation called 'nested sampling'.

A First Course in Optimization Theory


Rangarajan K. Sundaram - 1996
    The first of its three parts examines the existence of solutions to optimization problems in Rn, and how these solutions may be identified. The second part explores how solutions to optimization problems change with changes in the underlying parameters, and the last part provides an extensive description of the fundamental principles of finite- and infinite-horizon dynamic programming. A preliminary chapter and three appendices are designed to keep the book mathematically self-contained.

Challenging Problems in Geometry


Alfred S. Posamentier - 1996
    Within each topic, the problems are arranged in approximate order of difficulty. Detailed solutions (as well as hints) are provided for all problems, and specific answers for most.Invaluable as a supplement to a basic geometry textbook, this volume offers both further explorations on specific topics and practice in developing problem-solving techniques.

Field Quantization


Walter Greiner - 1996
    The initial chapters deal with the quantum mechanics of systems having many degrees of freedom and with classical Lagrangian field theory. Subsequently, both the traditional method of canonical quantization and the modern approach using path integrals are studied. The material is presented in considerable detail and accompanied by a large number of worked examples and exercises.

An Introduction to the Mathematics of Financial Derivatives


Salih N. Neftci - 1996
    This updated edition has six new chapters and chapter-concluding exercises, plus one thoroughly expanded chapter. The text answers the need for a resource targeting professionals, Ph.D. students, and advanced MBA students who are specifically interested in financial derivatives.This edition is also designed to become the main text in first year masters and Ph.D. programs for certain courses, and will continue to be an important manual for market professionals and professionals with mathematical, technical, or physics backgrounds.

Engineering Optimization: Theory and Practice


Singiresu S. Rao - 1996
    Covering both the latest and classical optimization methods, the text starts off with the basics and then progressively builds to advanced principles and applications.This comprehensive text covers nonlinear, linear, geometric, dynamic, and stochastic programming techniques as well as more specialized methods such as multiobjective, genetic algorithms, simulated annealing, neural networks, particle swarm optimization, ant colony optimization, and fuzzy optimization. Each method is presented in clear, straightforward language, making even the more sophisticated techniques easy to grasp. Moreover, the author provides:Case examples that show how each method is applied to solve real-world problems across a variety of industriesReview questions and problems at the end of each chapter to engage readers in applying their newfound skills and knowledgeExamples that demonstrate the use of MATLAB(R) for the solution of different types of practical optimization problemsReferences and bibliography at the end of each chapter for exploring topics in greater depthAnswers to Review Questions available on the author's Web site to help readers to test their understanding of the basic conceptsWith its emphasis on problem-solving and applications, Engineering Optimization is ideal for upper-level undergraduates and graduate students in mechanical, civil, electrical, chemical, and aerospace engineering. In addition, the text helps practicing engineers in almost any industry design improved, more efficient systems at less cost.

Mathematical Methods for Physicists: A Concise Introduction


Tai L. Chow - 1996
    It provides an accessible account of most of the current, important mathematical tools required in physics. The book bridges the gap between an introductory physics course and more advanced courses in classical mechanics, electricity and magnetism, quantum mechanics, and thermal and statistical physics. It contains a large number of worked examples to illustrate the mathematical techniques developed and to show their relevance to physics. The highly organized coverage allows instructors to teach the basics in one semester. The book could also be used in courses in engineering, astronomy, and mathematics.

The Quantum Theory of Fields 3 Volume Paperback Set


Steven Weinberg - 1996
    The first volume introduces the foundations of quantum field theory, the second volume examines modern applications, and finally, the third volume presents supersymmetry, an area of theoretical physics likely to be at the center of progress in the physics of elementary particles and gravitation. The development is fresh and logical throughout, with each step carefully motivated by what has preceded. The presentation of modern mathematical methods is interwoven with accounts of applications in both elementary particle and condensed matter physics. The three volumes contain much original material, and are enhanced with examples and insights drawn from the author's experience as a leader of elementary particle research. Hb ISBN (1995) Vol.1 0-521-55001-7 Hb ISBN (1996) Vol.2 0-521-55002-5 Hb ISBN (1996) Vols. 1 & 2 Set 0-521-58555-4 Hb ISBN (2000) Vol.3 0-521-66000-9 HB ISBN (2000) Vols. l-3 Set 0-521-78082-9

Theory of Functions, Parts I and II


Konrad Knopp - 1996
    Part I considers general foundations of the theory of functions; Part II stresses special functions and characteristic, important types of functions, selected from single-valued and multiple-valued classes. Demonstrations are full and proofs given in detail. Introduction. Bibliographies.

Black Scholes and Beyond: Option Pricing Models


Neil A. Chriss - 1996
    The Black-Scholes equation is discussed as well as other methods that have built upon the success of Black-Scholes, including Cox-Ross-Rubinstein binomial trees, the Derman-Kani theory on implied volatility trees and Mark Rubenstein's implied binomial trees. Other topics covered include, pricing and hedging options, volatility smiles and how to price options in the presence of a smile, pricing barrier options and current theoretical developments from Wall Street.

A Life of Bertrand Russell


Ray Monk - 1996
    

The Parsimonious Universe: Shape And Form In The Natural World


Stefan Hildebrandt - 1996
    Skillfully integrating striking full-color illustrations, the authors describe the efforts by scientists and mathematicians since the Renaissance to identify and describe the principles underlying the shape of natural forms. But can one set of laws account for both the symmetry and irregularity as well as the infinite variety of nature's designs? A complete answer to this question is likely never to be discovered. Yet, it is fascinating to see how the search for some simple universal laws down through the ages has increased our understanding of nature. The Parsimonious Universe looks at examples from the world around us at a non-mathematical, non-technical level to show that nature achieves efficiency by being stingy with the energy it expends.

The Principles of Mathematics Revisited


Jaakko Hintikka - 1996
    Jaakko Hintikka proposes a new basic first-order logic and uses it to explore the foundations of mathematics. This new logic enables logicians to express on the first-order level such concepts as equicardinality, infinity, and truth in the same language. Hintikka's new logic is highly original and will prove appealing to logicians, philosophers of mathematics, and mathematicians concerned with the foundations of the discipline.

Differential Forms: A Complement to Vector Calculus


Steven H. Weintraub - 1996
    Geared towards students taking courses in multivariable calculus, this innovative book aims to make the subject more readily understandable. Differential forms unify and simplify the subject of multivariable calculus, and students who learn the subject as it is presented in this book should come away with a better conceptual understanding of it than those who learn using conventional methods.* Treats vector calculus using differential forms* Presents a very concrete introduction to differential forms* Develops Stokess theorem in an easily understandable way* Gives well-supported, carefully stated, and thoroughly explained definitions and theorems.* Provides glimpses of further topics to entice the interested student

Foundations of Differential Geometry, Volume 1


Shoshichi Kobayashi - 1996
    It is completely self-contained and will serve as a reference as well as a teaching guide. Volume 1 presents a systematic introduction to the field from a brief survey of differentiable manifolds, Lie groups and fibre bundles to the extension of local transformations and Riemannian connections. The second volume continues with the study of variational problems on geodesics through differential geometric aspects of characteristic classes. Both volumes familiarize readers with basic computational techniques.

Computational Methods for Fluid Dynamics


Joel H. Ferziger - 1996
    Included are advanced methods in computational fluid dynamics, like direct and large-eddy simulation of turbulence, multigrid methods, parallel computing, moving grids, structured, block-structured and unstructured boundary-fitted grids, free surface flows. The 3rd edition contains a new section dealing with grid quality and an extended description of discretization methods. The book shows common roots and basic principles for many different methods. The book also contains a great deal of practical advice for code developers and users; it is designed to be equally useful to beginners and experts.The issues of numerical accuracy, estimation and reduction of numerical errors are dealt with in detail, with many examples.

Simulation


Sheldon M. Ross - 1996
    Readers learn to apply results of these analyses to problems in a wide variety of fields to obtain effective, accurate solutions and make predictions about future outcomes. This new edition provides a comprehensive, in-depth, and current guide for constructing probability models and simulations for a variety of purposes. It features new information, including the presentation of the Insurance Risk Model, generating a Random Vector, and evaluating an Exotic Option. Also new is coverage of the changing nature of statistical methods due to the advancements in computing technology.

Lectures on Elliptic and Parabolic Equations in Sobolev Spaces


N.V. Krylov - 1996
    The main areas covered in this book are the first boundary-value problem for elliptic equations and the Cauchy problem for parabolic equations.

Accuracy and Stability of Numerical Algorithms


Nicholas J. Higham - 1996
    It combines algorithmic derivations, perturbation theory, and rounding error analysis, all enlivened by historical perspective and informative quotations. The coverage of the first edition has been expanded and updated, involving numerous improvements. Two new chapters treat symmetric indefinite systems and skew-symmetric systems, and nonlinear systems and Newton's method. Twelve new sections include coverage of additional error bounds for Gaussian elimination, rank revealing LU factorizations, weighted and constrained least squares problems, and the fused multiply-add operation found on some modern computer architectures. This new edition is a suitable reference for an advanced course and can also be used at all levels as a supplementary text from which to draw examples, historical perspective, statements of results, and exercises. In addition the thorough indexes and extensive, up-to-date bibliography are in a readily accessible form.

Weak Convergence and Empirical Processes: With Applications to Statistics


Aad W. van der Vaart - 1996
    Part one reviews stochastic convergence in its various forms. Part two offers the theory of empirical processes in a form accessible to statisticians and probabilists. Part three covers a range of topics demonstrating the applicability of the theory to key questions such as measures of goodness of fit and the bootstrap.

Conformal Field Theory


Philippe Di Francesco - 1996
    The treatment is self-contained, pedagogical, and exhaustive, and includes a great deal of background material on quantum field theory, statistical mechanics, Lie algebras and affine Lie algebras. The many exercises, with a wide spectrum of difficulty and subjects, complement and in many cases extend the text. The text is thus not only an excellent tool for classroom teaching but also for individual study. Intended primarily for graduate students and researchers in theoretical high-energy physics, mathematical physics, condensed matter theory, statistical physics, the book will also be of interest in other areas of theoretical physics and mathematics. It will prepare the reader for original research in this very active field of theoretical and mathematical physics.

Fractal Art: The Mandelbrot Set (Postcard Portfolio)


NOT A BOOK - 1996
    Examine the wonders of this fractal set, which can also be used as a flip book. 30 cards. 30 color plates.

Formeln + Hilfen zur höheren Mathematik


Gerhard Merziger - 1996
    

Classic Set Theory: For Guided Independent Study


Derek Goldrei - 1996
    This includes:The definition of the real numbers in terms of rational numbers and ultimately in terms of natural numbersDefining natural numbers in terms of setsThe potential paradoxes in set theoryThe Zermelo-Fraenkel axioms for set theoryThe axiom of choiceThe arithmetic of ordered setsCantor's two sorts of transfinite number - cardinals and ordinals - and the arithmetic of these.The book is designed for students studying on their own, without access to lecturers and other reading, along the lines of the internationally renowned courses produced by the Open University. There are thus a large number of exercises within the main body of the text designed to help students engage with the subject, many of which have full teaching solutions. In addition, there are a number of exercises without answers so students studying under the guidance of a tutor may be assessed.Classic Set Theory gives students sufficient grounding in a rigorous approach to the revolutionary results of set theory as well as pleasure in being able to tackle significant problems that arise from the theory.

Elements of Modern Algebra


Jimmie Gilbert - 1996
    This text is intended for the introductory course in algebraic structures and covers groups before rings. This course often is used to bridge the gap from manipulative to theoretical mathematics and to help prepare secondary mathematics teachers for their careers. This text includes some optional sections to give instructors flexibility.

Chaos: An Introduction to Dynamical Systems


Kathleen T. Alligood - 1996
    Intended for courses in nonlinear dynamics offered either in Mathematics or Physics, the text requires only calculus, differential equations, and linear algebra as prerequisites. Along with discussions of the major topics, including discrete dynamical systems, chaos, fractals, nonlinear differential equations and bifurcations, the text also includes Lab Visits, short reports that illustrate relevant concepts from the physical, chemical and biological sciences. There are Computer Experiments throughout the text that present opportunities to explore dynamics through computer simulations, designed to be used with any software package. And each chapter ends with a Challenge, which provides students a tour through an advanced topic in the form of an extended exercise.

Handbook of Applied Cryptography


Alfred J. Menezes - 1996
    Standards are emerging to meet the demands for cryptographic protection in most areas of data communications. Public-key cryptographic techniques are now in widespread use, especially in the financial services industry, in the public sector, and by individuals for their personal privacy, such as in electronic mail. This Handbook will serve as a valuable reference for the novice as well as for the expert who needs a wider scope of coverage within the area of cryptography. It is a necessary and timely guide for professionals who practice the art of cryptography. The Handbook of Applied Cryptography provides a treatment that is multifunctional: It serves as an introduction to the more practical aspects of both conventional and public-key cryptographyIt is a valuable source of the latest techniques and algorithms for the serious practitionerIt provides an integrated treatment of the field, while still presenting each major topic as a self-contained unitIt provides a mathematical treatment to accompany practical discussionsIt contains enough abstraction to be a valuable reference for theoreticians while containing enough detail to actually allow implementation of the algorithms discussedNow in its third printing, this is the definitive cryptography reference that the novice as well as experienced developers, designers, researchers, engineers, computer scientists, and mathematicians alike will use.

Handbook of Analysis and Its Foundations


Eric Schechter - 1996
    It provides an introduction to a wide range of topics including set theory and mathematical logic; algebra; toplogy; normed spaces; integration theory; toplogical vector spaces; and differential equations. The author demonstrates the relationships between these topics and includes a few chapters on set theory and logic to explain the lack of examples in the presentation of classical pathological objects through nonconstructive proofs.

Foundations of Differential Geometry, Volume 2


Shoshichi Kobayashi - 1996
    It is completely self-contained and will serve as a reference as well as a teaching guide. Volume 1 presents a systematic introduction to the field from a brief survey of differentiable manifolds, Lie groups and fibre bundles to the extension of local transformations and Riemannian connections. The second volume continues with the study of variational problems on geodesics through differential geometric aspects of characteristic classes. Both volumes familiarize readers with basic computational techniques.

100% Mathematical Proof


Rowan Garnier - 1996
    Covering basic propositional and predicate logic as well as discussing axiom systems and formal proofs, the book seeks to explain what mathematicians understand by proofs and how they are communicated. The authors explore the principle techniques of direct and indirect proof including induction, existence and uniqueness proofs, proof by contradiction, constructive and non-constructive proofs, etc. Many examples from analysis and modern algebra are included. The exceptionally clear style and presentation ensures that the book will be useful and enjoyable to those studying and interested in the notion of mathematical "proof.

Planetary Harmonics of Speculative Markets


Larry Pesavento - 1996
    He includes a wealth of charted examples that provide "absolutely phenomenal" trend change dates with an explanation of the planetary and lunar, movements that precipitated these events. Other topics included are: Planetary Declinations and Retrogrades, hidden Fibonacci relationships, intertwined with lessons in attitude, money management, and discipline. Applies George Bayer's principles to financial markets; proves the validity of planetary harmonics; shows results from thousands of hours of computer research by the author. Deals with human aspects of discipline, flexibility, and intuition.

Which Way Did the Bicycle Go?: And Other Intriguing Mathematical Mysteries


Joseph D.E. Konhauser - 1996
    This collection will give students, teachers, and university professors a chance to experience the pleasure of wrestling with some beautiful problems of elementary mathematics. Readers can compare their sleuthing talents with those of Sherlock Holmes, who made a bad mistake regarding the first problem in the collection: Determine the direction of travel of a bicycle that has left its tracks in a patch of mud. The collection contains a variety of other unusual and interesting problems in geometry, algebra, combinatorics, and number theory. For example, if a pizza is sliced into eight 45-degree wedges meeting at a point other than the center of the pizza, and two people eat alternating wedges, will they get equal amounts of pizza? Or: Is an advertiser's claim that a certain unusual combination lock allows thousands of combinations justified? Complete solutions to the 191 problems are included with problem variations and topics for investigation.

Iterative Methods for Sparse Linear Systems


Yousef Saad - 1996
    Engineers and mathematicians will find its contents easily accessible, and practitioners and educators will value it as a helpful resource. The preface includes syllabi that can be used for either a semester- or quarter-length course in both mathematics and computer science.

Master Math: Algebra


Debra Anne Ross - 1996
    This math reference guide makes learning and understanding algebraic equations, inequalities, polynmials and linear equations as simple as "two plus two."

Lie Groups Beyond an Introduction


Anthony W. Knapp - 1996
    The book is very carefully organized [and] ends with 20 pages of useful historic comments. Such a comprehensive and carefully written treatment of fundamentals of the theory will certainly be a basic reference and text book in the future." -- Newsletter of the EMS "This is a fundamental book and none, beginner or expert, could afford to ignore it. Some results are really difficult to be found in other monographs, while others are for the first time included in a book." -- Mathematica "Each chapter begins with an excellent summary of the content and ends with an exercise section... This is really an outstanding book, well written and beautifully produced. It is both a graduate text and a monograph, so it can be recommended to graduate students as well as to specialists." -- Publicationes Mathematicae Lie Groups Beyond an Introduction takes the reader from the end of introductory Lie group theory to the threshold of infinite-dimensional group representations. Merging algebra and analysis throughout, the author uses Lie-theoretic methods to develop a beautiful theory having wide applications in mathematics and physics. A feature of the presentation is that it encourages the reader's comprehension of Lie group theory to evolve from beginner to expert: initial insights make use of actual matrices, while later insights come from such structural features as properties of root systems, or relationships among subgroups, or patterns among different subgroups. Topics include a description of all simply connected Lie groups in terms of semisimple Lie groups and semidirect products, the Cartan theory of complex semisimple Lie algebras, the Cartan-Weyl theory of the structure and representations of compact Lie groups and representations of complex semisimple Lie algebras, the classification of real semisimple Lie algebras, the structure theory of noncompact reductive Lie groups as it is now used in research, and integration on reductive groups. Many problems, tables, and bibliographical notes complete this comprehensive work, making the text suitable either for self-study or for courses in the second year of graduate study and beyond.

Partial Differential Equations III: Nonlinear Equations


Michael E. Taylor - 1996
    It looks at various equations in differential geometry, in areas such as minimal surfaces, isometric imbedding, conformal deformation, harmonic maps, and prescribed Gauss curvature. In addition, it addresses some non-linear diffusion problems. Analytical tools introduced in this volume include the theory of L DEGREESp Sobolev spaces, Holder spaces, Hardy spaces, Morrey spaces, and a development of Calderon-Zygmund theory and paradifferential operator ca

Selected Papers of Freeman Dyson with Commentary (Collected Works)


Freeman Dyson - 1996
    This collection offers a connected narrative of the developments in mathematics and physics in which the author was involved, beginning with his professional life as a student of G H Hardy.

Knot Theory and Its Applications


Kunio Murasugi - 1996
    This book is directed to a broad audience of researchers, beginning graduate students, and senior undergraduate students in these fields.The book contains most of the fundamental classical facts about the theory, such as knot diagrams, braid representations, Seifert surfaces, tangles, and Alexander polynomials; also included are key newer developments and special topics such as chord diagrams and covering spaces. The work introduces the fascinating study of knots and provides insight into applications to such studies as DNA research and graph theory. In addition, each chapter includes a supplement that consists of interesting historical as well as mathematical comments.The author clearly outlines what is known and what is not known about knots. He has been careful to avoid advanced mathematical terminology or intricate techniques in algebraic topology or group theory. There are numerous diagrams and exercises relating the material. The study of Jones polynomials and the Vassiliev invariants are closely examined."The book ...develops knot theory from an intuitive geometric-combinatorial point of view, avoiding completely more advanced concepts and techniques from algebraic topology...Thus the emphasis is on a lucid and intuitive exposition accessible to a broader audience... The book, written in a stimulating and original style, will serve as a first approach to this interesting field for readers with various backgrounds in mathematics, physics, etc. It is the first text developing recent topics as the Jones polynomial and Vassiliev invariants on a level accessible also for non-specialists in the field." -Zentralblatt Math

Introduction to Stochastic Calculus Applied to Finance


Damien Lamberton - 1996
    This book introduces the mathematical methods of financial modeling with clear explanations of the most useful models. Introduction to Stochastic Calculus begins with an elementary presentation of discrete models, including the Cox-Ross-Rubenstein model. This book will be valued by derivatives trading, marketing, and research divisions of investment banks and other institutions, and also by graduate students and research academics in applied probability and finance theory.

What's Happening in the Mathematical Sciences, Vol.3: 1995-1996


Barry Cipra - 1996
    In an accessible style, Cipra explores topics ranging from Fermat's Last Theorem to Computational Fluid Dynamics. The volumes in this series are intended to highlight the many roles mathematics plays in the modern world. This volume includes articles on Ultra-parallel supercomputing with DNA, and how a mathematician found the famous flaw in the Pentium chip.

Geometry


Richard G. Brown - 1996
    This textbook has some answers in the back of the book so students can check their work. Definitely worth buying if one is studying Geometry.

Poincaré and the Three Body Problem


June Barrow-Green - 1996
    It arose in the work of one of the greatest mathematicians of the late 19th century, Henri Poincare, on a problem in celestial mechanics: the three body problem. This ancient problem - to describe the paths of three bodies in mutual gravitational interaction - is one of those which is simple to pose but impossible to solve precisely. Poincare's famous memoir on the three body problem arose from his entry in King Oscar of Sweden's 60th birthday competition. His essay won the prize and was set up in print as a paper in Acta Mathematica when it was found to contain a deep and critical error. In correcting this error Poincare discovered mathematical chaos, as is now clear from the author's study of a copy of the original memoir annotated by Poincare himself, recently discovered in the Institut Mittag-Leffler in Stockholm. Poincare and the Three Body Problem opens with a discussion of the development of the three body problem itself and Poincare's related earlier work.

A History of Chinese Mathematics


Jean-Claude Martzloff - 1996
    Thus, the progressive increase in our knowledge of the content of Chinese mathematics has been accompanied by the realisation that, as far as results are concerned, there are numerous similarities between Chinese mathematics and other ancient and medieval mathematics. For example, Pythagoras' theorem, the double-false-position rules, Hero's formulae, and Ruffini-Harner's method are found almost everywhere. As far as the reasoning used to obtain these results is concerned, the fact that it is difficult to find rational justifications in the original texts has led to the reconstitution of proofs using appropriate tools of present-day elementary algebra. Consequently, the conclusion that Chinese mathematics is of a fundamentally algebraic nature has been ventured. However, in recent decades, new studies, particularly in China and Japan, have adopted a different approach to the original texts, in that they have considered the Chinese modes of reasoning, as these can be deduced from the rare texts which contain justifications. By studying the results and the methods explicitly mentioned in these texts hand in hand, this Chinese and Japanese research has attempted to reconstruct the conceptions of ancient authors within a given culture and period, without necessarily involving the convenient, but often distorting, social and conceptual framework of present-day mathematics.

Analytical Mechanics


Joseph-Louis Lagrange - 1996
    It marked the culmination of a line of research devoted to recasting Newton's synthetic, geomet ric methods in the analytic style of the Leibnizian calculus. Its sources extended well beyond the physics of central forces set forth in the Principia. Continental au thors such as Jakob Bernoulli, Daniel Bernoulli, Leonhard Euler, Alexis Clairaut and Jean d'Alembert had developed new concepts and methods to investigate problems in constrained interaction, fluid flow, elasticity, strength of materials and the operation of machines. The Mecanique Analytique was a remarkable work of compilation that became a fundamental reference for subsequent research in exact science. During the eighteenth century there was a considerable emphasis on extending the domain of analysis and algorithmic calculation, on reducing the dependence of advanced mathematics on geometrical intuition and diagrammatic aids. The analytical style that characterizes the Mecanique Analytique was evident in La grange's original derivation in 1755 of the 8-algorithm in the calculus of variations. It was expressed in his consistent attempts during the 1770s to prove theorems of mathematics and mechanics that had previously been obtained synthetically. The scope and distinctiveness of his 1788 treatise are evident if one compares it with an earlier work of similar outlook, Euler's Mechanica sive Motus Scientia Analyt 1 ice Exposita of 1736.

Partial Differential Equations I: Basic Theory


Michael E. Taylor - 1996
    It introduces basic examples of partial differential equations, arising in continuum mechanics, electromagnetism, complex analysis and other areas. It also develops a number of tools for their solution, including Fourier analysis, distribution theory and Sobolev spaces. These tools are applied to the treatment of basic problems in linear PDE, including the Laplace equation, heat equation and wave equation, as well as more general elliptic, parabolic and hyperbolic equations.

The Complete How to Figure It: Using Math in Everyday Life


Darrell Huff - 1996
    Now, with his trademark wry humor and simple language, Darrell Huff explains how to figure: the likely outcome of different investments; how much home insurance is enough; whether it makes more sense to buy or lease a new car; the most efficient way to save for future needs, from vacations to college tuition; air-conditioning and heating requirements for a new house; how many rolls of wallpaper you will need for a particular room; and much more. Here are tips for getting the most out of a modest pocket calculator or home computer to make tedious calcuations easy, a handy chapter on "Math in a Hurry," and even tips on improving your chances in tennis, horse racing, and blackjack.

Linear Algebra


Peter D. Lax - 1996
    The book grew out of Dr. Lax's course notes for the linear algebra classes he teaches at New York University. Geared to graduate students as well as advanced undergraduates, it assumes only limited knowledge of linear algebra and avoids subjects already heavily treated in other textbooks. And while it discusses linear equations, matrices, determinants, and vector spaces, it also in-cludes a number of exciting topics that are not covered elsewhere, such as eigenvalues, the Hahn-Banach theorem, geometry, game theory, and numerical analysis. The first four chapters are devoted to the abstract structure of finite dimensional vector spaces. Subsequent chapters deal with determinants as a blend of geometry, algebra, and general spectral theory. Euclidean structure is used to explain the notion of selfadjoint mappings and their spectral theory. Dr. Lax moves on to the calculus of vector and matrix valued functions of a single variable--a neglected topic in most undergraduate programs--and presents matrix inequalities from a variety of perspectives.Fundamentals--including duality, linear mappings, and matricesDeterminant, trace, and spectral theory Euclidean structure and the spectral theory of selfadjoint maps Calculus of vector and matrix valued functions Matrix inequalities Kinematics and dynamics Convexity and the duality theorem Normed linear spaces, linear mappings between normed spaces, and positive matrices Iterative methods for solving systems of linear equations Eight appendices devoted to important related topics, including special determinants, Pfaff's theorem, symplectic matrices, tensor product, lattices, fast matrix multiplication, Gershgorin's theorem, and multiplicity of eigenvalues Later chapters cover convexity and the duality theorem, describe the basics of normed linear spaces and linear maps between normed spaces, and discuss the dominant eigenvalue of matrices whose entries are positive or merely non-negative. The final chapter is devoted to numerical methods and describes Lanczos' procedure for inverting a symmetric, positive definite matrix. Eight appendices cover important topics that do not fit into the main thread of the book.Clear, concise, and superbly organized, Linear Algebra is an excellent text for advanced undergraduate and graduate courses and also serves as a handy professional reference.

Fractal Geometry in Architecture and Design


Carl Bovill - 1996
    Modern communication techniques enable us to transmit and reconstitute images without needing to know a specific verbal sequence language such as the Morse code or Hungarian. International traffic signs use international image symbols which are not specific to any particular verbal language. An image language differs from a verbal one in that the latter uses a linear string of symbols, whereas the former is multi- dimensional. Architectural renderings commonly show projections onto three mutual- ly perpendicular planes, or consist of cross sections at different altitudes capa- ble of being stacked and representing different floor plans. Such renderings make it difficult to imagine buildings comprising ramps and other features which disguise the separation between floors, and consequently limit the cre- ative process of the architect. Analogously, we tend to analyze natural struc- tures as if nature had used similar stacked renderings, rather than, for instance, a system of packed spheres, with the result that we fail to perceive the system of organization determining the form of such structures. Perception is a complex process. Our senses record; they are analogous to audio or video devices. We cannot, however, claim that such devices perceive.

Elementary Functional Analysis


Georgi E. Shilov - 1996
    Each chapter includes a set of problems, with hints and answers. Bibliography. 1974 edition.

A Primer of Mathematical Writing


Steven G. Krantz - 1996
    Issues addressed include: syntax, grammar, structure and style; mathematical exposition; use of the computer and TeX; e-mail etiquette; and all aspects of publishing a journal article. It also outlines how to write grant proposals, letters of recommendation, and book proposals.

Statistical Digital Signal Processing and Modeling


Monson H. Hayes - 1996
    While the focal point of the text is signal modeling, it integrates and explores the relationships of signal modeling to the important problems of optimal filtering, spectrum estimation, and adaptive filtering.Coverage is equally divided between the theory and philosophy of statistical signal processing, and the algorithms that are used to solve related problems. The text reflects the author's philosophy that a deep understanding of signal processing is accomplished best through working problems. For this reason, the book is loaded with worked examples, homework problems, and MATLAB computer exercises. While the examples serve to illustrate the ideas developed in the book, the problems seek to motivate and challenge the student and the computer exercises allow the student to experiment with signal processing algorithms on complex signals.Professor Hayes is recognized as a leader in the signal processing community, particularly for his work in signal reconstruction and image processing. This text is suitable for senior/graduate level courses in advanced DSP or digital filtering found in Electrical Engineering Departments. Prerequisites include basic courses in DSP and probability theory.

Topics in Complex Analysis


Mats Andersson - 1996
    As opposed to most introductory books on complex analysis, this one as- sumes that the reader has previous knowledge of basic real analysis. This makes it possible to follow a rather quick route through the most fundamen- tal material on the subject in order to move ahead to reach some classical highlights (such as Fatou theorems and some Nevanlinna theory), as well as some more recent topics (for example, the corona theorem and the HI_ BMO duality) within the time frame of a one-semester course. Sections 3 and 4 in Chapter 2, Sections 5 and 6 in Chapter 3, Section 3 in Chapter 5, and Section 4 in Chapter 7 were not contained in my original lecture notes and therefore might be considered special topics. In addition, they are completely independent and can be omitted with no loss of continuity. The order of the topics in the exposition coincides to a large degree with historical developments. The first five chapters essentially deal with theory developed in the nineteenth century, whereas the remaining chapters contain material from the early twentieth century up to the 1980s. Choosing methods of presentation and proofs is a delicate task. My aim has been to point out connections with real analysis and harmonic anal- ysis, while at the same time treating classical complex function theory.