Best of
Mathematics

2010

Quadrivium: The Four Classical Liberal Arts of Number, Geometry, Music, & Cosmology


John Martineau - 2010
    It was studied from antiquity to the Renaissance as a way of glimpsing the nature of reality. Geometry is number in space; music is number in time; and comology expresses number in space and time. Number, music, and geometry are metaphysical truths: life across the universe investigates them; they foreshadow the physical sciences.Quadrivium is the first volume to bring together these four subjects in many hundreds of years. Composed of six successful titles in the Wooden Books series-Sacred Geometry, Sacred Number, Harmonograph, The Elements of Music, Platonic & Archimedean Solids, and A Little Book of Coincidence-it makes ancient wisdom and its astonishing interconnectedness accessible to us today.Beautifully produced in six different colors of ink, Quadrivium will appeal to anyone interested in mathematics, music, astronomy, and how the universe works.

Doing Bayesian Data Analysis: A Tutorial Introduction with R and BUGS


John K. Kruschke - 2010
    Included are step-by-step instructions on how to carry out Bayesian data analyses.Download Link : readbux.com/download?i=0124058884            0124058884 Doing Bayesian Data Analysis: A Tutorial with R, JAGS, and Stan PDF by John Kruschke

Here's Looking at Euclid: A Surprising Excursion Through the Astonishing World of Math


Alex Bellos - 2010
    But, Alex Bellos says, "math can be inspiring and brilliantly creative. Mathematical thought is one of the great achievements of the human race, and arguably the foundation of all human progress. The world of mathematics is a remarkable place."Bellos has traveled all around the globe and has plunged into history to uncover fascinating stories of mathematical achievement, from the breakthroughs of Euclid, the greatest mathematician of all time, to the creations of the Zen master of origami, one of the hottest areas of mathematical work today. Taking us into the wilds of the Amazon, he tells the story of a tribe there who can count only to five and reports on the latest findings about the math instinct--including the revelation that ants can actually count how many steps they've taken. Journeying to the Bay of Bengal, he interviews a Hindu sage about the brilliant mathematical insights of the Buddha, while in Japan he visits the godfather of Sudoku and introduces the brainteasing delights of mathematical games.Exploring the mysteries of randomness, he explains why it is impossible for our iPods to truly randomly select songs. In probing the many intrigues of that most beloved of numbers, pi, he visits with two brothers so obsessed with the elusive number that they built a supercomputer in their Manhattan apartment to study it. Throughout, the journey is enhanced with a wealth of intriguing illustrations, such as of the clever puzzles known as tangrams and the crochet creation of an American math professor who suddenly realized one day that she could knit a representation of higher dimensional space that no one had been able to visualize. Whether writing about how algebra solved Swedish traffic problems, visiting the Mental Calculation World Cup to disclose the secrets of lightning calculation, or exploring the links between pineapples and beautiful teeth, Bellos is a wonderfully engaging guide who never fails to delight even as he edifies. "Here's Looking at Euclid "is a rare gem that brings the beauty of math to life.

Mathematics 1001: Absolutely Everything That Matters in Mathematics in 1001 Bite-Sized Explanations


Richard Elwes - 2010
    Distilled into 1001 mini-essays arranged thematically, this unique book moves steadily from the basics through to the most advanced areas of math, making it the ideal guide for both the beginner and the math wiz.The book covers all of the fundamental mathematical disciplines:Geometry Numbers Analysis Logic Algebra Probability and statistics Applied mathematics Discrete mathematics Games and recreational mathematics Philosophy and metamathematicsExpert mathematician Richard Elwes explains difficult concepts in the simplest language with a minimum of jargon. Along the way he reveals such mathematical magic as how to count to 1023 using just 10 fingers and how to make an unbreakable code.Enlightening and entertaining, Mathematics 1001 makes the language of math come alive.

Networks: An Introduction


M.E.J. Newman - 2010
    The rise of the Internet and the wide availability of inexpensive computers have made it possible to gather and analyze network data on a large scale, and the development of a variety of new theoretical tools has allowed us to extract new knowledge from many different kinds of networks.The study of networks is broadly interdisciplinary and important developments have occurred in many fields, including mathematics, physics, computer and information sciences, biology, and the social sciences. This book brings together for the first time the most important breakthroughs in each of these fields and presents them in a coherent fashion, highlighting the strong interconnections between work in different areas.Subjects covered include the measurement and structure of networks in many branches of science, methods for analyzing network data, including methods developed in physics, statistics, and sociology, the fundamentals of graph theory, computer algorithms, and spectral methods, mathematical models of networks, including random graph models and generative models, and theories of dynamical processes taking place on networks.

No bullshit guide to math and physics


Ivan Savov - 2010
    It shouldn't be like that. Learning calculus without mechanics is incredibly boring. Learning mechanics without calculus is missing the point. This textbook integrates both subjects and highlights the profound connections between them.This is the deal. Give me 350 pages of your attention, and I'll teach you everything you need to know about functions, limits, derivatives, integrals, vectors, forces, and accelerations. This book is the only math book you'll need for the first semester of undergraduate studies in science.With concise, jargon-free lessons on topics in math and physics, each section covers one concept at the level required for a first-year university course. Anyone can pick up this book and become proficient in calculus and mechanics, regardless of their mathematical background.Visit http://minireference.com for more details.

You Can Count on Monsters


Richard Evan Schwartz - 2010
    The playful and colorful monsters are designed to give children (and even older audiences) an intuitive understanding of the building blocks of numbers and the basics of multiplication. The introduction and appendices can also help adult readers answer questions about factoring from their young audience. The artwork is crisp and creative and the colors are bright and engaging, making this volume a welcome deviation from standard math texts. CRC Press Author and NPR's Math Guy Keith Devlin spoke with Scott Simon about how the book makes finding prime numbers fun. "This is one of the most amazing math books for kids I have ever seen…," Devlin says. "Great colors, it's wonderful, and yet because [Schwartz] knows the mathematics, he very skillfully and subtly embeds mathematical ideas into the drawings."

Emmy Noether's Wonderful Theorem


Dwight E. Neuenschwander - 2010
    Emmy Noether proved her theorem in 1915 and published it in 1918. This profound concept demonstrates the connection between conservation laws and symmetries. For instance, the theorem shows that a system invariant under translations of time, space, or rotation will obey the laws of conservation of energy, linear momentum, or angular momentum, respectively. This exciting result offers a rich unifying principle for all of physics.Dwight E. Neuenschwander's introduction to the theorem's genesis, applications, and consequences artfully unpacks its universal importance and unsurpassed elegance. Drawing from over thirty years of teaching the subject, Neuenschwander uses mechanics, optics,geometry, and field theory to point the way to a deep understanding of Noether's Theorem. The three sections provide a step-by-step, simple approach to the less-complex concepts surrounding the theorem, in turn instilling the knowledge and confidence needed to grasp the full wonder it encompasses. Illustrations and worked examples throughout each chapter serve as signposts on the way to this apex of physics.Noether's Theorem is an essential principle of post-introductory physics. This handy guide includes end-of-chapter questions for review and appendixes detailing key related physics concepts for further study.

Synergetics 2: Further Explorations in the Geometry of Thinking


R. Buckminster Fuller - 2010
    "It is the essence of synergy to produce unpredicted - indeed, unpredictable - results like the surprise geometrical discoveries of this second volume."

An Introduction to Infectious Disease Modelling


Emilia Vynnycky - 2010
    Applications include predicting the impact of vaccination strategies against common infections and determining optimal controlstrategies against HIV and pandemic influenza.This book introduces individuals interested in infectiousdiseases to this exciting and expanding area. Themathematical level of the book is kept as simple aspossible, which makes the book accessible to those who havenot studied mathematics to university level. Understandingis further enhanced by models that can be accessed online, which will allow readers to explore the impact of differentfactors and control strategies, and further adapt anddevelop the models themselves. The book is based on successful courses developed by theauthors at the London School of Hygiene and TropicalMedicine. It will be of interest to epidemiologists, publichealth researchers, policy makers, veterinary scientists, medical statisticians and infectious disease researchers.

Functional Analysis, Sobolev Spaces and Partial Differential Equations


Haïm Brézis - 2010
    The Hahn-Banach Theorems. Introduction to the Theory of Conjugate Convex Functions.- 2. The Uniform Boundedness Principle and the Closed Graph Theorem. Unbounded Operators. Adjoint. Characterization of Surjective Operators.- 3. Weak Topologies. Reflexive Spaces. Separable Spaces. Uniform Convexity.- 4. L^p Spaces.- 5. Hilbert Spaces.- 6. Compact Operators. Spectral Decomposition of Self-Adjoint Compact Operators.- 7. The Hille-Yosida Theorem.- 8. Sobolev Spaces and the Variational Formulation of Boundary Value Problems in One Dimension.- 9. Sobolev Spaces and the Variational Formulation of Elliptic Boundary Value Problems in N Dimensions.- 10. Evolution Problems: The Heat Equation and the Wave Equation.- 11. Some Complements.- Problems.- Solutions of Some Exercises and Problems.- Bibliography.- Index.

Elements Of Number Theory (Undergraduate Texts In Mathematics)


John Stillwell - 2010
    However, it is independent of the algebra book, and probably easier. In Elements oi Algebra we sought solution by radicals, and this led to the concepts of fields and groups and their fusion in the celebrated theory of Galois. In the present book we seek integer solutions, and this leads to the concepts of rings and ideals which merge in the equally celebrated theory of ideals due to Kummer and Dedekind. Solving equations in integers is the central problem of number theory, so this book is truly a number theory book, with most of the results found in standard number theory courses. However, numbers are best understood through their algebraic structure, and the necessary algebraic concepts- rings and ideals-have no better motivation than number theory. The first nontrivial examples of rings appear in the number theory of Euler and Gauss. The concept of ideal-today as routine in ring the- ory as the concept of normal subgroup is in group theory-also emerged from number theory, and in quite heroic fashion. Faced with failure of unique prime factorization in the arithmetic of certain generalized "inte- gers", Kummer created in the 1840s a new kind of number to overcome the difficulty. He called them "ideal numbers" because he did not know exactly what they were, though he knew how they behaved.

Mathematics: A complete introduction: Teach Yourself


Trevor Johnson - 2010
    Packed full of worked examples and useful exercises, it will guide you through the essentials quickly and easily, giving you the knowledge you need to gain maths confidence.NOT GOT MUCH TIME?One, five and ten-minute introductions to key principles to get you started.AUTHOR INSIGHTSLots of instant help with common problems and quick tips for success, based on the author's many years of experience.TEST YOURSELFTests in the book and online to keep track of your progress.FIVE THINGS TO REMEMBERQuick refreshers to help you remember the key facts.TRY THISInnovative exercises illustrate what you've learnt and how to use it.

Physics for Mathematicians: Mechanics I


Michael Spivak - 2010
    It is only necessary for me to explain what I mean by a mathematician, and what I mean byphysics.By a mathematician I mean some one who has been trained in modern mathematics and been inculcated with its general outlook. ... And by physics I mean -- well, physics, what physicists mean by physics, i.e., the actual study of physical objects ... (rather than the study of symplectic structures on cotangent bundles, for example). In addition to presenting the advanced physics, which mathematicians find so easy, I also want to explore the workings of elementary physics ... which I have always found so hard to fathom.As these remarks probably reveal, basically I have written this work in order to learn the subject myself, in a form that I find comprehensible. And readers familiar with some of my previous books probably realize that this has pretty much been the reason for those works also. ...Perhaps this travelogue of an innocent abroad in a very different field will also turn out to be a book that mathematicians will like.

Algebraic Number Theory


John William Scott Cassels - 2010
    It contains the lecture notes from an instructional conference held in Brighton in 1965, which was a milestone event that introduced class field theory as a standard tool of mathematics. There are landmark contributions from Serre and Tate. The book is a standard text for taught courses in algebraic number theory. This Second Edition includes a valuable list of errata compiled by mathematicians who have read and used the text over the years.

Advanced Calculus: A Geometric View


James J. Callahan - 2010
    The classic texts of Taylor [19], Buck [1], Widder [21], and Kaplan [9], for example, show some of the ways it was approached. Over time, certain aspects of the course came to be seen as more signi?cant--those seen as giving a rigorous foundation to calculus--and they - came the basis for a new course, an introduction to real analysis, that eventually supplanted advanced calculus in the core. Advanced calculus did not, in the process, become less important, but its role in the curriculum changed. In fact, a bifurcation occurred. In one direction we got c- culus on n-manifolds, a course beyond the practical reach of many undergraduates; in the other, we got calculus in two and three dimensions but still with the theorems of Stokes and Gauss as the goal. The latter course is intended for everyone who has had a year-long introduction to calculus; it often has a name like Calculus III. In my experience, though, it does not manage to accomplish what the old advancedcalculus course did. Multivariable calculusnaturallysplits intothreeparts: (1)severalfunctionsofonevariable, (2)one function of several variables, and (3) several functions of several variables. The ?rst two are well-developed in Calculus III, but the third is really too large and varied to be treated satisfactorily in the time remaining at the end of a semester. To put it another way: Green's theorem ?ts comfortably; Stokes' and Gauss' do not.

Group Theory: A Physicist's Survey


Pierre Ramond - 2010
    This book introduces physicists to many of the fascinating mathematical aspects of group theory, and mathematicians to its physics applications. Designed for advanced undergraduate and graduate students, this book gives a comprehensive overview of the main aspects of both finite and continuous group theory, with an emphasis on applications to fundamental physics. Finite groups are extensively discussed, highlighting their irreducible representations and invariants. Lie algebras, and to a lesser extent Kac-Moody algebras, are treated in detail, including Dynkin diagrams. Special emphasis is given to their representations and embeddings. The group theory underlying the Standard Model is discussed, along with its importance in model building. Applications of group theory to the classification of elementary particles are treated in detail.

The Tau Manifesto


Michael Hartl - 2010
    Building on the work of the mathematical heretics who preceded him, Michael Hartl published The Tau Manifesto on Tau Day (6/28), 2010, thereby launching what has become an international movement for mathematical sanity. Explore the reasons why pi is wrong—that is, why pi is a confusing and unnatural choice for the circle constant—and meet its replacement, tau. Skeptics beware: by the end of the manifesto you may be surprised to find yourself converted to tauism.

Geometries


Guillevic - 2010
    Translated from the French by Richard Sieburth. Guillevic wrote GEOMETRIES (Euclidiennes in French) in the early sixities, after his friend, the poet Andre Frenaud, recognizing in his poetry an inclination toward mathematics, and more specifically geometry, encouraged him to pursue this direction. Guillevic places a series of geometrical figures before our eyes, as they might appear in a schoolchild's primer, paired with poems that let us hear how these forms might speak. These talking circles, squares and angles--these articulations of space--are in turn meant to remind us of our own figures of speech. Guillevic's GEOMETRIES fits into the 1960s return to emblems, signs, and playful constraints both in art (Robert Indiana, Jasper Johns, Robert Rauschenberg and even Andy Warhol) and in writing (the Noigandres poets, Oulipo, Eugen Gomringer, the Robert Creeley of Pieces). But at the same time, the Euclidean world of forms here explored remains as timeless as the stones of Guillevic's own Carnac.

Thirty-Three Miniatures: Mathematical and Algorithmic Applications of Linear Algebra


Jiří Matoušek - 2010
    

Maths for Mums and Dads


Rob Eastaway - 2010
    Looking for a practical maths guide to help with home schooling? Maths for Mums and Dads is the solution.Maths for Mums and Dads guides you through the basics of primary school maths and covers the dilemmas and problems you are likely to be confronted with, including: * number bonds, place value and decimals * long multiplication and division * fractions, percentages and decimals * basic geometry, shapes, symmetry and angles * data-handling, combinations and chance Complete with sample questions, mock exam papers and examples of children's errors, Maths for Mums and Dads will challenge and reassure in equal measure.

Glimpses of Soliton Theory: The Algebra and Geometry of Nonlinear Pdes


Alex Kasman - 2010
    This is quite surprising, both mathematically and physically. Waves with these properties were once believed to be impossible by leading mathematical physicists, yet they are now not only accepted as a theoretical possibility but are regularly observed in nature and form the basis of modern fiber-optic communication networks. Glimpses of Soliton Theory addresses some of the hidden mathematical connections in soliton theory which have been revealed over the last half-century. It aims to convince the reader that, like the mirrors and hidden pockets used by magicians, the underlying algebro-geometric structure of soliton equations provides an elegant and surprisingly simple explanation of something seemingly miraculous. Assuming only multivariable calculus and linear algebra as prerequisites, this book introduces the reader to the KdV Equation and its multisoliton solutions, elliptic curves and Weierstrass $\wp$-functions, the algebra of differential operators, Lax Pairs and their use in discovering other soliton equations, wedge products and decomposability, the KP Equation and Sato's theory relating the Bilinear KP Equation to the geometry of Grassmannians. Notable features of the book include: careful selection of topics and detailed explanations to make this advanced subject accessible to any undergraduate math major, numerous worked examples and thought-provoking but not overly-difficult exercises, footnotes and lists of suggested readings to guide the interested reader to more information, and use of the software package MathematicaR to facilitate computation and to animate the solutions under study. This book provides the reader with a unique glimpse of the unity of mathematics and could form the basis for a self-study, one-semester special topics, or ''capstone'' course.

An Introduction to Diophantine Equations: A Problem-Based Approach


Titu Andreescu - 2010
    The presentation features some classical Diophantine equations, including linear, Pythagorean, and some higher degree equations, as well as exponential Diophantine equations. Many of the selected exercises and problems are original or are presented with original solutions. An Introduction to Diophantine Equations: A Problem-Based Approach is intended for undergraduates, advanced high school students and teachers, mathematical contest participants - including Olympiad and Putnam competitors - as well as readers interested in essential mathematics. The work uniquely presents unconventional and non-routine examples, ideas, and techniques.

More Good Questions: Great Ways to Differentiate Secondary Mathematics Instruction


Marian Small - 2010
    Yet DI challenges teachers, and nowhere more than in mathematics. In this new book, written specifically for secondary mathematics teachers, the authors cut through the difficulties with two powerful and universal strategies that teachers can use across all math content: Open Questions and Parallel Tasks. Showing teachers how to get started and become expert with these strategies, this book also demonstrates how to use more inclusive learning conversations to promote broader student participation. Strategies and examples are organized around Big Ideas within the National Council of Teachers of Mathematics (NCTM) content strands. With particular emphasis on Algebra, chapters also address Number and Operations, Geometry, Measurement, and Data Analysis and Probability, with examples included for Pre-Calculus.To help teachers differentiate math instruction with less difficulty and greater success, this resource:Underscores the rationale for differentiating secondary math instruction. Provides specific examples for secondary math content. Describes two easy-to-implement strategies designed to overcome the most common DI problems that teachers encounter. Offers almost 300 questions and tasks that teachers and coaches can adopt immediately, adapt, or use as models to create their own, along with scaffolding and consolidating questions. Includes Teaching Tips sidebars and an organizing template at the end of each chapter to help teachers build new tasks and open questions. Shows how to create a more inclusive classroom learning community with mathematical talk that engages participants from all levels. PROFESSIONAL DEVELOPMENT: Visit Marian Small's website onetwoinfinity.ca for in-person and online professional development.

Graph Theoretic Methods in Multiagent Networks


Mehran Mesbahi - 2010
    Such networks are of great interest in a wide range of areas in science and engineering, including: mobile sensor networks, distributed robotics such as formation flying and swarming, quantum networks, networked economics, biological synchronization, and social networks. Focusing on graph theoretic methods for the analysis and synthesis of dynamic multiagent networks, the book presents a powerful new formalism and set of tools for networked systems.The book's three sections look at foundations, multiagent networks, and networks as systems. The authors give an overview of important ideas from graph theory, followed by a detailed account of the agreement protocol and its various extensions, including the behavior of the protocol over undirected, directed, switching, and random networks. They cover topics such as formation control, coverage, distributed estimation, social networks, and games over networks. And they explore intriguing aspects of viewing networks as systems, by making these networks amenable to control-theoretic analysis and automatic synthesis, by monitoring their dynamic evolution, and by examining higher-order interaction models in terms of simplicial complexes and their applications.The book will interest graduate students working in systems and control, as well as in computer science and robotics. It will be a standard reference for researchers seeking a self-contained account of system-theoretic aspects of multiagent networks and their wide-ranging applications. This book has been adopted as a textbook at the following universities: ? University of Stuttgart, Germany Royal Institute of Technology, Sweden Johannes Kepler University, Austria Georgia Tech, USA University of Washington, USA Ohio University, USA

The Evolution of Logic


W.D. Hart - 2010
    Logic underwent a major renaissance beginning in the nineteenth century. Cantor almost tamed the infinite, and Frege aimed to undercut Kant by reducing mathematics to logic. These achievements were threatened by the paradoxes, like Russell's. This ferment generated excellent philosophy (and mathematics) by excellent philosophers (and mathematicians) up to World War II. This book provides a selective, critical history of the collaboration between logic and philosophy during this period. After World War II, mathematical logic became a recognized subdiscipline in mathematics departments, and consequently but unfortunately philosophers have lost touch with its monuments. This book aims to make four of them (consistency and independence of the continuum hypothesis, Post's problem, and Morley's theorem) more accessible to philosophers, making available the tools necessary for modern scholars of philosophy to renew a productive dialogue between logic and philosophy.

Quantify!: A Crash Course in Smart Thinking


Göran Grimvall - 2010
    Entertaining and enlightening, his latest book uses examples from sports, literature, and nature—as well as from the varied worlds of science—to illustrate how scientists make sense of and explain the world around us.Grimvall's fun-to-read essays and easy-to-follow examples detail how order-of-magnitude estimation, extreme cases, dimensional analysis, and other modeling methods work. They also reveal how nonscientists absorb these concepts and use them at home, school, and work.Grimvall's simple, elegant explanations will help you tap into your inner scientist. Read this book and enjoy your own "Aha!" moment.

Kurt G�del: Essays for His Centennial


Solomon Feferman - 2010
    This book on different aspects of his work and on subjects in which his ideas have contemporary resonance includes papers from a May 2006 symposium celebrating G�del's centennial as well as papers from a 2004 symposium. Proof theory, set theory, philosophy of mathematics, and the editing of G�del's writings are among the topics covered. Several chapters discuss his intellectual development and his relation to predecessors and contemporaries such as Hilbert, Carnap, and Herbrand. Others consider his views on justification in set theory in light of more recent work and contemporary echoes of his incompleteness theorems and the concept of constructible set.

NIST Handbook of Mathematical Functions Paperback and CD-ROM


Frank W.J. Olver - 2010
    These functions appear whenever natural phenomena are studied, engineering problems are formulated, and numerical simulations are performed. They also crop up in statistics, financial models, and economic analysis. Using them effectively requires practitioners to have ready access to a reliable collection of their properties. This handbook results from a 10-year project conducted by the National Institute of Standards and Technology with an international group of expert authors and validators. Printed in full color, it is destined to replace its predecessor, the classic but long-outdated Handbook of Mathematical Functions, edited by Abramowitz and Stegun. Included with every copy of the book is a CD with a searchable PDF of each chapter. Check out the news release and the video for this new book

Combinatorics: A Guided Tour (Maa Textbooks)


David R. Mazur - 2010
    This text focuses on the first three types of questions and covers basic counting and existence principles, distributions, generating functions, recurrence relations, P�lya theory, combinatorial designs, error correcting codes, partially ordered sets, and selected applications to graph theory including the enumeration of trees, the chromatic polynomial, and introductory Ramsey theory. The only prerequisites are single-variable calculus and familiarity with sets and basic proof techniques. It is flexible enough to be used for undergraduate courses in combinatorics, second courses in discrete mathematics, introductory graduate courses in applied mathematics programs, as well as for independent study or reading courses. It also features approximately 350 reading questions spread throughout its eight chapters. These questions provide checkpoints for learning and prepare the reader for the end-of-section exercises of which there are over 470.

The Dyscalculia Assessment


Jane Emerson - 2010
    A significant group of children fail to progress beyond counting in ones; they cannot calculate efficiently or learn their tables.This assessment tool is designed to explore which aspects of numeracy the child is struggling to acquire. The evidence from the assessment can then be used to draw up a personalized teaching plan. With clear, step-by-step instructions alongside photocopiable or downloadable assessment sheets, The Dyscalculia Assessment contains what you need to pinpoint a child's difficulties with numeracy, and use that information to help the child progress.The Assessment is ideal for use with primary school children, but can easily be adapted for older students, and is invaluable for SENCOs, TAs, educational psychologists and teachers wishing to support students with maths difficulties in their class.

Modal Logic for Open Minds (Center for the Study of Language and Information - Lecture Notes)


Johan van Benthem - 2010
    Van Benthem begins with the basic theories of modal logic, semantics, bisimulation, and axiomatics, and also covers more advanced topics, such as expressive power and computational complexity. The book then moves to a wide range of applications, including new developments in information flow, intelligent agency, and games. Taken together, the chapters show modal logic at the crossroads of philosophy, mathematics, linguistics, computer science, and economics. Most of the chapters are followed by exercises, making this volume ideal for undergraduate and graduate students in philosophy, computer science, symbolic systems, cognitive science, and linguistics.

Mathematical Tools for Physics


James Nearing - 2010
    Encouraging students' development of intuition, this original work begins with a review of basic mathematics and advances to infinite series, complex algebra, differential equations, and Fourier series. Succeeding chapters explore multivariable and vector calculus, partial differential equations, numerical and complex analysis, tensors, complex analysis, and more. 2010 edition.

Modern Computer Arithmetic


Richard P. Brent - 2010
    Brent and Zimmermann present algorithms that are ready to implement in your favorite language, while keeping a high-level description and avoiding too low-level or machine-dependent details. The book is intended for anyone interested in the design and implementation of efficient high-precision algorithms for computer arithmetic, and more generally efficient multiple-precision numerical algorithms. It may also be used in a graduate course in mathematics or computer science, for which exercises are included. These vary considerably in difficulty, from easy to small research projects, and expand on topics discussed in the text. Solutions are available from the authors.

Euclidean Geometry: A First Course


Mark Solomonovich - 2010
    The discussion is rigorous, axiom-based, written in a traditional manner, true to the Euclidean spirit. Transformations in the Euclidean plane are included as part of the axiomatics and as a tool for solving construction problems. The textbook can be used for teaching a high school or an introductory level college course. It can be especially recommended for schools with enriched mathematical programs and for homeschoolers looking for a rigorous traditional discussion of geometry. The text is supplied with over 1200 questions and problems, ranging from simple to challenging. The solutions sections of the book contain about 200 answers and hints to solutions and over 100 detailed solutions involving proofs and constructions. More solutions and some supplements for teachers are available in the Instructor s Manual, which is issued as a separate book. Book Reviews: In terms of presentation, this text is more rigorous than any existing high school textbook that I know of. It is based on a system of axioms that describe incidence, postulate a notion of congruence of line segments, and assume the existence of enough rigid motions ("free mobility") My gut reaction to the book is, wouldn't it be wonderful if American high school students could be exposed to this serious mathematical treatment of elementary geometry, instead of all the junk that is presented to them in existing textbooks. This book makes no concession to the TV-generation of students who want (or is it the publishers who want it for them?) pretty pictures, side bars, puzzles, games, historical references, cartoons, and all those colored images that clutter the pages of a typical modern textbook, while the mathematical content is diluted more and more with each successive edition. Professor Robin Hartshorne, University of California at Berkeley. The textbook Euclidean Geometry by Mark Solomonovich fills a big gap in the plethora of mathematical textbooks it provides an exposition of classical geometry with emphasis on logic and rigorous proofs I would be delighted to see this textbook used in Canadian schools in the framework of an improved geometry curriculum. Until this day comes, I highly recommend Euclidean Geometry by Mark Solomonovich to be used in Mathematics Enrichment Programs across Canada and the USA. Professor Yuly Billig, Carlton University.

The Adventure of Reason: Interplay Between Philosophy of Mathematics and Mathematical Logic, 1900-1940


Paolo Mancosu - 2010
    The Adventure of Reason is divided into five main sections: history of logic (from Russell to Tarski); foundational issues (Hilbert's program, constructivity, Wittgenstein, Godel); mathematics and phenomenology (Weyl, Becker, Mahnke); nominalism (Quine, Tarski); semantics (Tarski, Carnap, Neurath). Mancosu exploits extensive untapped archival sources to make available a wealth of new material that deepens in significant ways our understanding of these fascinating areas of modern intellectual history. At the same time, the book is a contribution to recent philosophical debates, in particular on the prospects for a successful nominalist reconstruction of mathematics, the nature of finitist intuition, the viability of alternative definitions of logical consequence, and the extent to which phenomenology can hope to account for the exact sciences.

Theoretical Statistics: Topics for a Core Course


Robert W. Keener - 2010
    Probability and Measure.- Exponential Families.- Risk, Sufficiency, Completeness, and Ancillarity.- Unbiased Estimation.- Curved Exponential Families.- Conditional Distributions.- Bayesian Estimation.- Large-Sample Theory.- Estimating Equations and Maximum Likelihood.- Equivariant Estimation.- Empirical Bayes and Shrinkage Estimators.- Hypothesis Testing.- Optimal Tests in Higher Dimensions.- General Linear Model.- Bayesian Inference: Modeling and Computation.- Asymptotic Optimality1.- Large-Sample Theory for Likelihood Ratio Tests.- Nonparametric Regression.- Bootstrap Methods.- Sequential Methods.

Numerical Methods for Ordinary Differential Equations: Initial Value Problems


David F. Griffiths - 2010
    Written for undergraduate students with a mathematical background, this book focuses on the analysis of numerical methods without losing sight of the practical nature of the subject.It covers the topics traditionally treated in a first course, but also highlights new and emerging themes. Chapters are broken down into `lecture' sized pieces, motivated and illustrated by numerous theoretical and computational examples.Over 200 exercises are provided and these are starred according to their degree of difficulty. Solutions to all exercises are available to authorized instructors.The book covers key foundation topics:o Taylor series methodso Runge--Kutta methodso Linear multistep methodso Convergenceo Stabilityand a range of modern themes:o Adaptive stepsize selectiono Long term dynamicso Modified equationso Geometric integrationo Stochastic differential equationsThe prerequisite of a basic university-level calculus class is assumed, although appropriate background results are also summarized in appendices. A dedicated website for the book containing extra information can be found via www.springer.com

Mathematical Methods for Optical Physics and Engineering


Gregory J. Gbur - 2010
    Containing detailed sections on the basic theory, the textbook places strong emphasis on connecting the abstract mathematical concepts to the optical systems to which they are applied. It covers many topics which usually only appear in more specialized books, such as Zernike polynomials, wavelet and fractional Fourier transforms, vector spherical harmonics, the z-transform, and the angular spectrum representation. Most chapters end by showing how the techniques covered can be used to solve an optical problem. Essay problems based on research publications and numerous exercises help to further strengthen the connection between the theory and its applications.

Rediscovering Mathematics: You Do The Math


Shai Simonson - 2010
    By focusing on problem solving, and discouraging rote memorisation, the book shows how to learn and teach mathematics through investigation, experimentation and discovery. Rediscovering Mathematics is also an excellent text for training mathematics teachers at all levels. Topics range in difficulty and cover a wide range of historical periods, with some examples demonstrating how to uncover mathematics in everyday life, including number theory and its application to secure communication over the Internet, the algebraic and combinatorial work of a medieval mathematician Rabbi, and applications of probability to sports, casinos, and everyday life. Rediscovering Mathematics provides a fresh view of mathematics for those who already like the subject, and offers a second chance for those who think they don't.

Understanding Game Theory: Introduction To The Analysis Of Many Agent Systems With Competition And Cooperation


Vasily N. Kolokoltsov - 2010
    

Algebraic Geometry I: Schemes, With Examples And Exercises (Vieweg Advanced Lectures In Mathematics)


Ulrich Görtz - 2010
    . ., x )=0, 1 1 n . . . f (x, . . ., x )=0. r 1 n Here the f ? k[X, . . ., X ] are polynomials in n variables with coe?cients in a ?eld k. i 1 n n ThesetofsolutionsisasubsetV(f, . . ., f)ofk . Polynomialequationsareomnipresent 1 r inandoutsidemathematics, andhavebeenstudiedsinceantiquity. Thefocusofalgebraic geometry is studying the geometric structure of their solution sets. n If the polynomials f are linear, then V(f, . . ., f ) is a subvector space of k. Its i 1 r size is measured by its dimension and it can be described as the kernel of the linear n r map k ? k, x=(x, . . ., x ) ? (f (x), . . ., f (x)). 1 n 1 r For arbitrary polynomials, V(f, . . ., f ) is in general not a subvector space. To study 1 r it, one uses the close connection of geometry and algebra which is a key property of algebraic geometry, and whose ?rst manifestation is the following: If g = g f +. . . g f 1 1 r r is a linear combination of the f (with coe?cients g ? k[T, . . ., T ]), then we have i i 1 n V(f, . . ., f)= V(g, f, . . ., f ). Thus the set of solutions depends only on the ideal 1 r 1 r a? k[T, . . ., T ] generated by the f ."

Graph Theory (Mathematical Olympiad Series)


Xiong Bin - 2010
    Over 200 years later, graph theory remains the skeleton content of discrete mathematics, which serves as a theoretical basis for computer science and network information science. This book introduces some basic knowledge and the primary methods in graph theory by many interesting problems and games Table Of Contents: Introduction Vii Chapter 1 Definition of Graph 1 Chapter 2 Degree of a Vertex 13 Chapter 3 Turán's Theorem 24 Chapter 4 Tree 40 Chapter 5 Euler's Problem 51 Chapter 6 Hamilton's Problem 63 Chapter 7 Planar Graph 75 Chapter 8 Ramsey's Problem 84 Chapter 9 Tournament 101 Solutions 110 Index 145 All Marketplace (--) New (--) Used (--) CLOSE X LOADING... We're sorry. Information from our Trusted Marketplace Sellers is currently unavailable. To try again, please visit the B&N Marketplace. Special Features: Graph Theory

Inequalities: Theory of Majorization and Its Applications


Albert W. Marshall - 2010
    Introduction.- Doubly Stochastic Matrices.- Schur-Convex Functions.- Equivalent Conditions for Majorization.- Preservation and Generation of Majorization.- Rearrangements and Majorization.- Combinatorial Analysis.- Geometric Inequalities.- Matrix Theory.- Numerical Analysis.- Stochastic Majorizations.- Probabilistic, Statistical, and Other Applications.- Additional Statistical Applications.- Orderings Extending Majorization.- Multivariate Majorization.- Convex Functions and Some Classical Inequalities.- Stochastic Ordering.- Total Positivity.- Matrix Factorizations, Compounds, Direct Products, and M-Matrices.- Extremal Representations of Matrix Functions.

Differential And Integral Calculus, Vol. 2 (Volume 2)


Richard Courant - 2010
    It has been reprinted more than twenty times and translated into several other languages, including Russian, and published in the Soviet Union and many other places. We especially want to thank Marvin Jay Greenberg, Emeritus Professor of Mathematics, University of California at Santa Cruz, for his Appendix on Infinitesimals, which includes recent discoveries on Hyperreals and Nilpotent Infinitesimals, and for his bibliography and references, which include up-to-date references to current publications in 2010. This foreword, which includes new mathematical discoveries, is included in Volume One of this work. A professor of mathematics writes: "I've enjoyed with great pleasure your foreword, discovering many interesting things about Courant's life and his thoughts. In particular, your citations about the antithesis between intuition and rigor were very illuminating, because it corresponds to the methodological thread I'm trying to follow developing the theory of Fermat reals. "Infinitesimals without "mysticism", explicit or fogged into unclear logical methods, seems possible. Now, I think we can make a step further, because the rigor increases our possibility to understand."

Musical Mathematics: On the Art and Science of Acoustic Instruments


Cris Forster - 2010
    Integrating mathematics, music history, and hands-on experience, this volume serves as a comprehensive guide to the tunings and scales of acoustic instruments from around the world. Author, composer, and builder Cris Forster illuminates the mathematical principles of acoustic music, offering practical information and new discoveries about both traditional and innovative instruments.With this knowledge readers can improve, or begin to build, their own instruments inspired by Forster's creationsshown in 16 color plates. For those ready to step outside musical conventions and those whose curiosity about the science of sound is never satisfied, Musical Mathematics is the map to a new musical world.

Population Games and Evolutionary Dynamics


William H. Sandholm - 2010
    Evolutionary game theory, which studies the behavior of large populations of strategically interacting agents, is used by economists to make predictions in settings where traditional assumptions about agents' rationality and knowledge may not be justified. Recently, computer scientists, transportation scientists, engineers, and control theorists have also turned to evolutionary game theory, seeking tools for modeling dynamics in multiagent systems. Population Games and Evolutionary Dynamics provides a point of entry into the field for researchers and students in all of these disciplines. The text first considers population games, which provide a simple, powerful model for studying strategic interactions among large numbers of anonymous agents. It then studies the dynamics of behavior in these games.By introducing a general model of myopic strategy revision by individual agents, the text provides foundations for two distinct approaches to aggregate behavior dynamics: the deterministic approach, based on differential equations, and the stochastic approach, based on Markov processes. Key results on local stability, global convergence, stochastic stability, and nonconvergence are developed in detail. Ten substantial appendixes present the mathematical tools needed to work in evolutionary game theory, offering a practical introduction to the methods of dynamic modeling. Accompanying the text are more than 200 color illustrations of the mathematics and theoretical results; many were created using the Dynamo software suite, which is freely available on the author's Web site. Readers are encouraged to use Dynamo to run quick numerical experiments and to create publishable figures for their own research.

Mathematical Foundations of Neuroscience


G. Bard Ermentrout - 2010
    These equations and the methods that arose from this combination of modeling and - periments have since formed the basis for nearly every subsequent model for active cells.TheHodgkin Huxleymodelandahostofsimpli?edequationsthatarederived fromit haveinspiredthedevelopmentofnewandbeautifulmathematics.Dynamical systems and computational methods are now being used to study activity patterns in a variety of neuronal systems. It is becoming increasingly recognized, by both experimentalists and theoreticians, that issues raised in neuroscience and the ma- ematical analysis of neuronal models provide unique interdisciplinary collaborative research and educational opportunities. This book is motivated by a perceived need for an overview of how dynamical systems and computational analysis have been used in understanding the types of models that come out of neuroscience. Our hope is that this will help to stimulate an increasing number of collaborations between mathematicians and other th- reticians, looking for interesting and relevant problems in applied mathematics and dynamical systems, and neuroscientists, looking for new ways to think about the biological mechanisms underlying experimental data. The book arose out of several courses that the authors have taught. One of these is a graduate course in computational neuroscience that has students from the d- ciplines of psychology, mathematics, computer science, physics, and neuroscience."

An Epsilon of Room, I: Pages from Year Three of a Mathematical Blog: A Textbook on Real Analysis


Terence Tao - 2010
    The first two years of the blog have already been published by the American Mathematical Society. The posts from the third year are being published in two volumes. The present volume consists of a second course in real analysis, together with related material from the blog. The real analysis course assumes some familiarity with general measure theory, as well as fundamental notions from undergraduate analysis. The text then covers more advanced topics in measure theory, notably the Lebesgue-Radon-Nikodym theorem and the Riesz representation theorem, topics in functional analysis, such as Hilbert spaces and Banach spaces, and the study of spaces of distributions and key function spaces, including Lebesgue's $L^p$ spaces and Sobolev spaces. There is also a discussion of the general theory of the Fourier transform. The second part of the book addresses a number of auxiliary topics, such as Zorn's lemma, the Caratheodory extension theorem, and the Banach-Tarski paradox. Tao also discusses the epsilon regularisation argument—a fundamental trick from soft analysis, from which the book gets its title. Taken together, the book presents more than enough material for a second graduate course in real analysis. The second volume consists of technical and expository articles on a variety of topics and can be read independently.

Computational Topology: An Introduction


Herbert Edelsbrunner - 2010
    

Mathematical Statistics with Applications


Richard L. Scheaffer - 2010
    Scheaffer present a solid foundation in statistical theory while conveying the relevance and importance of the theory in solving practical problems in the real world. The authors' use of practical applications and excellent exercises helps students discover the nature of statistics and understand its essential role in scientific research.Kindle textbooks are functionally equivalent to the print textbook. In some cases, individual items such as ancillary images or multimedia have been removed for digital delivery due to rights restrictions.

Graph Spectra for Complex Networks


Piet Van Mieghem - 2010
    Because any complex network can be represented by a graph, and therefore in turn by a matrix, graph theory has become a powerful tool in the investigation of network performance. This self-contained book provides a concise introduction to the theory of graph spectra and its applications to the study of complex networks. Covering a range of types of graphs and topics important to the analysis of complex systems, this guide provides the mathematical foundation needed to understand and apply spectral insight to real-world systems. In particular, the general properties of both the adjacency and Laplacian spectrum of graphs are derived and applied to complex networks. An ideal resource for researchers and students in communications networking as well as in physics and mathematics.

Activities to Undo Math Misconceptions, PreK-Grade 2


Honi Joyce Bamberger - 2010
    Book annotation not available for this title.Title: Activities to Undo Math MisconceptionsAuthor: Bamberger, Honi J./ Schultz-ferrell, KarrenPublisher: HeinemannPublication Date: 2010/09/28Number of Pages: 138Binding Type: PAPERBACKLibrary of Congress: 2010016302

Integral Geometry and Radon Transforms


Sigurdur Helgason - 2010
    Examples and far-reaching generalizations lead to fundamental problems such as: (i) injectivity, (ii) inversion formulas, (iii) support questions, (iv) applications (e.g., to tomography, partial di erential equations and group representations). For the case of the plane, the inversion theorem and the support theorem have had major applications in medicine through tomography and CAT scanning. While containing some recent research, the book is aimed at beginning graduate students for classroom use or self-study. A number of exercises point to further results with documentation. From the reviews: "Integral Geometry is a fascinating area, where numerous branches of mathematics meet together. the contents of the book is concentrated around the duality and double vibration, which is realized through the masterful treatment of a variety of examples. the book is written by an expert, who has made fundamental contributions to the area." --Boris Rubin, Louisiana State University

Elements of Structured Finance


Ann Rutledge - 2010
    These off-balance sheet structures allow credit exposures to be tailored to investor risk, asset class, and anever-increasing diversity of idiosyncratic needs on the part of issuers and investors. The discipline that addresses these structures, which is called structured finance or securitization, is almost twenty years old, and has become a ubiquitous element of modern financial management. Yet, it has notbeen systematically covered in a textbook designed for both the school and workplace contexts.Elements of Structured Finance, the text version of a program of instruction in structured finance that the authors have offered at universities, private training programs, and consultancies, fills this void spectacularly. Raynes and Rutledge, two very highly regarded teachers and consultants in thefield, bring clarity and logic to an inherently complex and frightening area of finance, using their extensive experience working with many of the top Wall Street securities houses. The book will start with the relatively simple concepts of static valuation models and the benchmark pool, and takethe reader through the more esoteric features of dynamic risk analysis, thus serving as both an excellent introduction for the beginner and an essential reference for the professional. In addition to participants in structured finance programs, this book will appeal to structured finance analystsand managers at banks, asset management companies, insurance companies, and a wide variety of other corporations.

3-D Shapes


Marina Cohen - 2010
    The aisles and shelves hold plenty of fun, too. As Justin helps his mother shop, he explores the variety of 3-D shapes all around him. As Justin can show you, there are always plenty of shapes to see!

New Structures For Physics (Lecture Notes In Physics)


Bob Coecke - 2010
    These include the theory of monoidal categories and corresponding graphical calculi, Girard's linear logic, Scott domains, lambda calculus and corresponding logics for typing, topos theory, and more general process structures. Most of these structures are very prominent in computer science; the chapters here are tailored towards an audience of physicists.

Topics in Physical Mathematics


Kishore Marathe - 2010
    Previously, science and mathematics were part of natural philosophy and many mathematical theories arose as a result of trying to understand natural phenomena. This situation changed at the beginning of last century as science and mathematics diverged. These two fields are collaborating once again; 'Topics in Mathematical Physics' takes the reader through this journey.The author discusses topics where the interaction of physical and mathematical theories has led to new points of view and new results in mathematics. The area where this is most evident is that of geometric topology of low dimensional manifolds. These include the theories of Donaldson, Chern-Simons, Floer-Fukaya, Seiberg-Witten, and Topological (Quantum) Field Theory.The author also discusses the interaction of CFT, Supersymmetry, String Theory and Gravity with diverse areas of mathematics. Several of these ideas have led to new insights into old mathematical structures and some have led to surprising new results The term "Physical Mathematics'' has been coined to describe collectively these new and fast growing areas of research, and regards the work of Donaldson and Witten as belonging to this new area of physical mathematics. Study of this work forms an important part of this book.

Accounting Savvy for Business Owners: A Guide to the Bare Essentials


Philip B. Goodman - 2010
    Demonstrating how to correctly maintain records and apply bookkeeping rules, this guide demonstrates how to keep track of all financial matters and monitor the overall health of any business. Avoiding complex and burdensome accounting jargon, this clear and concise overview translates the essentials into practical business language, answering the most frequently asked questions presented to accountants by small-business owners today. Topics covered include accounting components such as sales, expenses, assets, liabilities, and owners' profits.

In the Beginning: And Other Essays on Intelligent Design


Granville Sewell - 2010
    This book summarizes many of the traditional arguments for intelligent design, but presents some powerful new arguments as well.

A New Era of Thought


Charles Howard Hinton - 2010
    This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book.

Mathematics and Reality


Mary Leng - 2010
    Perhaps the most pressing challenge to mathematical fictionalism is the indispensability argument for the truth of our mathematical theories (and therefore for the existence of the mathematical objects posited by those theories). According to this argument, if we have reason to believe anything, we have reason to believe that the claims of our best empirical theories are (at least approximately) true. But since claims whose truth would require the existence of mathematical objects are indispensable in formulating our best empirical theories, it follows that we have good reason to believe in the mathematical objects posited by those mathematical theories used in empirical science, and therefore to believe that the mathematical theories utilized in empirical science are true. Previous responses to the indispensability argument have focussed on arguing that mathematical assumptions can be dispensed with in formulating our empirical theories. Leng, by contrast, offers an account of the role of mathematics in empirical science according to which the successful use of mathematics in formulating our empirical theories need not rely on the truth of the mathematics utilized.

The Chinese Roots of Linear Algebra


Roger Hart - 2010
    It argues convincingly that what the West "discovered" in the sixteenth and seventeenth centuries had already been known to the Chinese for 1,000 years.Accomplished historian and Chinese-language scholar Roger Hart examines Nine Chapters of Mathematical Arts—the classic ancient Chinese mathematics text—and the arcane art of fangcheng, one of the most significant branches of mathematics in Imperial China. Practiced between the first and seventeenth centuries by anonymous and most likely illiterate adepts, fangcheng involves manipulating counting rods on a counting board. It is essentially equivalent to the solution of systems of N equations in N unknowns in modern algebra, and its practice, Hart reveals, was visual and algorithmic. Fangcheng practitioners viewed problems in two dimensions as an array of numbers across counting boards. By "cross multiplying" these, they derived solutions of systems of linear equations that are not found in ancient Greek or early European mathematics. Doing so within a column equates to Gaussian elimination, while the same operation among individual entries produces determinantal-style solutions.Mathematicians and historians of mathematics and science will find in The Chinese Roots of Linear Algebra new ways to conceptualize the intellectual development of linear algebra.

Concrete: A Seven-Thousand-Year History


Reese Palley - 2010
    Reese Palley’s fascinating history of this ubiquitous and versatile material chronicles the repeated and often centuries-long losses of the technology and its many reemergences and the cultural, scientific, and engineering accomplishments it has enabled.Palley takes us from concrete’s earliest beginnings, including the startling proof that at least one of the pyramids was partially poured, through the building of the Eddystone Light, to the dramatic building explosion in the use of concrete during the twentieth century and the start of the twenty-first century. He discusses the environmental impact of the production of concrete and attempts to find substitutes for the burning of lime. He ends by contemplating outer space, where almost all of the elements needed to build extraterrestrial communities already exist in the chemical makeup of the moon and Mars.

A Kinetic View of Statistical Physics


Pavel L. Krapivsky - 2010
    It focuses on the development and application of theoretical methods to help students develop their problem-solving skills. The book begins with microscopic transport processes: diffusion, collision-driven phenomena, and exclusion. It then presents the kinetics of aggregation, fragmentation and adsorption, where the basic phenomenology and solution techniques are emphasized. The following chapters cover kinetic spin systems, both from a discrete and a continuum perspective, the role of disorder in non-equilibrium processes, hysteresis from the non-equilibrium perspective, the kinetics of chemical reactions, and the properties of complex networks. The book contains 200 exercises to test students' understanding of the subject. A link to a website hosted by the authors, containing supplementary material including solutions to some of the exercises, can be found at www.cambridge.org/9780521851039.

Undecidable Theories: Studies in Logic and the Foundation of Mathematics


Alfred Tarski - 2010
    It consists of three treatises from one of the greatest logicians of all time: "A General Method in Proofs of Undecidability," "Undecidability and Essential Undecidability in Mathematics," and "Undecidability of the Elementary Theory of Groups."

How to Read Historical Mathematics


Benjamin Wardhaugh - 2010
    Sourcebooks on the history of mathematics provide some guidance, but what has been lacking is a guide tailored to the needs of readers approaching these writings for the first time. How to Read Historical Mathematics fills this gap by introducing readers to the analytical questions historians ask when deciphering historical texts.Sampling actual writings from the history of mathematics, Benjamin Wardhaugh reveals the questions that will unlock the meaning and significance of a given text--Who wrote it, why, and for whom? What was its author's intended meaning? How did it reach its present form? Is it original or a translation? Why is it important today? Wardhaugh teaches readers to think about what the original text might have looked like, to consider where and when it was written, and to formulate questions of their own. Readers pick up new skills with each chapter, and gain the confidence and analytical sophistication needed to tackle virtually any text in the history of mathematics.Introduces readers to the methods of textual analysis used by historiansUses actual source material as examplesFeatures boxed summaries, discussion questions, and suggestions for further readingSupplements all major sourcebooks in mathematics historyDesigned for easy referenceIdeal for students and teachers

Figuring it out : entertaining encounters with everyday math


Nuno Crato - 2010
    It tells of villains who steal secrets, heroes who encode messages, highway confusions that result from ignoring Cartesian geometry, mistakes in calendars due to poor numerical approximations, and more.

Archimedes Men of Science


Thomas Little Heath - 2010
    You may find it for free on the web. Purchase of the Kindle edition includes wireless delivery.

Cellular Automata and Groups


Tullio Ceccherini-Silberstein - 2010
    This book presents a self-contained exposition of the theory of cellular automata on groups and explores its deep connections with recent developments in geometric group theory and other branches of mathematics and theoretical computer science.

Algebra Problems And Solutions From Mathematical Olympiads


Todev - 2010
    This is great collection of algebra problems and solutions from Mathematical Olympiads and competitions around the world.