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Philosophy of Mathematics Classic and Contemporary Studies

Philosophy of Mathematics Classic and Contemporary Studies

The philosophy of mathematics is an exciting subject. Philosophy of Mathematics: Classic and Contemporary Studies explores the foundations of mathematical thought. The aim of this book is to encourage young mathematicians to think about the philosophical issues behind fundamental concepts and about different views on mathematical objects and mathematical knowledge. With this new approach the author rekindles an interest in philosophical subjects surrounding the foundations of mathematics. He offers the mathematical motivations behind the topics under debate. He introduces various philosophical positions ranging from the classic views to more contemporary ones including subjects which are more engaged with mathematical logic. Most books on philosophy of mathematics have little to no focus on the effects of philosophical views on mathematical practice and no concern on giving crucial mathematical results and their philosophical relevance consequences reasons etc. This book fills this gap. The book can be used as a textbook for a one-semester or even one-year course on philosophy of mathematics. Other textbooks on the philosophy of mathematics are aimed at philosophers. This book is aimed at mathematicians. Since the author is a mathematician it is a valuable addition to the literature. Mark Balaguer California State University Los Angeles There are not many such texts available for mathematics students. I applaud efforts to foster the dialogue between mathematics and philosophy. Michele Friend George Washington University and CNRS Lille France | Philosophy of Mathematics Classic and Contemporary Studies

GBP 48.99
1

Handbook of Neuroimaging Data Analysis

Handbook of Neuroimaging Data Analysis

This book explores various state-of-the-art aspects behind the statistical analysis of neuroimaging data. It examines the development of novel statistical approaches to model brain data. Designed for researchers in statistics biostatistics computer science cognitive science computer engineering biomedical engineering applied mathematics physics and radiology the book can also be used as a textbook for graduate-level courses in statistics and biostatistics or as a self-study reference for Ph. D. students in statistics biostatistics psychology neuroscience and computer science. | Handbook of Neuroimaging Data Analysis

GBP 66.99
1

Banach Limit and Applications

Banach Limit and Applications

Banach Limit and Applications provides all the results in the area of Banach Limit its extensions generalizations and applications to various fields in one go (as far as possible). All the results in this field after Banach introduced this concept in 1932 were scattered till now. Sublinear functionals generating and dominating Banach Limit unique Banach Limit (almost convergence) invariant means and invariant limits absolute and strong almost convergence applications to ergodicity law of large numbers Fourier series uniform distribution of sequences uniform density core theorems and functional Banach limits are discussed in this book. The discovery of functional analysis such as the Hahn-Banach Theorem and the Banach-Steinhaus Theorem helped the researchers to develop a modern rich and unified theory of sequence spaces by encompassing classical summability theory via matrix transformations and the topics related to sequence spaces which arose from the concept of Banach limits all of which are presented in this book. The unique features of this book are as follows: All the results in this area which were scattered till now are in one place. The book is the first of its kind in the sense that there is no other competitive book. The contents of this monograph did not appear in any book form before. The audience of this book are the researchers in this area and Ph. D. and advanced master’s students. The book is suitable for one- or two-semester course work for Ph. D. students M. S. students in North America and Europe and M. Phil. and master’s students in India.

GBP 130.00
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Random Circulant Matrices

Random Circulant Matrices

Circulant matrices have been around for a long time and have been extensively used in many scientific areas. This book studies the properties of the eigenvalues for various types of circulant matrices such as the usual circulant the reverse circulant and the k-circulant when the dimension of the matrices grow and the entries are random. In particular the behavior of the spectral distribution of the spectral radius and of the appropriate point processes are developed systematically using the method of moments and the various powerful normal approximation results. This behavior varies according as the entries are independent are from a linear process and are light- or heavy-tailed. Arup Bose obtained his B. Stat. M. Stat. and Ph. D. degrees from the Indian Statistical Institute. He has been on its faculty at the Theoretical Statistics and Mathematics Unit Kolkata India since 1991. He is a Fellow of the Institute of Mathematical Statistics and of all three national science academies of India. He is a recipient of the S. S. Bhatnagar Prize and the C. R. Rao Award. He is the author of three books: Patterned Random Matrices Large Covariance and Autocovariance Matrices (with Monika Bhattacharjee) and U-Statistics M_m-Estimators and Resampling (with Snigdhansu Chatterjee). Koushik Saha obtained a B. Sc. in Mathematics from Ramakrishna Mission Vidyamandiara Belur and an M. Sc. in Mathematics from Indian Institute of Technology Bombay. He obtained his Ph. D. degree from the Indian Statistical Institute under the supervision of Arup Bose. His thesis on circulant matrices received high praise from the reviewers. He has been on the faculty of the Department of Mathematics Indian Institute of Technology Bombay since 2014. | Random Circulant Matrices

GBP 44.99
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Fundamentals of Ramsey Theory

Fundamentals of Ramsey Theory

Ramsey theory is a fascinating topic. The author shares his view of the topic in this contemporary overview of Ramsey theory. He presents from several points of view adding intuition and detailed proofs in an accessible manner unique among most books on the topic. This book covers all of the main results in Ramsey theory along with results that have not appeared in a book before. The presentation is comprehensive and reader friendly. The book covers integer graph and Euclidean Ramsey theory with many proofs being combinatorial in nature. The author motivates topics and discussion rather than just a list of theorems and proofs. In order to engage the reader each chapter has a section of exercises. This up-to-date book introduces the field of Ramsey theory from several different viewpoints so that the reader can decide which flavor of Ramsey theory best suits them. Additionally the book offers: A chapter providing different approaches to Ramsey theory e. g. using topological dynamics ergodic systems and algebra in the Stone-Čech compactification of the integers. A chapter on the probabilistic method since it is quite central to Ramsey-type numbers. A unique chapter presenting some applications of Ramsey theory. Exercises in every chapter The intended audience consists of students and mathematicians desiring to learn about Ramsey theory. An undergraduate degree in mathematics (or its equivalent for advanced undergraduates) and a combinatorics course is assumed. TABLE OF CONENTS Preface List of Figures List of Tables Symbols 1. Introduction 2. Integer Ramsey Theory 3. Graph Ramsey Theory 4. Euclidean Ramsey Theory 5. Other Approaches to Ramsey Theory 6. The Probabilistic Method 7. Applications Bibliography Index Biography Aaron Robertson received his Ph. D. in mathematics from Temple University under the guidance of his advisor Doron Zeilberger. Upon finishing his Ph. D. he started at Colgate University in upstate New York where he is currently Professor of Mathematics. He also serves as Associate Managing editor of the journal Integers. After a brief detour into the world of permutation patterns he has focused most of his research on Ramsey theory. | Fundamentals of Ramsey Theory

GBP 82.99
1

Bayesian Analysis with R for Drug Development Concepts Algorithms and Case Studies

Bayesian Analysis with R for Drug Development Concepts Algorithms and Case Studies

Drug development is an iterative process. The recent publications of regulatory guidelines further entail a lifecycle approach. Blending data from disparate sources the Bayesian approach provides a flexible framework for drug development. Despite its advantages the uptake of Bayesian methodologies is lagging behind in the field of pharmaceutical development. Written specifically for pharmaceutical practitioners Bayesian Analysis with R for Drug Development: Concepts Algorithms and Case Studies describes a wide range of Bayesian applications to problems throughout pre-clinical clinical and Chemistry Manufacturing and Control (CMC) development. Authored by two seasoned statisticians in the pharmaceutical industry the book provides detailed Bayesian solutions to a broad array of pharmaceutical problems. Features Provides a single source of information on Bayesian statistics for drug development Covers a wide spectrum of pre-clinical clinical and CMC topics Demonstrates proper Bayesian applications using real-life examples Includes easy-to-follow R code with Bayesian Markov Chain Monte Carlo performed in both JAGS and Stan Bayesian software platforms Offers sufficient background for each problem and detailed description of solutions suitable for practitioners with limited Bayesian knowledge Harry Yang Ph. D. is Senior Director and Head of Statistical Sciences at AstraZeneca. He has 24 years of experience across all aspects of drug research and development and extensive global regulatory experiences. He has published 6 statistical books 15 book chapters and over 90 peer-reviewed papers on diverse scientific and statistical subjects including 15 joint statistical works with Dr. Novick. He is a frequent invited speaker at national and international conferences. He also developed statistical courses and conducted training at the FDA and USP as well as Peking University. Steven Novick Ph. D. is Director of Statistical Sciences at AstraZeneca. He has extensively contributed statistical methods to the biopharmaceutical literature. Novick is a skilled Bayesian computer programmer and is frequently invited to speak at conferences having developed and taught courses in several areas including drug-combination analysis and Bayesian methods in clinical areas. Novick served on IPAC-RS and has chaired several national statistical conferences. | Bayesian Analysis with R for Drug Development Concepts Algorithms and Case Studies

GBP 38.99
1

Statistical and Econometric Methods for Transportation Data Analysis

Statistical and Econometric Methods for Transportation Data Analysis

The book's website (with databases and other support materials) can be accessed here. Praise for the Second Edition: The second edition introduces an especially broad set of statistical methods … As a lecturer in both transportation and marketing research I find this book an excellent textbook for advanced undergraduate Master’s and Ph. D. students covering topics from simple descriptive statistics to complex Bayesian models. … It is one of the few books that cover an extensive set of statistical methods needed for data analysis in transportation. The book offers a wealth of examples from the transportation field. —The American Statistician Statistical and Econometric Methods for Transportation Data Analysis Third Edition offers an expansion over the first and second editions in response to the recent methodological advancements in the fields of econometrics and statistics and to provide an increasing range of examples and corresponding data sets. It describes and illustrates some of the statistical and econometric tools commonly used in transportation data analysis. It provides a wide breadth of examples and case studies covering applications in various aspects of transportation planning engineering safety and economics. Ample analytical rigor is provided in each chapter so that fundamental concepts and principles are clear and numerous references are provided for those seeking additional technical details and applications. New to the Third Edition Updated references and improved examples throughout. New sections on random parameters linear regression and ordered probability models including the hierarchical ordered probit model. A new section on random parameters models with heterogeneity in the means and variances of parameter estimates. Multiple new sections on correlated random parameters and correlated grouped random parameters in probit logit and hazard-based models. A new section discussing the practical aspects of random parameters model estimation. A new chapter on Latent Class Models. A new chapter on Bivariate and Multivariate Dependent Variable Models. Statistical and Econometric Methods for Transportation Data Analysis Third Edition can serve as a textbook for advanced undergraduate Masters and Ph. D. students in transportation-related disciplines including engineering economics urban and regional planning and sociology. The book also serves as a technical reference for researchers and practitioners wishing to examine and understand a broad range of statistical and econometric tools required to study transportation problems.

GBP 69.99
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Algebraic Number Theory A Brief Introduction

Algebraic Number Theory A Brief Introduction

This book offers the basics of algebraic number theory for students and others who need an introduction and do not have the time to wade through the voluminous textbooks available. It is suitable for an independent study or as a textbook for a first course on the topic. The author presents the topic here by first offering a brief introduction to number theory and a review of the prerequisite material then presents the basic theory of algebraic numbers. The treatment of the subject is classical but the newer approach discussed at the end provides a broader theory to include the arithmetic of algebraic curves over finite fields and even suggests a theory for studying higher dimensional varieties over finite fields. It leads naturally to the Weil conjecture and some delicate questions in algebraic geometry. About the Author Dr. J. S. Chahal is a professor of mathematics at Brigham Young University. He received his Ph. D. from Johns Hopkins University and after spending a couple of years at the University of Wisconsin as a post doc he joined Brigham Young University as an assistant professor and has been there ever since. He specializes and has published several papers in number theory. For hobbies he likes to travel and hike. His book Fundamentals of Linear Algebra is also published by CRC Press. | Algebraic Number Theory A Brief Introduction

GBP 52.99
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Pencils of Cubics and Algebraic Curves in the Real Projective Plane

Pencils of Cubics and Algebraic Curves in the Real Projective Plane

Pencils of Cubics and Algebraic Curves in the Real Projective Plane thoroughly examines the combinatorial configurations of n generic points in RP². Especially how it is the data describing the mutual position of each point with respect to lines and conics passing through others. The first section in this book answers questions such as can one count the combinatorial configurations up to the action of the symmetric group? How are they pairwise connected via almost generic configurations? These questions are addressed using rational cubics and pencils of cubics for n = 6 and 7. The book’s second section deals with configurations of eight points in the convex position. Both the combinatorial configurations and combinatorial pencils are classified up to the action of the dihedral group D8. Finally the third section contains plentiful applications and results around Hilbert’s sixteenth problem. The author meticulously wrote this book based upon years of research devoted to the topic. The book is particularly useful for researchers and graduate students interested in topology algebraic geometry and combinatorics. Features: Examines how the shape of pencils depends on the corresponding configurations of points Includes topology of real algebraic curves Contains numerous applications and results around Hilbert’s sixteenth problem About the Author: Séverine Fiedler-le Touzé has published several papers on this topic and has been invited to present at many conferences. She holds a Ph. D. from University Rennes1 and was a post-doc at the Mathematical Sciences Research Institute in Berkeley California.

GBP 115.00
1

Advanced Spatial Modeling with Stochastic Partial Differential Equations Using R and INLA

Advanced Spatial Modeling with Stochastic Partial Differential Equations Using R and INLA

Modeling spatial and spatio-temporal continuous processes is an important and challenging problem in spatial statistics. Advanced Spatial Modeling with Stochastic Partial Differential Equations Using R and INLA describes in detail the stochastic partial differential equations (SPDE) approach for modeling continuous spatial processes with a Matérn covariance which has been implemented using the integrated nested Laplace approximation (INLA) in the R-INLA package. Key concepts about modeling spatial processes and the SPDE approach are explained with examples using simulated data and real applications. This book has been authored by leading experts in spatial statistics including the main developers of the INLA and SPDE methodologies and the R-INLA package. It also includes a wide range of applications:* Spatial and spatio-temporal models for continuous outcomes* Analysis of spatial and spatio-temporal point patterns* Coregionalization spatial and spatio-temporal models* Measurement error spatial models* Modeling preferential sampling* Spatial and spatio-temporal models with physical barriers* Survival analysis with spatial effects* Dynamic space-time regression* Spatial and spatio-temporal models for extremes* Hurdle models with spatial effects* Penalized Complexity priors for spatial modelsAll the examples in the book are fully reproducible. Further information about this book as well as the R code and datasets used is available from the book website at http://www. r-inla. org/spde-book. The tools described in this book will be useful to researchers in many fields such as biostatistics spatial statistics environmental sciences epidemiology ecology and others. Graduate and Ph. D. students will also find this book and associated files a valuable resource to learn INLA and the SPDE approach for spatial modeling.

GBP 44.99
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Handbook of Approximation Algorithms and Metaheuristics Methologies and Traditional Applications Volume 1

Handbook of Approximation Algorithms and Metaheuristics Methologies and Traditional Applications Volume 1

Handbook of Approximation Algorithms and Metaheuristics Second Edition reflects the tremendous growth in the field over the past two decades. Through contributions from leading experts this handbook provides a comprehensive introduction to the underlying theory and methodologies as well as the various applications of approximation algorithms and metaheuristics. Volume 1 of this two-volume set deals primarily with methodologies and traditional applications. It includes restriction relaxation local ratio approximation schemes randomization tabu search evolutionary computation local search neural networks and other metaheuristics. It also explores multi-objective optimization reoptimization sensitivity analysis and stability. Traditional applications covered include: bin packing multi-dimensional packing Steiner trees traveling salesperson scheduling and related problems. Volume 2 focuses on the contemporary and emerging applications of methodologies to problems in combinatorial optimization computational geometry and graphs problems as well as in large-scale and emerging application areas. It includes approximation algorithms and heuristics for clustering networks (sensor and wireless) communication bioinformatics search streams virtual communities and more. About the EditorTeofilo F. Gonzalez is a professor emeritus of computer science at the University of California Santa Barbara. He completed his Ph. D. in 1975 from the University of Minnesota. He taught at the University of Oklahoma the Pennsylvania State University and the University of Texas at Dallas before joining the UCSB computer science faculty in 1984. He spent sabbatical leaves at the Monterrey Institute of Technology and Higher Education and Utrecht University. He is known for his highly cited pioneering research in the hardness of approximation; for his sublinear and best possible approximation algorithm for k-tMM clustering; for introducing the open-shop scheduling problem as well as algorithms for its solution that have found applications in numerous research areas; as well as for his research on problems in the areas of job scheduling graph algorithms computational geometry message communication wire routing etc. | Handbook of Approximation Algorithms and Metaheuristics Methologies and Traditional Applications Volume 1

GBP 44.99
1

Statistical Machine Learning A Unified Framework

Statistical Machine Learning A Unified Framework

The recent rapid growth in the variety and complexity of new machine learning architectures requires the development of improved methods for designing analyzing evaluating and communicating machine learning technologies. Statistical Machine Learning: A Unified Framework provides students engineers and scientists with tools from mathematical statistics and nonlinear optimization theory to become experts in the field of machine learning. In particular the material in this text directly supports the mathematical analysis and design of old new and not-yet-invented nonlinear high-dimensional machine learning algorithms. Features: Unified empirical risk minimization framework supports rigorous mathematical analyses of widely used supervised unsupervised and reinforcement machine learning algorithms Matrix calculus methods for supporting machine learning analysis and design applications Explicit conditions for ensuring convergence of adaptive batch minibatch MCEM and MCMC learning algorithms that minimize both unimodal and multimodal objective functions Explicit conditions for characterizing asymptotic properties of M-estimators and model selection criteria such as AIC and BIC in the presence of possible model misspecification This advanced text is suitable for graduate students or highly motivated undergraduate students in statistics computer science electrical engineering and applied mathematics. The text is self-contained and only assumes knowledge of lower-division linear algebra and upper-division probability theory. Students professional engineers and multidisciplinary scientists possessing these minimal prerequisites will find this text challenging yet accessible. About the Author: Richard M. Golden (Ph. D. M. S. E. E. B. S. E. E. ) is Professor of Cognitive Science and Participating Faculty Member in Electrical Engineering at the University of Texas at Dallas. Dr. Golden has published articles and given talks at scientific conferences on a wide range of topics in the fields of both statistics and machine learning over the past three decades. His long-term research interests include identifying conditions for the convergence of deterministic and stochastic machine learning algorithms and investigating estimation and inference in the presence of possibly misspecified probability models. | Statistical Machine Learning A Unified Framework

GBP 99.99
1

Probability and Statistics for Computer Scientists

Probability and Statistics for Computer Scientists

Praise for the Second Edition: The author has done his homework on the statistical tools needed for the particular challenges computer scientists encounter. [He] has taken great care to select examples that are interesting and practical for computer scientists. . The content is illustrated with numerous figures and concludes with appendices and an index. The book is erudite and … could work well as a required text for an advanced undergraduate or graduate course. Computing Reviews Probability and Statistics for Computer Scientists Third Edition helps students understand fundamental concepts of Probability and Statistics general methods of stochastic modeling simulation queuing and statistical data analysis; make optimal decisions under uncertainty; model and evaluate computer systems; and prepare for advanced probability-based courses. Written in a lively style with simple language and now including R as well as MATLAB this classroom-tested book can be used for one- or two-semester courses. Features: Axiomatic introduction of probability Expanded coverage of statistical inference and data analysis including estimation and testing Bayesian approach multivariate regression chi-square tests for independence and goodness of fit nonparametric statistics and bootstrap Numerous motivating examples and exercises including computer projects Fully annotated R codes in parallel to MATLAB Applications in computer science software engineering telecommunications and related areas In-Depth yet Accessible Treatment of Computer Science-Related TopicsStarting with the fundamentals of probability the text takes students through topics heavily featured in modern computer science computer engineering software engineering and associated fields such as computer simulations Monte Carlo methods stochastic processes Markov chains queuing theory statistical inference and regression. It also meets the requirements of the Accreditation Board for Engineering and Technology (ABET). About the Author Michael Baron is David Carroll Professor of Mathematics and Statistics at American University in Washington D. C. He conducts research in sequential analysis and optimal stopping change-point detection Bayesian inference and applications of statistics in epidemiology clinical trials semiconductor manufacturing and other fields. M. Baron is a Fellow of the American Statistical Association and a recipient of the Abraham Wald Prize for the best paper in Sequential Analysis and the Regents Outstanding Teaching Award. M. Baron holds a Ph. D. in statistics from the University of Maryland. In his turn he supervised twelve doctoral students mostly employed on academic and research positions.

GBP 99.99
1

Nonequilibrium Statistical Mechanics An Introduction with Applications

Nonequilibrium Statistical Mechanics An Introduction with Applications

Nonequilibrium statistical mechanics (NESM) practically synonymous with time-dependent statistical mechanics (TDSM) is a beautiful and profound subject vast in scope diverse in applications and indispensable in understanding the changing natural phenomena we encounter in the physical chemical and biological world. Although time dependent phenomena have been studied from antiquity the modern subject the nonequilibrium statistical mechanics has its genesis in Boltzmann’s 1872 classic paper that aimed at extending Maxwell’s kinetic theory of gases by including intermolecular interactions. Subsequent development of the subject drew upon the seminal work of Einstein and Langevin on Brownian motion Rayleigh and Stokes on hydrodynamics and on the works of Onsager Prigogine Kramers Kubo Mori and Zwanzig. One major goal of this book is to develop and present NESM in an organized fashion so that students can appreciate and understand the flow of the subject from postulates to practical uses. This book takes the students on a journey from fundamentals to applications mostly using simple mathematics and fundamental concepts. With the advent of computers and computational packages and techniques a deep intuitive understanding can allow the students to tackle fairly complex problems like proteins in lipid membranes or solvation of ions in electrolytes used in batteries. The subject is still evolving rapidly with forays into complex biological events and materials science. Nonequilibrium Statistical Mechanics: An Introduction with Applications is thus an introductory text that aims to provide students with a background and skill essential to study and understand time-dependent (relaxation) phenomena. It will allow students to calculate transport properties like diffusion and conductivity. The book also teaches the methods to calculate reaction rate on a multi-dimensional energy surface in another such application. For a beginner in the field especially for one with an aim to study chemistry and biology and also physics one major difficulty faced is a lack of organization of the available study material. Since NESM is a vast subject with many different theoretical tools the above poses a problem. This book lays the foundations towards understanding time- dependent phenomena in a simple and systematic fashion. It is accessible to students and researchers who have basic training in physics and mathematics. The book can be used to teach advanced undergraduates. Some involved topics like the projection operator technique and mode coupling theory are more suitable for Ph. D. level. | Nonequilibrium Statistical Mechanics An Introduction with Applications

GBP 89.99
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3D Animation for the Raw Beginner Using Autodesk Maya 2e

3D Animation for the Raw Beginner Using Autodesk Maya 2e

3D Animation for the Raw Beginner Using Autodesk Maya is a hands-on academic textbook as well as a do-it-yourself training manual for the individual animator. This second edition has been completely rewritten to take into account updates to Autodesk Maya including Autodesk’s renderer Arnold. It contains entirely new examples and tutorial lessons. All 612 images are in full color. The book directs the reader to the parts of Maya that must be mastered in order to create complete 3D projects and thus it simplifies the process of taking on Maya’s vast and intricate interface while giving the reader a firm foundation on which to build future knowledge of Maya. It also presents brief examples of other popular 3D applications and rendering engines. This principles-based yet pragmatic book: Introduces the basic steps of the 3D modeling materials animation lighting and rendering processes. Presents clear and concise tutorials that link key concepts to practical techniques. Includes access to a webpage for the book: https://buzzking. com/AnimationTextbook/AnimationTextbook. html. On this webpage are videos that cover many of the lessons in the book as well as video tutorials that present bonus material not included in the book. Frees instructors from the painstaking task of developing step-by-step examples to present Maya’s complex interface and basic capabilities. Boasts an easy-to-follow tutorial-based learning style ideal for individual study by aspiring animators and do-it yourselfers. Roger Buzz King is a Professor Emeritus at the University of Colorado at Boulder where he teaches 3D Animation for the Computer Science Department and the Alliance for Technology Learning and Society (ATLAS) an institute dedicated to the application of technology to the arts. Buzz is an independent 3D animator who serves on the board of directors of a 3D animation startup. Buzz has a B. A. in Mathematics from Occidental College an M. S. and Ph. D. in Computer Science from the University of Southern California and an M. Div. from the Iliff School of Theology. Key Features Introduces critical aspects of the 3D animation process Presents clear and concise tutorials that link key concepts to practical techniques Includes access to a dedicated Web site http://3dbybuzz. com featuring useful videos lessons and updates Frees instructors from developing step-by-step examples to present Maya’s complex interface and basic Boasts an easy-to-follow hands-on learning style ideal for individual study by aspiring animators and do-ityourselfers | 3D Animation for the Raw Beginner Using Autodesk Maya 2e

GBP 48.99
1

An Introduction to Analysis

An Introduction to Analysis

The third edition of this widely popular textbook is authored by a master teacher. This book provides a mathematically rigorous introduction to analysis of real­valued functions of one variable. This intuitive student-friendly text is written in a manner that will help to ease the transition from primarily computational to primarily theoretical mathematics. The material is presented clearly and as intuitive as possible while maintaining mathematical integrity. The author supplies the ideas of the proof and leaves the write-up as an exercise. The text also states why a step in a proof is the reasonable thing to do and which techniques are recurrent. Examples while no substitute for a proof are a valuable tool in helping to develop intuition and are an important feature of this text. Examples can also provide a vivid reminder that what one hopes might be true is not always true. Features of the Third Edition: Begins with a discussion of the axioms of the real number system. The limit is introduced via sequences. Examples motivate what is to come highlight the need for hypothesis in a theorem and make abstract ideas more concrete. A new section on the Cantor set and the Cantor function. Additional material on connectedness. Exercises range in difficulty from the routine getting your feet wet types of problems to the moderately challenging problems. Topology of the real number system is developed to obtain the familiar properties of continuous functions. Some exercises are devoted to the construction of counterexamples. The author presents the material to make the subject understandable and perhaps exciting to those who are beginning their study of abstract mathematics. Table of Contents Preface Introduction The Real Number System Sequences of Real Numbers Topology of the Real Numbers Continuous Functions Differentiation Integration Series of Real Numbers Sequences and Series of Functions Fourier Series Bibliography Hints and Answers to Selected Exercises Index Biography James R. Kirkwood holds a Ph. D. from University of Virginia. He has authored fifteen published mathematics textbooks on various topics including calculus real analysis mathematical biology and mathematical physics. His original research was in mathematical physics and he co-authored the seminal paper in a topic now called Kirkwood-Thomas Theory in mathematical physics. During the summer he teaches real analysis to entering graduate students at the University of Virginia. He has been awarded several National Science Foundation grants. His texts Elementary Linear Algebra Linear Algebra and Markov Processes are also published by CRC Press. | An Introduction to Analysis

GBP 82.99
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Games Gambling and Probability An Introduction to Mathematics

Games Gambling and Probability An Introduction to Mathematics

Many experiments have shown the human brain generally has very serious problems dealing with probability and chance. A greater understanding of probability can help develop the intuition necessary to approach risk with the ability to make more informed (and better) decisions. The first four chapters offer the standard content for an introductory probability course albeit presented in a much different way and order. The chapters afterward include some discussion of different games different ideas that relate to the law of large numbers and many more mathematical topics not typically seen in such a book. The use of games is meant to make the book (and course) feel like fun! Since many of the early games discussed are casino games the study of those games along with an understanding of the material in later chapters should remind you that gambling is a bad idea; you should think of placing bets in a casino as paying for entertainment. Winning can obviously be a fun reward but should not ever be expected. Changes for the Second Edition: New chapter on Game Theory New chapter on Sports Mathematics The chapter on Blackjack which was Chapter 4 in the first edition appears later in the book. Reorganization has been done to improve the flow of topics and learning. New sections on Arkham Horror Uno and Scrabble have been added. Even more exercises were added! The goal for this textbook is to complement the inquiry-based learning movement. In my mind concepts and ideas will stick with the reader more when they are motivated in an interesting way. Here we use questions about various games (not just casino games) to motivate the mathematics and I would say that the writing emphasizes a just-in-time mathematics approach. Topics are presented mathematically as questions about the games themselves are posed. Table of Contents Preface1. Mathematics and Probability 2. Roulette and Craps: Expected Value 3. Counting: Poker Hands 4. More Dice: Counting and Combinations and Statistics 5. Game Theory: Poker Bluffing and Other Games 6. Probability/Stochastic Matrices: Board Game Movement 7. Sports Mathematics: Probability Meets Athletics 8. Blackjack: Previous Methods Revisited 9. A Mix of Other Games 10. Betting Systems: Can You Beat the System? 11. Potpourri: Assorted Adventures in Probability Appendices Tables Answers and Selected Solutions Bibliography Biography Dr. David G. Taylor is a professor of mathematics and an associate dean for academic affairs at Roanoke College in southwest Virginia. He attended Lebanon Valley College for his B. S. in computer science and mathematics and went to the University of Virginia for his Ph. D. While his graduate school focus was on studying infinite dimensional Lie algebras he started studying the mathematics of various games in order to have a more undergraduate-friendly research agenda. Work done with two Roanoke College students Heather Cook and Jonathan Marino appears in this book! Currently he owns over 100 different board games and enjoys using probability in his decision-making while playing most of those games. In his spare time he enjoys reading cooking coding playing his board games and spending time with his six-year-old dog Lilly. | Games Gambling and Probability An Introduction to Mathematics

GBP 82.99
1