Tuesday, April 30, 2013

Numerical Recipes: The Art of Scientific Computing 3e

Numerical Recipes: The Art of Scientific Computing 3rd Edition PDF Download Ebook. William H. Press, Saul A. Teukolsky, William T. Vetterling and Brian P. Flannery describe basic mathematics and computer science and proceeds to complete, working routines. Widely recognized as the most comprehensive, accessible and practical basis for scientific computing, this new edition incorporates more than 400 Numerical Recipes routines, many of them new or upgraded.

The executable C++ code, now printed in color for easy reading, adopts an object-oriented style particularly suited to scientific applications. The whole book is presented in the informal, easy-to-read style that made earlier editions so popular. The book includes commented full listings of now more than 400 unique C++ routines that can be downloaded in machine-readable form (see right) for inclusion in users' programs.

This text has 2 new chapters, 25 new sections, and is about 25% longer than the 2nd edition. Its code is wholeheartedly object oriented, demonstrating diverse techniques for using the full power of C++. Color and marginal labels add clarity to the text and code. Journal references now include article titles.

New or expanded topics include classification and inference (including Gaussian mixture models, hidden Markov modeling, hierarchical clustering, support vector machines); computational geometry (including KD trees, quad- and octrees, Delaunay triangulation, polygons, triangles, spheres); many new statistical distributions; completely new ODE routines; expanded random deviates; spectral and pseudospectral methods for PDEs.

Other topics include interior point methods for linear programming; expanded sparse matrices; interpolation in multidimensions; quadrature by variable transformation; fast spherical harmonic transforms; fast incremental quantile estimation; information theoretic properties of distributions; wavelets on the interval; kriging; phylogenetic trees; soft error decoding; stochastic simulation of reaction networks; and much, much more!

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Numerical Analysis 2nd Edition by Timothy Sauer

Numerical Analysis 2nd Edition PDF Download Ebook. Timothy Sauer covers not only the standard topics but also some more advanced numerical methods being used by computational scientists and engineers—topics such as compression, forward and backward error analysis, and iterative methods of solving equations—all while maintaining a level of discussion appropriate for undergraduates.

Each chapter contains a Reality Check, which is an extended exploration of relevant application areas that can launch individual or team projects. MATLAB® is used throughout to demonstrate and implement numerical methods. The Second Edition features many noteworthy improvements based on feedback from users, such as new coverage of Cholesky factorization, GMRES methods, and nonlinear PDEs.

Chapter 0 (optional) provides students with the fundamental building blocks they will need in later chapters. The entire text is designed to move from elementary ideas to more sophisticated concepts to avoid sudden jumps in level.

Spotlights throughout the text highlight the five major ideas of Numerical Analysis. These spotlights comment on the topic at hand and make informal connections to other expressions of the same concept elsewhere in the book helping students connect what they already know to a new concept.

Reality Checks appear throughout the text to provide concrete examples of the way numerical methods lead to solutions of important technological problems showing students how numerical analysis applies to their lives.

Optional MATLAB® expositions are used throughout the text, giving students and instructors the ability to use a common computing language to solve all of the interface problems: data input/output, plotting, etc. in one fell swoop. Appendix B is a short MATLAB tutorial that can be used as a first introduction to students who have not used MATLAB, or as a reference to students already familiar with MATLAB.

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Numerical Analysis 9th Edition, Richard Burden and Faires

Numerical Analysis 9th Edition PDF Download Ebook. Richard L. Burden and J. Douglas Faires offer introduction to the theory and application of modern numerical approximation techniques for students taking a one- or two-semester course in numerical analysis. With an accessible treatment that only requires a calculus prerequisite, Burden and Faires explain how, why, and when approximation techniques can be expected to work, and why, in some situations, they fail.

A wealth of examples and exercises develop students' intuition, and demonstrate the subject's practical applications to important everyday problems in math, computing, engineering, and physical science disciplines. The first book of its kind built from the ground up to serve a diverse undergraduate audience, three decades later Burden and Faires remains the definitive introduction to a vital and practical subject.

Balances theory and methods to stake a wide middle ground between audiences who need to know the mathematics and audiences who only need to know the essential techniques. Flexible coverage to suit one- or two-semester courses and differing student levels, with careful attention paid to marking optional material and alternate paths for instructors. Specific instructions are given for Maple in limited cases where software-specific questions are absolutely required.

Language and software neutral programs in book are supported on companion website by specific program code for Maple, Mathematica, MATLAB, C, FORTRAN, Java, and Pascal to cover all technologies the majority of the market will use. Author website includes mid-cycle updates and additions to this program code to keep up with new software releases.

Virtually every concept in the text is illustrated by example, and this edition contains more than 2000 class-tested exercises ranging from elementary applications of methods and algorithms to generalizations and extensions of the theory. The exercise sets include many applied problems from diverse areas of engineering, as well as from the physical, computer, biological, and social sciences.

The design of the text gives instructors flexibility in choosing topics they wish to cover, selecting the level of theoretical rigor desired, and deciding which applications are most appropriate or interesting for their classes. Theory coverage emphasizes mathematical thought and is especially accessible for students who've optionally taken undergrad math foundations courses like Real Analysis or Transition to Advanced Math.

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Monday, April 29, 2013

Engineering Mathematics 7th Edition, Stroud and Booth

Engineering Mathematics 7th Edition PDF Download Ebook. K. A. Stroud and Dexter J. Booth offer unique programmed approach that takes users through the mathematics in a step-by-step fashion with a wealth of worked examples and exercises.

This book contains Quizzes, Learning Outcomes and Checklists that guide readers through each topic and focus understanding, updated throughout for the latest calculators and Excel spreadsheets. A groundbreaking and comprehensive reference that's been a bestseller since it first debuted in 1970, the book has been thoroughly revised and expanded. Providing a broad mathematical survey, this innovative volume covers a full range of topics from the very basic to the advanced.

Whether you're an engineer looking for a useful on-the-job reference or want to improve your mathematical skills, or you are a student who needs an in-depth self-study guide, Engineering Mathematics is sure to come in handy time and time again. It is by far the bestselling book of its kind with well over half a million copies sold.

Widely recommended by lecturers it is also a huge word-of-mouth seller. Its unique programmed approach takes the student through the mathematics in an interactive, step-by-step fashion with a wealth of worked examples and exercises. It is the most comprehensive course of its type.

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Calculus Early Transcendentals 10th Edition, Howard Anton

Calculus Early Transcendentals 10th Edition PDF Download Ebook. Howard Anton, Irl C. Bivens and Stephen Davis fulfill the needs of a changing market by providing flexible solutions to teaching and learning needs of all kinds. The text continues to focus on and incorporate new ideas that have withstood the objective scrutiny of many skilled and thoughtful instructors and their students.

This 10th edition retains Anton's trademark clarity of exposition, sound mathematics, excellent exercises and examples, and appropriate level. Exercise sets have been modified to correspond more closely to questions in Wiley Plus. In addition, more WileyPLUS questions now correspond to specific exercises in the text.

New applied exercises have been added to the book and existing applied exercises have been updated. The authors' goal is to present precise mathematics to the fullest extent possible in an introductory treatment. Clear writing, effective pedagogy--including special exercises designed for self-assessment--and visual representations of the mathematics help students from a variety of backgrounds to learn.

Recognizing variations in learning styles, the authors take a "rule of four" approach, presenting concepts from the verbal, algebraic, visual, and numerical points of view to foster deeper understanding whenever appropriate. Anton provides thorough topic coverage organized to fit standard curricula and carefully-constructed exercise sets that users of previous editions have come to depend upon.

This edition is designed to serve a broad spectrum of calculus philosophies-from traditional to "reform." Technology can be emphasized or not, and the order of many topics can be adapted to accommodate each instructor's specific needs. Each exercise set begins with approximately five exercises (answers included) that are designed to provide the student with an immediate assessment of whether he or she has mastered key ideas from the section. They require a minimum of computation and can usually be answered by filling in the blanks.

Most sections include exercises that are designed to be solved using either a graphing calculator or a computer algebra system such as Mathematica, Maple, or Derive. These exercises are marked with an icon for easy identification. The book is written at a mathematical level that is suitable for students planning on careers in engineering or science.

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Calculus 4th Edition by Michael Spivak

Calculus 4th Edition PDF Download Ebook. Michael Spivak combines leisurely explanations, a profusion of examples, a wide range of exercises and plenty of illustrations in an easy-going approach that enlightens difficult concepts and rewards effort. It is ideal for honors students and mathematics majors seeking an alternative to doorstop textbooks and more formidable introductions to real analysis.

Every aspect of this book was influenced by the desire to present calculus not merely as a prelude to but as the first real encounter with mathematics. Since the foundations of analysis provided the arena in which modern modes of mathematical thinking developed, calculus ought to be the place in which to expect, rather than avoid, the strengthening of insight with logic.

In addition to developing the students' intuition about the beautiful concepts of analysis, it is surely equally important to persuade them that precision and rigor are neither deterrents to intuition, nor ends in themselves, but the natural medium in which to formulate and think about mathematical questions.

This goal implies a view of mathematics which, in a sense, the entire book attempts to defend. No matter how well particular topics may be developed, the goals of this book will be realized only if it succeeds as a whole. For this reason, it would be of little value merely to list the topics covered, or to mention pedagogical practices and other innovations. Even the cursory glance customarily bestowed on new calculus texts will probably tell more than any such extended advertisement, and the teacher with strong feelings about particular aspects of calculus will know just where to look to see if this book fulfills his requirements.

A few features do require explicit comment, however. Of the twenty-nine chapters in the book, two (starred) chapters are optional, and the three chapters comprising Part V have been included only for the benefit of those students who might want to examine on their own a construction of the real numbers. Moreover, the appendices to Chapters 3 and 1 1 also contain optional material.

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Sunday, April 28, 2013

Calculus: Concepts and Contexts 4th Edition, Stewart

Calculus: Concepts and Contexts 4th Edition PDF Download Ebook. James Stewart offers a streamlined approach to teaching calculus, focusing on major concepts and supporting those with precise definitions, patient explanations, and carefully graded problems. This text is highly regarded because this text offers a balance of theory and conceptual work to satisfy more progressive programs as well as those who are more comfortable teaching in a more traditional fashion.

Each title is just one component in a comprehensive calculus course program that carefully integrates and coordinates print, media, and technology products for successful teaching and learning. This text also features meticulous accuracy, patient explanations, and carefully graded problems. The content has been refined and the examples and exercises have been updated. In addition, this book now includes a free CD-ROM for students with animations, activities, and homework hints.

The book integrates the use of the CD throughout by using icons that show students when to use the CD to deepen their understanding of a difficult concept. The respected author emphasizes conceptual understanding - motivating students with real world applications and stressing the Rule of Four in numerical, visual, algebraic, and verbal interpretations.

All concepts are presented in the classic Stewart style: with simplicity, character, and attention to detail. In addition to his clear exposition, Stewart also creates well thought-out problems and exercises. The definitions are precise and the problems create an ideal balance between conceptual understanding and algebraic skills.

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Single Variable Calculus: Early Transcendentals 7e, Stewart

Single Variable Calculus: Early Transcendentals 7th Edition PDF Download Ebook. James Stewart offers clear, accurate, and filled with relevant, real-world examples. With this book, Stewart conveys not only the utility of calculus to help you develop technical competence, but also gives you an appreciation for the intrinsic beauty of the subject.

Four carefully crafted diagnostic tests in algebra, analytic geometry, functions, and trigonometry appear at the beginning of the text. These provide students with a convenient way to test their pre-existing knowledge and brush up on skill techniques they need to successfully begin the course. Answers are included, and students who need to improve will be referred to points in the text or on the book's website where they can seek help.

Stewart's writing style speaks clearly and directly to students, guiding them through key ideas, theorems, and problem-solving steps, and encouraging them to think as they read and learn calculus. Every concept is supported by thoughtfully worked examples—many with step-by-step explanations—and carefully chosen exercises. The quality of this pedagogical system is what sets Stewart's texts above others.

Examples are not only models for problem solving or a means of demonstrating techniques; they also encourage students to develop an analytic view of the subject. To provide further insight into mathematical concepts, many of these detailed examples display solutions that are presented graphically, analytically, and/or numerically. Margin notes expand on and clarify the steps of the solution.

The text's clean, user-friendly design provides a clear presentation of calculus. The art program, with its functional and consistent use of color, helps students identify and review mathematical concepts more easily. It offers an extensive collection of more than 8,000 quality exercises. Each exercise set is carefully graded, progressing from skill-development problems to more challenging problems involving applications and proofs.

The wide variety of types of exercises includes many technology-oriented, thought-provoking, real, and engaging problems. Conceptual exercises encourage the development of communication skills by explicitly requesting descriptions, conjectures, and explanations. These exercises stimulate critical thinking and reinforce the concepts of calculus.

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Calculus 10th Edition by Ron Larson and Bruce Edwards

Calculus 10th Edition PDF Download Ebook. Ron Larson and Bruce H. Edwards address the needs of a broad range of teaching and learning styles and environments. Each title is just one component in a comprehensive calculus course program that carefully integrates and coordinates print, media, and technology products for successful teaching and learning.

The Larson CALCULUS program has a long history of innovation in the calculus market. It has been widely praised by a generation of students and professors for its solid and effective pedagogy. To eliminate any possible confusion, all Study Tips and Notes have been combined into one feature, Remarks. These hints and tips can be used to reinforce or expand upon concepts, help you learn how to study mathematics, caution you about common errors, address special cases, or show alternative or additional steps to a solution of an example.

The exercise sets have been carefully and extensively examined to ensure they are rigorous, relevant, and cover all topics suggested by our users. The exercises have been reorganized and titled so you can better see the connections between examples and exercises. Multi-step, real-life exercises reinforce problem-solving skills and mastery of concepts by giving you the opportunity to apply the concepts in real-life situations. Putnam Exam questions to push the limits of students’ understanding of calculus. Graphing technology exercises for students to make us of a graphing utility to help find solutions.

Online homework and tests are evaluated using powerful Maple software to ensure mathematical accuracy. Instructors control point values, weighting grades, and whether of not an item is graded. An electronic gradebook helps instructors manage course information easily and can be exported to other files, such as Excel.

Many examples throughout the book are accompanied by CAS Investigations. These are collaborative investigations using a computer algebra system (e.g., Maple) to further explore the related example. CAS Investigations are located online and in the Multimedia eBook.

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Friday, April 26, 2013

Probability, Statistics and Random Processes For Electrical Engineering 3e

Probability, Statistics, and Random Processes For Electrical Engineering 3rd Edition PDF Download Ebook. Alberto Leon-Garcia offers an interesting, straightforward introduction to probability and random processes. While helping readers to develop their problem-solving skills, the book enables them to understand how to make the transition from real problems to probability models for those problems.

To keep users motivated, the author uses a number of practical applications from various areas of electrical and computer engineering that demonstrate the relevance of probability theory to engineering practice. Discrete-time random processes are used to bridge the transition between random variables and continuous-time random processes. Additional material has been added to the second edition to provide a more substantial introduction to random processes.

The book's first five chapters form the basis of a traditional, introduction to probability and random variables. In addition to the standard topics, it offers optional sections on modeling, computer methods, combinatories, reliability, and entropy. Chapters 4 through 9 can accommodate a one-semester senior/first-year graduate course on random processes and linear systems, as well as Markov chains and queuing theory.

Additional coverage includes cyclostationary random processes, Fourier series and Karhunen-Loeve expansion, continuity, derivatives and integrals, amplitude modulation. Wiener and Kalman filters, and time reversed Markov chains. In Chapter 4, a section on the joint characteristic function has been added and the discussion of jointly Gaussian random variables has been expanded.

Section 5.5 discusses the various types of convergence of sequences of random variables. A carefully selected set of examples is presented to demonstrate the differences in the various types of convergence.

Section 6.6 uses these results to develop the notions of mean square continuity, derivatives, and integrals of random processes. This section presents the relations between the Wiener process and white Gaussian noise. It also develops the Ornstein-Uhlenbeck process as the transient solution to a first-order linear system driven by noise.

Section 6.8 uses Fourier series to introduce the notion of representing a random process by a linear combination of deterministic functions weighted by random variables. It then proceeds to develop the Karhunen-Loeve expansion for vector random variables and then random processes.

Section 7.4 now contains a separate section on prediction and the Levinson algorithm. Finally, Section 7.5 presents a discussion of the Kalman filter to complement the Wiener filter introduced in Section 7.4. Acknowledgments

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Probability Theory: A Comprehensive Course, Achim Klenke

Probability Theory: A Comprehensive Course PDF Download Ebook. Achim Klenke covers a wide variety of topics, many of which are not usually found in introductory textbooks. Aimed primarily at graduate students and researchers, this text is a comprehensive course in modern probability theory and its measure-theoretical foundations.

Probabilistic concepts play an increasingly important role in mathematics, physics, biology, financial engineering and computer science. They help us to understand magnetism, amorphous media, genetic diversity and the perils of random developments on the financial markets, and they guide us in constructing more efficient algorithms.

The topics in this book are not usually found in introductory textbooks, such as: limit theorems for sums of random variables; martingales; percolation; Markov chains and electrical networks; construction of stochastic processes; Poisson point processes and infinite divisibility; large deviation principles and statistical physics; Brownian motion; and stochastic integral and stochastic differential equations.

The theory is developed rigorously and in a self-contained way, with the chapters on measure theory interlaced with the probabilistic chapters in order to display the power of the abstract concepts in the world of probability theory. In addition, plenty of figures, computer simulations, biographic details of key mathematicians, and a wealth of examples support and enliven the presentation.

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A First Course in Probability 9th Edition, Sheldon Ross

A First Course in Probability 9th Edition PDF Download Ebook. Sheldon Ross offers clear and intuitive explanations of the mathematics of probability theory, outstanding problem sets, and a variety of diverse examples and applications.

The coverage includes Combinatorial Analysis; Axioms of Probability; Conditional Probability and Independence; Random Variables; Continuous Random Variables; Jointly Distributed Random Variables; Properties of Expectation; Limit Theorems; Additional Topics in Probability; Simulation. This book is ideal for an upper-level undergraduate or graduate level introduction to probability for math, science, engineering and business students. It assumes a background in elementary calculus.

Stream-lined exposition focuses on improved clarity and deeper understanding. New examples and exercises added throughout this edition pique students’ interest while building their understanding of probability. New Examples 3h and 4k, found in Chapter 3,engage students by discussing estimating the fraction of twin pairs that are identical and with analyzing serve and rally games.

Intuitive explanations are supported with an abundance of examples to give readers a thorough introduction to both the theory and applications of probability. Analysis is unique to the text and elegantly designed. Examples include the knockout tournament and multiple players gambling ruin problem, as well as the new results concerning the sum of uniform and the sum of geometric random variables.

Three sets of exercises are given at the end of each chapter. These include Problems, Theoretical Exercises, and Self-Test Problems and Exercises. The Self-Test Problems and Exercises include complete solutions in the appendix, allowing students to test their comprehension and study for exams.

Sheldon M. Ross is a professor in the Department of Industrial Engineering and Operations Research at the University of Southern California. He received his Ph.D. in statistics at Stanford University in 1968. He has published many technical articles and textbooks in the areas of statistics and applied probability. Among his texts are A First Course in Probability, Introduction to Probability Models, Stochastic Processes, and Introductory Statistics.

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Thursday, April 25, 2013

Probability Theory: The Logic of Science, E. T. Jaynes

Probability Theory: The Logic of Science PDF Download Ebook. E. T. Jaynes and G. Larry Bretthorst discuss new results, along with applications of probability theory to a variety of problems. Going beyond the conventional mathematics of probability theory, this study views the subject in a wider context.

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

This is a work written by a scientist for scientists. As such it is to be welcomed. The reader will certainly find things with which he disagrees, but he will also find much that will cause him to think deeply not only on his usual practice by also on statistics and probability in general. This is not an ordinary text. It is an unabashed, hard sell of the Bayesian approach to statistics.

It is wonderfully down to earth, with hundreds of telling examples. Everyone who is interested in the problems or applications of statistics should have a serious look. If you deal at all with probability theory, statistics, data analysis, pattern recognition, automated diagnosis, any forms of reasoning from inconclusive or uncertain information, you need to read this book. It will give you new perspectives on these problems.

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Probability and Statistics for Engineering and the Sciences 8e

Probability and Statistics for Engineering and the Sciences 8th Edition PDF Download Ebook. Jay L. Devore provides a comprehensive introduction to probability and statistics for engineering students in all specialties. Proven, accurate, and lauded for its excellent examples, this text evidences Jay Devore's reputation as an outstanding author and leader in the academic community.

Author emphasizes concepts, models, methodology, and applications as opposed to rigorous mathematical development and derivations. Aided by his lively and realistic examples, students go beyond simply learning about statistics; they also learn how to put statistical methods to use. More than 40 new examples and 100 new problems were carefully researched and written using the most up-to-date real data.

Chapter 1, "Overview and Descriptive Statistics," contains a new subsection, "The Scope of Modern Statistics," which describes and exemplifies how statistics is used in modern disciplines. A significantly revised and simplified Chapter 8, "Tests of Hypotheses Based on a Single Sample," also has a new subsection entitled "More on Interpreting P-values." Wherever possible throughout the book, the language has been tightened and simplified to improve clarity.

"Simulation Experiments" help students gain an understanding of sampling distributions and the insight they provide, especially when a derivation is too complex to carry out. Strong computer coverage, especially with ANOVA and regression, is supported by an abundance of computer output from SAS® and MINITAB® and coverage of computer methods. Inclusion of JavaTM Applets from Gary McClelland's Seeing Statistics, specifically designed for this calculus-based text, allows students to experience statistics firsthand.

Sample exams help students build confidence and master concepts prior to taking class exams; the glossary of symbols/acronyms, which includes text page references, is another useful study aid. Several exercises refer to material covered in earlier sections and chapters, allowing students to more easily see the connections between concepts. Virtually every example and exercise has a real-world context. Real data in exercises and examples stimulate students' interest and enhance their comprehension of concepts.

Notable content includes a strong emphasis on the role that variation plays in statistics, emphasis on the nature of variation in the slope estimate in simple linear regression, and inclusion of a detailed description of pooled t procedures to provide a balance between un-pooled and pooled analyses.

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Probability and Statistics 4th Edition, DeGroot and Schervish

Probability and Statistics 4th Edition PDF Download Ebook. Morris H. DeGroot and Mark J. Schervish offer balanced approach of the classical and Bayesian methods and now includes a chapter on simulation (including Markov chain Monte Carlo and the Bootstrap), coverage of residual analysis in linear models, and many examples using real data.

Calculus is assumed as a prerequisite, and a familiarity with the concepts and elementary properties of vectors and matrices is a plus. A new chapter on simulation has been added. This includes methods for simulating specific distributions, importance sampling, Markov chain Monte Carlo, and the bootstrap.

New sections or subsections on conditionally independent events and random variables, the log normal distribution, quantiles, prediction and prediction intervals, improper priors, Bayes tests, power functions, M-estimators, residual plots in linear models, and Bayesian analysis of simple linear regression are now included.

Brief introductions and summaries have been added to each technical section. The introductory paragraphs give readers a hint about what they are going to encounter. The summaries list the most important ideas. The author has added special notes where it is useful to briefly summarize or make a connection to a point made elsewhere in the text.

Some material has been reorganized. Independence is now introduced after conditional probability. The first five chapters of the text are devoted to probability and can serve as the text for a one-semester course on probability. In addition to examples using current data, some elementary concepts of probability are illustrated by famous examples such as the birthday problem, the tennis tournament problem, the matching problem, and the collector's problem.

Included as a special feature are sections on Markov chains, the Gambler's Ruin problem, and utility and preferences among gambles. These topics are treated in a completely elementary fashion, and can be omitted without loss of continuity if time is limited. Optional sections of the book are indicated by an asterisk in the Table of Contents.

Chapters 6 through 10 are devoted to statistical inference. Both classical and Bayesian statistical methods are developed in an integrated presentation which will be useful to students when applying the concepts to the real world.

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Wednesday, April 24, 2013

Topology, Geometry and Gauge fields: Foundations 2e

Topology, Geometry and Gauge fields: Foundations 2nd Edition PDF Download Ebook. Gregory L. Naber takes the view that the rekindled interest that mathematics and physics have shown in each other of late should be fostered, and that this is best accomplished by allowing them to cohabit. The book weaves together rudimentary notions from the classical gauge theory of physics with the topological and geometrical concepts that became the mathematical models of these notions.

The reader is asked to join the author on some vague notion of what an electromagnetic field might be, to be willing to accept a few of the more elementary pronouncements of quantum mechanics, and to have a solid background in real analysis and linear algebra and some of the vocabulary of modern algebra. In return, the book offers an excursion that begins with the definition of a topological space and finds its way eventually to the moduli space of anti-self-dual SU(2) connections on S4 with instanton number -1.

This is a book on topology and geometry, and like any book on subjects as vast as these, it has a point of view that guided the selection of topics. The author’s point of view is that the rekindled interest that mathematics and physics have shown in each other of late should be fostered, and that this is best accomplished by allowing them to cohabit.

The goal is to weave together rudimentary notions from the classical gauge theories of physics and the topological and geometrical concepts that became the mathematical models of these notions. The reader is assumed to have a minimal understanding of what an electromagnetic field is, a willingness to accept a few of the more elementary pronouncements of quantum mechanics, and a solid background in real analysis and linear algebra with some of the vocabulary of modern algebra.

To such a reader we offer an excursion that begins with the definition of a topological space and finds its way eventually to the moduli space of anti-self-dual SU(2)-connections on S4 with instanton number -1. It includes a new chapter on singular homology theory and a new appendix outlining Donaldson’s beautiful application of gauge theory to the topology of compact, simply connected , smooth 4-manifolds with definite intersection form.

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Essential Topology by Martin D. Crossley

Essential Topology PDF Download Ebook. Martin D. Crossley brings the most important aspects of modern topology within reach of a second-year undergraduate student. It successfully unites the most exciting aspects of modern topology with those that are most useful for research, leaving readers prepared and motivated for further study.

This book presents the most important aspects of modern topology, essential subjects of research in algebraic topology. The book contains all the key results of basic topology and the focus throughout on providing interesting examples that clarify the ideas and motivate the student. It contains enough material for two-semester courses and offers interesting material for undergraduate-level topology, motivating students for post-graduate study in the field and giving them a solid foundation.

This text provides a concise and well-focused introduction to point set and algebraic topology. The main purpose is to quickly move to relevant notions from algebraic topology (homotopy and homology). Throughout the book the author has taken great care to explain topological concepts by well-chosen examples. It is written in a clear and pleasant style and can certainly be recommended as a basis for an introductory course on the subject.

Written from a thoroughly modern perspective, every topic is introduced with an explanation of why it is being studied, and a huge number of examples provide further motivation. The book is ideal for self-study and assumes only a familiarity with the notion of continuity and basic algebra.

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Tuesday, April 23, 2013

Introduction to Topology: Pure and Applied, Colin Adams

Introduction to Topology: Pure and Applied PDF Download Ebook. Colin Adams and Robert Franzosa describe the basics of point-set topology with the understanding of its real-world application to a variety of other subjects including science, economics, engineering, and other areas of mathematics.

This book introduces topology as an important and fascinating mathematics discipline to retain the readers interest in the subject. Written in an accessible way for readers to understand the usefulness and importance of the application of topology to other fields, this book introduces topology concepts combined with their real-world application to subjects such DNA, heart stimulation, population modeling, cosmology, and computer graphics.

Author covers topics including knot theory, degree theory, dynamical systems and chaos, graph theory, metric spaces, connectedness, and compactness. It is useful reference for readers wanting an intuitive introduction to topology. Numerous figures allow students to visualize and understand the material presented.

The authors focus on the basic concepts of topology and their utility using real-world applications. Applications cover a wide variety of disciplines, including molecular biology, digital image processing, robotics, population dynamics, medicine, economics, synthetic chemistry, electronic circuit design, and cosmology.

Intuitive and accessibly written text, this book offers rigorous presentation of the mathematics with intuitive descriptions and discussions to increase student understand. Examples of real world application keep students engrossed in the material.

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Topology 2nd Edition by James Munkres

Topology 2nd Edition PDF Download Ebook. James Munkres provides separate, in-depth coverage of both general topology and algebraic topology with many examples and figures. This text is designed to provide instructors with a convenient single text resource for bridging between general and algebraic topology courses.

Two separate, distinct sections (one on general, point set topology, the other on algebraic topology) are each suitable for a one-semester course and are based around the same set of basic, core topics. Optional, independent topics and applications can be studied and developed in depth depending on course needs and preferences.

What follows is a wealth of applications-to the topology of the plane (including the Jordan curve theorem), to the classification of compact surfaces, and to the classification of covering spaces. A final chapter provides an application to group theory itself. This book follows the present-day trend in the teaching of topology which explores the subject much more extensively with one semester devoted to general topology and a second to algebraic topology.

Order of topics proceeds naturally from the familiar to the unfamiliar begins with the familiar set theory, moves on to a thorough and careful treatment of topological spaces, then explores connectedness and compactness (with their many ties to calculus and analysis), and then branches out to the new and different topics mentioned above.

Author carefully guides students through transitions to more advanced topics being careful not to overwhelm them. Each of the text's two parts is suitable for a one-semester course, giving instructors a convenient single text resource for bridging between the courses. The text can also be used where algebraic topology is studied only briefly at the end of a single-semester course.

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Monday, April 22, 2013

Geometry and Its Applications 2nd Edition, Walter Meyer

Geometry and Its Applications 2nd Edition PDF Download Ebook. Walter A. Meyer combines traditional geometry with current ideas to present a modern approach that is grounded in real-world applications. It balances the deductive approach with discovery learning, and introduces axiomatic, Euclidean geometry, non-Euclidean geometry, and transformational geometry.

The text integrates applications and examples throughout and includes historical notes in many chapters. It is a significant text for any college or university that focuses on geometry's usefulness in other disciplines. It is especially appropriate for engineering and science majors, as well as future mathematics teachers.

The author's emphasis on applications sets this proposed text apart from the standard ones. His examples make the point that geometry plays a vital role in the modern world. A unique blend of modern applications and theory is presented with excellent balance of mathematical rigor and informal style. CD-ROM (included) offers courseware for use with The Geometer's Sketchpad, polyhedra and planar maps.

This text offers balance between deductive geometry and coordinate geometry using vectors with over 700 exercises with complete solutions available. Real strengths of the text include the applications, the treatment of symmetry, and the attention to isometrics. The style is conversational and the approaches to problems are sensible. I appreciate the large number of problems. Walter Meyer is experienced in employing geometry as an industrial researcher and developer and has researched and taught geometry for nearly thirty years. The National Science Foundation, COMAP, and the Sloan Foundation have supported his work.

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Geometry, Topology and Physics 2nd Edition, Nakahara

Geometry, Topology and Physics 2nd Edition PDF Download Ebook. Mikio Nakahara describes considerably expanded first chapter, reviewing aspects of path integral quantization and gauge theories. Chapter 2 introduces the mathematical concepts of maps, vector spaces, and topology.

Differential geometry and topology have become essential tools for many theoretical physicists. In particular, they are indispensable in theoretical studies of condensed matter physics, gravity, and particle physics. This book introduces the ideas and techniques of differential geometry and topology at a level suitable for postgraduate students and researchers in these fields. It incorporates a number of changes designed to meet the needs of the reader and reflect the development of the subject.

The following chapters focus on more elaborate concepts in geometry and topology and discuss the application of these concepts to liquid crystals, superfluid helium, general relativity, and bosonic string theory. Later chapters unify geometry and topology, exploring fiber bundles, characteristic classes, and index theorems. New to this second edition is the proof of the index theorem in terms of supersymmetric quantum mechanics.

The final two chapters are devoted to the most fascinating applications of geometry and topology in contemporary physics, namely the study of anomalies in gauge field theories and the analysis of Polakov's bosonic string theory from the geometrical point of view. It is an ideal introduction to differential geometry and topology for postgraduate students and researchers in theoretical and mathematical physics.

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Perspectives on Projective Geometry by Richter-Gebert

Perspectives on Projective Geometry: A Guided Tour Through Real and Complex Geometry PDF Download Ebook. Jürgen Richter-Gebert offers a comprehensive introduction to this fascinating field and its applications. In particular, it explains how metric concepts may be best understood in projective terms.

The major theme that appears throughout this book is the beauty of the interplay between geometry, algebra and combinatorics. This book can especially be used as a guide that explains how geometric objects and operations may be most elegantly expressed in algebraic terms, making it a valuable resource for mathematicians, as well as for computer scientists and physicists.

Projective geometry is one of the most fundamental and at the same time most beautiful branches of geometry. It can be considered the common foundation of many other geometric disciplines like Euclidean geometry, hyperbolic and elliptic geometry or even relativistic space-time geometry. The book is based on the author’s experience in implementing geometric software and includes hundreds of high-quality illustrations.

The author covers most of the traditional topics in real projective geometry, and extends the concepts through complex projective geometry. He provides the reader with concise proofs, clear and insightful presentations, and a coherent development of the topic. Richter-Gebert presents algebraic, visual, and diagrammatic approaches to unify the subject, while his fresh writing style make for a very readable text. Additionally, the student and teacher will enjoy the quotations introducing each section.

The author describes his work as ‘a guided tour through real and complex geometry’, and these words explain perfectly the aim of the book. The prerequisites for reading the book are just the basics of linear algebra (in terms of coordinates), so that the book seems accessible to a wide audience ranging from mathematicians to computer scientists and physicists.

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Friday, April 19, 2013

Differential Geometry: Curves - Surfaces - Manifolds 2e

Differential Geometry: Curves - Surfaces – Manifolds 2nd Edition PDF Download Ebook. Wolfgang Kühnel describes all the topics which could be necessary later for learning higher level differential geometry. The material is very carefully sorted and easy-to-read.

It is extraordinarily welcome that this comprehensive textbook containing all the high points of differential geometry is now available in an English translation. Required reading for all mathematicians. Here we learn about line and surface integrals, divergence and curl, and the various forms of Stokes' Theorem. If we are fortunate, we may encounter curvature and such things as the Serret-Frenet formulas.

With just the basic tools from multivariable calculus, plus a little knowledge of linear algebra, it is possible to begin a much richer and rewarding study of differential geometry, which is what is presented in this book. It starts with an introduction to the classical differential geometry of curves and surfaces in Euclidean space, then leads to an introduction to the Riemannian geometry of more general manifolds, including a look at Einstein spaces.

An important bridge from the low-dimensional theory to the general case is provided by a chapter on the intrinsic geometry of surfaces. The first half of the book, covering the geometry of curves and surfaces, would be suitable for a one-semester undergraduate course. The local and global theories of curves and surfaces are presented, including detailed discussions of surfaces of rotation, ruled surfaces, and minimal surfaces.

The second half of the book, which could be used for a more advanced course, begins with an introduction to differentiable manifolds, Riemannian structures, and the curvature tensor. Two special topics are treated in detail: spaces of constant curvature and Einstein spaces. The main goal of the book is to get started in a fairly elementary way, then to guide the reader toward more sophisticated concepts and more advanced topics.

There are many examples and exercises to help along the way. Numerous figures help the reader visualize key concepts and examples, especially in lower dimensions. For the second edition, a number of errors were corrected and some text and a number of figures have been added.

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An Invitation to Algebraic Geometry by Karen E. Smith

An Invitation to Algebraic Geometry PDF Download Ebook. Karen E. Smith, Lauri Kahanpää, Pekka Kekäläinen and William Traves describe the underlying principles of algebraic geometry, some of its important developments in the twentieth century, and some of the problems that occupy its practitioners today.

It is intended for the working or the aspiring mathematician who is unfamiliar with algebraic geometry but wishes to gain an appreciation of its foundations and its goals with a minimum of prerequisites. Few algebraic prerequisites are presumed beyond a basic course in linear algebra. The author has some stunning graphs and pictures to help understand material. Long stretches of the book apply just as well over any field or any algebraically complete field.

This book sets aside a lot of the tedious background required to get started in algebraic geometry and lets you get acquainted with the actual ideas of the subject. The book does geometry over the complex numbers. It is good old conservative material, with terrific graphics of curves and surfaces. The proofs and partial proofs are very clear, intuitive and to the point.

Affine Algebraic Varieties.- Algebraic Foundations.- Projective Varieties.- Quasi-projective Varieties.- Classical Constructions.- Smoothness.- Birational Geometry.- Maps to Projective Space.- Appendix: Sheaves and Abstract Varieties.

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Algebraic Geometry by Robin Hartshorne Ebook

Algebraic Geometry PDF Download Ebook. Robin Hartshorne provides complete introduction to abstract algebraic geometry, with the only prerequisites being results from commutative algebra, which are stated as needed, and some elementary topology.

More than 400 exercises distributed throughout the book offer specific examples as well as more specialized topics not treated in the main text, while three appendices present brief accounts of some areas of current research. This book can thus be used as textbook for an introductory course in algebraic geometry following a basic graduate course in algebra.

Robin Hartshorne studied algebraic geometry with Oscar Zariski and David Mumford at Harvard, and with J.-P. Serre and A. Grothendieck in Paris. After receiving his Ph.D. from Princeton in 1963, Hartshorne became a Junior Fellow at Harvard, then taught there for several years. In 1972 he moved to California where he is now Professor at the University of California at Berkeley. He is the author of "Residues and Duality" (1966), "Foundations of Projective Geometry (1968), "Ample Subvarieties of Algebraic Varieties" (1970), and numerous research titles.

His current research interest is the geometry of projective varieties and vector bundles. He has been a visiting professor at the College de France and at Kyoto University, where he gave lectures in French and in Japanese, respectively. Professor Hartshorne is married to Edie Churchill, educator and psychotherapist, and has two sons. He has travelled widely, speaks several foreign languages, and is an experienced mountain climber. He is also an accomplished amateur musician: he has played the flute for many years, and during his last visit to Kyoto he began studying the shakuhachi.

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A Walk Through Combinatorics 3rd Edition, Miklos Bona

A Walk Through Combinatorics: An Introduction to Enumeration and Graph Theory 3rd Edition PDF Download Ebook. Miklos Bona encourages students to learn more combinatorics, every effort has been made to provide them with a not only useful, but also enjoyable and engaging reading. It is extremely lively yet mathematically accurate, and the writing is lucid and very entertaining at the same time.

This is a textbook for an introductory combinatorics course lasting one or two semesters. An extensive list of problems, ranging from routine exercises to research questions, is included. In each section, there are also exercises that contain material not explicitly discussed in the preceding text, so as to provide instructors with extra choices if they want to shift the emphasis of their course.

Just as with the first two editions, the new edition walks the reader through the classic parts of combinatorial enumeration and graph theory, while also discussing some recent progress in the area: on the one hand, providing material that will help students learn the basic techniques, and on the other hand, showing that some questions at the forefront of research are comprehensible and accessible to the talented and hardworking undergraduate.

The basic topics discussed are: the twelvefold way, cycles in permutations, the formula of inclusion and exclusion, the notion of graphs and trees, matchings, Eulerian and Hamiltonian cycles, and planar graphs.

The selected advanced topics are: Ramsey theory, pattern avoidance, the probabilistic method, partially ordered sets, the theory of designs (new to this edition), enumeration under group action (new to this edition), generating functions of labeled and unlabeled structures and algorithms and complexity.

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Introductory Combinatorics 5th Edition, Richard Brualdi

Introductory Combinatorics 5th Edition PDF Download Ebook. Richard A. Brualdi emphasizes combinatorial ideas, including the pigeon-hole principle, counting techniques, permutations and combinations, Polya counting, binomial coefficients, inclusion-exclusion principle, generating functions and recurrence relations, and combinatortial structures (matchings, designs, graphs).

Written to be entertaining and readable, this book's lively style reflects the author's joy for teaching the subject. It presents an excellent treatment of Polya's Counting Theorem that doesn't assume the student is familiar with group theory. It also includes problems that offer good practice of the principles it presents.

The book has been updated to include new material on partially ordered sets, Dilworth's Theorem, partitions of integers and generating functions. In addition, the chapters on graph theory have been completely revised. It is valuable book for any reader interested in learning more about combinatorics. It clarifies the exposition throughout and adds a wealth of new exercises, appropriate for one- or two-semester, junior- to senior-level combinatorics courses.

A clear and accessible presentation, written from the student's perspective, facilitates understanding of basic concepts and principles. An excellent treatment of Polya's Counting Theorem that does not assume students have studied group theory. Use of the term “combination” as it applies to a set has been de-emphasized; the author now uses the essentially equivalent term of “subset” for clarity.

A new section (Section 1.6) on mutually overlapping circles has been moved from Chapter 7 to illustrate some of the counting techniques covered in later chapters. Chapter 2 now contains a short section (Section 3.6) on finite probability. Chapter 3 now contains a proof of Ramsey’s theorem in the case of pairs as well as Pascal’s formula.

An extensively revised Chapter 7 moves up generating functions and exponential generating functions to Sections 7.2 and 7.3, giving them a more central treatment. Coverage of more topics of graph theory and digraphs and networks has been reversed. Chapter 12 now covers more topics of graph theory and Chapter 13 now covers digraphs and networks.

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Principles and Techniques in Combinatori Ebook

Principles and Techniques in Combinatori PDF Download Ebook. Chen Chuan-Chong and Koh Khee-Meng offer wide range of examples, about 500 combinatorial problems taken from various mathematical competitions and exercises. It is textbook suitable for undergraduate courses. The materials are presented very explicitly so that students will find it very easy to read.

Moreover, this book also discusses sequence creation using generating functions, something that Tucker leaves out. This book has solid introduction to combinatorics, explicitly detailing every step of every proof--something direly missing in most other texts of this type. Most people taking this class have only had a rudimentary sampling of proof techniques and this book helps fill in the missing gaps left in slightly higher-flyers such as Tucker's.

Author assumes you can do that already. His chapter on modeling is light on problems and doesn't explain the examples as clearly as this one does. This book also shows some incredibly creative problem solutions that crafty students have devised (being trainers) that help you think about other implications in things such as Pascal's triangle. It does a great job of improving mathematical thinking.

Contents include: Permutations and Combinations, Binomial Coefficients and Multinomial Coefficients, The Pigeonhole Principle and Ramsey Numbers, The Principle of Inclusion and Exclusion, Generating Functions and Recurrence Relations.

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Applied Combinatorics 6th Edition by Alan Tucker

Applied Combinatorics 6th Edition PDF Download Ebook. Alan Tucker offers in depth analysis of computer systems in order to help develop proficiency in basic discrete math problem solving. As one of the most widely used book in combinatorial problems, this edition explains how to reason and model combinatorically while stressing the systematic analysis of different possibilities, exploration of the logical structure of a problem, and ingenuity.

Although important uses of combinatorics in computer science, operations research, and finite probability are mentioned, these applications are often used solely for motivation. Numerical examples involving the same concepts use more interesting settings such as poker probabilities or logical games. This new sixth edition has new examples, expanded discussions, and additional exercises throughout the text.

The game of Mastermind that appeared at the beginning of the first edition has been brought back to this edition. New material is added including: chromatic polynomials, the transportation problem, and NP-completeness. The chapter on formal languages and finite-state machines from the second edition is back in abbreviated form.

A closing postlude about crytoanalysis has been added. A greater emphasis on underlying reasoning in combinatorial problem-solving has been stressed throughout the text. Theory is always first motivated by examples, and proofs are given only when their reasoning is needed to solve applied problems. Elsewhere, results are stated without proof, such as the form of solutions to various recurrence relations, and then applied in problem solving.

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Wednesday, April 17, 2013

Combinatorics and Graph Theory 2nd Edition, John Harris

Combinatorics and Graph Theory 2nd Edition PDF Download Ebook. John Harris, Jeffry L. Hirst and Michael Mossinghoff offer wide variety of topics in combinatorics and graph theory. It includes results and problems that cross subdisciplines, emphasizing relationships between different areas of mathematics.

In addition, recent results appear in the text, illustrating the fact that mathematics is a living discipline. The second edition includes many new topics and features new sections in graph theory on distance, Eulerian trails, and Hamiltonian paths. New material on partitions, multinomial coefficients, and the pigeonhole principle is presented with expanded coverage of Pólya Theory to include de Bruijn’s method for counting arrangements when a second symmetry group acts on the set of allowed colors.

There are topics in combinatorial geometry, including Erdos and Szekeres’ development of Ramsey Theory in a problem about convex polygons determined by sets of points. This book also offers expanded coverage of stable marriage problems, and new sections on marriage problems for infinite sets, both countable and uncountable with numerous new exercises throughout the book.

The narrative and proofs are well written, and the authors are given to frequent uses of humor. Students should find this book as easy to read as any other good-quality text written with them in mind. Each of the three chapters concludes with several paragraphs describing an excellent selection of more advanced texts or papers to consider for further study.

There is a short section on References in each chapter introducing briefly other books dealing with the topics covered in the respective chapter. A full list of 293 references, about 550 exercises and an index with 13 pages are also provided.

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Combinatorics Topics, Techniques, Algorithms by Peter Cameron

Combinatorics: Topics, Techniques, Algorithms PDF Download Ebook. Peter J. Cameron stresses common techniques (such as generating functions and recursive construction) that underlie the great variety of subject matter, and the fact that a constructive or algorithmic proof is more valuable than an existence proof.

The author emphasizes techniques as well as topics and includes many algorithms described in simple terms. The text should provide essential background for students in all parts of discrete mathematics. Combinatorics is a subject of increasing importance because of its links with computer science, statistics, and algebra.

This book gives number brief case studies. Its 18 chapters (not counting intro and closing) span a variety of interesting topics. Cameron doesn't write down to the reader - it takes serious thought and some mathematical background to get full value from the reading. The examples are nowhere near as concrete as you'd expect in a popularized version. Still, the author avoids opaque references to specialist terms, and keeps the text approachable.

The book is divided into two parts corresponding roughly to undergraduate material and graduate. The selection of topics is robust; the writing is clear and consise. The level is senior and above. The reader should have some knowledge of advanced math such as group theory, and analysis of algorithms.

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A Course in Combinatorics 2nd Edition, van Lint and Wilson

A Course in Combinatorics 2nd Edition PDF Download Ebook. J. H. van Lint and R. M. Wilson describe subject dealing with ways of arranging and distributing objects, and which involves ideas from geometry, algebra and analysis. There are also many applications, so workers in many scientific fields need some familiarity with the subject.

The extensive depth and breadth of the coverage make the book a unique guide to the whole of the subject, so that it is ideal for courses at the advanced undergraduate or beginning graduate level and also for working mathematicians and scientists. The authors have made the text as comprehensive as possible, dealing in a unified manner with such topics as graph theory, extremal problems, designs, colorings, and codes.

The depth and breadth of the coverage make the book a unique guide to the whole of the subject. It is ideal for courses on combinatorical mathematics at the advanced undergraduate or beginning graduate level, and working mathematicians and scientists will also find it a valuable introduction and reference.

The writing is very clear and there is a lot of explanation. Exercises are mixed in with the text, which I like very much; it makes them seem more natural, and it makes the book well-suited for self-study. I would say the difficulty level of this book is a bit inconsistent--but this is more a function of the material than of the writing style. The authors make everything as clear as possible, but they choose to include some difficult topics which require more thought.

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Tuesday, April 16, 2013

Real Analysis: Measure Theory, Integration and Hilbert Spaces

Real Analysis: Measure Theory, Integration, and Hilbert Spaces PDF Download Ebook. Elias M. Stein and Rami Shakarchi focus on the development of measure and integration theory, differentiation and integration, Hilbert spaces, and Hausdorff measure and fractals.

This book reflects the objective of the series as a whole: to make plain the organic unity that exists between the various parts of the subject, and to illustrate the wide applicability of ideas of analysis to other fields of mathematics and science.

After setting forth the basic facts of measure theory, Lebesgue integration, and differentiation on Euclidian spaces, the authors move to the elements of Hilbert space, via the L2 theory. They next present basic illustrations of these concepts from Fourier analysis, partial differential equations, and complex analysis.

The final part of the book introduces the reader to the fascinating subject of fractional-dimensional sets, including Hausdorff measure, self-replicating sets, space-filling curves, and Besicovitch sets. Each chapter has a series of exercises, from the relatively easy to the more complex, that are tied directly to the text. A substantial number of hints encourage the reader to take on even the more challenging exercises.

As with the other volumes in the series, this book is accessible to students interested in such diverse disciplines as mathematics, physics, engineering, and finance, at both the undergraduate and graduate levels. It is the third volume in the Princeton Lectures in Analysis, a series of four textbooks that aim to present, in an integrated manner, the core areas of analysis.

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Analysis of Financial Time Series 3rd Edition, Ruey S. Tsay

Analysis of Financial Time Series 3rd Edition PDF Download Ebook. Ruey S. Tsay provides a broad, mature, and systematic introduction to current financial econometric models and their applications to modeling and prediction of financial time series data. It utilizes real-world examples and real financial data throughout the book to apply the models and methods described.

The author begins with basic characteristics of financial time series data before covering three main topics: analysis and application of univariate financial time series, the return series of multiple assets and Bayesian inference in finance methods. Key features include additional coverage of modern day topics such as arbitrage, pair trading, realized volatility, and credit risk modeling; a smooth transition from S-Plus to R; and expanded empirical financial data sets.

This text utilizes the freely available R software package to explore empirical financial data and illustrate related computation and analyses using real-world examples. Retaining the fundamental and hands-on style of its predecessor, this new edition continues to serve as the cornerstone for understanding the important statistical methods and techniques for working with financial data.

The latest developments in financial econometrics are explored in-depth, such as realized volatility, volatility with skew innovations, conditional value at risk, statistical arbitrage, and applications of duration and dynamic-correlation models. The use of both R and S-PLUS software with the book's numerous examples and exercises ensures that readers can reproduce the results shown in the book and apply the detailed steps and procedures to their own work.

New and updated exercises throughout provide opportunities to test comprehension of the presented material, and a related Web site houses additional data sets and related software programs. The overall objective of the book is to provide some knowledge of financial time series, introduce some statistical tools useful for analyzing these series and gain experience in financial applications of various econometric methods.

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Elementary Analysis: The Theory of Calculus, Kenneth A. Ross

Elementary Analysis: The Theory of Calculus PDF Download Ebook. Kenneth A. Ross has tried to write in an informal but precise style, stressing motivation and methods of proof, and, in this reviewer’s opinion, has succeeded admirably.

Designed for students having no previous experience with rigorous proofs, this text can be used immediately after standard calculus courses. It is highly recommended for anyone planning to study advanced analysis, as well as for future secondary school teachers. A limited number of concepts involving the real line and functions on the real line are studied, while many abstract ideas, such as metric spaces and ordered systems, are avoided completely.

A thorough treatment of sequences of numbers is used as a basis for studying standard calculus topics, and optional sections invite students to study such topics as metric spaces and Riemann-Stieltjes integrals. This book occupies a niche between a calculus course and a full-blown real analysis course. I think the book should be viewed as a text for a bridge or transition course that happens to be about analysis.

This book is intended for the student who has a good, but naïve, understanding of elementary calculus and now wishes to gain a thorough understanding of a few basic concepts in analysis, such as continuity, convergence of sequences and series of numbers, and convergence of sequences and series of functions. There are many nontrivial examples and exercises, which illuminate and extend the material.

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