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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

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Using the R Commander A Point-and-Click Interface for R

This book provides a general introduction to the R Commander graphical user interface (GUI) to R for readers who are unfamiliar with R. It is suitable for use as a supplementary text in a basic or intermediate-level statistics course. It is not intended to replace a basic or other statistics text but rather to complement it although it does promote sound statistical practice in the examples. The book should also be useful to individual casual or occasional users of R for whom the standard command-line interface is an obstacle. tinyurl. com/RcmdrBookThe site includes data files used in the book and an errata list. http://socserv. mcmaster. ca/jfox/Books/RCommander/Writing-Rcmdr-Plugins. pdf Writing R Commander Plug-in Packages | Using the R Commander A Point-and-Click Interface for R

GBP 175.00

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Handbook of Discrete and Computational Geometry

The Handbook of Discrete and Computational Geometry is intended as a reference book fully accessible to nonspecialists as well as specialists covering all major aspects of both fields. The book offers the most important results and methods in discrete and computational geometry to those who use them in their work both in the academic world—as researchers in mathematics and computer science—and in the professional world—as practitioners in ﬁelds as diverse as operations research molecular biology and robotics. Discrete geometry has contributed signiﬁcantly to the growth of discrete mathematics in recent years. This has been fueled partly by the advent of powerful computers and by the recent explosion of activity in the relatively young ﬁeld of computational geometry. This synthesis between discrete and computational geometry lies at the heart of this Handbook. A growing list of application fields includes combinatorial optimization computer-aided design computer graphics crystallography data analysis error-correcting codes geographic information systems motion planning operations research pattern recognition robotics solid modeling and tomography.

GBP 240.00

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Start Programming Using HTML CSS and JavaScript

A Beginner‘s Guide to Computer Programming Start Programming Using HTML CSS and JavaScript is a manual for undergraduate students in engineering and the natural sciences to discover how computer programming works. Using a dialog format between two students and a professor the text teaches students how the mainstream web languages HTML CSS and JavaScript interact and how to harness their capabilities in practical settings. Each chapter focuses on a specific theme supported by a gradual development of engaging worked examples of live web documents and applications using the three languages. Students can follow most of the examples and experiments using any modern browser and plain text editor. A practical homework problem is included at the end of every chapter and then is discussed at the beginning of the next chapter. In addition a related keywords list helps students review key topics. By focusing on important established principles and concrete examples this introductory book shows students how to write cleaner and more easily maintainable code. It augments the basic language syntax and rules with contents and structure while keeping the material simple and manageable.

GBP 175.00

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An Advanced Course in Probability and Stochastic Processes

An Advanced Course in Probability and Stochastic Processes provides a modern and rigorous treatment of probability theory and stochastic processes at an upper undergraduate and graduate level. Starting with the foundations of measure theory this book introduces the key concepts of probability theory in an accessible way providing full proofs and extensive examples and illustrations. Fundamental stochastic processes such as Gaussian processes Poisson random measures Lévy processes Markov processes and Itô processes are presented and explored in considerable depth showcasing their many interconnections. Special attention is paid to martingales and the Wiener process and their central role in the treatment of stochastic integrals and stochastic calculus. This book includes many exercises designed to test and challenge the reader and expand their skillset. An Advanced Course in Probability and Stochastic Processes is meant for students and researchers who have a solid mathematical background and who have had prior exposure to elementary probability and stochastic processes. Key Features: Focus on mathematical understanding Rigorous and self-contained Accessible and comprehensive High-quality illustrations Includes essential simulation algorithms Extensive list of exercises and worked-out examples Elegant and consistent notation

GBP 89.99

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Sharpening Your Advanced SAS Skills

Sharpening Your Advanced SAS® Skills presents sophisticated SAS programming techniques procedures and tools such as Proc SQL hash tables and SAS Macro programming for any industry. Drawing on his more than 20 years’ experience of SAS programming in the pharmaceutical industry the author provides a unique approach that empowers both advanced programmers who need a quick refresher and programmers interested in learning new techniques. The book helps you easily search for key points by summarizing and differentiating the syntax between similar SAS statements and options. Each chapter begins with an overview so you can quickly locate the detailed examples and syntax. The basic syntax expected data and descriptions are organized in summary tables to facilitate better memory recall. General rules list common points about similar statements or options. Real-world examples of SAS programs and code statements are line numbered with references such as SAS papers and websites for more detailed explanations. The text also includes end-of-chapter questions to reinforce your knowledge of the topics and prepare you for the advanced SAS certification exam. In addition the author’s website offers mindmaps and process flowcharts that connect concepts and relationships. | Sharpening Your Advanced SAS Skills

GBP 59.99

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Smooth Homogeneous Structures in Operator Theory

Geometric ideas and techniques play an important role in operator theory and the theory of operator algebras. Smooth Homogeneous Structures in Operator Theory builds the background needed to understand this circle of ideas and reports on recent developments in this fruitful field of research. Requiring only a moderate familiarity with functional analysis and general topology the author begins with an introduction to infinite dimensional Lie theory with emphasis on the relationship between Lie groups and Lie algebras. A detailed examination of smooth homogeneous spaces follows. This study is illustrated by familiar examples from operator theory and develops methods that allow endowing such spaces with structures of complex manifolds. The final section of the book explores equivariant monotone operators and Kähler structures. It examines certain symmetry properties of abstract reproducing kernels and arrives at a very general version of the construction of restricted Grassmann manifolds from the theory of loop groups. The author provides complete arguments for nearly every result. An extensive list of references and bibliographic notes provide a clear picture of the applicability of geometric methods in functional analysis and the open questions presented throughout the text highlight interesting new research opportunities. Daniel Beltit is a Principal Researcher at the Institute of Mathematics Simion Stoilow of the Romanian Academy Bucharest Romania.

GBP 59.99

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Algebraic Number Theory and Fermat's Last Theorem

Updated to reflect current research Algebraic Number Theory and Fermat’s Last Theorem Fourth Edition introduces fundamental ideas of algebraic numbers and explores one of the most intriguing stories in the history of mathematics—the quest for a proof of Fermat’s Last Theorem. The authors use this celebrated theorem to motivate a general study of the theory of algebraic numbers from a relatively concrete point of view. Students will see how Wiles’s proof of Fermat’s Last Theorem opened many new areas for future work. New to the Fourth EditionProvides up-to-date information on unique prime factorization for real quadratic number fields especially Harper’s proof that Z(√14) is EuclideanPresents an important new result: Mihăilescu’s proof of the Catalan conjecture of 1844Revises and expands one chapter into two covering classical ideas about modular functions and highlighting the new ideas of Frey Wiles and others that led to the long-sought proof of Fermat’s Last TheoremImproves and updates the index figures bibliography further reading list and historical remarksWritten by preeminent mathematicians Ian Stewart and David Tall this text continues to teach students how to extend properties of natural numbers to more general number structures including algebraic number fields and their rings of algebraic integers. It also explains how basic notions from the theory of algebraic numbers can be used to solve problems in number theory. | Algebraic Number Theory and Fermat's Last Theorem

GBP 39.99

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A Primer on Wavelets and Their Scientific Applications

In the first edition of his seminal introduction to wavelets James S. Walker informed us that the potential applications for wavelets were virtually unlimited. Since that time thousands of published papers have proven him true while also necessitating the creation of a new edition of his bestselling primer. Updated and fully revised to include the latest developments this second edition of A Primer on Wavelets and Their Scientific Applications guides readers through the main ideas of wavelet analysis in order to develop a thorough appreciation of wavelet applications. Ingeniously relying on elementary algebra and just a smidgen of calculus Professor Walker demonstrates how the underlying ideas behind wavelet analysis can be applied to solve significant problems in audio and image processing as well in biology and medicine. Nearly twice as long as the original this new edition provides 104 worked examples and 222 exercises constituting a veritable book of review material Two sections on biorthogonal wavelets A mini-course on image compression including a tutorial on arithmetic compression Extensive material on image denoising featuring a rarely covered technique for removing isolated randomly positioned clutter Concise yet complete coverage of the fundamentals of time-frequency analysis showcasing its application to audio denoising and musical theory and synthesis An introduction to the multiresolution principle a new mathematical concept in musical theory Expanded suggestions for research projects An enhanced list of references

GBP 180.00

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Combinatorial Nullstellensatz With Applications to Graph Colouring

Combinatorial Nullstellensatz is a novel theorem in algebra introduced by Noga Alon to tackle combinatorial problems in diverse areas of mathematics. This book focuses on the applications of this theorem to graph colouring. A key step in the applications of Combinatorial Nullstellensatz is to show that the coefficient of a certain monomial in the expansion of a polynomial is nonzero. The major part of the book concentrates on three methods for calculating the coefficients: Alon-Tarsi orientation: The task is to show that a graph has an orientation with given maximum out-degree and for which the number of even Eulerian sub-digraphs is different from the number of odd Eulerian sub-digraphs. In particular this method is used to show that a graph whose edge set decomposes into a Hamilton cycle and vertex-disjoint triangles is 3-choosable and that every planar graph has a matching whose deletion results in a 4-choosable graph. Interpolation formula for the coefficient: This method is in particular used to show that toroidal grids of even order are 3-choosable r-edge colourable r-regular planar graphs are r-edge choosable and complete graphs of order p+1 where p is a prime are p-edge choosable. Coefficients as the permanents of matrices: This method is in particular used in the study of the list version of vertex-edge weighting and to show that every graph is (2 3)-choosable. It is suited as a reference book for a graduate course in mathematics. | Combinatorial Nullstellensatz With Applications to Graph Colouring

GBP 52.99

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Differential Geometry of Curves and Surfaces

Through two previous editions the third edition of this popular and intriguing text takes both an analytical/theoretical approach and a visual/intuitive approach to the local and global properties of curves and surfaces. Requiring only multivariable calculus and linear algebra it develops students’ geometric intuition through interactive graphics applets. Applets are presented in Maple workbook format which readers can access using the free Maple Player. The book explains the reasons for various definitions while the interactive applets offer motivation for definitions allowing students to explore examples further and give a visual explanation of complicated theorems. The ability to change parametric curves and parametrized surfaces in an applet lets students probe the concepts far beyond what static text permits. Investigative project ideas promote student research. At users of the previous editions' request this third edition offers a broader list of exercises. More elementary exercises are added and some challenging problems are moved later in exercise sets to assure more graduated progress. The authors also add hints to motivate students grappling with the more difficult exercises. This student-friendly and readable approach offers additional examples well-placed to assist student comprehension. In the presentation of the Gauss-Bonnet Theorem the authors provide more intuition and stepping-stones to help students grasp phenomena behind it. Also the concept of a homeomorphism is new to students even though it is a key theoretical component of the definition of a regular surface. Providing more examples show students how to prove certain functions are homeomorphisms. | Differential Geometry of Curves and Surfaces

GBP 56.99

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Introduction to Real Analysis

This classic textbook has been used successfully by instructors and students for nearly three decades. This timely new edition offers minimal yet notable changes while retaining all the elements presentation and accessible exposition of previous editions. A list of updates is found in the Preface to this edition. This text is based on the author’s experience in teaching graduate courses and the minimal requirements for successful graduate study. The text is understandable to the typical student enrolled in the course taking into consideration the variations in abilities background and motivation. Chapters one through six have been written to be accessible to the average student w hile at the same time challenging the more talented student through the exercises. Chapters seven through ten assume the students have achieved some level of expertise in the subject. In these chapters the theorems examples and exercises require greater sophistication and mathematical maturity for full understanding. In addition to the standard topics the text includes topics that are not always included in comparable texts. Chapter 6 contains a section on the Riemann-Stieltjes integral and a proof of Lebesgue’s t heorem providing necessary and sufficient conditions for Riemann integrability. Chapter 7 also includes a section on square summable sequences and a brief introduction to normed linear spaces. C hapter 8 contains a proof of the Weierstrass approximation theorem using the method of aapproximate identities. The inclusion of Fourier series in the text allows the student to gain some exposure to this important subject. The final chapter includes a detailed treatment of Lebesgue measure and the Lebesgue integral using inner and outer measure. The exercises at the end of each section reinforce the concepts. Notes provide historical comments or discuss additional topics. | Introduction to Real Analysis

GBP 46.99

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Financial Mathematics Two Volume Set

This textbook provides complete coverage of discrete-time financial models that form the cornerstones of financial derivative pricing theory. Unlike similar texts in the field this one presents multiple problem-solving approaches linking related comprehensive techniques for pricing different types of financial derivatives. Key features: In-depth coverage of discrete-time theory and methodology. Numerous fully worked out examples and exercises in every chapter. Mathematically rigorous and consistent yet bridging various basic and more advanced concepts. Judicious balance of financial theory mathematical and computational methods. Guide to Material. This revision contains: Almost 200 pages worth of new material in all chapters. A new chapter on elementary probability theory. An expanded the set of solved problems and additional exercises. Answers to all exercises. This book is a comprehensive self-contained and unified treatment of the main theory and application of mathematical methods behind modern-day financial mathematics. Table of Contents List of Figures and Tables Preface I Introduction to Pricing and Management of Financial Securities 1 Mathematics of Compounding 2 Primer on Pricing Risky Securities 3 Portfolio Management 4 Primer on Derivative Securities II Discrete-Time Modelling 5 Single-Period Arrow–Debreu Models 6 Introduction to Discrete-Time Stochastic Calculus 7 Replication and Pricing in the Binomial Tree Model 8 General Multi-Asset Multi-Period Model Appendices A Elementary Probability Theory B Glossary of Symbols and Abbreviations C Answers and Hints to Exercises References Index Biographies Giuseppe Campolieti is Professor of Mathematics at Wilfrid Laurier University in Waterloo Canada. He has been Natural Sciences and Engineering Research Council postdoctoral research fellow and university research fellow at the University of Toronto. In 1998 he joined the Masters in Mathematical Finance as an instructor and later as an adjunct professor in financial mathematics until 2002. Dr. Campolieti also founded a financial software and consulting company in 1998. He joined Laurier in 2002 as Associate Professor of Mathematics and as SHARCNET Chair in Financial Mathematics. Roman N. Makarov is Associate Professor and Chair of Mathematics at Wilfrid Laurier University. Prior to joining Laurier in 2003 he was an Assistant Professor of Mathematics at Siberian State University of Telecommunications and Informatics and a senior research fellow at the Laboratory of Monte Carlo Methods at the Institute of Computational Mathematics and Mathematical Geophysics in Novosibirsk Russia. | Financial Mathematics Two Volume Set

GBP 130.00

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