Mathematics Books

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Book Synopsis

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Book Synopsis

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Book Synopsis

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Book SynopsisExam Board: OCRLevel: A-levelSubject: MathematicsFirst Teaching: September 2017First Exam: June 2018An OCR endorsed textbook Grow your students'' confidence in applying mathematical techniques to solving problems with resources developed specifically for the OCR specification subject experts and in conjunction with MEI (Mathematics in Education and Industry).- Develop reasoning and problem-solving skills with practice questions and differentiated exercises that build mathematical techniques.- Help students to overcome misconceptions and develop insight into problem-solving with annotated worked examples.- Build connections between topics with points of interest and things to notice such as links to real world examples and noticing patterns in the mathematics.- Enhance individual understanding with discussion points designed for the classroom.- Consolidate understanding with en

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Book SynopsisWhat is Big Data, and why should you care?Big data knows where you''ve been and who your friends are. It knows what you like and what makes you angry. It can predict what you''ll buy, where you''ll be the victim of crime and when you''ll have a heart attack. Big data knows you better than you know yourself, or so it claims.But how well do you know big data?You''ve probably seen the phrase in newspaper headlines, at work in a marketing meeting, or on a fitness-tracking gadget. But can you understand it without being a Silicon Valley nerd who writes computer programs for fun?Yes. Yes, you can.Timandra Harkness writes comedy, not computer code. The only programmes she makes are on the radio. If you can read a newspaper you can read this book.Starting with the basics what IS data? And what makes it big? Timandra takes you on a whirlwind tour of how people are using big data today: from science to smart cities, business to politics, self-quantification to the Internet of ThiTrade ReviewA superb explanation of how we got to today. * Evening Standard *Harkness has the perfect combination of wit, charm and statistical insight to crunch big data. It's the book about stats, life and big data we've all been waiting for. -- Matt Parker, Stand-up MathematicianHarkness raises some very big questions indeed, not just about the grandiose claims of the big data evangelists, but also about how in the age of universal surveillance we can defend the concept of privacy. * The Herald *A wonderful collection of fascinating data stories, all told in Timandra's smart and chatty style. But this book also asks the important questions. If big data brings new opportunities, just what are the implications? -- Hannah Fry, author and mathematicianA brilliant guide to our brave new world. -- Brian CleggThis book is a great read – full of interesting stories and fun interviews. But it is not just another credulous tale of technological wonders – Harkness is suitably sceptical of the hype about data analytics, and serious about the challenges is brings. -- David Spiegelhalter, author and mathematicianTable of ContentsIntroduction: What is it? Where did it come from? 1: What Is Data? And what makes it big? 2: Death and Taxes. And Babies. 3: Thinking Machines What Has Big Data Done For Us? 4: Big Business 5: Big Science 6: Big Society 7: Data Driven Democracy Big Ideas? 8: Big Brother 9: Who Do We Think You Are? 10: Are You A Data Point Or A Human Being? Appendix - things you can do to keep your data private Acknowledgements

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Book SynopsisFoundations of Analysis covers the basics of real analysis for a one- or two-semester course. In a straightforward and concise way, it helps students understand the key ideas and apply the theorems. The bookâs accessible approach will appeal to a wide range of students and instructors.Each section begins with a boxed introduction that familiarizes students with the upcoming topics and sets the stage for the work to be done. Each section ends with several questions that ask students to review what they have just learned. The text is also scattered with notes pointing out places where different pieces of terminology seem to conflict with each other or where different ideas appear not to fit together properly. In addition, many remarks throughout help put the material in perspective.As with any real analysis text, exercises are powerful and effective learning tools. This book is no exception. Each chapter generally contains at least 50 exercises that builTrade Review"… there is a good set of exercises in each section … . If real analysis is to be dealt with in a one-semester course, this book appears to provide a reasonable text for the course."—Mathematical Reviews, April 2015Table of ContentsNumber Systems. Sequences. Series of Numbers. Basic Topology. Limits and Continuity of Functions. Differentiation of Functions. The Integral. Sequences and Series of Functions. Elementary Transcendental Functions. Appendices. Table of Notation. Glossary. Bibliography. Index.

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Book SynopsisActuarial Models: The Mathematics of Insurance, Second Edition thoroughly covers the basic models of insurance processes. It also presents the mathematical frameworks and methods used in actuarial modeling. This second edition provides an even smoother, more robust account of the main ideas and models, preparing students to take exams of the Society of Actuaries (SOA) and the Casualty Actuarial Society (CAS).New to the Second Edition Revises all chapters, especially material on the surplus process Takes into account new results and current trends in teaching actuarial modeling Presents a new chapter on pension models Includes new problems from the 2011-2013 CAS examinations Like its best-selling, widely adopted predecessor, this edition is designed for students, actuaries, mathematicians, and researchers interested in insurance processes and economic and social models. The authTable of ContentsPreliminary Facts from Probability and Interest. Comparison of Random Variables. Preferences of Individuals. An Individual Risk Model for a Short Period. A Collective Risk Model for a Short Period. Random Processes and Their Applications I. Random Processes and Their Applications II. Global Characteristics of the Surplus Process. Survival Distributions. Life Insurance Models. Annuity Models. Premiums and Reserves. Pensions Plans. Risk Exchange: Reinsurance and Coinsurance. Appendix. References. Answers to Exercises. Index.

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Book SynopsisA Classroom-Tested, Alternative Approach to Teaching Math for Liberal Arts Puzzles, Paradoxes, and Problem Solving: An Introduction to Mathematical Thinking uses puzzles and paradoxes to introduce basic principles of mathematical thought. The text is designed for students in liberal arts mathematics courses. Decision-making situations that progress from recreational problems to important contemporary applications develop the critical-thinking skills of non-science and non-technical majors. The logical underpinnings of this textbook were developed and refined throughout many years of classroom feedback and in response to commentary from presentations at national conferences. The text's five units focus on graphs, logic, probability, voting, and cryptography. The authors also cover related areas, such as operations research, game theory, number theory, combinatorics, statistics, and circuit design. The text uses a core set oTrade Review"… an interesting approach to the world of mathematics. … The layout is good, as is the coverage. … The reinforcing exercises are excellent. Using logic and other techniques, the text lays out methods to help students learn to think in a mathematical manner. Summing up: Recommended. General readers, lower- and upper-division undergraduates."—M. D. Sanford, Felician College, Lodi, New Jersey, USA for CHOICE, November 2015Table of ContentsGraphs: Puzzles and Optimization. Logic: Rational Inference and Computer Circuits. Probability: Predictions and Expectations. Counting: Voting Methods and Apportionment. Numbers: Cryptosystems and Security. Appendices. Index.

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Book SynopsisDesigned for a one-semester course at the junior undergraduate level, Transformational Plane Geometry takes a hands-on, interactive approach to teaching plane geometry. The book is self-contained, defining basic concepts from linear and abstract algebra gradually as needed.The text adheres to the National Council of Teachers of Mathematics Principles and Standards for School Mathematics and the Common Core State Standards Initiative Standards for Mathematical Practice. Future teachers will acquire the skills needed to effectively apply these standards in their classrooms. Following Felix Klein's Erlangen Program, the book provides students in pure mathematics and students in teacher training programs with a concrete visual alternative to Euclid's purely axiomatic approach to plane geometry. It enables geometrical visualization in three ways: Key concepts are motivated with explorTrade Review"This book is designed for a one-semester course at the junior undergraduate level and turns especially to future educators in the USA. … The arrangement and clarity of the text meet the most demanding pedagogical and mathematical requirements. Highlights of the book are the classification of isometries and similarities of the Euclidean plane. … a wonderful first step into transformational plane geometry …"—Zentralblatt MATH 1311 Table of ContentsAxioms of Euclidean Plane Geometry. Theorems of Euclidean Plane Geometry. Introduction to Transformations, Isometries, and Similarities. Translations, Rotations, and Reflections. Compositions of Translations, Rotations, and Reflections. Classification of Isometries. Symmetry of Plane Figures. Similarity. Appendix. Bibliography. Index.

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Book SynopsisAnalyze Global Nonlinear Problems Using MetasolutionsMetasolutions of Parabolic Equations in Population Dynamics explores the dynamics of a generalized prototype of semilinear parabolic logistic problem. Highlighting the author's advanced work in the field, it covers the latest developments in the theory of nonlinear parabolic problems.The book reveals how to mathematically determine if a species maintains, dwindles, or increases under certain circumstances. It explains how to predict the time evolution of species inhabiting regions governed by either logistic growth or exponential growth. The book studies the possibility that the species grows according to the Malthus law while it simultaneously inherits a limited growth in other regions.The first part of the book introduces large solutions and metasolutions in the context of population dynamics. In a self-contained way, tTable of ContentsExistence of Large Solutions and Metasolutions. Dynamics. Uniqueness of the Large Solution. Metasolutions Do Arise Everywhere. Bibliography. Index.

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Book SynopsisSet Theoretical Aspects of Real Analysis is built around a number of questions in real analysis and classical measure theory, which are of a set theoretic flavor. Accessible to graduate students, and researchers the beginning of the book presents introductory topics on real analysis and Lebesgue measure theory. These topics highlight the boundary between fundamental concepts of measurability and nonmeasurability for point sets and functions. The remainder of the book deals with more specialized material on set theoretical real analysis. The book focuses on certain logical and set theoretical aspects of real analysis. It is expected that the first eleven chapters can be used in a course on Lebesque measure theory that highlights the fundamental concepts of measurability and non-measurability for point sets and functions. Provided in the book are problems of varying difficulty that range from simple observations to advanced results. Relatively difficult Table of ContentsZF theory and some point sets on the real line. Countable versions of AC and real analysis. Uncountable versions of AC and Lebesgue nonmeasurable sets. The Continuum Hypothesis and Lebesgue nonmeasurable sets. Measurability properties of sets and functions. Radon measures and nonmeasurable sets. Real-valued step functions with strange measurability properties. Relationships between certain classical constructions of Lebesgue nonmeasurable sets. Measurability properties of Vitali sets. A relationship between the measurability and continuity of real-valued functions. A relationship between absolutely nonmeasurable functions and Sierpinski-Zygmund functions. Sums of absolutely nonmeasurable injective functions. A large group of absolutely nonmeasurable additive functions. Additive properties of certain classes of pathological functions. Absolutely nonmeasurable homomorphisms of commutative groups. Measurable and nonmeasurable sets with homogeneous sections. A combinatorial problem on translation invariant extensions of the Lebesgue measure. Countable almost invariant partitions of G-spaces. Nonmeasurable unions of measure zero sections of plane sets. Measurability properties of well-orderings. Appendices. Bibliography. Subject Index.

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Book SynopsisSince the start of modern computing, the studies of living organisms have inspired the progress in developing computers and intelligent machines. In particular, the methods of search and foraging are the benchmark problems for robotics and multi-agent systems. The highly developed theory of search and screening involves optimal search plans that are obtained by standard optimization techniques while the foraging theory addresses search plans that mimic the behavior of living foragers.Search and Foraging: Individual Motion and Swarm Dynamics examines how to program artificial search agents so that they demonstrate the same behavior as predicted by the foraging theory for living organisms. For cybernetics, this approach yields techniques that enable the best online search planning in varying environments. For biology, it allows reasonable insights regarding the internal activity of living organisms performing foraging tasks.The book discusses foraTrade Review"The book is valuable reading both for teaching inspiration as well as for research insights into optimization, modeling, mathematical biology, and robot programming."—Zentralblatt MATH 1327Table of ContentsIntroduction. Methods of Optimal Search and Screening. Methods of Optimal Foraging. Models of Individual Search and Foraging. Coalitional Search and Swarm Dynamics. Remarks on Swarm Robotic Systems for Search and Foraging. Conclusion. Bibliography. Index.

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Book SynopsisLike its popular predecessors, A First Course in Abstract Algebra: Rings, Groups, and Fields, Third Edition develops ring theory first by drawing on studentsâ familiarity with integers and polynomials. This unique approach motivates students in the study of abstract algebra and helps them understand the power of abstraction. The authors introduce groups later on using examples of symmetries of figures in the plane and space as well as permutations.New to the Third Edition Makes it easier to teach unique factorization as an optional topic Reorganizes the core material on rings, integral domains, and fields Includes a more detailed treatment of permutations Introduces more topics in group theory, including new chapters on Sylow theorems Provides many new exercises on Galois theory The text includes straightforward exercises within each chapter for students to quickly verify facts, waTrade Review"I am a fan of the rings-first approach to algebra, agreeing with the authors that students’ familiarity with the integers and with polynomials renders rings more intuitive and accessible than groups. But this book has many other virtues besides presenting the material in this order. For example, each section is preceded and followed by short sections that try to put the material into a broader context. … This is definitely a book worth considering for textbook adoption."—MAA Reviews, November 2014Praise for the Second Edition:"I was quickly won over by the book … . The book is very complete, containing more than enough material for a two semester course in undergraduate abstract algebra … . Even though there was a great deal of material presented, I found the book to be very well organized. … There are a lot of things that I like about this book. … [It is] well written and will help students to see the big picture. … All in all it seems that a lot of thought went into this book, resulting in a comprehensive, well-written, readable book for undergraduates first learning abstract algebra."—MAA Online"A remarkable feature of the book is that it starts first with the concept of a ring, while groups are introduced later. The reason of that is that students are usually more familiar with various number domains rather than the mappings and matrices. There is a huge number of examples in the book … . The book contains a lot of nice exercises of various degrees of difficulty so that it can also be used as a practice book."—EMS Newsletter, March 2006Table of ContentsNumbers, Polynomials, and Factoring. Rings, Domains, and Fields. Ring Homomorphisms and Ideals. Groups. Group Homomorphisms. Topics from Group Theory. Unique Factorization. Constructibility Problems. Vector Spaces and Field Extensions. Galois Theory. Hints and Solutions. Guide to Notation. Index.

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Book SynopsisEquivalence: Elizabeth L. Scott at Berkeley is the compelling story of one pioneering statistician's relentless twenty-year effort to promote the status of women in academe and science. Part biography and part microhistory, the book provides the context and background to understand Scott's masterfulness at using statistics to help solve societal problems. In addition to being one of the first researchers to work at the interface of astronomy and statistics and an early practitioner of statistics using high-speed computers, Scott worked on an impressively broad range of questions in science, from whether cloud seeding actually works to whether ozone depletion causes skin cancer. Later in her career, Scott became swept up in the academic women's movement. She used her well-developed scientific research skills together with the advocacy skills she had honed, in such activities as raising funds for Martin Luther King Jr. and keeping Free Speech Movement students outTrade Review "This book is an amazing tour de force." ~ Juliet Shaffer, University of California-Berkeley"What an intriguing life Scott led!" ~ Deborah Bennett, Lawrence Livermore National Laboratory, Ret. "The details of what was done when in response to situations are revealing and instructive. We should all have access to her story." ~ Brian Yandell, University of Wisconsin"The way in which Scott was able to continue her research while simultaneously serving the University system through her gender discrimination work is exemplary and should be inspirational to the academic women of today. Women are still recognised as being under-represented at higher levels of academia, particularly in science, even though it is now 50 years after Scott commenced her investigations! Men and women who are interested in the history of statistics and in the history of gender equity in universities will want to own this book. There is inspiration to be gained and lessons to be learnt by those who still face gender inequity in academia today." ~ Alice Richardson, ANU College of Medicine, Canberra"Equivalence tells the captivating story of statistician Elizabeth L. Scott, who was a trail blazer for all women in academia, and especially in statistics . . . During her entire time in the Statistics Department, she overlapped with only four other women . . . It is a story of the love, passion, and commitment exhibited by Betty throughout her personal and professional life. It also illustrates the love, passion, and commitment of the author (statistician Amanda Golbeck) for telling Betty’s story. . . Reading Equivalence was an eye-opening experience for me. Having received my PhD in Statistics in 1978, the book helped me place my academic career in a larger context. It felt somewhat like I had boarded a train part way through a treacherous journey, and only slowly came to realize the hardships the passengers had faced before reaching my embarkation point. It brought back memories of some of my early experiences . . ." ~ Jessica Utts, American Statistician"This book is an amazing tour de force." ~ Juliet Shaffer, University of California-Berkeley"What an intriguing life Scott led!" ~ Deborah Bennett, Lawrence Livermore National Laboratory, Ret. "The details of what was done when in response to situations are revealing and instructive. We should all have access to her story." ~ Brian Yandell, University of Wisconsin"The way in which Scott was able to continue her research while simultaneously serving the University system through her gender discrimination work is exemplary and should be inspirational to the academic women of today. Women are still recognised as being under-represented at higher levels of academia, particularly in science, even though it is now 50 years after Scott commenced her investigations! Men and women who are interested in the history of statistics and in the history of gender equity in universities will want to own this book. There is inspiration to be gained and lessons to be learnt by those who still face gender inequity in academia today." ~ Alice Richardson, ANU College of Medicine, Canberra"Equivalence tells the captivating story of statistician Elizabeth L. Scott, who was a trail blazer for all women in academia, and especially in statistics . . . During her entire time in the Statistics Department, she overlapped with only four other women . . . It is a story of the love, passion, and commitment exhibited by Betty throughout her personal and professional life. It also illustrates the love, passion, and commitment of the author (statistician Amanda Golbeck) for telling Betty’s story. . . Reading Equivalence was an eye-opening experience for me. Having received my PhD in Statistics in 1978, the book helped me place my academic career in a larger context. It felt somewhat like I had boarded a train part way through a treacherous journey, and only slowly came to realize the hardships the passengers had faced before reaching my embarkation point. It brought back memories of some of my early experiences . . ." ~ Jessica Utts, American StatisticianTable of ContentsIntroduction. Framing the local research questions (1968). West Point and the field artillery family (ancestry I). Collecting, managing, and summarizing the local data (1969). Aunt Phoebe the astronomer (ancestry II). Reporting the local data (1970). Becoming an outlier. Using the local data for advocacy (1971). 10,000 hours of professional practice. Regressing national data (1972). The UC - Berkeley department of statistics. Focusing on salary data (1973). With Jerzy Neyman. Advocating for data quality improvement (1974). Loyalty oath, civil rights, free speech. Using statistical reasoning toward affirmative action (1975). Productivity as a statistical scientist. Creating the salary evaluation kit (1976). Influencing academic salaries (1977). Continuing efforts to further the careers of academic women (1978 - 1981). After Neyman. (1982 - 1988).

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Book SynopsisThis book deals with certain aspects of material science, particularly with the release of thermal energy associated with bond breaking. It clearly establishes the connection between heat transfer rates and product quality. The editors then sharply draw the thermal distinctions between the various categories of welding processes, and demonstrate how these distinctions are translated into simulation model uniqueness. The book discusses the incorporation of radiative heat transfer processes into the simulation model.Table of ContentsPrefaceEditorsContributorsChapter 1 Heat Exchangers and Their Fan/Blower Partners Modeled as a Single Interacting System by Numerical SimulationE. M. Sparrow, J. M. Gorman, J. P. Abraham, and W. J. MinkowyczChapter 2 On Computational Heat Transfer Procedures for Heat Exchangers in Single-Phase Flow OperationBengt SundénChapter 3 Utilization of Numerical Methods and Experiments for the Design and Tests of Gasketed Plate Heat ExchangersSelin Aradag, Sadik Kakac, and Ece ÖzkayaChapter 4 Numerical Methods for Micro Heat ExchangersBengt Sundén, Zan Wu, and Mohammad FaghriChapter 5 Review of Advances in Heat Pipe Analysis and Numerical SimulationAmir Faghri and Theodore L. BergmanIndex

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Book SynopsisBlow-up for Higher-Order Parabolic, Hyperbolic, Dispersion and Schrödinger Equations shows how four types of higher-order nonlinear evolution partial differential equations (PDEs) have many commonalities through their special quasilinear degenerate representations. The authors present a unified approach to deal with these quasilinear PDEs.The book first studies the particular self-similar singularity solutions (patterns) of the equations. This approach allows four different classes of nonlinear PDEs to be treated simultaneously to establish their striking common features. The book describes many properties of the equations and examines traditional questions of existence/nonexistence, uniqueness/nonuniqueness, global asymptotics, regularizations, shock-wave theory, and various blow-up singularities.Preparing readers for more advanced mathematical PDE analysis, the book demonstrates that quasilinear degenerate higher-order PDEs, even exoticTrade Review"This volume gives a collection of results on self-similar singular solutions for nonlinear partial differential equations (PDEs), with special emphasis on ‘exotic’ equations of higher order …"—Zentralblatt MATH 1320Table of ContentsIntroduction. Complicated Self-Similar Blow-Up, Compacton, and Standing Wave Patterns for Four Nonlinear PDEs: A Unified Variational Approach to Elliptic Equations. Classification of Global Sign-Changing Solutions of Semilinear Heat Equations in the Subcritical Fujita Range: Second- and Higher-Order Diffusion. Global and Blow-Up Solutions for Kuramoto–Sivashinsky, Navier–Stokes, and Burnett Equations. Regional, Single-Point, and Global Blow-Up for a Fourth-Order Porous Medium-Type Equation with Source. Semilinear Fourth-Order Hyperbolic Equation: Two Types of Blow-Up Patterns. Quasilinear Fourth-Order Hyperbolic Boussinesq Equation: Shock, Rarefaction, and Fundamental Solutions. Blow-Up and Global Solutions for Korteweg–de Vries-Type Equations. Higher-Order Nonlinear Dispersion PDEs: Shock, Rarefaction, and Blow-Up Waves. Higher-Order Schrödinger Equations: From "Blow-Up" Zero Structures to Quasilinear Operators. References.

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Book SynopsisThe Essentials of a First Linear Algebra Course and MoreLinear Algebra, Geometry and Transformation provides students with a solid geometric grasp of linear transformations. It stresses the linear case of the inverse function and rank theorems and gives a careful geometric treatment of the spectral theorem.An Engaging Treatment of the Interplay among Algebra, Geometry, and MappingsThe text starts with basic questions about images and pre-images of mappings, injectivity, surjectivity, and distortion. In the process of answering these questions in the linear setting, the book covers all the standard topics for a first course on linear algebra, including linear systems, vector geometry, matrix algebra, subspaces, independence, dimension, orthogonality, eigenvectors, and diagonalization. A Smooth Transition to the Conceptual Realm of Higher MathematicsThis book guides students on a journey from Trade Review"All the standard topics of a first course are covered, but the treatment omits abstract vector spaces. … What is unusual is the author's aim to interpret every concept and result geometrically, thus motivating the student to learn to visualize what is going on, rather than just relying on calculations. This is a strong and useful feature. … The book has very many practice sections with over 500 exercises, most of them numerical. … As the author mentions in the preface, it was his aim to provide a sound mathematical introduction, and in the reviewer's opinion he has succeeded in doing this."—Zentralblatt MATH 1314Table of ContentsVectors, Mappings, and Linearity. Solving Linear Systems. Linear Geometry. The Algebra of Matrices. Subspaces. Orthogonality. Linear Transformation. Appendices. Index.

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Book SynopsisThe Discrete.- Integers.- Natural Numbers and Induction.- Some Points of Logic.- Recursion.- Underlying Notions in Set Theory.- Equivalence Relations and Modular Arithmetic.- Arithmetic in Base Ten.- The Continuous.- Real Numbers.- Embedding Z in R.- Limits and Other Consequences of Completeness.- Rational and Irrational Numbers.- Decimal Expansions.- Cardinality.- Final Remarks.- Further Topics.- Continuity and Uniform Continuity.- Public-Key Cryptography.- Complex Numbers.- Groups and Graphs.- Generating Functions.- Cardinal Number and Ordinal Number.- Remarks on Euclidean Geometry.Trade ReviewFrom the reviews:"The Art of Proof is a surprising union of rigor with taste and wit. The authors take a hard-core axiomatic approach, but the writing is never dry. Instead, topics are carefully chosen and meticulously developed with grace and humor, careful attention to detail, and just the right number of skill-building exercises and thought-provoking problems."The text is spare—well under two hundred pages—but contains a thorough axiomatic development of the integers and the reals, along with non-standard optional topics such as Cayley graphs and generating functions. Instead of the standard scattershot "symbolic logic-set theory-functions-proof by contradiction-zzzz..." books, this text keeps its focus on just a few fundamental ideas, of which induction is the most important. This helps my students to feel that they are participants in a grand undertaking—the construction of a number system—rather than passive victims of one proof technique after another." —Paul Zeitz (Mathematics Professor at the University of San Francisco)“This qualitative transition presents a most acute pedagogical challenge. … This book does feature definite mathematical content, contrasting with works that aim at decoupling purely logical apparatus from strictly mathematical concerns. … The authors write with the authority of research mathematicians and clearly mean to open that avenue to students. Summing Up: Recommended. Upper-division undergraduates through professionals.” (D. V. Feldman, Choice, Vol. 48 (8), April, 2011)“This book offers an approach well-balanced between rigor and clarifying simplification. Dilbert and Foxtrot cartoons with philosophical quotes presage the introduction of axioms and preliminary propositions. This graceful and witty blend succeeds well in a textbook for a post-calculus course transitioning a student to higher mathematics. The Art of Proof can also well serve independent readers looking for a solitary path to a vista on higher mathematics.” (Tom Schulte, The Mathematical Association of America, November, 2010)“This is an undergraduate text to extend, in a deeper and formal way, the usual initial knowledge of mathematics. The book deals with classical topics like integers, induction, algorithms, real numbers, rational numbers, modular arithmetic, limits, uncountable sets … . The publication may be useful for people using the book to teach a course on the above mentioned topics. … The aim behind this textbook is teaching how to read and write mathematics as well as understanding key methods and concepts.” (Claudi Alsina, Zentralblatt MATH, Vol. 1198, 2010)Table of ContentsPreface.- Notes for the Student.- Notes for Instructors.- Part I: The Discrete.- 1 Integers.- 2 Natural Numbers and Induction.- 3 Some Points of Logic.- 4 Recursion.- 5 Underlying Notions in Set Theory.- 6 Equivalence Relations and Modular Arithmetic.- 7 Arithmetic in Base Ten.- Part II: The Continuous.- 8 Real Numbers.- 9 Embedding Z in R.- 10. Limits and Other Consequences of Completeness.- 11 Rational and Irrational Numbers.- 12 Decimal Expansions.- 13 Cardinality.- 14 Final Remarks.- Further Topics.- A Continuity and Uniform Continuity.- B Public-Key Cryptography.- C Complex Numbers.- D Groups and Graphs.- E Generating Functions.- F Cardinal Number and Ordinal Number.- G Remarks on Euclidean Geometry.- List of Symbols.- Index.

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Trade ReviewFrom the book reviews:“This text has resulted from the author’s teaching of introductory statistics to engineering students in the USA. Dealing both with the theoretical aspects of statistical methods and the need to implement software that engineers are familiar with, the book is a delight to read. … I recommend the book to any one intending to use either MATLAB or/and WinBUGS for statistical modelling and analysis.” (Carl M. O’Brien, International Statistical Review, Vol. 81 (3), 2014)“Although there are many engineering statistics books, this is the first one I have seen devoted to bioengineering. It is a very comprehensive book with many good features. … I would say that Statistics for Bioengineering Sciences would make a wonderful text for a first course in statistics for biomedical engineering students and is a great reference for engineers and statisticians.” (Michael R. Chernick, Technometrics, Vol. 55 (1), February, 2013)Table of ContentsIntroduction.- The Sample and Its Properties.- Probability, Conditional Probability, and Bayes' Rule.- Sensitivity, Specificity, and Relatives.- Random Variables.- Normal Distribution.- Point and Interval Estimators.- Bayesian Approach to Inference.- Testing Statistical Hypotheses.- Two Samples.- ANOVA and Elements of Experimental Design.- Distribution-Free Tests.- Goodness-of-Fit Tests.- Models for Tables.- Correlation.- Regression.- Regression for Binary and Count Data.- Inference for Censored Data and Survival Analysis.- Bayesian Inference Using Gibbs Sampling - BUGS Project.

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Book SynopsisThe Multiphase Flow Handbook, Second Edition is a thoroughly updated and reorganized revision of the late Clayton Crowe's work, and provides a detailed look at the basic concepts and the wide range of applications in this important area of thermal/fluids engineering. Revised by the new editors, Efstathios E. (Stathis) Michaelides and John D. Schwarzkopf, the new Second Edition begins with two chapters covering fundamental concepts and methods that pertain to all the types and applications of multiphase flow. The remaining chapters cover the applications and engineering systems that are relevant to all the types of multiphase flow and heat transfer. The twenty-one chapters and several sections of the book include the basic science as well as the contemporary engineering and technological applications of multiphase flow in a comprehensive way that is easy to follow and be understood. The editors created a common set of nomenclature that is used throughout the book, allowing reaTrade Review"The second edition of the Multiphase Flow Handbook represents a comprehensive and thorough treatment of the field of multiphase fluid mechanics – from fundamentals to applications – written by top experts in the field. It is an indispensable resource for student and researcher alike."— Michael L. Calvisi, University of Colorado Colorado Springs, USATable of ContentsFundamentals of Multiphase Flow. Computational Methods. Gas-Liquid Flow in Ducts. Fluid-Solid Flow in Ducts. Compressible Multiphase Flow. Combustion with Particles and Drops. Microgravity Two-Phase Flow. Boiling. Condensation. Powder and Granular Flow. Multiphase Flow in Porous Media. Turbulence Interactions. Bubble Dynamics and Cavitation. Aggregation, Collisions and Break-up. Particle Separation Methods and Systems. Biological Systems and Bio-mimetics. Fluidized Bed Reactors. Nanofluids. Sprays. Aerosols. Dispersed Flow in Non-Newtonian Fluids.

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Book SynopsisWinner of the 2017 De Groot Prize awarded by the International Society for Bayesian Analysis (ISBA)A relatively new area of research, adversarial risk analysis (ARA) informs decision making when there are intelligent opponents and uncertain outcomes. Adversarial Risk Analysis develops methods for allocating defensive or offensive resources against intelligent adversaries. Many examples throughout illustrate the application of the ARA approach to a variety of games and strategic situations.Focuses on the recent subfield of decision analysis, ARA Compares ideas from decision theory and game theoryUses multi-agent influence diagrams (MAIDs) throughout to help readers visualize complex information structuresApplies the ARA approach to simultaneous games, auctions, sequential games, and defend-attack gamesContains an extended case study based on a real application in railway security, whichTrade Review"This well-written and concise text is an introduction to the field of adversarial risk analysis (ARA), which is a form of decision and risk analysis which incorporates uncertainty and game theory to model strategies of an adversary…There is an appropriate amount of detail throughout the book, making it suitable for a reference text as well as a book which may be read cover to cover and it is both thought provoking and enlightening."—Matthew Craven, Plymouth University, Journal of the Royal Statistical Society, Series A, January 2017 "Here, Banks (Duke Univ.), Rios (IBM), and Insua (ICMAT-CSIC, Spain) identify three categories of uncertainty for the strategist: aleatory uncertainty—nondeterminism of outcomes even after players make choices; epistemic uncertainty—hidden information concerning opponents' preferences, beliefs, and capabilities; and concept uncertainty—hidden information concerning opponents' strategies. Adversarial risk analysis, a new field with roots in modern efforts to defeat terrorism, provides a framework, in principle, to cope with these uncertainties. Solving the models seems generally intractable, but the heart of the book, the first of its kind, offers exemplary case studies. Summing up: Recommended. Lower-division undergraduates and above; informed general audiences."—D. V. Feldman, University of New Hampshire, Durham, USA, for CHOICE, March 2016 Table of ContentsGames and Decisions. Simultaneous Games. Auctions. Sequential Games. Variations on Sequential Defend-Attack Games. A Security Case Study. Other Issues. Solutions to Selected Exercises. References. Index.

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Book SynopsisThis book provides engineers and scientists with a single source introduction to the concepts, models, and case studies for making credible reliability assessments. It satisfies the need for thorough discussions of several fundamental subjects.Section I contains a comprehensive overview of assessing and assuring reliability that is followed by discussions of: Concept of randomness and its relationship to chaos Uses and limitations of the binomial and Poisson distributions Relationship of the chi-square method and Poisson curves Derivations and applications of the exponential, Weibull, and lognormal models Examination of the human mortality bathtub curve as a template for componentsSection II introduces the case study modeling of failure data and is followed by analyses of: 5 sets of ideal Weibull, lognormal, and normal failure data 83 sets of actual (real) failure data The intent of the modeling was Table of ContentsSelected Topics. Overview of Reliability Assessments. Concept of Random. Probability & Sampling. Reliability Functions. Reliability Model: Exponential. Reliability Models: Weibull & Lognormal. Bathtub Curves for Humans & Components. Introduction & Case Studies. Introduction to Case Study Modeling of Failure Data.

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Book SynopsisThis book focuses on process simulation in chemical engineering with a numerical algorithm based on the moving finite element method (MFEM). It offers new tools and approaches for modeling and simulating time-dependent problems with moving fronts and with moving boundaries described by time-dependent convection-reaction-diffusion partial differential equations in one or two-dimensional space domains. It provides a comprehensive account of the development of the moving finite element method, describing and analyzing the theoretical and practical aspects of the MFEM for models in 1D, 1D+1d, and 2D space domains. Mathematical models are universal, and the book reviews successful applications of MFEM to solve engineering problems. It covers a broad range of application algorithm to engineering problems, namely on separation and reaction processes presenting and discussing relevant numerical applications of the moving finite element method derived from real-world process simulations.Table of Contents1. Modeling and Simulation in Chemical Engineering. 2. The Moving Finite Elements Method. 3. Solving 1D Time-Dependent Models. 4. Solving 2D Time-Dependent Problems. 5. Solving Two Scales 1D+1d Time-Dependent Problems. 6. Solving Moving Boundary Problems. 7. Looking Ahead. 8. Index

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Book SynopsisPrepare Your Students for Statistical Work in the Real WorldStatistics for Engineering and the Sciences, Sixth Edition is designed for a two-semester introductory course on statistics for students majoring in engineering or any of the physical sciences. This popular text continues to teach students the basic concepts of data description and statistical inference as well as the statistical methods necessary for real-world applications. Students will understand how to collect and analyze data and think critically about the results.New to the Sixth Edition Many new and updated exercises based on contemporary engineering and scientific-related studies and real data More statistical software printouts and corresponding instructions for use that reflect the latest versions of the SAS, SPSS, and MINITAB software Introduction of the case studies at the beginning of each chapter Streamlined materiTrade Review"A salient feature of this book is the clarity with which many statistical concepts have been presented. A very nice blend of theory and applications. It contains a wealth of illustrative examples and problem sets. All the important concepts have been highlighted; real-life data has been extensively used throughout the book. Students will find it very appealing and useful on their way to learning the basic statistical concepts and tools."—Dharam V. Chopra, Wichita State University "I like the problems because they are all based on engineering applications of probability and statistics. I especially like the problems at the end of chapters because students have to think more to solve them. I favor problems that require calculations because engineers are problem solvers." —Charles H. Reilly, University of Central Florida "I think this text is one of the best I have seen when it comes down to real data sets. The authors successfully included small and large real data sets from various real-world problems in engineering, mathematical sciences, and natural sciences."—Edward J. Danial, Morgan State University Table of ContentsIntroduction. Descriptive Statistics. Probability. Discrete Random Variables. Continuous Random Variables. Bivariate Probability Distributions and Sampling Distributions. Estimation Using Confidence Intervals. Tests of Hypotheses. Categorical Data Analysis. Simple Linear Regression. Multiple Regression Analysis. Model Building. Principles of Experimental Design. The Analysis of Variance for Designed Experiments. Nonparametric Statistics. Statistical Process and Quality Control. Product and System Reliability.

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Book SynopsisDynamical Biostatistical Models presents statistical models and methods for the analysis of longitudinal data. The book focuses on models for analyzing repeated measures of quantitative and qualitative variables and events history, including survival and multistate models. Most of the advanced methods, such as multistate and joint models, can be applied using SAS or R software.The book describes advanced regression models that include the time dimension, such as mixed-effect models, survival models, multistate models, and joint models for repeated measures and time-to-event data. It also explores the possibility of unifying these models through a stochastic process point of view and introduces the dynamic approach to causal inference.Drawing on much of their own extensive research, the authors use three main examples throughout the text to illustrate epidemiological questions and methodological issues. Readers will see how each method is Trade Review"The properties of this book may be summarized in two words: rich and concise. . . this is a very well-written book that manages to cover a lot of ground in a remarkably succinct way. . . I can highly recommend the book."—Per Kragh Andersen, International Society for Clinical Biostatistics"I think that those whose research is or will be in the area of dynamical biostatistics would benefit from having a copy on their shelves."—Alice M. Richardson, Faculty of Education, Science, Technology and Mathematics, University of Canberra, Australia"This book aims at describing methods of biostatistics modeling, in particular, dynamical model approaches for statisticians, as well as serving as a textbook for postgraduate students... The balance between theory and application is appropriate for both researchers performing biostatistics modeling and for students taking graduate level courses… The book is concisely written so that it covers a wide range of basic and dynamic models and modeling approaches with examples. Statisticians in the industry may feel a large part of the book too technical but can use the book for reference and may also benefit from the rich examples and R-codes, some with translation to SAS, in the appendix." —Pharmaceutical Statistics"One of my favorite features of this book is that the same three examples are used throughout, and all the approaches discussed are applied to these examples. This allows readers to identify the similarities and differences of various techniques. Furthermore, it is a good way for readers to learn so-called data mining since diverse information can be mined by applying different statistical methods to the same dataset . . . I believe this book will be a successful text for graduate level courses focusing on dynamical biostatistical models that analyze time-dependent data. Its presentation of conventional methods is very effective."~Hongjian Zhu, Table of ContentsIntroduction. Classical Biostatistical Models: Inference. Survival Analysis. Models for Longitudinal Data. Advanced Biostatistical Models: Extensions of Mixed Models. Advanced Survival Models. Multistate Models. Joint Models for Longitudinal and Time-to-Event Data. The Dynamic Approach to Causality. Appendix: Software. Index.

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Book SynopsisUncover the Useful Interactions of Fixed Point Theory with Topological StructuresNonlinear Functional Analysis in Banach Spaces and Banach Algebras: Fixed Point Theory under Weak Topology for Nonlinear Operators and Block Operator Matrices with Applications is the first book to tackle the topological fixed point theory for block operator matrices with nonlinear entries in Banach spaces and Banach algebras. The book provides researchers and graduate students with a unified survey of the fundamental principles of fixed point theory in Banach spaces and algebras. The authors present several extensions of Schauder's and Krasnosel'skii's fixed point theorems to the class of weakly compact operators acting on Banach spaces and algebras, particularly on spaces satisfying the DunfordPettis property. They also address under which conditions a 2×2 block operator matrix with single- and multi-valued nonlinear entries will have a fixed point.Table of ContentsFixed Point Theory: Fundamentals. Fixed Point Theory under Weak Topology. Fixed Point Theory in Banach Algebras. Fixed Point Theory for BOM on Banach Spaces and Banach Algebras. Applications in Mathematical Physics and Biology: Existence of Solutions for Transport Equations. Exsistence of Solutions for Nonlinear Integral Equations. Two-Dimensional Boundary Value Problems.

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Book SynopsisDifferential Equations: Theory, Technique, and Practice with Boundary Value Problems presents classical ideas and cutting-edge techniques for a contemporary, undergraduate-level, one- or two-semester course on ordinary differential equations. Authored by a widely respected researcher and teacher, the text covers standard topics such as partial differential equations (PDEs), boundary value problems, numerical methods, and dynamical systems. Lively historical notes and mathematical nuggets of information enrich the reading experience by offering perspective on the lives of significant contributors to the discipline. Anatomy of an Application sections highlight applications from engineering, physics, and applied science. Problems for review and discovery provide students with open-ended material for further exploration and learning. Streamlined for the interests of engineers, this version:Includes new coverage of Sturm-Liouville theory and problemsTrade ReviewPraise for Differential Equations: Theory, Technique, and Practice, Second Edition "Krantz is a very prolific writer. He … creates excellent examples and problem sets."—Albert Boggess, Professor and Director of the School of Mathematics and Statistical Sciences, Arizona State University, Tempe, USA A first course in differential equations lends itself to the introduction of many interesting applications of mathematics. In this well-written text, Krantz (mathematics, Washington Univ. in St. Louis) emphasizes the differential equations needed to succeed as an engineer. This work is similar to Krantz and Simmons’s Differential Equations: Theory, Technique, and Practice (2007), yet the current work adds the necessary exposure to Sturm-Liouville problems and boundary value problems for the intended engineering audience. This enables the reader access to the all-important introduction to the partial differential equations; namely, the heat and wave equations, as well as the Dirichlet problem. This text has two features that differentiate it from all others on the market at this level: the sections entitled, “Anatomy of an Application” and “Problems for Review and Discovery.” The former analyzes a particular application, while the latter introduces open-ended material for further student exploration. These features will serve students well in their pursuit of garnishing the applied fruits of the subject. This text sets a new standard for the modern undergraduate course in differential equations.--J. T. Zerger, Catawba College Table of ContentsWhat Is a Differential Equation? Second-Order Linear Equations. Power Series Solutions and Special Functions. Numerical Methods. Fourier Series: Basic Concepts. Sturm–Liouville Problems and Boundary Value Problems. Partial Differential Equations and Boundary Value Problems. Laplace Transforms. Systems of First-Order Equations. The Nonlinear Theory. Appendix: Review of Linear Algebra.

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Book SynopsisThis book focuses on the role of modeling in the design of alloys and intermetallic compounds. It includes an introduction to the most important and most used modeling techniques, such as CALPHAD and ab-initio methods, as well as a section devoted to the latest developments in applications of alloys. The book emphasizes the correlation between modeling and technological developments while discussing topics such as wettability of Ultra High Temperature Ceramics by metals, active brazing of diamonds to metals in cutting tools, surface issues in medicine, novel Fe-based superconductors, metallic glasses, high entropy alloys, and thermoelectric materials.Table of ContentsModeling Techniques and Prediction of Properties. Computational Thermodynamics: From Experiments to Applications. Thermophysical Properties of Metallic Alloys from Ab Initio Methods and Applications to Thermodynamic Modeling. The Formation Volume in Rare Earth Intermetallic Systems: A Representation by Means of Atomic Physical Quantities. Role of Modeling on the Design of Alloys and Intermetallic Compounds. Metal-Ceramic Interactions in Brazing Ultra High Temperature Diboride Ceramics. Metal Surfaces in Medicine: Current Knowledge of Properties, Modeling and Biological Response. Fe-based Superconductors: Crystallochemistry, Band Structure and Phase Diagrams. Electronic and Magnetic Properties of Highly Disordered Fe-based Frank Kasper-Phases in View of First Principles Calculation and Experimental Study. Atomistic Modeling to Design Favored Compositions for the Metallic Glass Formation. Shape Memory Alloys: Constitutive Modeling and Engineering Simulations. Prediction of the Thermoelectric Properties of Half-Heusler Phases from the Density Functional Theory. Skutterudites for Thermoelectric Applications: Properties, Synthesis and Modeling.

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Book SynopsisUnderstand the Strategic Behavior in Queueing SystemsRational Queueing provides one of the first unified accounts of the dynamic aspects involved in the strategic behavior in queues. It explores the performance of queueing systems where multiple agents, such as customers, servers, and central managers, all act but often in a noncooperative manner.The book first addresses observable queues and models that assume state-dependent behavior. It then discusses other types of information in queueing systems and compares observable and unobservable variations and incentives for information disclosure. The next several chapters present relevant models for the maximization of individual utilities, social welfare, and profits. After covering queueing networks, from simple parallel servers to general network structures, the author describes models for planned vacations and forced vacations (such as breakdowns). Focusing on supply chaiTrade Review"This unique bibliographical volume by a foremost researcher in the area of strategic queues, or game theoretical analysis of queueing systems, provides a complete panorama of the extensive literature that was published in this area in recent years, spanning the period since the by-now classical monograph of Hassin and Haviv (2003) up to the present day. With over 700 references, individual papers are typically summarized in a paragraph or two, highlighting their essential contribution. The surveyed articles are arranged within a thoughtful subject classification, which makes it easy to focus on topics of interest, while the chronological ordering within each subject clearly displays the progression of ideas and results. Anyone who works in the area of strategic queues should have this book handy on his or her bookshelf. A newcomer may first study the above-mentioned monograph and come back to the present book to fully realize the state of the art."- Nahum Shimkin, Professor of Electrical Engineering, Technion"Rational Queueing provides a comprehensive and authoritative survey of recent research on strategic behavior in queueing systems. Focusing on advances in the field since the publication of the classic To Queue or Not to Queue, the author brings the reader up to date by summarizing and organizing over 700 papers from multiple disciplines in a unifying framework. This book will serve as an indispensable reference for researchers, students, and teachers in this area."- Philipp Afèche, Associate Professor of Operations Management, Rotman School of Management, University of Toronto"Rational Queueing is the book that defines and summarizes the important area of operations research that combines queueing with game theory. This is a must-have reference for anyone that is interested in game-theoretic considerations in queueing models. It will be immensely useful as an introduction for beginners and as a reference for mature researchers in the area. Professor Hassin has done a superb job. The book can be used for independent study, but also as the main source for graduate seminars on production, service, and operations management."- Antonis Economou, Department of Mathematics, University of Athens"This really is a must read for researchers in game theory, from those just starting out in this field through to more established researchers. It is also a valuable teaching resource, covering both undergraduate topics through to a comprehensive and state-of-the-art review of modern trends in the subject for postgraduate students."- Paul Harper, Professor of Operational Research and Deputy Head of School of Mathematics, Cardiff University"With the gross domestic product (GDP) in the service sector accounting for over 90 percent of the whole GDP in many countries and areas such as the United States and Hong Kong, service management is becoming increasingly important. Different from a manufacturing system, a service system has direct contact with customers, a feature that has inspired an increasing trend on studying service management with strategic customers. This book provides a timely and inclusive summary of studies on strategic customer behavior and games among service providers in recent years. I was amazed by two main features of the book. One, the number of papers surveyed is enormous. With over 700 papers surveyed, the book covers a wide range of topics on games among customers and games among service providers. In particular, it surveys those cutting-edge topics in the field such as bounded-rationality and loss-aversion customer behavior. Two, the reviews on papers are extremely accurate. I heard from many researchers that the author of the book, Prof. Refael Hassin, contacted them individually, asking for feedback on the review of their work. I was also requested to provide comments on my work during the writing of this book. These steps assure the high quality of the book. This book can serve as an excellent reference book for researchers and graduate students in the fields of operations management, operations research, industry engineering, civil engineering, and computer science. This is a must-have book and is greatly helpful and handy for researchers in fields involving strategic customers."- Dr. Pengfei Guo, Associate Professor and Associate Head, Department of Logistics and Maritime Studies, The Hong Kong Polytechnic University"In this book, the author gives an extensive survey on queueing systems in which the agents interact to maximize certain goals. The book is a follow-up of a book on strategic queueing co-authored by the author and M. Haviv [To queue or not to queue: equilibrium behavior in queueing systems, Internat. Ser. Oper. Res. Management Sci., 59, Kluwer Acad. Publ., Boston, MA, 2003; MR2006433]. [..] This book is excellent reading for any researcher interested in the state of the art of rational queueing. It provides an overview on recent work combining queueing systems and game theory."- Judith Timmer, Mathematical Reviews, January 2017"This unique bibliographical volume by a foremost researcher in the area of strategic queues, or game theoretical analysis of queueing systems, provides a complete panorama of the extensive literature that was published in this area in recent years, spanning the period since the by-now classical monograph of Hassin and Haviv (2003) up to the present day. With over 700 references, individual papers are typically summarized in a paragraph or two, highlighting their essential contribution. The surveyed articles are arranged within a thoughtful subject classification, which makes it easy to focus on topics of interest, while the chronological ordering within each subject clearly displays the progression of ideas and results. Anyone who works in the area of strategic queues should have this book handy on his or her bookshelf. A newcomer may first study the above-mentioned monograph and come back to the present book to fully realize the state of the art."- Nahum Shimkin, Professor of Electrical Engineering, Technion"Rational Queueing provides a comprehensive and authoritative survey of recent research on strategic behavior in queueing systems. Focusing on advances in the field since the publication of the classic To Queue or Not to Queue, the author brings the reader up to date by summarizing and organizing over 700 papers from multiple disciplines in a unifying framework. This book will serve as an indispensable reference for researchers, students, and teachers in this area."- Philipp Afèche, Associate Professor of Operations Management, Rotman School of Management, University of Toronto"Rational Queueing is the book that defines and summarizes the important area of operations research that combines queueing with game theory. This is a must-have reference for anyone that is interested in game-theoretic considerations in queueing models. It will be immensely useful as an introduction for beginners and as a reference for mature researchers in the area. Professor Hassin has done a superb job. The book can be used for independent study, but also as the main source for graduate seminars on production, service, and operations management."- Antonis Economou, Department of Mathematics, University of Athens"This really is a must read for researchers in game theory, from those just starting out in this field through to more established researchers. It is also a valuable teaching resource, covering both undergraduate topics through to a comprehensive and state-of-the-art review of modern trends in the subject for postgraduate students."- Paul Harper, Professor of Operational Research and Deputy Head of School of Mathematics, Cardiff University"With the gross domestic product (GDP) in the service sector accounting for over 90 percent of the whole GDP in many countries and areas such as the United States and Hong Kong, service management is becoming increasingly important. Different from a manufacturing system, a service system has direct contact with customers, a feature that has inspired an increasing trend on studying service management with strategic customers. This book provides a timely and inclusive summary of studies on strategic customer behavior and games among service providers in recent years. I was amazed by two main features of the book. One, the number of papers surveyed is enormous. With over 700 papers surveyed, the book covers a wide range of topics on games among customers and games among service providers. In particular, it surveys those cutting-edge topics in the field such as bounded-rationality and loss-aversion customer behavior. Two, the reviews on papers are extremely accurate. I heard from many researchers that the author of the book, Prof. Refael Hassin, contacted them individually, asking for feedback on the review of their work. I was also requested to provide comments on my work during the writing of this book. These steps assure the high quality of the book. This book can serve as an excellent reference book for researchers and graduate students in the fields of operations management, operations research, industry engineering, civil engineering, and computer science. This is a must-have book and is greatly helpful and handy for researchers in fields involving strategic customers."- Dr. Pengfei Guo, Associate Professor and Associate Head, Department of Logistics and Maritime Studies, The Hong Kong Polytechnic University"The book summarizes a big amount of actual results concerning the combination of queueing theory and game theory. It indicates the results of over 700 papers appearing in the bibliography in this area and very accurately refers their contents reecting the most actual achievements in a wide range of topics on games among customers and service providers. It can highly be recommended to researchers, teachers and students working in this area, even one can say it is an indispensable handbook for them."- L□aszl□o Lakatos (Budapest)"In this book, the author gives an extensive survey on queueing systems in which the agents interact to maximize certain goals. The book is a follow-up of a book on strategic queueing co-authored by the author and M. Haviv [To queue or not to queue: equilibrium behavior in queueing systems, Internat. Ser. Oper. Res. Management Sci., 59, Kluwer Acad. Publ., Boston, MA, 2003; MR2006433]. [..] This book is excellent reading for any researcher interested in the state of the art of rational queueing. It provides an overview on recent work combining queueing systems and game theory."- Judith Timmer, Mathematical Reviews, January 2017Table of ContentsIntroduction. Observable queues. Information. Customer decisions. Social optimization and cooperation. Monopoly. Competition. Routing in queueing networks. Supply chains, outsourcing, and contracting. Vacations. Bounded rationality. Bibliography. Indices.

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Book SynopsisFilling a gap in the literature, Delay Differential Evolutions Subjected to Nonlocal Initial Conditions reveals important results on ordinary differential equations (ODEs) and partial differential equations (PDEs). It presents very recent results relating to the existence, boundedness, regularity, and asymptotic behavior of global solutions for differential equations and inclusions, with or without delay, subjected to nonlocal implicit initial conditions.After preliminaries on nonlinear evolution equations governed by dissipative operators, the book gives a thorough study of the existence, uniqueness, and asymptotic behavior of global bounded solutions for differential equations with delay and local initial conditions. It then focuses on two important nonlocal cases: autonomous and quasi-autonomous. The authors next discuss sufficient conditions for the existence of almost periodic solutions, describe evolution systems with delay and nonlocal initial cTrade Review"This book will be useful to researchers and graduate students interested in delay evolution equations and inclusions subjected to nonlocal initial conditions." - Sotiris K. Ntouyas (Ioannina)Table of ContentsPreliminaries. Local Initial Conditions. Nonlocal Initial Conditions: The Autonomous Case. Nonlocal Initial Conditions: The Quasi-Autonomous Case. Almost Periodic Solutions. Evolution Systems with Nonlocal Initial Conditions. Delay Evolution Inclusions. Multivalued Reaction-Diffusion Systems. Viability for Nonlocal Evolution Inclusions. Bibliography. Index.

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Book SynopsisHeat transfer enhancement has seen rapid development and widespread use in both conventional and emerging technologies.  Improvement of heat transfer fluids requires a balance between experimental and numerical work in nanofluids and new refrigerants. Recognizing the uncertainties in development of new heat transfer fluids, Advances in New Heat Transfer Fluids:  From Numerical to Experimental Techniques contains both theoretical and practical coverage. Table of ContentsList of Contributors Preface 1. Experimental studies on the influence of metal and metal oxide nanofluid properties on forced convection heat transfer and fluid flow Viswanatha Sharma Korada, Seshu Kumar Vandrangi, Subhash Kamal, and Alina Adriana Minea 2. Comparative methods in convective heat transfer enhancement by nanofluids: entropy generation Vincenzo BIANCO, Oronzio MANCA, Alina Adriana MINEA, and Sergio NARDINI 3. Static and flow heat transfer status of ethylene glycol-based nanofluids S M Sohel MURSHED and Carlos A. NIETO DE CASTRO 4. Carbon based nanofluids characteristics: basics and applications on heat pipes Gabriela HUMINIC, Angel HUMINIC, Florian DUMITRACHE, and Claudiu FLEACĂ 5. Numerical studies on metallic nanofluids flow and heat transfer in tangential microtube heat sink with multiple inlets Dorin LELEA 6. Heat transfer augmentation with nanocomposite based hybrid nanofluids flowing in a tube with inserts L. Syam SUNDAR, Manoj K. SINGH, and Antonio C.M. SOUSA 7. Magnetohydrodynamic with nanofluids for heat transfer applications Fatih SELIMEFENDIGIL and Hakan F. OZTOP 8. Enhancing the Thermal Properties of Water and Ethylene Glycol with Nanoadditives and Surface Functionalization Ronald J. WARZOHA 9. Rheological characteristics of nanofluids for advance heat transfer S M Sohel MURSHED and Patrice ESTELLÉ 10. Heat transfer enhancement in cavities filled with nanofluids Teodor GROSAN, Mikhail A. SHEREMET, and Ioan POP 11. New high temperature heat transfer and thermal storage molten salt-based nanofluids: preparation, stabilization and characterization Rosa MONDRAGON, Nuria NAVARRETE, Alexandra GIMENO-FURIO, Leonor HERNANDEZ, Luis CABEDO, and J. Enrique JULIA 12. Liquid metals as heat transfer fluids for science and technology Alexandru ONEA, Sara PEREZ-MARTIN, Wadim JÄGER, Wolfgang HERING, and Robert STIEGLITZ 13. Comparison of environmentally friendly working fluids for Organic Rankine cycles Kostantinos BRAIMAKIS, Tryfonas ROUMPEDAKIS, Aris-Dimitrios LEONTARITIS, and Sotirios KARELLAS 14. Thermodynamic properties of refrigerants with low GWP Sergio BOBBO and Laura FEDELE 15. Refrigerants for vapour compression refrigeration systems: a review on natural and artificial heat transfer fluids Rodrigo LLOPIS, Daniel SÁNCHEZ, and Ramón CABELLO

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Book SynopsisThis book covers both theoretical and practical results for graph polynomials. Graph polynomials have been developed for measuring combinatorial graph invariants and for characterizing graphs. Various problems in pure and applied graph theory or discrete mathematics can be treated and solved efficiently by using graph polynomials. Graph polynomials have been proven useful areas such as discrete mathematics, engineering, information sciences, mathematical chemistry and related disciplines.Table of ContentsThe Alliance Polynomial of a Graph. Aspects of the Interlace Polynomial of a Graph. The clique-transversal set problem in clawfree graphs with degree at most 4. Permanental Polynomials of Graphs. Tutte polynomial and its generalizations. Graphs characterized by various polynomials. Recurrence relations of graph polynomials. Independence polynomials of k-tree related graphs. Generatingfunctionology for Graph Polynomials. Symmetric representations and the connection with linear recurrences. From the Ising and Potts model to the general graph homomorphism polynomial.

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Book SynopsisThis book presents a unified algebraic approach to stabilization problems of linear boundary control systems with no assumption on finite-dimensional approximations to the original systems, such as the existence of the associated Riesz basis. A new proof of the stabilization result for linear systems of finite dimension is also presented, leading to an explicit design of the feedback scheme. The problem of output stabilization is discussed, and some interesting results are developed when the observability or the controllability conditions are not satisfied.Table of ContentsPreliminary results - Stabilization of linear systems of finite dimension. Preliminary results: Basic theory of elliptic operators. Stabilization of linear systems of infinite dimension: Static feedback. Stabilization of linear systems of infinite dimension: Dynamic feedback. Stabilization of linear systems with Riesz Bases: Dynamic feedback. Output stabilization: lack of the observability and/or the controllability conditions. Stabilization of a class of linear control systems generating C0- semigroups. A Computational Algorhism for an Infinite-Dimensional Sylvester’s Equation.

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Book SynopsisIterative Methods without Inversion presents the iterative methods for solving operator equations f(x) = 0 in Banach and/or Hilbert spaces. It covers methods that do not require inversions of f (or solving linearized subproblems). The typical representatives of the class of methods discussed are Ulm's and Broyden's methods. Convergence analyses of the methods considered are based on Kantorovich's majorization principle which avoids unnecessary simplifying assumptions like differentiability of the operator or solvability of the equation. These analyses are carried out under a more general assumption about degree of continuity of the operator than traditional Lipschitz continuity: regular continuity.Key Features The methods discussed are analyzed under the assumption of regular continuity of divided difference operator, which is more general and more flexible than the traditional Lipschitz continuity. An attention is given toTrade Review"The book is well organised and clearly written and presents a limited but illustrative number of computational examples that are intended to provide results that can be used to validate the reader's own implementations and to give a sense of how the algorithms perform. It will be accessible to anyone who has reasonable knowledge of basic nonlinear functional analysis. Among many other positive features of the book, I especially appreciate the fact that Chapters 2-7 begin with a motivation, give numerical examples and end by stating research project(s), thus enabling and challenging interested readers to pursue further developments. The book will be very useful to graduate students and young researchers beginning their scientific careers in the field of computational mathematics and to anyone else interested in numerical analysis." - Vasile Berinde, Mathematical Reviews, August 2017 "The book is well organised and clearly written and presents a limited but illustrative number of computational examples that are intended to provide results that can be used to validate the reader's own implementations and to give a sense of how the algorithms perform. It will be accessible to anyone who has reasonable knowledge of basic nonlinear functional analysis. Among many other positive features of the book, I especially appreciate the fact that Chapters 2-7 begin with a motivation, give numerical examples and end by stating research project(s), thus enabling and challenging interested readers to pursue further developments. The book will be very useful to graduate students and young researchers beginning their scientific careers in the field of computational mathematics and to anyone else interested in numerical analysis." - Vasile Berinde, Mathematical Reviews, August 2017 Table of ContentsIntroduction. Some useful tools of the trade. Ulm’s method. Ulm’s method without derivatives. Broyden’s method. Optimal secantupdates of low rank. Optimal secant-type methods. Majorant generators and their convergence domains. Bibliography

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Book SynopsisExploring Geometry, Second Edition promotes student engagement with the beautiful ideas of geometry. Every major concept is introduced in its historical context and connects the idea with real-life. A system of experimentation followed by rigorous explanation and proof is central. Exploratory projects play an integral role in this text. Students develop a better sense of how to prove a result and visualize connections between statements, making these connections real. They develop the intuition needed to conjecture a theorem and devise a proof of what they have observed.Features:Second edition of a successful textbook for the first undergraduate courseEvery major concept is introduced in its historical context and connects the idea with real lifeFocuses on experimentationProjects help enhance student learningAll major software programs can be used; free software from authorTable of ContentsGeometry and the Axiomatic MethodEarly Origins of GeometryThales and PythagorasProject 1 - The Ratio Made of GoldThe Rise of the Axiomatic MethodProperties of the Axiomatic SystemsEuclid's Axiomatic GeometryProject 2 - A Concrete Axiomatic SystemEuclidean GeometryAngles, Lines, and Parallels ANGLES, LINES, AND PARALLELS 51Congruent Triangles and Pasch's AxiomProject 3 - Special Points of a TriangleMeasurement and AreaSimilar TrianglesCircle GeometryProject 4 - Circle Inversion and OrthogonalityAnalytic GeometryThe Cartesian Coordinate SystemVector GeometryProject 5 - Bezier CurvesAngles in Coordinate GeometryThe Complex PlaneBirkhoff's Axiomatic SystemConstructionsEuclidean ConstructionsProject 6 - Euclidean EggsConstructibilityTransformational GeometryEuclidean IsometriesReflectionsTranslationsRotationsProject 7 - Quilts and TransformationsGlide ReflectionsStructure and Representation of IsometriesProject 8 - Constructing CompositionsSymmetryFinite Plane Symmetry GroupsFrieze GroupsWallpaper GroupsTilting the PlaneProject 9 - Constructing TesselationsHyperbollic GeometryBackground and HistoryModels of Hyperbolic GeometryBasic Results in Hyperbolic GeometryProject 10 - The Saccheri QuadrilateralLambert Quadrilaterals and TrianglesArea in Hyperbolic GeometryProject 11 - Tilting the Hyperbolic PlaneElliptic GeometryBackground and HistoryPerpendiculars and Poles in Elliptic GeometryProject 12 - Models of Elliptic GeometryBasic Results in Elliptic GeometryTriangles and Area in Elliptic GeometryProject 13 - Elliptic TilingProjective GeometryUniversal ThemesProject 14 - Perspective and ProjectionFoundations of Projective GeometryTransformations and Pappus's TheoremModels of Projective GeometryProject 15 - Ratios and HarmonicsHarmonic SetsConics and CoordinatesFractal GeometryThe Search for a "Natural" GeometrySelf-SimilaritySimilarity DimensionProject 16 - An Endlessly Beautiful SnowflakeContraction MappingsFractal DimensionProject 17 - IFS FernsAlgorithmic GeometryGrammars and ProductionsProject 18 - Words Into PlantsAppendix A: A Primer on ProofsAppendix A □ A Primer on Proofs 497Appendix B □ Book I of Euclid’s Elements Appendix C □ Birkhoff’s Axioms Appendix D □ Hilbert’s Axioms Appendix E □ Wallpaper Groups

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Book SynopsisConvective Flow and Heat Transfer from Wavy Surfaces: Viscous Fluids, Porous Media, and Nanofluids addresses the wavy irregular surfaces in heat transfer devices. Fluid flow and heat transfer studies from wavy surfaces have received attention, since they add complexity and require special mathematical techniques. This book considers the flow and heat transfer characteristics from wavy surfaces, providing an understanding of convective behavioral changes.Table of ContentsIntroduction. Governing Equations. Natural and Mixed Convection Flow in Viscous Fluids. Natural and Mixed Convection Flow in Fluid-Saturated Porous Media. Natural and Mixed Convection Flow in Nanofluids. Wavy Vertical Channels. Natural and Mixed Convection Flow in Viscous Fluids. Natural and Mixed Convection Flow in Fluid-Saturated Porous Media. Natural and Mixed Convection Flow in Nanofluids. Wavy Cavities. Natural and Mixed Convection Flow in Viscous Fluids. Natural and Mixed Convection.. Natural and Mixed Convection Flow in Fluid-Saturated Porous Media. Natural and Mixed Convection Flow in Nanofluids. Concluding Remarks. Nomenclature. References. Index.

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Book SynopsisIterative processes are the tools used to generate sequences approximating solutions of equations describing real life problems. Intended for researchers in computational sciences and as a reference book for advanced computational method in nonlinear analysis, this book is a collection of the recent results on the convergence analysis of numerical algorithms in both finite-dimensional and infinite-dimensional spaces and presents several applications and connections with fixed point theory. It contains an abundant and updated bibliography and provides comparisons between various investigations made in recent years in the field of computational nonlinear analysis.The book also provides recent advancements in the study of iterative procedures and can be used as a source to obtain the proper method to use in order to solve a problem. The book assumes a basic background in Mathematical Statistics, Linear Algebra and Numerical Analysis and may be used as a self-study referTable of ContentsHalley’s method. Newton’s method for k-Fréchet differentiable operators. Nonlinear Ill-posed quations. Sixth-order iterative methods. Local convergence and basins of attraction of a two-step Newton like method for equations with solutions of multiplicity greater than one. Extending the Kantorovich theory for solving equations. Robust convergence for inexact Newton method. Inexact Gauss-Newton-like method for least square problems. Lavrentiev Regularization Methods for Ill-posed Equations. King-Werner-type methods of order 1+sqrt(2). Generalized equations and Newton’s method. Newton’s method for generalized equations using restricted domains. Secant-like methods. King-Werner-like methods free of derivatives. Müller’s method. Generalized Newton Method with applications. Newton-secant methods with values in a cone. Gauss-Newton method with applications to convex optimization. Directional Newton methods and restricted domains. Gauss-Newton method for convex optimization. Ball Convergence for eighth order method. Expanding Kantorovich’s theorem for solving generalized equations.

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Book SynopsisQuantum Effects in Tribology is devoted to the study of quantum foundations of materials friction interaction and evolutionary formation of tribosystem's operating parameters. At the start of the book, large consideration is given to the analysis of the existing diversity of friction, wear, and lubrication models and their relationship with each other, as well as to the quantum nature of the measurement process and the wave function reduction caused by the act of measurement. Consideration of measurement as a process of defining the output parameters of tribosystem is carried out with the apparatus of second quantization and conceptions associated with non-local quantum effects. Such an approach makes it possible not only to take another look to the evolution of tribosystems but discover previously unknown regularities of friction. The book is intended for professionals working in the field of tribology, but will be also useful for graduate students spTable of ContentsPreface. Problems of Creation of the Generalized Physical Model of Friction and Wear. Quantum Algorithm for Solving the "Fundamental Paradox of Tribology". Quantum Spaces of Tribosystems. Quantum Dynamics of Tribosystems. Quantum States of Manifested Tribosystem. Afterword. Bibliography.

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Book SynopsisData Mining: A Tutorial-Based Primer, Second Edition provides a comprehensive introduction to data mining with a focus on model building and testing, as well as on interpreting and validating results. The text guides students to understand how data mining can be employed to solve real problems and recognize whether a data mining solution is a feasible alternative for a specific problem. Fundamental data mining strategies, techniques, and evaluation methods are presented and implemented with the help of two well-known software tools. Several new topics have been added to the second edition including an introduction to Big Data and data analytics, ROC curves, Pareto lift charts, methods for handling large-sized, streaming and imbalanced data, support vector machines, and extended coverage of textual data mining. The second edition contains tutorials for attribute selection, dealing with imbalanced data, outlier analysis, time series analysis, mining textual data, and morTrade Review"Dr. Roiger does an excellent job of describing in step by step detail formulae involved in various data mining algorithms, along with illustrations. In addition, his tutorials in Weka software provide excellent grounding for students in comprehending the underpinnings of Machine Learning as applied to Data Mining. The inclusion of RapidMiner software tutorials and examples in the book is also a definite plus since it is one of the most popular Data Mining software platforms in use today."--Robert Hughes, Golden Gate University, San Francisco, CA, USATable of ContentsData Mining: A First View. Data Mining: A Closer Look. Basic Data Mining Techniques. Weka – A Tool for Knowledge Discovery.Pre Processing & Visualization Techniques. Knowledge Discovery in Databases. Formal Evaluation Techniques. The DataWarehouse. Neural Networks. Building Neural Networks with BpKNet. Statistical Methods. Specialized Techniques. A Case Studyin Knowledge Discovery. Rule-Based Systems. Managing Uncertainty in Rule-Based Systems. Intelligent Agents

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Book SynopsisThe book presents qualitative results for different classes of fractional equations, including fractional functional differential equations, fractional impulsive differential equations, and fractional impulsive functional differential equations, which have not been covered by other books. It manifests different constructive methods by demonstrating how these techniques can be applied to investigate qualitative properties of the solutions of fractional systems. Since many applications have been included, the demonstrated techniques and models can be used in training students in mathematical modeling and in the study and development of fractional-order models.Table of ContentsIntroduction. Preliminary Notes. Qualitative Properties Definitions. Lyapunov Functions and their Fractional Derivatives. Fractional Comparison Lemmas. Stability and Boundedness. Lyapunov Stability. Theorems on Boundedness. Global Stability. Mittag-Leffler Stability. Practical Stability. Lipschitz Stability. Stability of Sets. Stability of Integral Manifolds. Almost Periodicity. Almost Periodic Solutions. Lyapunov Method for Almost Periodic Solutions. Uncertain Fractional Differential Systems. Applications. Fractional Impulsive Neural Networks. Stability and Synchronization. Almost Periodic Solutions. The Uncertain Case. Fractional Impulsive Biological Models. Lasota-Wazewska Models. Lotka-Volterra Models. Kolmogorov-type Models. Fractional Impulsive Models in Economics.

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Book SynopsisA properly structured financial model can provide decision makers with a powerful planning tool that helps them identify the consequences of their decisions before they are put into practice. Introduction to Financial Models for Management and Planning, Second Edition enables professionals and students to learn how to develop and use computer-based models for financial planning. This volume provides critical tools for the financial toolbox, then shows how to use them tools to build successful models.Table of ContentsAn Overview of Financial Planning and Modeling. Part I: Tools for Financial Planning and Modeling: Financial Analysis. The Tools for Financial Planning I: Financial Analysis. Appendix A: Using Names in the Excel Spreadsheet. Appendix B: Constructing a Data Table. The Tools for Financial Planning II: Growth and Cash Flows. Part II: Tools for Financial Planning and Modeling: Simulation. Financial Statement Simulation. Monte Carlo Simulation. Part III: Introduction to Forecasting Methods. Forecasting I: Time Trend Extrapolation. Forecasting II: Econometric Forecasting. Forecasting III: Smoothing Data for Forecasts. Part IV: A Closer Look at the Details of a Financial Model. Modeling Value. Modeling Long-Term Assets. Debt Financing. Modeling Working Capital Accounts. PART V: Modeling Security Prices and Investment Portfolios. Modeling Security Prices. Constructing Optimal Security Portfolios. Options. Part VI: Optimization Models. Optimization Models for Financial Planning. Planning and Managing Working Capital with LP. References. Index

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Book SynopsisThe first part of this book introduces the Schubert Cells and varieties of the general linear group Gl (k^(r+1)) over a field k according to Ehresmann geometric way. Smooth resolutions for these varieties are constructed in terms of Flag Configurations in k^(r+1) given by linear graphs called Minimal Galleries. In the second part, Schubert Schemes, the Universal Schubert Scheme and their Canonical Smooth Resolution, in terms of the incidence relation in a Tits relative building are constructed for a Reductive Group Scheme as in Grothendieck''s SGAIII. This is a topic where algebra and algebraic geometry, combinatorics, and group theory interact in unusual and deep ways.Table of ContentsGrassmannians and Flag Varieties. Schubert Cell Decomposition of Grassmannians and Flag Varieties. Resolution of Singularities of a Schubert Variety. The Singular Locus of a Schubert Variety. The Flag Complex. Configurations and Galleries Varieties. Configurations Varieties as Galleries Varieties. The Coxeter Complex. Minimal Generalized Galleries in a Coxeter Complex. Minimal Generalized Galleries in a Reductive Group Building. Parabolic Subgroups in a Reductive Group Scheme. Associated Schemes to the Relative Building. Incidence Type Schemes of the Relative Building. Smooth Resolutions of Schubert Schemes. Contracted Products and Galleries Configurations Schemes. Functoriality of Schubert Schemes Smooth Resolutions and Base Changes. About the Coxeter Complex. Generators and Relations and the Building of a Reductive Group.

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Book SynopsisA Bridge to Higher Mathematics is more than simply another book to aid the transition to advanced mathematics. The authors intend to assist students in developing a deeper understanding of mathematics and mathematical thought. The only way to understand mathematics is by doing mathematics. The reader will learn the language of axioms and theorems and will write convincing and cogent proofs using quantifiers. Students will solve many puzzles and encounter some mysteries and challenging problems. The emphasis is on proof. To progress towards mathematical maturity, it is necessary to be trained in two aspects: the ability to read and understand a proof and the ability to write a proof. The journey begins with elements of logic and techniques of proof, then with elementary set theory, relations and functions. Peano axioms for positive integers and for natural numbers follow, in particular mathematical and other forms of induction. Next Trade ReviewThis is one of the shorter books for a course that introduces students to the concept of mathematical proofs. The brevity is due to the "bare-bones" nature of the treatment. The number of topics covered, the number of examples, and the number of exercises are not smaller than what appears in competing textbooks; what is shorter is the text that one finds between theorems, lemmas, examples, and exercises. Besides the topics found in similar textbooks (i.e., proof techniques, logic, set theory, relations, and functions), there are chapters on (very) elementary number theory, combinatorial counting techniques, and Peano axioms on the set of positive integers. Several chapters are devoted to the construction of various kinds of numbers, such as integers, rationals, real numbers, and complex numbers. Answers to around half the exercises are included at the end of the book, and a few have complete solutions. This reviewer finds the book more enjoyable than the average competing textbook. --M. Bona, University of FloridaTable of ContentsElements of logicTrue and false statementsLogical connectives and truth tablesLogical equivalenceQuantifiersProofs: Structures and strategiesAxioms, theorems and proofsDirect proofContrapositive proofProof by equivalent statementsProof by casesExistence proofsProof by counterexampleProof by mathematical inductionElementary Theory of Sets. FunctionsAxioms for set theoryInclusion of setsUnion and intersection of setsComplement, difference and symmetric difference of setsOrdered pairs and the Cartersian productFunctionsDefinition and examples of functionsDirect image, inverse imageRestriction and extension of a functionOne-to-one and onto functionsComposition and inverse functions*Family of sets and the axiom of choiceRelationsGeneral relations and operations with relationsEquivalence relations and equivalence classesOrder relations*More on ordered sets and Zorn's lemmaAxiomatic theory of positive integersPeano axioms and additionThe natural order relation and subtractionMultiplication and divisibilityNatural numbersOther forms of inductionElementary number theoryAboslute value and divisibility of integersGreatest common divisor and least common multipleIntegers in base 10 and divisibility testsCardinality. Finite sets, infinite setsEquipotent setsFinite and infinite setsCountable and uncountable setsCounting techniques and combinatoricsCounting principlesPigeonhole principle and parityPermutations and combinationsRecursive sequences and recurrence relationsThe construction of integers and rationals Definition of integers and operationsOrder relation on integersDefinition of rationals, operations and orderDecimal representation of rational numbersThe construction of real and complex numbersThe Dedekind cuts approachThe Cauchy sequences approachDecimal representation of real numbersAlgebraic and transcendental numbersComples numbersThe trigonometric form of a complex number

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Book SynopsisThe book reviews inequalities for weighted entry sums of matrix powers. Applications range from mathematics and CS to pure sciences. It unifies and generalizes several results for products and powers of sesquilinear forms derived from powers of Hermitian, positive-semidefinite, as well as nonnegative matrices. It shows that some inequalities are valid only in specific cases. How to translate the Hermitian matrix results into results for alternating powers of general rectangular matrices? Inequalities that compare the powers of the row and column sums to the row and column sums of the matrix powers are refined for nonnegative matrices. Lastly, eigenvalue bounds and derive results for iterated kernels are improved.Table of ContentsIntroduction. Notation and Basic Facts. Motivation. Diagonalization and Spectral Decomposition. Undirected Graphs / Hermitian Matrices. General Results. Restricted Graph Classes. Directed Graphs / Nonsymmetric. Walks and Alternating Walks in Directed Graphs. Powers of Row and Column Sums. Applications. Bounds for the Largest Eigenvalue. Iterated Kernels. Conclusion. Bibliography. Index.

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