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An Introduction to Optimization with Applications in Machine Learning and Data Analytics (Textbooks in Mathematics)
by Jeffrey Paul WheelerThe primary goal of this text is a practical one. Equipping students with enough knowledge and creating an independent research platform, the author strives to prepare students for professional careers. Providing students with a marketable skill set requires topics from many areas of optimization. The initial goal of this text is to develop a marketable skill set for mathematics majors as well as for students of engineering, computer science, economics, statistics, and business. Optimization reaches into many different fields. This text provides a balance where one is needed. Mathematics optimization books are often too heavy on theory without enough applications; texts aimed at business students are often strong on applications, but weak on math. The book represents an attempt at overcoming this imbalance for all students taking such a course. The book contains many practical applications but also explains the mathematics behind the techniques, including stating definitions and proving theorems. Optimization techniques are at the heart of the first spam filters, are used in self-driving cars, play a great role in machine learning, and can be used in such places as determining a batting order in a Major League Baseball game. Additionally, optimization has seemingly limitless other applications in business and industry. In short, knowledge of this subject offers an individual both a very marketable skill set for a wealth of jobs as well as useful tools for research in many academic disciplines. Many of the problems rely on using a computer. Microsoft’s Excel is most often used, as this is common in business, but Python and other languages are considered. The consideration of other programming languages permits experienced mathematics and engineering students to use MATLAB® or Mathematica, and the computer science students to write their own programs in Java or Python.
An Introduction to Optimization: With Applications to Machine Learning (Wiley Series In Discrete Mathematics And Optimization Ser. #77)
by Edwin K. Chong Wu-Sheng Lu Stanislaw H. ŻakAn Introduction to Optimization Accessible introductory textbook on optimization theory and methods, with an emphasis on engineering design, featuring MATLAB® exercises and worked examples Fully updated to reflect modern developments in the field, the Fifth Edition of An Introduction to Optimization fills the need for an accessible, yet rigorous, introduction to optimization theory and methods, featuring innovative coverage and a straightforward approach. The book begins with a review of basic definitions and notations while also providing the related fundamental background of linear algebra, geometry, and calculus. With this foundation, the authors explore the essential topics of unconstrained optimization problems, linear programming problems, and nonlinear constrained optimization. In addition, the book includes an introduction to artificial neural networks, convex optimization, multi-objective optimization, and applications of optimization in machine learning. Numerous diagrams and figures found throughout the book complement the written presentation of key concepts, and each chapter is followed by MATLAB® exercises and practice problems that reinforce the discussed theory and algorithms. The Fifth Edition features a new chapter on Lagrangian (nonlinear) duality, expanded coverage on matrix games, projected gradient algorithms, machine learning, and numerous new exercises at the end of each chapter. An Introduction to Optimization includes information on: The mathematical definitions, notations, and relations from linear algebra, geometry, and calculus used in optimization Optimization algorithms, covering one-dimensional search, randomized search, and gradient, Newton, conjugate direction, and quasi-Newton methods Linear programming methods, covering the simplex algorithm, interior point methods, and duality Nonlinear constrained optimization, covering theory and algorithms, convex optimization, and Lagrangian duality Applications of optimization in machine learning, including neural network training, classification, stochastic gradient descent, linear regression, logistic regression, support vector machines, and clustering. An Introduction to Optimization is an ideal textbook for a one- or two-semester senior undergraduate or beginning graduate course in optimization theory and methods. The text is also of value for researchers and professionals in mathematics, operations research, electrical engineering, economics, statistics, and business.
An Introduction to Ordinary Differential Equations
by Earl A. Coddington"Written in an admirably cleancut and economical style." -- Mathematical Reviews. This concise text offers undergraduates in mathematics and science a thorough and systematic first course in elementary differential equations. Presuming a knowledge of basic calculus, the book first reviews the mathematical essentials required to master the materials to be presented. The next four chapters take up linear equations, those of the first order and those with constant coefficients, variable coefficients, and regular singular points. The last two chapters address the existence and uniqueness of solutions to both first order equations and to systems and n-th order equations. Throughout the book, the author carries the theory far enough to include the statements and proofs of the simpler existence and uniqueness theorems. Dr. Coddington, who has taught at MIT, Princeton, and UCLA, has included many exercises designed to develop the student's technique in solving equations. He has also included problems (with answers) selected to sharpen understanding of the mathematical structure of the subject, and to introduce a variety of relevant topics not covered in the text, e.g. stability, equations with periodic coefficients, and boundary value problems.
An Introduction to Ordinary Differential Equations
by James C. RobinsonThis refreshing, introductory textbook covers both standard techniques for solving ordinary differential equations, as well as introducing students to qualitative methods such as phase-plane analysis. The presentation is concise, informal yet rigorous; it can be used either for 1-term or 1-semester courses. Topics such as Euler's method, difference equations, the dynamics of the logistic map, and the Lorenz equations, demonstrate the vitality of the subject, and provide pointers to further study. The author also encourages a graphical approach to the equations and their solutions, and to that end the book is profusely illustrated. The files to produce the figures using MATLAB are all provided in an accompanying website. Numerous worked examples provide motivation for and illustration of key ideas and show how to make the transition from theory to practice. Exercises are also provided to test and extend understanding: solutions for these are available for teachers.
An Introduction to Orthogonal Polynomials (Dover Books On Mathematics Ser.)
by Theodore S ChiharaAssuming no further prerequisites than a first undergraduate course in real analysis, this concise introduction covers general elementary theory related to orthogonal polynomials. It includes necessary background material of the type not usually found in the standard mathematics curriculum. Suitable for advanced undergraduate and graduate courses, it is also appropriate for independent study. Topics include the representation theorem and distribution functions, continued fractions and chain sequences, the recurrence formula and properties of orthogonal polynomials, special functions, and some specific systems of orthogonal polynomials. Numerous examples and exercises, an extensive bibliography, and a table of recurrence formulas supplement the text.
An Introduction to PHP for Scientists and Engineers: Beyond JavaScript
by David R. BrooksThis book provides an introduction to PHP and server-side programming. It presents readers with a science or engineering background with the information to write their own online applications requiring reading, creating and manipulating data files stored as text on a server, overcoming the limitations of a client-side language. It focuses only on those elements of the language, such as file input/output, arrays, built-in math functions, and user-created functions that are essential for solving a wide range of scientific/engineering computing problems - and assumes a working knowledge of programming concepts and HTML, JavaScript, C or a similar language. It contains complete applications and hence offers a very compact and efficient way for working professionals to take advantage of the possibilities offered by server-side programming. Written for a technical audience, this book is an effective learning tool to the essentials of PHP and is also ideal for self-study.
An Introduction to Panel Data QCA in R
by Preya BhattacharyaIn the last few years, Qualitative Comparative Analysis (QCA) has become one of the most important research approaches in social science. This has encouraged researchers to apply QCA, to analyze cross-sectional and panel data, leading to the development of a variety of cross-sectional and panel data QCA models.This book compares four different panel data QCA models: Cluster QCA, Multiple Sub-QCA, Remote-Proximate Panel, and Relevant Variation Panel. It starts by introducing QCA as a research approach, then discusses the assumptions, and steps in a QCA research process. It then applies these assumptions and steps to demonstrate each of the 4 afore-mentioned panel data QCA models. Each chapter also provides a step-by-step guide, that researchers can follow while building any of these 4 panel data QCA models. Finally, it compares the strengths and weaknesses of each of these models and suggests scenarios where researchers can apply them. This book is supplemented by materials like datasets and codes, available at the end of each chapter, and online on Harvard Dataverse. This book can be used as a textbook for introductory and advanced courses on panel data QCA.
An Introduction to Partial Differential Equations
by Yehuda Pinchover Jacob RubinsteinA complete introduction to partial differential equations. A textbook aimed at students of mathematics, physics and engineering.
An Introduction to Partial Differential Equations with MATLAB (Advances in Applied Mathematics)
by Matthew P. ColemanAn Introduction to Partial Differential Equations with MATLAB, Second Edition illustrates the usefulness of PDEs through numerous applications and helps students appreciate the beauty of the underlying mathematics. Updated throughout, this second edition of a bestseller shows students how PDEs can model diverse problems, including the flow of heat,
An Introduction to Partial Differential Equations with MATLAB (ISSN #27)
by Matthew P. Coleman Vladislav BukshtynovThe first two editions of An Introduction to Partial Differential Equations with MATLAB® gained popularity among instructors and students at various universities throughout the world. Plain mathematical language is used in a friendly manner to provide a basic introduction to partial differential equations (PDEs).Suitable for a one- or two-semester introduction to PDEs and Fourier series, the book strives to provide physical, mathematical, and historical motivation for each topic. Equations are studied based on method of solution, rather than on type of equation.This third edition of this popular textbook updates the structure of the book by increasing the role of the computational portion, compared to previous editions. The redesigned content will be extremely useful for students of mathematics, physics, and engineering who would like to focus on the practical aspects of the study of PDEs, without sacrificing mathematical rigor. The authors have maintained flexibility in the order of topics.In addition, students will be able to use what they have learned in some later courses (for example, courses in numerical analysis, optimization, and PDE-based programming). Included in this new edition is a substantial amount of material on reviewing computational methods for solving ODEs (symbolically and numerically), visualizing solutions of PDEs, using MATLAB®'s symbolic programming toolbox, and applying various schemes from numerical analysis, along with suggestions for topics of course projects.Students will use sample MATLAB® or Python codes available online for their practical experiments and for completing computational lab assignments and course projects.
An Introduction to Phase-Integral Methods (Dover Books on Mathematics)
by John HeadingThe phase-integral method in mathematics, also known as the Wentzel-Kramers-Brillouin (WKB) method, is the focus of this introductory treatment. Author John Heading successfully steers a course between simplistic and rigorous approaches to provide a concise overview for advanced undergraduates and graduate students in mathematics and physics. Since the number of applications is vast, the text considers only a brief selection of topics and emphasizes the method itself rather than detailed applications. The process, once derived, is shown to be one of essential simplicity that involves merely the application of certain well-defined rules. Starting with a historical survey of the problem and its solutions, subjects include the Stokes phenomenon, one and two transition points, and applications to physical problems. An appendix and bibliography conclude the text.
An Introduction to Physical Oncology: How Mechanistic Mathematical Modeling Can Improve Cancer Therapy Outcomes (Chapman & Hall/CRC Mathematical Biology Series)
by Vittorio Cristini Eugene Koay Zhihui WangPhysical oncology has the potential to revolutionize cancer research and treatment. The fundamental rationale behind this approach is that physical processes, such as transport mechanisms for drug molecules within tissue and forces exchanged by cancer cells with tissue, may play an equally important role as biological processes in influencing progression and treatment outcome. <P><P>This book introduces the emerging field of physical oncology to a general audience, with a focus on recent breakthroughs that help in the design and discovery of more effective cancer treatments. It describes how novel mathematical models of physical transport processes incorporate patient tissue and imaging data routinely produced in the clinic to predict the efficacy of many cancer treatment approaches, including chemotherapy and radiation therapy. By helping to identify which therapies would be most beneficial for an individual patient, and quantifying their effects prior to actual implementation in the clinic, physical oncology allows doctors to design treatment regimens customized to each patient’s clinical needs, significantly altering the current clinical approach to cancer treatment and improving the outcomes for patients.
An Introduction to Political and Social Data Analysis (With R)
by Thomas M. HolbrookAn Introduction to Political and Social Data Analysis (With R) provides students with an accessible overview of practical data analysis while also providing a gentle introduction to R. By starting with statistics first and using just enough R code to generate results, this text helps students focus on learning how to do data analysis while slowly gaining confidence in using R as they progress through the material. This book is structured around learning by doing. Students can follow along in each chapter by reading about statistics and their applications in R, and then running the R code on their own as they work through contemporary political science and social science examples. Author Thomas M. Holbrook patiently explains each step in in the process, avoiding overly complicated jargon and commands. Exercises at the end of chapters feature both conceptual and calculation-based questions so students can check their understanding of data analysis and practice using R. At the end of the semester, students can confidently add skills in data analysis with R to their resumes.
An Introduction to Political and Social Data Analysis (With R)
by Thomas M. HolbrookAn Introduction to Political and Social Data Analysis (With R) provides students with an accessible overview of practical data analysis while also providing a gentle introduction to R. By starting with statistics first and using just enough R code to generate results, this text helps students focus on learning how to do data analysis while slowly gaining confidence in using R as they progress through the material. This book is structured around learning by doing. Students can follow along in each chapter by reading about statistics and their applications in R, and then running the R code on their own as they work through contemporary political science and social science examples. Author Thomas M. Holbrook patiently explains each step in in the process, avoiding overly complicated jargon and commands. Exercises at the end of chapters feature both conceptual and calculation-based questions so students can check their understanding of data analysis and practice using R. At the end of the semester, students can confidently add skills in data analysis with R to their resumes.
An Introduction to Polynomial and Semi-Algebraic Optimization
by Jean Bernard LasserreThis is the first comprehensive introduction to the powerful moment approach for solving global optimization problems (and some related problems) described by polynomials (and even semi-algebraic functions). In particular, the author explains how to use relatively recent results from real algebraic geometry to provide a systematic numerical scheme for computing the optimal value and global minimizers. Indeed, among other things, powerful positivity certificates from real algebraic geometry allow one to define an appropriate hierarchy of semidefinite (SOS) relaxations or LP relaxations whose optimal values converge to the global minimum. Several extensions to related optimization problems are also described. Graduate students, engineers and researchers entering the field can use this book to understand, experiment with and master this new approach through the simple worked examples provided.
An Introduction to Population Geographies: Lives Across Space
by Holly R. Barcus Keith HalfacreeAn Introduction to Population Geographies provides a foundation to the incredibly diverse, topical and interesting field of twenty-first-century population geography. It establishes the substantive concerns of the subdiscipline, acknowledges the sheer diversity of its approaches, key concepts and theories and engages with the resulting major areas of academic debate that stem from this richness. Written in an accessible style and assuming little prior knowledge of topics covered, yet drawing on a wide range of diverse academic literature, the book’s particular originality comes from its extended definition of population geography that locates it firmly within the multiple geographies of the life course. Consequently, issues such as childhood and adulthood, family dynamics, ageing, everyday mobilities, morbidity and differential ability assume a prominent place alongside the classic population geography triumvirate of births, migrations and deaths. This broader framing of the field allows the book to address more holistically aspects of lives across space often provided little attention in current textbooks. Particular note is given to how these lives are shaped though hybrid social, biological and individual arenas of differential life course experience. By engaging with traditional quantitative perspectives and newer qualitative insights, the authors engage students from the quantitative macro scale of population to the micro individual scale. Aimed at higher-level undergraduate and graduate students, this introductory text provides a well-developed pedagogy, including case studies that illustrate theory, concepts and issues.
An Introduction to Probabilistic Number Theory (Cambridge Studies in Advanced Mathematics #192)
by Emmanuel KowalskiDespite its seemingly deterministic nature, the study of whole numbers, especially prime numbers, has many interactions with probability theory, the theory of random processes and events. This surprising connection was first discovered around 1920, but in recent years the links have become much deeper and better understood. Aimed at beginning graduate students, this textbook is the first to explain some of the most modern parts of the story. Such topics include the Chebychev bias, universality of the Riemann zeta function, exponential sums and the bewitching shapes known as Kloosterman paths. Emphasis is given throughout to probabilistic ideas in the arguments, not just the final statements, and the focus is on key examples over technicalities. The book develops probabilistic number theory from scratch, with short appendices summarizing the most important background results from number theory, analysis and probability, making it a readable and incisive introduction to this beautiful area of mathematics.
An Introduction to Probability and Inductive Logic
by Ian HackingThis is an introductory textbook on probability and induction written by one of the world's foremost philosophers of science. The book has been designed to offer maximal accessibility to the widest range of students (not only those majoring in philosophy) and assumes no formal training in elementary symbolic logic. It offers a comprehensive course covering all basic definitions of induction and probability, and considers such topics as decision theory, Bayesianism, frequency ideas, and the philosophical problem of induction. The key features of the book are: * A lively and vigorous prose style* Lucid and systematic organization and presentation of the ideas* Many practical applications* A rich supply of exercises drawing on examples from such fields as psychology, ecology, economics, bioethics, engineering, and political science* Numerous brief historical accounts of how fundamental ideas of probability and induction developed. * A full bibliography of further reading Although designed primarily for courses in philosophy, the book could certainly be read and enjoyed by those in the social sciences (particularly psychology, economics, political science and sociology) or medical sciences such as epidemiology seeking a reader-friendly account of the basic ideas of probability and induction. Ian Hacking is University Professor, University of Toronto. He is Fellow of the Royal Society of Canada, Fellow of the British Academy, and Fellow of the American Academy of Arts and Sciences. he is author of many books including five previous books with Cambridge (The Logic of Statistical Inference, Why Does Language Matter to Philosophy?, The Emergence of Probability, Representing and Intervening, and The Taming of Chance).
An Introduction to Probability and Statistics
by Vijay K. Rohatgi A.K. Md. SalehA well-balanced introduction to probability theory and mathematical statistics Featuring a comprehensive update, An Introduction to Probability and Statistics, Third Edition remains a solid overview to probability theory and mathematical statistics. Divided into three parts, the Third Edition begins by presenting the fundamentals and foundations of probability. The second part addresses statistical inference, and the remaining chapters focus on special topics. Featuring a substantial revision to include recent developments, An Introduction to Probability and Statistics, Third Edition also includes: A new section on regression analysis to include multiple regression, logistic regression, and Poisson regression A reorganized chapter on large sample theory to emphasize the growing role of asymptotic statistics Additional topical coverage on bootstrapping, estimation procedures, and resampling Discussions on invariance, ancillary statistics, conjugate prior distributions, and invariant confidence intervals Over 550 problems and answers to most problems, as well as 350 worked-out examples and 200 remarks Numerous figures to further illustrate examples and proofs throughout An Introduction to Probability and Statistics, Third Edition is an ideal reference and resource for scientists and engineers in the fields of statistics, mathematics, physics, industrial management, and engineering. The book is also an excellent text for upper-undergraduate and graduate- level students majoring in probability and statistics.
An Introduction to Probability and Stochastic Processes (Dover Books on Mathematics)
by Andrew P. Sage James L. MelsaGeared toward college seniors and first-year graduate students, this text is designed for a one-semester course in probability and stochastic processes. Topics covered in detail include probability theory, random variables and their functions, stochastic processes, linear system response to stochastic processes, Gaussian and Markov processes, and stochastic differential equations. 1973 edition.
An Introduction to Proof through Real Analysis
by Daniel J. Madden Jason A. AubreyAn engaging and accessible introduction to mathematical proof incorporating ideas from real analysis A mathematical proof is an inferential argument for a mathematical statement. Since the time of the ancient Greek mathematicians, the proof has been a cornerstone of the science of mathematics. The goal of this book is to help students learn to follow and understand the function and structure of mathematical proof and to produce proofs of their own. An Introduction to Proof through Real Analysis is based on course material developed and refined over thirty years by Professor Daniel J. Madden and was designed to function as a complete text for both first proofs and first analysis courses. Written in an engaging and accessible narrative style, this book systematically covers the basic techniques of proof writing, beginning with real numbers and progressing to logic, set theory, topology, and continuity. The book proceeds from natural numbers to rational numbers in a familiar way, and justifies the need for a rigorous definition of real numbers. The mathematical climax of the story it tells is the Intermediate Value Theorem, which justifies the notion that the real numbers are sufficient for solving all geometric problems. • Concentrates solely on designing proofs by placing instruction on proof writing on top of discussions of specific mathematical subjects • Departs from traditional guides to proofs by incorporating elements of both real analysis and algebraic representation • Written in an engaging narrative style to tell the story of proof and its meaning, function, and construction • Uses a particular mathematical idea as the focus of each type of proof presented • Developed from material that has been class-tested and fine-tuned over thirty years in university introductory courses An Introduction to Proof through Real Analysis is the ideal introductory text to proofs for second and third-year undergraduate mathematics students, especially those who have completed a calculus sequence, students learning real analysis for the first time, and those learning proofs for the first time. Daniel J. Madden, PhD, is an Associate Professor of Mathematics at The University of Arizona, Tucson, Arizona, USA. He has taught a junior level course introducing students to the idea of a rigorous proof based on real analysis almost every semester since 1990. Dr. Madden is the winner of the 2015 Southwest Section of the Mathematical Association of America Distinguished Teacher Award. Jason A. Aubrey, PhD, is Assistant Professor of Mathematics and Director, Mathematics Center of the University of Arizona.
An Introduction to Psychological Tests and Scales
by Kate Loewenthal Christopher Alan LewisIn its first edition this book successfully enabled readers, with little or no prior knowledge of computing or statistics, to develop reliable and valid tests and scales for assessment or research purposes. In this edition, the author has thoroughly updated the text to include new recent advances in computer software and provide information on relevant internet resources. The book contains detailed guidelines for locating and constructing psychological measures, including descriptions of popular psychological measures and step-by-step instructions for composing a measure, entering data and computing reliability and validity of test results. Advanced techniques such as factor analysis, analysis of covariance and multiple regression analysis are presented for the beginner.An Introduction to Psychological Tests and Scales provides a clear, concise and jargon-free primer for all those embarking in fieldwork or research analysis. It will be an invaluable tool for undergraduates and postgraduates in psychology and a useful text for students and professionals in related disciplines.
An Introduction to Quantitative Research Methods for Marketing: Tools and Techniques Using SPSS and R
by Ahmad DaryantoThis introductory text covers the foundational concepts and statistical applications of quantitative research techniques using SPSS and R.Using step-by-step examples throughout, the book is broken down into six core sections: Part 1 covers an introduction to quantitative research methods and how to get started with SPSS and R; Part 2 covers basic concepts in measurement, data descriptions, and distributions; Part 3 discusses hypothesis testing, and basic statistical tests; Part 4 covers regression analysis; Part 5 discusses advanced topics in regression analysis and analysis of variance; and finally Part 6 covers advanced statistical methods. Each chapter contains learning objectives and summaries to structure learning, while breakout boxes provide tips and draw students’ attention to dos and don’ts in statistical research. SPSS and R Action Boxes present step-by-step instructions on how to perform statistical tests and procedures with SPSS and R. Review questions prompt self-reflection on concepts taught in each chapter and are complemented by exercises that allow students to put their learning into practice.A very applied text designed to make this complex subject accessible to students with no background in quantitative methods, this book is valuable recommended and core reading for advanced undergraduate and postgraduate students studying business and marketing research methods, business analytics, marketing analytics, statistical skills and quantitative methods.Online supplementary resources include data sets and programming files.
An Introduction to Quantum and Vassiliev Knot Invariants (CMS Books in Mathematics)
by Iain Moffatt David M. JacksonThis book provides an accessible introduction to knot theory, focussing on Vassiliev invariants, quantum knot invariants constructed via representations of quantum groups, and how these two apparently distinct theories come together through the Kontsevich invariant. Consisting of four parts, the book opens with an introduction to the fundamentals of knot theory, and to knot invariants such as the Jones polynomial. The second part introduces quantum invariants of knots, working constructively from first principles towards the construction of Reshetikhin-Turaev invariants and a description of how these arise through Drinfeld and Jimbo's quantum groups. Its third part offers an introduction to Vassiliev invariants, providing a careful account of how chord diagrams and Jacobi diagrams arise in the theory, and the role that Lie algebras play. The final part of the book introduces the Konstevich invariant. This is a universal quantum invariant and a universal Vassiliev invariant, and brings together these two seemingly different families of knot invariants. The book provides a detailed account of the construction of the Jones polynomial via the quantum groups attached to sl(2), the Vassiliev weight system arising from sl(2), and how these invariants come together through the Kontsevich invariant.
An Introduction to Quasigroups and Their Representations (Studies in Advanced Mathematics)
by Jonathan D. SmithCollecting results scattered throughout the literature into one source, An Introduction to Quasigroups and Their Representations shows how representation theories for groups are capable of extending to general quasigroups and illustrates the added depth and richness that result from this extension.To fully understand representation theory,