Introduction to the Theory of Statistical Inference
Based on the authors' lecture notes, this text presents concise yet complete coverage of statistical inference theory, focusing on the fundamental classical principles. Unlike related textbooks, it combines the theoretical basis of statistical inference with a useful applied toolbox that includes linear models. Suitable for a second semester undergraduate course on statistical inference, the text offers proofs to support the mathematics and does not require any use of measure theory. It illustrates core concepts using cartoons and provides solutions to all examples and problems.
The Number Mysteries
Every time we download music, take a flight across the Atlantic or talk on our cell phones, we are relying on great mathematical inventions. In The Number Mysteries, one of our generation's foremost mathematicians Marcus du Sautoy offers a playful and accessible examination of numbers and how, despite efforts of the greatest minds, the most fundamental puzzles of nature remain unsolved. Du Sautoy tells about the quest to predict the future--from the flight of asteroids to an impending storm, from bending a ball like Beckham to forecasting population growth. He brings to life the beauty behind five mathematical puzzles that have contributed to our understanding of the world around us and have helped develop the technology to cope with it. With loads of games to play and puzzles to solve, this is a math book for everyone.
Statistics Demystified, 2nd Edition
MULTIPLY your chances of learning STATISTICS Trying to understand statistics but feeling a bit uncertain? Here's your solution. Statistics Demystifed, Second Edition helps you master this fundamental topic with ease. Written in a step-by-step format, this practical guide begins by reviewing background mathematics, probability basics, and descriptive measures. The book goes on to demonstrate statistics in action with coverage of sampling, estimation, hypotheses, prediction, regression, correlation, causation, order, and chaos. Detailed examples, concise explanations, and worked-out problems make it easy to understand the material, and end-of-chapter quizzes and a final exam help reinforce learning. It's a no-brainer! You'll learn about: The probability fallacy Random sampling Estimation Assumptions and testing Chaos, bounds, and randomness Variance and standard deviation Correlation and cause/effect relations The use of statistics in medicine, law, math, and engineering Simple enough for a beginner, but challenging enough for an advanced student, Statistics Demystified, Second Edition helps you master this essential subject.
A First Look at Numerical Functional Analysis
Functional analysis arose from traditional topics of calculus and integral and differential equations. This text starts with problems in numerical analysis, showing how they lead naturally to the concepts of functional analysis. Topics include Banach and Hilbert spaces, contraction mappings, convergence, differentiation and integration, and Euclidean space. 1978 edition.
The Predictioneer's Game
Bruce Bueno de Mesquita is a master of game theory, which is a fancy label for a simple idea: People compete, and they always do what they think is in their own best interest. Bueno de Mesquita uses game theory and its insights into human behavior to predict and even engineer political, financial, and personal events. His forecasts, which have been employed by everyone from the CIA to major business firms, have an amazing 90 percent accuracy rate, and in this dazzling and revelatory book he shares his startling methods and lets you play along in a range of high-stakes negotiations and conflicts. Revealing the origins of game theory and the advances made by John Nash, the Nobel Prize--winning scientist perhaps best known from A Beautiful Mind, Bueno de Mesquita details the controversial and cold-eyed system of calculation that he has since created, one that allows individuals to think strategically about what their opponents want, how much they want it, and how they might react to every move. From there, Bueno de Mesquita games such events as the North Korean disarmament talks and the Middle East peace process and recalls, among other cases, how he correctly predicted which corporate clients of the Arthur Andersen accounting firm were most likely engaged in fraudulent activity (hint: one of them started with an E). And looking as ever to the future, Bueno de Mesquita also demonstrates how game theory can provide successful strategies to combat both global warming (instead of relying on empty regulations, make nations compete in technology) and terror (figure out exactly how much U.S. aid will make Pakistan fight the Taliban). But as Bueno de Mesquita shows, game theory isn't just for saving the world. It can help you in your own life, whether you want to succeed in a lawsuit (lawyers argue too much the merits of the case and question too little the motives of their opponents), elect the CEO of your company (change the system of voting on your board to be more advantageous to your candidate), or even buy a car (start by knowing exactly what you want, call every dealer in a fifty-mile radius, and negotiate only over the phone). Savvy, provocative, and shockingly effective, The Predictioneer's Game will change how you understand the world and manage your future. Life's a game, and how you play is whether you win or lose.
Matlab Primer
Highlighting the new aspects of MATLAB(R) 7.10 and expanding on many existing features, this eighth edition continues to offer a hands-on, step-by-step introduction to using the powerful tools of MATLAB. It includes a new chapter on object-oriented programming, a new discussion of the MATLAB File Exchange window, major changes to the MATLAB Editor, and an explanation of more powerful Help tools. It also presents a synopsis of the most frequently used functions, operators, and special characters-providing quick and easy access to frequently used information. M-files and MEX-files for large examples are available online.
Practice Makes Perfect Statistics
A no-nonsense practical guide to statistics, providing concise summaries, clear model examples, and plenty of practice, making this workbook the ideal complement to class study or self-study, preparation for exams or a brush-up on rusty skills. About the Book Established as a successful practical workbook series with over 20 titles in the language learning category, Practice Makes Perfect now provides the same clear, concise approach and extensive exercises to key fields within mathematics. The key to the Practice Makes Perfect series is the extensive exercises that provide learners with all the practice they need for mastery. Not focused on any particular test or exam, but complementary to most statistics curricula Deliberately all-encompassing approach: international perspective and balance between traditional and newer approaches. Large trim allows clear presentation of worked problems, exercises, and explained answers. Features No-nonsense approach: provides clear presentation of content. Over 500 exercises and answers covering all aspects of statistics Successful series: "Practice Makes Perfect" has sales of 1,000,000 copies in the language category - now applied to mathematics Workbook is not exam specific, yet it provides thorough coverage of the statistics skills required in most math tests.
Foundations of Mathematical Analysis
This classroom-tested volume offers a definitive look at modern analysis, with views of applications to statistics, numerical analysis, Fourier series, differential equations, mathematical analysis, and functional analysis. Upper-level undergraduate students with a background in calculus will benefit from its teachings, along with beginning graduate students seeking a firm grounding in modern analysis. A self-contained text, it presents the necessary background on the limit concept, and the first seven chapters could constitute a one-semester introduction to limits. Subsequent chapters discuss differential calculus of the real line, the Riemann-Stieltjes integral, sequences and series of functions, transcendental functions, inner product spaces and Fourier series, normed linear spaces and the Riesz representation theorem, and the Lebesgue integral. Supplementary materials include an appendix on vector spaces and more than 750 exercises of varying degrees of difficulty. Hints and solutions to selected exercises, indicated by an asterisk, appear at the back of the book.
Professor Stewart's Hoard of Mathematical Treasures
Opening another drawer in his Cabinet of Curiosities, renowned mathematics professor Ian Stewart presents a new medley of games, paradoxes, and riddles in Professor Stewart's Hoard of Mathematical Treasures. With wit and aplomb, Stewart mingles casual puzzles with grander forays into ancient and modern mathematical thought. Amongst a host of arcane and astonishing facts about every kind of number from irrational and imaginary to complex and cuneiform, we learn: How to organize chaosHow matter balances anti-matterHow to turn a sphere inside out (without creasing it) How to calculate pi by observing the stars . . . and why you can't comb a hairy ball. Along the way Stewart offers the reader tantalizing glimpses of the mathematics underlying life and the universe. Mind-stretching, enlightening, and endlessly amusing, Professor Stewart's Hoard of Mathematical Treasures will stimulate, delight, and enthrall.
Stochastic Financial Models
Developed from the esteemed author's advanced undergraduate and graduate courses at the University of Cambridge, this text provides a hands-on, sound introduction to mathematical finance. Assuming no prior knowledge of stochastic calculus or measure-theoretic probability, the author includes the relevant mathematical background as well as many exercises with solutions. He first presents the classical topics of utility and the mean-variance approach to portfolio choice. Focusing on derivative pricing, the text then covers the binomial model, the general discrete-time model, Brownian motion, the Black-Scholes model, and various interest-rate models.
Multiple Testing Problems in Pharmaceutical Statistics
Bringing together leading statisticians, scientists, and clinicians from the pharmaceutical industry, academia, and regulatory agencies, this volume explores the rapidly growing area of multiple comparison research with an emphasis on pharmaceutical applications. It describes important multiplicity problems encountered in pre-clinical and clinical trial settings. The book includes numerous case studies from actual pre-clinical experiments and clinical trials to help readers quickly learn common multiple testing methods and apply them to real-life problems. It also reviews relevant regulatory guidelines and implements the methods using SAS and R. The data sets and code are available on the book's website.
Good Thinking
These sparkling essays by a gifted thinker offer philosophical views on the roots of statistical interference. A pioneer in the early development of computing, Irving J. Good made fundamental contributions to the theory of Bayesian inference and was a key member of the team that broke the German Enigma code during World War II. Good maintains that a grasp of probability is essential to answering both practical and philosophical questions. This compilation of his most accessible works concentrates on philosophical rather than mathematical subjects, ranging from rational decisions, randomness, and the nature of probability to operational research, artificial intelligence, cognitive psychology, and chess. These twenty-three self-contained articles represent the author's work in a variety of fields but are unified by a consistently rational approach. Five closely related sections explore Bayesian rationality; probability; corroboration, hypothesis testing, and simplicity; information and surprise; and causality and explanation. A comprehensive index, abundant references, and a bibliography refer readers to classic and modern literature. Good's thought-provoking observations and memorable examples provide scientists, mathematicians, and historians of science with a coherent view of probability and its applications.
200% of Nothing
Acclaim for "In today's world, 'innumeracy' is an even greaterdanger than illiteracy, and is perhaps even more common.Advertisers and politicians exploit it; intellectuals (self-styled)even flaunt it. I hope that this wise and witty book will providecures where they are possible, and warnings where they arenecessary. "It's also a lot of fun. I can guarantee that 100%."--Arthur C.Clarke "Dewdney retells with charm and wit magnificent morsels ofmathematical mayhem discovered by his army of volunteer 'abusedetectives.' From 'sample trashing' to 'numerical terrorism, ' from'percentage pumping' to 'dimensional dementia, ' 200% of Nothingplumbs the depths of innumeracy in daily life and reveals whatordinary people can do about it. A rich, readable, instructive, and persuasive book."--Lynn ArthurSteen, Professor of Mathematics, St. Olaf College
Cryptic Cross Numbers
Extending the principle of cross numbers, these puzzles aim at those of above average mathematical ability, particularly those who enjoy games of strategy. Written from a classroom perspective, the puzzles focus on key aspects of the curriculum and are graded according to difficulty. Solved deductively, the puzzles difficulty can be moderated by using hints provided. Answers are also provided for teacher or selfmarking.
Mathematical Amazements and Surprises
If you've been waiting for a book that will evoke the delight and intrigue that mathematics has to offer, this is the book for you. What are the odds of finding two people who share the same birth date in a room of thirty-five? Most people would guess they're pretty low. In actuality, the probability is better than 80 percent. This is just one of many entertaining examples of mathematical curiosities presented. Two veteran math educators have created the perfect introduction to the wonders of mathematics for the general reader, requiring only a high school background in the subject. Among the entertaining and useful tricks they teach are shortcuts in arithmetic, such as ways to determine at a glance the exact divisors of any given number. They also demonstrate how the properties of certain numbers can lead to infinite loops. What is particularly exciting is how many correct answers turn out to be counterintuitive. Exploring all these features will instill insights into the nature of numbers, improve your ability to manipulate them, and give you an appreciation for the inherent elegance of mathematics. As you marvel at the many unusual relationships and novelties revealed in this ingenious and delightful presentation, you'll be learning more math than you ever thought possible - and will be relishing every moment of it!
Schaum's Outline of Theory and Problems of Basic Mathematics with Applications to Science
Confusing Textbooks? Missed Lectures? Not Enough Time? Fortunately for you, there's Schaum's Outlines. More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. You also get hundreds of examples, solved problems, and practice exercises to test your skills. This Schaum's Outline gives you Practice problems with full explanations that reinforce knowledge Coverage of the most up-to-date developments in your course field In-depth review of practices and applications Fully compatible with your classroom text, Schaum's highlights all the important facts you need to know. Use Schaum's to shorten your study time-and get your best test scores! Schaum's Outlines-Problem Solved.
The Concept of a Riemann Surface
This classic on the general history of functions was written by one of the twentieth century's best-known mathematicians. Hermann Weyl, who worked with Einstein at Princeton, combined function theory and geometry in this high-level landmark work, forming a new branch of mathematics and the basis of the modern approach to analysis, geometry, and topology.The author intended this book not only to develop the basic ideas of Riemann's theory of algebraic functions and their integrals but also to examine the related ideas and theorems with an unprecedented degree of rigor. Weyl's two-part treatment begins by defining the concept and topology of Riemann surfaces and concludes with an exploration of functions of Riemann surfaces. His teachings illustrate the role of Riemann surfaces as not only devices for visualizing the values of analytic functions but also as indispensable components of the theory.
Lattice Theory
Lattice theory extends into virtually every area of mathematics and offers an ideal framework for understanding basic concepts. This outstanding text is written in clear, direct language and enhanced with many research problems, exercises, diagrams, and concise proofs. The author discusses historical developments as well as future directions and provides extensive end-of-chapter materials and references.Both novices and experts will benefit from this treatment, which combines the techniques of an introductory text with those of a monograph. It begins with a concise development of the fundamentals of lattice theory and a detailed exploration of free lattices. The core of the text focuses upon the theory of distributive lattices. Diagrams constitute an integral part of the book, along with 500 exercises and 67 original research problems. Eight appendixes, contributed by a group of experts, complement this accessible and informative text.
Introduction to Complex Variables
A mathematics textbook providing an introduction to fundamental concepts from the theory of complex variables together with numerous worked examples and applications. The textbook contains both elementary and advanced material which is suitable for a one or two semester course in complex variable theory for beginning graduate students in mathematics, physics, engineering and the sciences. There is sufficient elementary material so that the textbook would be suitable for an upper level undergraduate course in complex variable theory. The textbook contains numerous worked examples and a large number of exercises at the end of each chapter. The appendix C contains hints and answers to over 85 percent of the exercise problems. Some of the more difficult problems are worked out in step-by-step detail. An examination of the table of contents and exercise problems at the end of each chapter will illustrate the variety of applications presented. In addition to fundamentals the reader is provided with an introduction to many specialized topics involving complex variables. The text material concludes with a chapter on the Fourier, Laplace and Z-transforms followed by a chapter on special functions. For additional information and sample pages go to the web site: http: //www.math.odu.edu/ jhh/counter8.html.
Nonstandard Methods in Stochastic Analysis and Mathematical Physics
Two-part treatment begins with a self-contained introduction to the subject, followed by applications to stochastic analysis and mathematical physics. "A welcome addition." - Bulletin of the American Mathematical Society. 1986 edition.
Statistics
" Our objective in this book is to present an exposition of basic principles of statistics along with some indication of applications which satisfies the following ten commandments: The focus should be placed on a clear development of basic ideas and principles. The exposition of these basic ideas and principles should be streamlined so as to avoid having the undergrowth get in the way of the statistical forest. High priority should be given to the assumptions which underlie the application of statistical principles. Understanding of abuses, misuses, and misunderstandings which have arisen from the application of statistics is essential for a correct understanding of statistics. The coverage should provide students with sufficient preparation for continued study of intermediate and advanced level statistics or disciplines which use statistical methodology. The exposition should be readable and understandable by students without sacrifice of mathematical accuracy. The organization should clearly distinguish mainstream topics inherent in every basic level statistics course, irrespective of applied interests, from topics of special interest to particular audience segments. The computation dimension should not be given equal billing with statistical principles and ideas. Statistics is the master and, important as it is, the computation tool is the servant. Exercises to provoke-thought - exercise the little grey cells, as Hercule Poirot would put it - should be a prominent part of the exposition. Exercise banks to help the student see statistics as a whole are important.
Statistics
" Our objective in this book is to present an exposition of basic principles of statistics along with some indication of applications which satisfies the following ten commandments: The focus should be placed on a clear development of basic ideas and principles. The exposition of these basic ideas and principles should be streamlined so as to avoid having the undergrowth get in the way of the statistical forest. High priority should be given to the assumptions which underlie the application of statistical principles. Understanding of abuses, misuses, and misunderstandings which have arisen from the application of statistics is essential for a correct understanding of statistics. The coverage should provide students with sufficient preparation for continued study of intermediate and advanced level statistics or disciplines which use statistical methodology. The exposition should be readable and understandable by students without sacrifice of mathematical accuracy. The organization should clearly distinguish mainstream topics inherent in every basic level statistics course, irrespective of applied interests, from topics of special interest to particular audience segments. The computation dimension should not be given equal billing with statistical principles and ideas. Statistics is the master and, important as it is, the computation tool is the servant. Exercises to provoke-thought - exercise the little grey cells, as Hercule Poirot would put it - should be a prominent part of the exposition. Exercise banks to help the student see statistics as a whole are important.
Modern Regression Methods
"Over the years, I have had the opportunity to teach several regression courses, and I cannot think of a better undergraduate text than this one."--The American Statistician "The book is well written and has many exercises. It can serve as a very good textbook for scientists and engineers, with only basic statistics as a prerequisite. I also highly recommend it to practitioners who want to solve real-life prediction problems." (Computing Reviews) Modern Regression Methods, Second Edition maintains the accessible organization, breadth of coverage, and cutting-edge appeal that earned its predecessor the title of being one of the top five books for statisticians by an Amstat News book editor in 2003. This new edition has been updated and enhanced to include all-new information on the latest advances and research in the evolving field of regression analysis. The book provides a unique treatment of fundamental regression methods, such as diagnostics, transformations, robust regression, and ridge regression. Unifying key concepts and procedures, this new edition emphasizes applications to provide a more hands-on and comprehensive understanding of regression diagnostics. New features of the Second Edition include: A revised chapter on logistic regression, including improved methods of parameter estimation A new chapter focusing on additional topics of study in regression, including quantile regression, semiparametric regression, and Poisson regression A wealth of new and updated exercises with worked solutions An extensive FTP site complete with Minitab macros, which allow the reader to compute analyses, and specialized procedures Updated references at the end of each chapter that direct the reader to the appropriate resources for further study An accessible guide to state-of-the-art regression techniques, Modern Regression Methods, Second Edition is an excellent book for courses in regression analysis at the upper-undergraduate and graduate levels. It is also a valuable reference for practicing statisticians, engineers, and physical scientists.
Introduction to Spatial Econometrics
Introduction to Spatial Econometrics presents a variety of regression methods for analyzing spatial data samples that violate the traditional assumption of independence between observations. It explores a range of alternative topics, including maximum likelihood and Bayesian estimation, various types of spatial regression specifications, and applied modeling situations involving different circumstances. The authors clarify the often-mystifying phenomenon of simultaneous spatial dependence. By presenting new methods, they help with the interpretation of spatial regression models. MATLAB(R) toolboxes useful for spatial econometric estimation are made available on the authors' websites.
Number Systems and the Foundations of Analysis
This study of basic number systems explores natural numbers, integers, rational numbers, real numbers, and complex numbers. Written by a noted expert on logic and set theory, it assumes no background in abstract mathematical thought. Undergraduates and beginning graduate students will find this treatment an ideal introduction to number systems, particularly in terms of its detailed proofs.Starting with the basic facts and notions of logic and set theory, the text offers an axiomatic presentation of the simplest structure, the system of natural numbers. It proceeds, by set-theoretic methods, to an examination of integers that covers rings and integral domains, ordered integral domains, and natural numbers and integers of an integral domain. A look at rational numbers and ordered fields follows, along with a survey of the real number system that includes considerations of least upper bounds and greatest lower bounds, convergent and Cauchy sequences, and elementary topology. Numerous exercises and several helpful appendixes supplement the text.
Splines and Variational Methods
One of the clearest available introductions to variational methods, this text requires only a minimal background in calculus and linear algebra. Its self-contained treatment explains the application of theoretic notions to the kinds of physical problems that engineers regularly encounter. The text's first half concerns approximation theoretic notions, exploring the theory and computation of one- and two-dimensional polynomial and other spline functions. Later chapters examine variational methods in the solution of operator equations, focusing on boundary value problems in one and two dimensions. Additional topics include least squares and other Galerkin methods. Many helpful definitions, examples, and exercises appear throughout the book. A classic reference in spline theory, this volume will benefit experts as well as students of engineering and mathematics.
Statistics
Statistical ideas and methods underlie just about every aspect of modern life. From randomized clinical trials in medical research, to statistical models of risk in banking and hedge fund industries, to the statistical tools used to probe vast astronomical databases, the field of statistics has become centrally important to how we understand our world. But the discipline underlying all these is not the dull statistics of the popular imagination. Long gone are the days of manual arithmetic manipulation. Nowadays statistics is a dynamic discipline, revolutionized by the computer, which uses advanced software tools to probe numerical data, seeking structures, patterns, and relationships. This Very Short Introduction sets the study of statistics in context, describing its history and giving examples of its impact, summarizes methods of gathering and evaluating data, and explains the role played by the science of chance, of probability, in statistical methods. The book also explores deep philosophical issues of induction--how we use statistics to discern the true nature of reality from the limited observations we necessarily must make. About the Series: Combining authority with wit, accessibility, and style, Very Short Introductions offer an introduction to some of life's most interesting topics. Written by experts for the newcomer, they demonstrate the finest contemporary thinking about the central problems and issues in hundreds of key topics, from philosophy to Freud, quantum theory to Islam.
Set Theory and the Continuum Hypothesis
This exploration of a notorious mathematical problem is the work of the man who discovered the solution. The independence of the continuum hypothesis is the focus of this study by Paul J. Cohen. It presents not only an accessible technical explanation of the author's landmark proof but also a fine introduction to mathematical logic. An emeritus professor of mathematics at Stanford University, Dr. Cohen won two of the most prestigious awards in mathematics: in 1964, he was awarded the American Mathematical Society's B繫cher Prize for analysis; and in 1966, he received the Fields Medal for Logic. In this volume, the distinguished mathematician offers an exposition of set theory and the continuum hypothesis that employs intuitive explanations as well as detailed proofs. The self-contained treatment includes background material in logic and axiomatic set theory as well as an account of Kurt G繹del's proof of the consistency of the continuum hypothesis. An invaluable reference book for mathematicians and mathematical theorists, this text is suitable for graduate and postgraduate students and is rich with hints and ideas that will lead readers to further work in mathematical logic.
An Introduction to Stability Theory
This introductory treatment covers the basic concepts and machinery of stability theory. Lemmas, corollaries, proofs, and notes assist readers in working through and understanding the material and applications. Full of examples, theorems, propositions, and problems, it is suitable for graduate students in logic and mathematics, professional mathematicians, and computer scientists. Chapter 1 introduces the notions of definable type, heir, and coheir. A discussion of stability and order follows, along with definitions of forking that follow the approach of Lascar and Poizat, plus a consideration of forking and the definability of types. Subsequent chapters examine superstability, dividing and ranks, the relation between types and sets of indiscernibles, and further properties of stable theories. The text concludes with proofs of the theorems of Morley and Baldwin-Lachlan and an extension of dimension theory that incorporates orthogonality of types in addition to regular types.
Rock, Paper, Scissors
Praised by Entertainment Weekly as "the man who put the fizz into physics," Dr. Len Fisher turns his attention to the science of cooperation in his lively and thought-provoking book. Fisher shows how the modern science of game theory has helped biologists to understand the evolution of cooperation in nature, and investigates how we might apply those lessons to our own society. In a series of experiments that take him from the polite confines of an English dinner party to crowded supermarkets, congested Indian roads, and the wilds of outback Australia, not to mention baseball strategies and the intricacies of quantum mechanics, Fisher sheds light on the problem of global cooperation. The outcomes are sometimes hilarious, sometimes alarming, but always revealing. A witty romp through a serious science, Rock, Paper, Scissors will both teach and delight anyone interested in what it what it takes to get people to work together.
Hexaflexagons, Probability Paradoxes, and the Tower of Hanoi
Hexaflexagons, Probability Paradoxes, and the Tower of Hanoi is the inaugural volume in The New Martin Gardner Mathematical Library series. Based off of Gardener's enormously popular Scientific American columns, his puzzles and challenges can now fascinate a whole new generation! Paradoxes and paper-folding, Moebius variations and mnemonics, fallacies, magic square, topological curiosities, parlor tricks, and games ancient and modern, from Polyminoes, Nim, Hex, and the Tower of Hanoi to four-dimensional ticktacktoe. These mathematical recreations, clearly and cleverly presented by Martin Gardner, delight and perplex while demonstrating principles of logic, probability, geometry, and other fields of mathematics. Now the author, in consultation with experts, has added updates to all the chapters, including new game variations, mathematical proofs, and other developments and discoveries.
Origami, Eleusis, and the Soma Cube
Martin Gardner continues to delight readers in Origami, Eleusis, and the Soma Cube, which is the second volume in the new Cambridge series, The New Martin Gardner Mathematical Library, based off his enormously popular Scientific American columns. He introduces young and old readers alike to the Generalized Ham Sandwich Theorem, origami, digital roots, magic squares, the mathematics of cooling coffee, the induction game of Eleusis, Dudeney puzzles, the maze at Hampton Court Palace, and many more mathematical puzzles and principles. Now the author, in consultation with experts, has added updates to all the chapters, including new game variations, mathematical proofs, and other developments and discoveries, to challenge and fascinate a new generation of readers.
Hexaflexagons, Probability Paradoxes, and the Tower of Hanoi
Hexaflexagons, Probability Paradoxes, and the Tower of Hanoi is the inaugural volume in The New Martin Gardner Mathematical Library series. Based off of Gardener's enormously popular Scientific American columns, his puzzles and challenges can now fascinate a whole new generation! Paradoxes and paper-folding, Moebius variations and mnemonics, fallacies, magic square, topological curiosities, parlor tricks, and games ancient and modern, from Polyminoes, Nim, Hex, and the Tower of Hanoi to four-dimensional ticktacktoe. These mathematical recreations, clearly and cleverly presented by Martin Gardner, delight and perplex while demonstrating principles of logic, probability, geometry, and other fields of mathematics. Now the author, in consultation with experts, has added updates to all the chapters, including new game variations, mathematical proofs, and other developments and discoveries.
Origami, Eleusis, and the Soma Cube
Martin Gardner continues to delight readers in Origami, Eleusis, and the Soma Cube, which is the second volume in the new Cambridge series, The New Martin Gardner Mathematical Library, based off his enormously popular Scientific American columns. He introduces young and old readers alike to the Generalized Ham Sandwich Theorem, origami, digital roots, magic squares, the mathematics of cooling coffee, the induction game of Eleusis, Dudeney puzzles, the maze at Hampton Court Palace, and many more mathematical puzzles and principles. Now the author, in consultation with experts, has added updates to all the chapters, including new game variations, mathematical proofs, and other developments and discoveries, to challenge and fascinate a new generation of readers.
Head First Statistics
Wouldn't it be great if there were a statistics book that made histograms, probability distributions, and chi square analysis more enjoyable than going to the dentist? Head First Statistics brings this typically dry subject to life, teaching you everything you want and need to know about statistics through engaging, interactive, and thought-provoking material, full of puzzles, stories, quizzes, visual aids, and real-world examples.Whether you're a student, a professional, or just curious about statistical analysis, Head First's brain-friendly formula helps you get a firm grasp of statistics so you can understand key points and actually use them. Learn to present data visually with charts and plots; discover the difference between taking the average with mean, median, and mode, and why it's important; learn how to calculate probability and expectation; and much more.Head First Statistics is ideal for high school and college students taking statistics and satisfies the requirements for passing the College Board's Advanced Placement (AP) Statistics Exam. With this book, you'll: Study the full range of topics covered in first-year statisticsTackle tough statistical concepts using Head First's dynamic, visually rich format proven to stimulate learning and help you retain knowledge Explore real-world scenarios, ranging from casino gambling to prescription drug testing, to bring statistical principles to lifeDiscover how to measure spread, calculate odds through probability, and understand the normal, binomial, geometric, and Poisson distributionsConduct sampling, use correlation and regression, do hypothesis testing, perform chi square analysis, and moreBefore you know it, you'll not only have mastered statistics, you'll also see how they work in the real world. Head First Statistics will help you pass your statistics course, and give you a firm understanding of the subject so you can apply the knowledge throughout your life.
Statistical Rules of Thumb
Praise for the First Edition: "For a beginner [this book] is a treasure trove; for an experienced person it can provide new ideas on how better to pursue the subject of applied statistics." --Journal of Quality Technology Sensibly organized for quick reference, Statistical Rules of Thumb, Second Edition compiles simple rules that are widely applicable, robust, and elegant, and each captures key statistical concepts. This unique guide to the use of statistics for designing, conducting, and analyzing research studies illustrates real-world statistical applications through examples from fields such as public health and environmental studies. Along with an insightful discussion of the reasoning behind every technique, this easy-to-use handbook also conveys the various possibilities statisticians must think of when designing and conducting a study or analyzing its data. Each chapter presents clearly defined rules related to inference, covariation, experimental design, consultation, and data representation, and each rule is organized and discussed under five succinct headings: introduction; statement and illustration of the rule; the derivation of the rule; a concluding discussion; and exploration of the concept's extensions. The author also introduces new rules of thumb for topics such as sample size for ratio analysis, absolute and relative risk, ANCOVA cautions, and dichotomization of continuous variables. Additional features of the Second Edition include: Additional rules on Bayesian topics New chapters on observational studies and Evidence-Based Medicine (EBM) Additional emphasis on variation and causation Updated material with new references, examples, and sources A related Web site provides a rich learning environment and contains additional rules, presentations by the author, and a message board where readers can share their own strategies and discoveries. Statistical Rules of Thumb, Second Edition is an ideal supplementary book for courses in experimental design and survey research methods at the upper-undergraduate and graduate levels. It also serves as an indispensable reference for statisticians, researchers, consultants, and scientists who would like to develop an understanding of the statistical foundations of their research efforts. A related website www.vanbelle.org provides additional rules, author presentations and more.
Basic Probability Theory
This introduction to more advanced courses in probability and real analysis emphasizes the probabilistic way of thinking, rather than measure-theoretic concepts. Geared toward advanced undergraduates and graduate students, its sole prerequisite is calculus.Taking statistics as its major field of application, the text opens with a review of basic concepts, advancing to surveys of random variables, the properties of expectation, conditional probability and expectation, and characteristic functions. Subsequent topics include infinite sequences of random variables, Markov chains, and an introduction to statistics. Complete solutions to some of the problems appear at the end of the book.
Competition
What do chess-playing computer programs, biological evolution, competitive sports, gambling, alternative voting systems, public auctions, corporate globalization, and class warfare have in common? All are manifestations of a new paradigm in scientific thinking, one that the author calls "the emerging science of competition." Drawing in part on the pioneering work of mathematicians such as John von Neumann, John Nash (of A Beautiful Mind fame), and Robert Axelrod, James Case explores the common game-theoretical strands that tie these seemingly unrelated fields together, showing how each can be better understood in the shared light of the others. Not since James Gleick's bestselling book Chaos brought widespread public attention to the new sciences of chaos and complexity has a general-interest science book served such an eye-opening purpose. Competition will appeal to a wide range of readers, from policy wonks and futurologists to former jocks and other ordinary citizens seeking to make sense of a host of novel--and frequently controversial--issues.
Fourier Series, Transforms, And Boundary Value Problems
This introduction to Fourier and transform methods emphasizes basic techniques rather than theoretical concepts. It explains the essentials of the Fourier method and presents detailed considerations of modeling and solutions of physical problems. All solutions feature well-drawn outlines that allow students to follow an appropriate sequence of steps, and many of the exercises include answers.The chief focus of this text is the application of the Fourier method to physical problems, which are described mathematically in terms of boundary value problems. Problems involving separation of variables, Sturm-Liouville theory, superposition, and boundary complaints are addressed in a logical sequence. Multidimensional Fourier series solutions and Fourier integral solutions on unbounded domains are followed by the special functions of Bessel and Legendre, which are introduced to deal with the cylindrical and spherical geometry of boundary value problems. Students and professionals in mathematics, the physical sciences, and engineering will find this volume an excellent study guide and resource.
Mathematics For The Physical Sciences
This exploration of the mathematical methods of physics takes a careful look at mathematical entities and explains their elementary properties. Its examples, drawn from the physical sciences, illustrate the application of concepts. The theory of distributions is introduced early and employed throughout the text.Concise rather than comprehensive, this text states only essential results in its proofs. Topics include preliminary results in the integral calculus, elementary theory of distributions, convolution, Fourier series and the Fourier transform, the Laplace transform, wave and heat conduction equations, the gamma function, and Bessel functions. Prerequisites include a familiarity with linear algebra and functions of a complex variable.
Guesstimation
Guesstimation is a book that unlocks the power of approximation--it's popular mathematics rounded to the nearest power of ten! The ability to estimate is an important skill in daily life. More and more leading businesses today use estimation questions in interviews to test applicants' abilities to think on their feet. Guesstimation enables anyone with basic math and science skills to estimate virtually anything--quickly--using plausible assumptions and elementary arithmetic. Lawrence Weinstein and John Adam present an eclectic array of estimation problems that range from devilishly simple to quite sophisticated and from serious real-world concerns to downright silly ones. How long would it take a running faucet to fill the inverted dome of the Capitol? What is the total length of all the pickles consumed in the US in one year? What are the relative merits of internal-combustion and electric cars, of coal and nuclear energy? The problems are marvelously diverse, yet the skills to solve them are the same. The authors show how easy it is to derive useful ballpark estimates by breaking complex problems into simpler, more manageable ones--and how there can be many paths to the right answer. The book is written in a question-and-answer format with lots of hints along the way. It includes a handy appendix summarizing the few formulas and basic science concepts needed, and its small size and French-fold design make it conveniently portable. Illustrated with humorous pen-and-ink sketches, Guesstimation will delight popular-math enthusiasts and is ideal for the classroom.
Intermediate Mathematical Analysis
Geared toward those who have studied elementary calculus and intend to progress to more advanced mathematics, this book stresses concepts rather than techniques. It emphasizes the simplest setting of basic theorems so that students may progress from "one-space" to ""n"-space" calculus.An introductory section by the author reviews the roles of sets, relations, and functions. Subsequent chapters explore real numbers, the limit concept, useful theorems, continuity, differentiability, and integrability. The author focuses on real-valued functions of a real variable. Considerations ofcomplex numbers appear only in optional supplements to certain chapters, as well asin the final two chapters, which consist of in-depth explorations of sequences of functions and Fourier series. Each chapter features several helpful exercises."
A Treatise on Probability
John Maynard Keynes's classic work on the study of probability.
Monte Carlo Principles and Neutron Transport Problems
This two-part treatment introduces the general principles of the Monte Carlo method within a unified mathematical point of view, applying them to problems in neutron transport. It describes several efficiency-enhancing approaches, including the method of superposition and simulation of the adjoint equation based on reciprocity.The first half of the book presents an exposition of the fundamentals of Monte Carlo methods, examining discrete and continuous random walk processes and standard variance reduction techniques. The second half of the text focuses directly on the methods of superposition and reciprocity, illustrating their applications to specific neutron transport problems. Topics include the computation of thermal neutron fluxes and the superposition principle in resonance escape computations.
