Mathematics Books

Book SynopsisEtale cohomology is an important branch in arithmetic geometry. This book covers the main materials in SGA 1, SGA 4, SGA 4 1/2 and SGA 5 on etale cohomology theory, which includes decent theory, etale fundamental groups, Galois cohomology, etale cohomology, derived categories, base change theorems, duality, and ℓ-adic cohomology. The prerequisites for reading this book are basic algebraic geometry and advanced commutative algebra.Table of ContentsDescent Theory; Etale Morphisms and Smooth Morphisms; Etale Fundamental Groups; Group Cohomology and Galois Cohomology; Etale Cohomology; Derived Categories and Derived Functors; Base Change Theorems; Duality; Finiteness Theorems; -Adic Cohomology;

Read more less

Book SynopsisIn China, lots of excellent students who are good at maths takes an active part in various maths contests and the best six senior high school students will be selected to form the IMO National Team to compete in the International Mathematical Olympiad. In the past ten years China's IMO Team has achieved outstanding results — they have won the first place almost every year.The author is one of the coaches of China's IMO National Team, whose students have won many gold medals many times in IMO.This book is part of the Mathematical Olympiad Series which discusses several aspects related to maths contests, such as algebra, number theory, combinatorics, graph theory and geometry. The book elaborates on methods of discrete extremization, such as inequality control, repeated extremum, partial adjustment, exploiting symmetry, polishing transform, space estimates, etc.Table of ContentsInequality Control; Repeated Extremum; Partial Adjustment; Exploiting Symmetry; Polishing Transform; Space Estimates; Block Estimates; Guesses and Contradiction; Global Estimates; Parameter Estimates; Counting in Two Ways; Shrinking the Encirclement; Considering Special Cases; Solutions to Exercises;

Read more less

Book SynopsisChapter 1. Thales of Miletus, First of The Seven Sages.- Chapter 2. Archimedes: The God of Mathematics.- Chapter 3. The World of Omar Khayyam.- Chapter 4. Qin Jiushao, Daogu Bridge, and the Mathematical Treatise in Nine Sections.- Chapter 5. The Reclusive Frenchmen:Descartes and Pascal .- Chapter 6. Leibniz: Unattainable Heights.- Chapter 7. John von Neumann, Who Made the World a Better Place.- Chapter 8. Paul Erdos: A Narrowly Missed Opportunity.- Chapter 9. Mathematicians and Poets.- Chapter 10. Mathematicians and Political Leaders.- Chapter 11. Hua Luogeng and Shiing-Shen Chern Two Contemporary Chinese Masters. Chapter 12. "My life can be said to form a circle." An interview with Nobel laureate Professor Chen-Ning Yang.

Read more less

Book SynopsisMathematical Excursions, 5th Edition, will help you develop mathematical and analytical thinking skills for wherever your own excursions may lead. The authors prepare you for success with study strategies and an introduction to problem solving at the start and then help you discover key mathematical concepts and why they matter. This new edition focuses on what you need to know for your life and career. The coverage will help you make more informed decisions, including financial decisions as well as quick decisions in a variety of contexts. Relatable applications include social media, streaming services, wind energy and hybrid vehicles. We hope you enjoy the journey!

Read more less

Book SynopsisGain essential mathematical skills for machine trades and manufacturing with Peterson/McGarry/Smith's MATHEMATICS FOR MACHINE TECHNOLOGY, 9th Edition. This comprehensive book seamlessly connects math concepts to practical machine applications, featuring industry-specific examples, realistic illustrations and actual machine functions. From general math to trigonometry, solid geometry and introductory G- and M-codes for CNC programming, this book prepares you for success in the fields of machine trades and manufacturing. Strengthen your mathematical abilities and unlock your potential for a rewarding career.

Read more less

Book SynopsisProbability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.Trade ReviewFrom the reviews: "This beautifully produced book is intended for advanced undergraduates, PhD students, and researchers and practitioners, primarily in the machine learning or allied areas...A strong feature is the use of geometric illustration and intuition...This is an impressive and interesting book that might form the basis of several advanced statistics courses. It would be a good choice for a reading group." John Maindonald for the Journal of Statistical Software "In this book, aimed at senior undergraduates or beginning graduate students, Bishop provides an authoritative presentation of many of the statistical techniques that have come to be considered part of ‘pattern recognition’ or ‘machine learning’. … This book will serve as an excellent reference. … With its coherent viewpoint, accurate and extensive coverage, and generally good explanations, Bishop’s book is a useful introduction … and a valuable reference for the principle techniques used in these fields." (Radford M. Neal, Technometrics, Vol. 49 (3), August, 2007) "This book appears in the Information Science and Statistics Series commissioned by the publishers. … The book appears to have been designed for course teaching, but obviously contains material that readers interested in self-study can use. It is certainly structured for easy use. … For course teachers there is ample backing which includes some 400 exercises. … it does contain important material which can be easily followed without the reader being confined to a pre-determined course of study." (W. R. Howard, Kybernetes, Vol. 36 (2), 2007) "Bishop (Microsoft Research, UK) has prepared a marvelous book that provides a comprehensive, 700-page introduction to the fields of pattern recognition and machine learning. Aimed at advanced undergraduates and first-year graduate students, as well as researchers and practitioners, the book assumes knowledge of multivariate calculus and linear algebra … . Summing Up: Highly recommended. Upper-division undergraduates through professionals." (C. Tappert, CHOICE, Vol. 44 (9), May, 2007) "The book is structured into 14 main parts and 5 appendices. … The book is aimed at PhD students, researchers and practitioners. It is well-suited for courses on machine learning, statistics, computer science, signal processing, computer vision, data mining, and bio-informatics. Extensive support is provided for course instructors, including more than 400 exercises, lecture slides and a great deal of additional material available at the book’s web site … ." (Ingmar Randvee, Zentralblatt MATH, Vol. 1107 (9), 2007) "This new textbook by C. M. Bishop is a brilliant extension of his former book ‘Neural Networks for Pattern Recognition’. It is written for graduate students or scientists doing interdisciplinary work in related fields. … In summary, this textbook is an excellent introduction to classical pattern recognition and machine learning (in the sense of parameter estimation). A large number of very instructive illustrations adds to this value." (H. G. Feichtinger, Monatshefte für Mathematik, Vol. 151 (3), 2007) "Author aims this text at advanced undergraduates, beginning graduate students, and researchers new to machine learning and pattern recognition. … Pattern Recognition and Machine Learning provides excellent intuitive descriptions and appropriate-level technical details on modern pattern recognition and machine learning. It can be used to teach a course or for self-study, as well as for a reference. … I strongly recommend it for the intended audience and note that Neal (2007) also has given this text a strong review to complement its strong sales record." (Thomas Burr, Journal of the American Statistical Association, Vol. 103 (482), June, 2008) "This accessible monograph seeks to provide a comprehensive introduction to the fields of pattern recognition and machine learning. It presents a unified treatment of well-known statistical pattern recognition techniques. … The book can be used by advanced undergraduates and graduate students … . The illustrative examples and exercises proposed at the end of each chapter are welcome … . The book, which provides several new views, developments and results, is appropriate for both researchers and students who work in machine learning … ." (L. State, ACM Computing Reviews, October, 2008) "Chris Bishop’s … technical exposition that is at once lucid and mathematically rigorous. … In more than 700 pages of clear, copiously illustrated text, he develops a common statistical framework that encompasses … machine learning. … it is a textbook, with a wide range of exercises, instructions to tutors on where to go for full solutions, and the color illustrations that have become obligatory in undergraduate texts. … its clarity and comprehensiveness will make it a favorite desktop companion for practicing data analysts." (H. Van Dyke Parunak, ACM Computing Reviews, Vol. 49 (3), March, 2008)Table of ContentsProbability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Read more less

Book SynopsisWinner of the 2024 De Groot Prize awarded by the International Society for Bayesian Analysis (ISBA)Statistical Rethinking: A Bayesian Course with Examples in R and Stan builds your knowledge of and confidence in making inferences from data. Reflecting the need for scripting in today's model-based statistics, the book pushes you to perform step-by-step calculations that are usually automated. This unique computational approach ensures that you understand enough of the details to make reasonable choices and interpretations in your own modeling work.The text presents causal inference and generalized linear multilevel models from a simple Bayesian perspective that builds on information theory and maximum entropy. The core material ranges from the basics of regression to advanced multilevel models. It also presents measurement error, missing data, and Gaussian process models for spatial and phylogenetic confounding.The second edition emphasizes the directed acyclic graph (DAG) approach to causal inference, integrating DAGs into many examples. The new edition also contains new material on the design of prior distributions, splines, ordered categorical predictors, social relations models, cross-validation, importance sampling, instrumental variables, and Hamiltonian Monte Carlo. It ends with an entirely new chapter that goes beyond generalized linear modeling, showing how domain-specific scientific models can be built into statistical analyses.Features Integrates working code into the main text. Illustrates concepts through worked data analysis examples. Emphasizes understanding assumptions and how assumptions are reflected in code. Offers more detailed explanations of the mathematics in optional sections. Presents examples of using the dagitty R package to analyze causal graphs. Provides the rethinking R package on the author's website and on GitHub. Trade Review"The first edition (and this second edition) of *Statistical Rethinking* beautifully outlines the key steps in the statistical analysis cycle, starting from formulating the research question. I find that many statistics textbooks omit the issue of problem formulation and either jump into data acquisition or further into analysis after the fact. McElreath has created a fantastic text for students of applied statistics to not only learn about the Bayesian paradigm, but also to gain a deep appreciation for the statistical thought process. I also found that many students appreciated McElreath’s engaging writing style and humor, and personally found the infusion of humor quite refreshing."- Adam Loy, Carleton College"(The chapter) ‘Generalized Linear Madness’ represents another great chapter of an even better edition of an already awesome textbook."- Benjamin K. Goodrich, Columbia University"(Chapter 16) is a worthy concluding chapter to a masterful book. Eminently readable and enjoyable. Brimful of small thought-provoking bits which may inspire deeper studies, but first and foremost a window on the trial and error process involved in building a statistical model or rather, indeed, any scientific theory."- Josep Fortiana Gregori, University of Barcelona"I do regard the manuscript as technically correct, clearly written, and at an appropriate level of difficulty. The technical approaches and the R codes of the book are perfect for our students. They can learn concepts of Bayesian models, data analysis, and model validation methods through using the R codes. The codes help students to have better understanding of the models and data analysis process." - Nguyet Nguyen, Youngstown State University "As a textbook it successfully brings the statistician’s toolbox to a wider audience with an accessible style and good humour. It should be recommended to statistics students, both old and new."- Nathan Green, Journal of the Royal Statistical Society, 2021, https://doi.org/10.1111/rssa.12755"In conclusion, Statistical Rethinking frames usual methods and tools taught in graduate statistical courses into a different way to encourage the reader to understand the details and appreciate the underlying assumptions. The accompanying R package offers example codes for some interesting problems that are not available in standard library or other popular packages. This book can be used as a supplement to a graduate course or it can be used by practitioners wanting to brush up their knowledge with better understanding of statistical techniques."- Abhirup Mallik in Technometrics, August 2021"The first edition (and this second edition) of *Statistical Rethinking* beautifully outlines the key steps in the statistical analysis cycle, starting from formulating the research question. I find that many statistics textbooks omit the issue of problem formulation and either jump into data acquisition or further into analysis after the fact. McElreath has created a fantastic text for students of applied statistics to not only learn about the Bayesian paradigm, but also to gain a deep appreciation for the statistical thought process. I also found that many students appreciated McElreath’s engaging writing style and humor, and personally found the infusion of humor quite refreshing."~Adam Loy, Carleton College"(The chapter) ‘Generalized Linear Madness’ represents another great chapter of an even better edition of an already awesome textbook."~Benjamin K. Goodrich, Columbia University"(Chapter 16) is a worthy concluding chapter to a masterful book. Eminently readable and enjoyable. Brimful of small thought-provoking bits which may inspire deeper studies, but first and foremost a window on the trial and error process involved in building a statistical model or rather, indeed, any scientific theory."~Josep Fortiana Gregori, University of Barcelona"I do regard the manuscript as technically correct, clearly written, and at an appropriate level of difficulty. The technical approaches and the R codes of the book are perfect for our students. They can learn concepts of Bayesian models, data analysis, and model validation methods through using the R codes. The codes help students to have better understanding of the models and data analysis process." ~Nguyet Nguyen, Youngstown State University"In conclusion, Statistical Rethinking frames usual methods and tools taught in graduate statistical courses into a different way to encourage the reader to understand the details and appreciate the underlying assumptions. The accompanying R package offers example codes for some interesting problems that are not available in standard library or other popular packages. This book can be used as a supplement to a graduate course or it can be used by practitioners wanting to brush up their knowledge with better understanding of statistical techniques."~Abhirup Mallik in Technometrics, August 2021"As a textbook it successfully brings the statistician’s toolbox to a wider audience with an accessible style and good humour. It should be recommended to statistics students, both old and new."~ Nathan Green, Journal of the Royal Statistical Society, 2021Table of Contents1. The Golem of Prague. 2. Small Worlds and Large Worlds. Chapter 3. Sampling the Imaginary. 4. Geocentric Models. 5. The Many Variables & The Spurious Waffles. 6. The Haunted DAG & The Causal Terror. 7. Ulysses’ Compass. 8. Conditional Manatees. 8. Conditional Manatees. 9. Markov Chain Monte Carlo. 10. Big Entropy and the Generalized Linear Model. 11. God Spiked the Integers. 12. Monsters and Mixtures. 13. Models With Memory. 14. Adventures in Covariance. 15. Missing Data and Other Opportunities. 16. Generalized Linear Madness. 17. Horoscopes.

Read more less

Book SynopsisExam Board: SQALevel: National 5Subject: MathsFirst Teaching: September 2017First Exam: Summer 2018Get your best grade with How to Pass National 5 Applications of Mathematics.Fully updated to account for the changes to the National 5 exam, this book contains all the advice and support you need to revise successfully. It combines an overview of the course syllabus with advice from a top expert on how to improve exam performance, so you have the best chance of success.- Refresh your knowledge with complete course notes- Prepare for the exam with top tips and hints on revision technique- Get your best grade with advice on how to gain those vital extra marks

Read more less

Book Synopsis

Read more less

Book SynopsisThis book offers a lively exploration of the mathematics, physics, and neuroscience that underlie music. Written for musicians and music lovers with any level of science and math proficiency, including none, Music, Math, and Mind demystifies how music works while testifying to its beauty and wonder.Trade ReviewIt is rare that one finds a book where on opening any page, one is drawn to read on and . . . to read back. Every page has a story, every page a fascinating connection between the universal joy we find in music and some biological or mathematical fact. Here is the place to find out about the way crickets make music, and the McGurk effect! The science comes along gently, never intimidating. Only a neurobiologist who is a master composer and musician could have written this wonderful book! -- Roald Hoffmann, author and recipient of the Nobel Prize in ChemistryIf you ever suspected that musicians belonged to a secret society, this is the book that blows the mysteries wide open. Using a potent cocktail of math, physics, history, biology, and neurology, Dave Sulzer explains why music is the medicine most of us can’t live without. This is a book written for the initiate and the noninitiate about the universal way sound and music connect us, both human and nonhuman. -- Peter Gabriel, singer-songwriter, musician, and activistThis is an amazing book. Readers will come back to it again and again for its clear explanations, breadth of content, and “listening” advice. Importantly, it includes a chapter on animals, acknowledging that the sophisticated production and perception of music is not limited to humans. It is accessible to all readers but does not shy away from the direct presentation of science—it gives the reader things that anyone interested in this topic needs to begin to think about. It raises important philosophical questions while allowing the reader to gain the skills to explore these questions further and stops there—giving the reader the chance to pursue or ignore. -- Susan Savage-Rumbaugh, primatologist and psychologist, specialist in communication by bonobosDave Soldier’s excellent book turns into an encyclopedia of our tonal imagination as it catalogues the nefarious passion that gives our creativity its edge. -- John Cale, songwriter, composer, performerIf you think you love music as much as you possibly could, think again. Music, which is so hard to define, and which connects to everything, has yet to reveal every level of its joy to you. This book will help you experience music as an animal, a neural pathway, or a mathematical principle. -- Jaron Lanier, writer, computer scientist, and musicianWhen your band protests, “Whaddaya mean ‘dynamics’? I’m playing as loud as I can!”—turn them onto the solid matter in Music, Math, and Mind. As to Soldier’s confection? A ribald reality check on what makes music matter and why we should mind. I’ve waited seventy-six years in a musical immersion to put a buzz on Dave Soldier’s fly-leaf. -- Van Dyke Parks, performer, arranger, producer, composer, and lyricist, including with the Beach BoysPutting the worlds of science and music together is an ambitious, and potentially intimidating, endeavor. But David Sulzer had me at paragraph one, where he writes “no one needs this book!” No, I don’t need it—but I find I do want it. -- John Schaefer, host of New Sounds, WNYCMusicians shouldn’t be intimidated by the title Music, Math, and Mind: The Physics and Neuroscience of Music. This is a book that any musician or music fan will find both enjoyable and educational. The questions regarding the science, biology, and math related to music are made easily understandable, and the book is grounded in David’s passion for both creating and enjoying music. At the end, anyone reading this book will have a greater appreciation for the creative spirit and a way to understand music in even deeper ways. -- Bob Neuwirth, singer-songwriter and record producerWith his whimsical, philosophical deep dive into the musical interplay of science and mathematics, Sulzer draws on his dual roles – as professor of psychiatry, neurology, and pharmacology at Columbia University and as an experimental musician (under the name Dave Soldier). Each chapter unfolds with theory, history, mathematical notation, and riveting storytelling. * Library Journal *At last, the book for science nerds no musical home should be without. * Limelight Magazine *A jaunty, conversational manner...you barely realize that you're learning some rather heady stuff. * Memphis Flyer *[Music, Math, and Mind: the Physics and Neuroscience of Music] is exactly the sort of book that science written for a general audience should be—accessible on multiple levels from the neophyte to the expert, engagingly written, and informative in a way that stimulates curiosity and prompts further investigation. . . . Highly recommended. * Choice *Table of ContentsNota BeneIntroduction1. The Parameters of Sound2. The Math of Pitch, Scales, and Harmony3. Waves and Harmonics4. The Math of Sound and Resonance5. Math and Rhythmic StructureCenterpiece: The Sense of Hearing6. Brain Mechanisms of Rhythm7. Neural Mechanisms of Emotion8. Ear Physiology: How Air Waves Become Sound9. Deep Brain Physiology of Sound10. Sound Disorders, Illusions, and Hallucinations11. Animal Sound, Song, and MusicAcknowledgmentsAppendix 1: Musical Pitch to Frequency TableAppendix 2: Further ReadingBibliographyAuthor’s Selected Compositions and DiscographyIndex

Read more less

Book SynopsisThis book is an introduction to programming with Python for MBA students and others in business positions who need a crash course. Beginning with fundamentals such as variables, strings, lists, and functions, it builds up to data analytics and practical ways to derive value from large and complex datasets.Trade ReviewBusiness leaders everywhere increasingly need top technology and data skills to stay competitive. Mattan Griffel and Daniel Guetta bring Python to life through clear and compelling stories and case studies, showing you how to use the power of variables, strings, and lists to immediately help your business and analytics. -- Glenn Hubbard, dean emeritus and Russell L. Carson Professor of Finance and Economics, Columbia Business SchoolIn the data-driven economy, there is an enormous demand for hybrid professionals who are simultaneously broad and deep across business and technical fields. Mattan Griffel and Daniel Guetta have done a great job providing a practical, step-by-step guide for commercially minded individuals to upskill quickly in the technical arena. This will be required reading for all those in my team who need to rapidly learn fundamental data and analytical skills. -- Afsheen Afshar, founder and CEO, Pilot Wave Holdings ManagementBusiness education is changing to prepare MBA students for careers in the digital age and to provide an understanding of the technological capabilities and analytics tools driving this digital transformation. Griffel and Guetta are experts in Python and its use in business analytics. This book will be an incredible resource for teaching programming to students in MBA programs and for business practitioners and managers. -- Costis Maglaras, dean and David and Lyn Silfen Professor of Business, Columbia Business SchoolTable of ContentsIntroductionPart I1. Getting Started with Python2. Python Basics, Part 13. Python Basics, Part 24. Python Basics, Part 3Part II5. Introduction to Data in Python6. Exploring, Plotting, and Modifying Data in Python7. Bringing Together Datasets8. Aggregation9. PracticeWhat’s Next?NotesIndex

Read more less

Book SynopsisTrade Review"Nahin includes gems from all over mathematics, ranging from engineering applications to beautiful pure-mathematical identities... It would be good to have more books like this."--Timothy Gowers, Nature "Nahin's tale of the formula e[pi] i+1=0, which links five of the most important numbers in mathematics, is remarkable. With a plethora of historical and anecdotal material and a knack for linking events and facts, he gives the reader a strong sense of what drove mathematicians like Euler."--Matthew Killeya, New Scientist "It is very difficult to sum up the greatness of Euler... This excellent book goes a long way to explaining the kind of mathematician he really was."--Steve Humble, Mathematics Today "What a treasure of a book this is! This is the fourth enthusiastic, informative, and delightful book Paul Nahin has written about the beauties of various areas of mathematics... This book is a marvelous tribute to Euler's genius and those who built upon it and would make a great present for students of mathematics, physics, and engineering and their professors."--Henry Ricardo, MAA Reviews "The heart and soul of the book are the final three chapters on Fourier series, Fourier integrals, and related engineering. One can recommend them to all applied math students for their historical development and sensible content."--Robert E. O'Malley, Jr., SIAM Review "This is a book for mathematicians who enjoy historically motivated mathematical explanations on a high mathematical level."--Eberhard Knobloch, Mathematical Reviews "It is a 'popular' book, written for a general reader with some mathematical background equivalent to a first-year undergraduate course in the UK."--Robin Wilson, London Mathematical Society NewsletterTable of Contents*FrontMatter, pg. i*Contents, pg. ix*Preface to the Paperback Edition, pg. xiii*Preface, pg. xxix*Introduction, pg. 1*Chapter 1. Complex Numbers, pg. 13*Chapter 2. Vector Trips, pg. 68*Chapter 3. The Irrationality of pi2, pg. 92*Chapter 4. Fourier Series, pg. 114*Chapter 5. Fourier Integrals, pg. 188*Chapter 6. Electronics and -1, pg. 275*Euler: The Man and the Mathematical Physicist, pg. 324*Notes, pg. 347*Acknowledgments, pg. 375*Index, pg. 377

Read more less

Book SynopsisTrade Review"Sports fans will learn much from probability theory and statistical models as they abandon empty clichés (time to throw momentum out of the informed fan's lexicon) and confront institutionalized injustices (such as those built into the protocols for selecting a national champion in college football and for seeding the NCAA's basketball tournament). A rare fusion of sports enthusiasm and numerical acumen." * Booklist *"Who is Wayne Winston? Maybe we should begin by telling you who he is not. He is not some barstool fan or uninformed sportswriter who fuels his opinions with information gleaned from SportsCenter highlights or newspaper box scores. He is a professor of decision sciences at Indiana University's Kelley School of Business, and until this year was the statistical guru for the Dallas Mavericks. He is author of the book Mathletics, which explains what statistics really tell us about sports."---Ken Berger, CBSSports.com"[A] terrific read for anyone trying to model markets statistically and make trading decisions based on statistical data. . . . Reading Winston's book is a mind-opening experience."---Brenda Jubin, Reading the Markets blog"[Huge] and highly interesting."---Mathematics Magazine, Paul J. Campbell

Read more less

Book SynopsisTrade Review"A thorough, very clearly written overview on the subject of machine learning for those with the prerequisite mathematical tools of calculus, linear algebra and probability."---Jonathan Shock, Mathemafrica"Valuable."---J. Brzezinski, Choice

Read more less

Book Synopsis

Read more less

Book Synopsis

Read more less

Book SynopsisTable of ContentsIntroduction 1 About This Book 1 Foolish Assumptions 2 Icons Used in This Book 2 Beyond the Book 3 Where to Go from Here 3 Unit 1: Getting Started with Basic Math & Pre-algebra 5 Chapter 1: Playing the Numbers Game 7 Inventing Numbers 8 Understanding Number Sequences 8 Evening the odds 8 Counting by threes, fours, fives, and so on 9 Getting square with square numbers 9 Composing yourself with composite numbers 10 Stepping out of the box with prime numbers 11 Multiplying quickly with exponents 12 Four Important Sets of Numbers 13 Counting on the counting numbers 13 Introducing integers 13 Staying rational 14 Getting real 14 Chapter 2: The Big Four Operations 15 The Big Four Operations 15 Adding things up: Addition 16 Take it away: Subtraction 16 A sign of the times: Multiplication 17 Doing math lickety-split: Division 18 Applying the Big Four Operations to Larger Numbers 18 Calculating stacked addition 18 Performing stacked subtraction 19 Calculating with stacked multiplication 21 Understanding long division 22 Unit 2: the Big Four Operations: Addition, Subtraction, Multiplication, and Division 25 Chapter 3: Counting on Success: Numbers and Digits 27 Knowing Your Place Value 28 Counting to ten and beyond 28 Telling placeholders from leading zeros 29 Reading long numbers 30 Close Enough for Rock ‘n’ Roll: Rounding and Estimating 30 Rounding numbers 30 Estimating value to make problems easier 32 Practice Questions Answers and Explanations 34 Whaddya Know? Chapter 3 Quiz 35 Answers to Chapter 3 Quiz 36 Chapter 4: Staying Positive with Negative Numbers 37 Understanding Where Negative Numbers Come From 38 Sign-Switching: Understanding Negation and Absolute Value 39 Addition and Subtraction with Negative Numbers 41 Starting with a negative number 41 Adding a negative number 41 Subtracting a negative number 42 Knowing Signs of the Times (and Division) for Negative Numbers 44 Practice Questions Answers and Explanations 47 Whaddya Know? Chapter 4 Quiz 51 Answers to Chapter 4 Quiz 52 Chapter 5: Putting the Big Four Operations to Work 55 Switching Things Up with Inverse Operations and the Commutative Property 56 Getting with the In-Group: Parentheses and the Associative Property 59 Distribution to lighten the load 61 Understanding Inequalities 63 Doesn’t equal (≠) 63 Less than (<) and greater than (>) 63 Less than or equal to (≤) and greater than or equal to (≥) 64 Approximately equals (≈) 64 Moving Beyond the Big Four: Exponents and Square Roots 65 Understanding exponents 66 Discovering your roots 67 Practice Questions Answers and Explanations 69 Whaddya Know? Chapter 5 Quiz 72 Answers to Chapter 5 Quiz 73 Unit 3: Getting a Handle on Whole Numbers 75 Chapter 6: Please Excuse My Dear Aunt Sally: Evaluating Arithmetic Expressions with PEMDAS 77 The Three E’s of Math: Equations, Expressions, and Evaluation 78 Seeking equality for all: Equations 78 Hey, it’s just an expression 78 Evaluating the situation 79 Putting the Three E’s together 79 Introducing Order of Operations (PEMDAS) 80 Expressions with only addition and subtraction 81 Expressions with only multiplication and division 81 Mixed-operator expressions 82 Handling Powers Responsibly 83 Prioritizing parentheses 84 Pulling apart parentheses and powers 85 Figuring out nested parentheses 86 Bringing It All Together: The Order of Operations 87 Practice Questions Answers and Explanations 89 Whaddya Know? Chapter 6 Quiz 98 Answers to Chapter 6 Quiz 99 Chapter 7: Turning Words into Numbers: Basic Math Word Problems 103 Dispelling Two Myths about Word Problems 104 Word problems aren’t always hard 104 Word problems are useful 104 Solving Basic Word Problems 105 Turning word problems into word equations 105 Plugging in numbers for words 109 Send in the clowns 109 Our house in the middle of our street 110 I hear the train a-comin’ 110 Solving More-Complex Word Problems 113 When numbers get serious 113 Too much information 115 Practice Questions Answers and Explanations 120 Whaddya Know? Chapter 7 Quiz 124 Answers to Chapter 7 Quiz 125 Chapter 8: Divisibility and Prime Numbers 127 Knowing the Divisibility Tricks 128 Counting everyone in: Numbers you can divide everything by 128 In the end: Looking at the final digits 128 Count it up: Checking divisibility by adding and subtracting digits 130 Less is more: Checking divisibility by subtracting 134 Cross-checking: Using multiple tests 135 Identifying Prime and Composite Numbers 136 Practice Questions Answers and Explanations 139 Whaddya Know? Chapter 8 Quiz 142 Answers to Chapter 8 Quiz 143 Chapter 9: Divided Attention: Factors and Multiples 145 Knowing Six Ways to Say the Same Thing 146 Understanding Factors and Multiples 146 Finding Fabulous Factors 148 Deciding when one number is a factor of another 148 Understanding factor pairs 148 Generating a Number’s Factors 149 Decomposing a Number into Its Prime Factors 150 Finding the Greatest Common Factor 151 Generating the Multiples of a Number 153 Finding the Least Common Multiple 153 Practice Questions Answers and Explanations 155 Whaddya Know? Chapter 9 Quiz 158 Answers to Chapter 9 Quiz 159 Unit 4: Fractions 161 Chapter 10: Understanding Fractions 163 Slicing a Cake into Fractions 164 Knowing the Fraction Facts of Life 165 Telling the numerator from the denominator 165 Flipping for reciprocals 166 Using ones and zeros 166 Mixing things up 167 Knowing proper from improper 167 Increasing and Reducing Terms of Fractions 169 Increasing the terms of fractions 170 Reducing fractions to lowest terms (simplifying fractions) 171 Converting between Improper Fractions and Mixed Numbers 174 Knowing the parts of a mixed number 174 Converting a mixed number to an improper fraction 175 Converting an improper fraction to a mixed number 176 Comparing Fractions with Cross-Multiplication 178 Working with Ratios and Proportions 180 Practice Questions Answers and Explanations 182 Whaddya Know? Chapter 10 Quiz 188 Answers to Chapter 10 Quiz 189 Chapter 11: Fractions and the Big Four Operations 191 Multiplying and Dividing Fractions 192 Multiplying numerators and denominators straight across 192 Doing a flip to divide fractions 194 Adding and Subtracting Fractions with the Same Denominator 196 Adding and Subtracting Fractions with Different Denominators 198 The easy case: Increasing the terms of one fraction 198 The difficult case: Increasing the terms of both fractions 200 Practice Questions Answers and Explanations 202 Whaddya Know? Chapter 11 Quiz 208 Answers to Chapter 11 Quiz 209 Chapter 12: Mixing Things Up with Mixed Numbers 213 Multiplying and Dividing Mixed Numbers 214 Adding Mixed Numbers 216 Adding mixed numbers that have the same denominator 216 Adding mixed numbers that have different denominators 217 Adding mixed numbers with carrying 217 Subtracting Mixed Numbers 220 Subtracting mixed numbers that have the same denominator 220 Subtracting mixed numbers that have different denominators 221 Subtracting mixed numbers with borrowing 222 Practice Questions Answers and Explanations 225 Whaddya Know? Chapter 12 Quiz 233 Answers to Chapter 12 Quiz 234 Unit 5: Decimals and Percents 241 Chapter 13: Getting to the Point with Decimals 243 Understanding Basic Decimal Stuff 244 Counting dollars and decimals 244 Identifying the place value of decimals 246 Knowing the decimal facts of life 247 Performing the Big Four Operations with Decimals 252 Adding decimals 253 Subtracting decimals 254 Multiplying decimals 256 Dividing decimals 257 Converting between Decimals and Fractions 262 Simple Decimal-Fraction Conversions 262 Changing decimals to fractions 264 Changing fractions to decimals 267 Practice Questions Answers and Explanations 271 Whaddya Know? Chapter 13 Quiz 279 Answers to Chapter 13 Quiz 280 Chapter 14: Playing the Percentages 285 Making Sense of Percentages 285 Dealing with Percentages Greater than 100% 286 Converting to and from Percentages, Decimals, and Fractions 287 Converting Percentages to Decimals 287 Changing Decimals to Percentages 288 Switching from Percentages to Fractions 288 Converting Fractions to Percentages 289 Solving Percentage Problems 290 Figuring out simple percent problems 291 Turning the problem around 292 Deciphering more-difficult percent problems 293 Putting All the Percent Problems Together 294 Identifying the three types of percent problems 294 Solving Percent Problems with Equations 295 Practice Questions Answers and Explanations 299 Whaddya Know? Chapter 14 Quiz 303 Answers to Chapter 14 Quiz 304 Chapter 15: Word Problems with Fractions, Decimals, and Percentages 307 Adding and Subtracting Parts of the Whole in Word Problems 308 Sharing a pizza: Fractions 308 Buying by the pound: Decimals 309 Splitting the vote: Percentages 309 Problems about Multiplying Fractions 310 Renegade grocery shopping: Buying less than they tell you to 310 Easy as pie: Working out what’s left on your plate 311 Multiplying Decimals and Percentages in Word Problems 313 To the end: Figuring out how much money is left 313 Finding out how much you started with 314 Handling Percent Increases and Decreases in Word Problems 316 Raking in the dough: Finding salary increases 316 Earning interest on top of interest 316 Getting a deal: Calculating discounts 317 Practice Questions Answers and Explanations 319 Whaddya Know? Chapter 15 Quiz 322 Answers to Chapter 15 Quiz 324 Unit 6: Reaching the Summit: Advanced Pre-algebra Topics 327 Chapter 16: Powers and Roots 329 Memorizing Powers and Roots 329 Remembering square numbers and square roots 330 Keeping track of cubic numbers and cube roots 330 Knowing a few powers of 2 and their related roots 331 Changing the Base 332 Negating a number raised to an exponent 332 Finding powers of negative numbers 332 Finding powers of fractions 333 Mixing negative numbers and fractions with exponents 333 Exponents of 0 and Negative Numbers 334 Exponents of 0 334 Negative exponents 335 Fractional Exponents 337 Exponents of 1 2 337 Exponents of 1 3 338 Exponents of 1 4 , 1 5 , 1 , and so forth 6 339 Other fractional exponents 339 Practice Questions Answers and Explanations 341 Whaddya Know? Chapter 16 Quiz 343 Answers to Chapter 16 Quiz 344 Chapter 17: A Perfect Ten: Condensing Numbers with Scientific Notation 347 First Things First: Using Powers of Ten as Exponents 348 Counting zeros and writing exponents 348 Exponential Arithmetic: Multiplying and Dividing Powers of Ten 350 Working with Scientific Notation 352 Writing in scientific notation 352 Understanding order of magnitude 354 Multiplying with scientific notation 355 Dividing with Scientific Notation 356 Practice Questions Answers and Explanations 357 Whaddya Know? Chapter 17 Quiz 360 Answers to Chapter 17 Quiz 361 Chapter 18: How Much Have You Got? Weights and Measures 363 Understanding Units 364 Adding and subtracting units 364 Multiplying and dividing units 364 Examining Differences between the English and Metric Systems 365 Looking at the English system 365 Looking at the metric system 369 Estimating and Converting between the English and Metric Systems 372 Estimating in the metric system 373 Converting units of measurement 375 Converting between English and Metric Units 377 Practice Questions Answers and Explanations 381 Whaddya Know? Chapter 18 Quiz 388 Answers to Chapter 18 Quiz 389 Chapter 19: Getting the Picture with Geometry 393 Getting on the Plane: Points, Lines, Angles, and Shapes 394 Making some points 394 Knowing your lines 394 Figuring the angles 395 Shaping things up 396 Getting in Shape: Polygon (and Non-Polygon) Basics 396 Closed Encounters: Shaping Up Your Understanding of 2-D Shapes 397 Polygons 397 Circles 399 Squaring Off with Quadrilaterals 400 Making a Triple Play with Triangles 403 Getting Around with Circle Measurements 405 Taking a Trip to Another Dimension: Solid Geometry 406 The many faces of polyhedrons 407 3-D shapes with curves 408 Building Solid Measurement Skills 409 Solving Geometry Word Problems 413 Working from words and images 413 Breaking out those sketching skills 415 Practice Questions Answers and Explanations 418 Whaddya Know? Chapter 19 Quiz 425 Answers to Chapter 19 Quiz 427 Chapter 20: Figuring Your Chances: Statistics and Probability 431 Gathering Data Mathematically: Basic Statistics 432 Understanding differences between qualitative and quantitative data 432 Working with qualitative data 433 Working with quantitative data 436 Looking at Likelihoods: Basic Probability 439 Figuring the probability 440 Oh, the possibilities! Counting outcomes with multiple coins 441 Practice Questions Answers and Explanations 444 Whaddya Know? Chapter 20 Quiz 447 Answers to Chapter 20 Quiz 449 Chapter 21: Setting Things Up with Basic Set Theory 451 Understanding Sets 451 Elementary, my dear: Considering what’s inside sets 452 Sets of numbers 454 Performing Operations on Sets 455 Union: Combined elements 455 Intersection: Elements in common 456 Relative complement: Subtraction (sorta) 457 Complement: Feeling left out 457 Practice Questions Answers and Explanations 459 Whaddya Know? Chapter 21 Quiz 461 Answers to Chapter 21 Quiz 462 Unit 7: the X-files: Introduction to Algebra 463 Chapter 22: Working with Algebraic Expressions 465 Seeing How X Marks the Spot 466 Expressing Yourself with Algebraic Expressions 466 Evaluating Algebraic Expressions 467 Knowing the Terms 470 Making the commute: Rearranging your terms 471 Identifying the coefficient and variable 472 Adding and Subtracting Like Terms 473 Identifying like terms 473 Adding and subtracting terms 474 Multiplying and Dividing Terms 475 Simplifying Expressions by Combining Like Terms 479 Removing Parentheses from an Algebraic Expression 481 Drop everything: Parentheses with a plus sign 481 Sign turnabout: Parentheses with a negative sign 481 Distribution: Parentheses with no sign 482 FOILing: Dealing with Two Sets of Parentheses 484 Practice Questions Answers and Explanations 487 Whaddya Know? Chapter 22 Quiz 495 Answers to Chapter 22 Quiz 496 Chapter 23: Solving Algebraic Equations 499 Understanding Algebraic Equations 500 Using X in Equations 500 Choosing among four ways to solve algebraic equations 501 The Balancing Act: Solving for x 503 Striking a balance 504 Using the Balance Scale to Isolate X 504 Rearranging Equations and Isolating x 506 Rearranging terms on one side of an equation 506 Moving terms to the other side of the equals sign 507 Removing parentheses from equations 509 Cross-multiplying 512 Practice Questions Answers and Explanations 515 Whaddya Know? Chapter 23 Quiz 525 Answers to Chapter 23 Quiz 526 Chapter 24: Tackling Algebra Word Problems 531 Solving Algebra Word Problems in Five Steps 531 Declaring a variable 532 Setting up the equation 533 Solving the equation 533 Answering the question 534 Checking your work 534 Choosing Your Variable Wisely 536 Solving More-Complex Algebraic Problems 539 Charting four people 539 Crossing the finish line with five people 540 Practice Questions Answers and Explanations 545 Whaddya Know? Chapter 24 Quiz 549 Answers to Chapter 24 Quiz 550 Chapter 25: Graphing Algebraic Equations 553 Graphing on the xy-Plane 554 Understanding the axes, the origin, and the quadrants 554 Plotting coordinates on the xy-plane 554 Graphing equations on the xy-plane 555 Understanding Linear Equations 559 Knowing the most basic linear equation 559 Changing the slope (m) 560 Changing the y-intercept (b) 561 Understanding slope-intercept form 562 Measuring the Slope of a Line 564 Estimating slope 564 Eyeballing slope on the xy-plane 566 Using the two-point slope formula 569 Graphing Linear Equations Using the Slope and y-intercept 572 Practice Questions Answers and Explanations 574 Whaddya Know? Chapter 25 Quiz 577 Answers to Chapter 25 Quiz 581 Index 583

Read more less

Book SynopsisThis 3rd edition of Modern Mathematical Statistics with Applications tries to strike a balance between mathematical foundations and statistical practice. The book provides a clear and current exposition of statistical concepts and methodology, including many examples and exercises based on real data gleaned from publicly available sources. Here is a small but representative selection of scenarios for our examples and exercises based on information in recent articles: Use of the “Big Mac index” by the publication The Economist as a humorous way to compare product costs across nations Visualizing how the concentration of lead levels in cartridges varies for each of five brands of e-cigarettes Describing the distribution of grip size among surgeons and how it impacts their ability to use a particular brand of surgical stapler Estimating the true average odometer reading of used Porsche Boxsters listed for sale on www.cars.com Comparing head acceleration after impact when wearing a football helmet with acceleration without a helmet Investigating the relationship between body mass index and foot load while running The main focus of the book is on presenting and illustrating methods of inferential statistics used by investigators in a wide variety of disciplines, from actuarial science all the way to zoology. It begins with a chapter on descriptive statistics that immediately exposes the reader to the analysis of real data. The next six chapters develop the probability material that facilitates the transition from simply describing data to drawing formal conclusions based on inferential methodology. Point estimation, the use of statistical intervals, and hypothesis testing are the topics of the first three inferential chapters. The remainder of the book explores the use of these methods in a variety of more complex settings. This edition includes many new examples and exercises as well as an introduction to the simulation of events and probability distributions. There are more than 1300 exercises in the book, ranging from very straightforward to reasonably challenging. Many sections have been rewritten with the goal of streamlining and providing a more accessible exposition. Output from the most common statistical software packages is included wherever appropriate (a feature absent from virtually all other mathematical statistics textbooks). The authors hope that their enthusiasm for the theory and applicability of statistics to real world problems will encourage students to pursue more training in the discipline. Trade Review“The textbook Modern Mathematical Statistics with Applications can be recommended for applied mathematics and statistics majors as well as prospective scientists, business, social and medical science majors interested in the applying modern statistical methods for their disciplines.” (Maria Ivanchuk, ISCB News, iscb.info, June, 2022)Table of Contents

Read more less

Book SynopsisCovid-19 has shown us the importance of mathematical and statistical models to interpret reality, provide forecasts, and explore future scenarios. Algorithms, artificial neural networks, and machine learning help us discover the opportunities and pitfalls of a world governed by mathematics and artificial intelligence.Trade Review“Alfio Quarteroni invites us to the stage of contemporary science and technology in which multidisciplinarity and transferability are combined to contribute to the construction of the wisdom of life … . A great master. Its access does not present difficulties beyond the decision to satisfy an intellectual and spiritual curiosity with a future edge: a book to be read with ease and understood with great quality.” (Melio Sáenz, ResearchGate, researchgate.net, June, 2023)Table of Contents1 Epidemic.- 2 Retrospective.- 3 Interlude: the revolution that did not happen and the revolution that was unforeseen.- 4 Artificial intelligence, learning computers, artificial neural networks.- 5 A bit of maths (behind artificial intelligence and machine learning).- 6 BIG DATA - BIG BROTHER (or, on the ethical and moral aspects of artificial intelligence).

Read more less

Book SynopsisIntroductory courses in combinatorial optimization are popular at the upper undergraduate/graduate levels in computer science, industrial engineering, and business management/OR, owed to its wide applications in these fields. There are several published textbooks that treat this course and the authors have used many of them in their own teaching experiences. This present text fills a gap and is organized with a stress on methodology and relevant content, providing a step-by-step approach for the student to become proficient in solving combinatorial optimization problems. Applications and problems are considered via recent technology developments including wireless communication, cloud computing, social networks, and machine learning, to name several, and the reader is led to the frontiers of combinatorial optimization. Each chapter presents common problems, such as minimum spanning tree, shortest path, maximum matching, network flow, set-cover, as well as key algorithms, such as greedy algorithm, dynamic programming, augmenting path, and divide-and-conquer. Historical notes, ample exercises in every chapter, strategically placed graphics, and an extensive bibliography are amongst the gems of this textbook.Trade Review“This book introduces combinatorial optimization with a methodology-oriented organization. It targets undergraduate and graduate students and contains a good mix of theoretical results (with proof) and examples, which helps the reader acquire ideas and concepts. The chapters end with a list of exercises for the students.” (Francisco Chicano, Mathematical Reviews, January, 2024)“The book can appropriately be used as a textbook in a graduate course. All the algorithms are clearly explained and presented. It is a very valuable book for successful application of real problems from combinatorial optimization. … this book is an excellent contribution to the field of combinatorial optimization, and it is highly recommended to the students and researchers in optimization.” (Samir Kumar Neogy, zbMATH 1512.90001, 2023)Table of Contents1. Introduction.-2. Divide-and-Conquer.- 3. Dynamic Programming and Shortest Path.- 4. Greedy Algorithm and Spanning Tree.- 5. Incremental Method and Maximum Network Flow.- 6. Linear Programming.- 7. Primal-Dual Methods and Minimum Cost Flow.- 8. NP-hard Problems and Approximation Algorithms.- 9. Restriction and Steiner Tree.- 10. Greedy Approximation and Submodular Optimization.- 11. Relaxation and Rounding. 12. Nonsubmodular Optimization.- Bibliography.

Read more less

Book SynopsisThis book introduces the reader to the study of Hamiltonian systems, focusing on the stability of autonomous and periodic systems and expanding to topics that are usually not covered by the canonical literature in the field. It emerged from lectures and seminars given at the Federal University of Pernambuco, Brazil, known as one of the leading research centers in the theory of Hamiltonian dynamics. This book starts with a brief review of some results of linear algebra and advanced calculus, followed by the basic theory of Hamiltonian systems. The study of normal forms of Hamiltonian systems is covered by Ch.3, while Chapters 4 and 5 treat the normalization of Hamiltonian matrices. Stability in non-linear and linear systems are topics in Chapters 6 and 7. This work finishes with a study of parametric resonance in Ch. 8. All the background needed is presented, from the Hamiltonian formulation of the laws of motion to the application of the Krein-Gelfand-Lidskii theory of strongly stable systems. With a clear, self-contained exposition, this work is a valuable help to advanced undergraduate and graduate students, and to mathematicians and physicists doing research on this topic.Table of ContentsForeword.- Preliminaries on Advanced Calculus.- Hamiltonian Systems Theory.- Normal Forms of Hamiltonian Systems.- Spectral Decomposition of Hamiltonian Matrices.- The General Linear Normalization.- Stability of Equilibria.- Stability of Linear Hamiltonian Systems.- Parametric Resonance.- References.- Index.

Read more less

Book SynopsisThis memoir chronicles the journey of an academic, tracing a path from primary school in Zambia to a career in higher education as a mathematician and educational leader. Set against the backdrop of the 20th century, the book explores how early influences and historical events shape an individual's life and professional trajectory. The author shares childhood experiences across three parts of Africa, providing an original perspective as a witness to the post-colonial period. Through personal reflections, the memoir delves into the emergence of ideas and collaborations in mathematics and how these shape career choices. It also offers candid observations on the major changes in British higher education since the 1980s. Intended for a general audience, this book provides a compelling read for anyone interested in the experience of becoming a mathematician, and higher education in general.Table of Contents1 Dorset and Ghana.- 2 Lusaka.- 3 Swaziland.- 4 Dorchester.- 5 Coventry.- 6 Seattle, Shuffleboard, Vitaly.- 7 College Park, Maryland.- 8 Columbus.- 9 Norwich and Graham.- 10 Columbus Revisited.- 11 Norwich Revisited.- 12 Two New Roles in Norwich.- 13 From Sillery to the Office for Students.- 14 Durham.- 15 Leeds.- 16 Newcastle.- 17 Looking back.

Read more less

Book SynopsisKofi Annan, former Secretary General of the United Nations, argued that We need to create a world that is equitable, that is stable and a world where we bear in mind the needs of others, and not only what we need immediately. We are all in the same boat.American businessman, John Landgraf stated: I hope that most of us believe that we actually would all benefit from living in a more equitable society. If that's not happening, we're squandering human potential. For the world to be fair, one needs to know how to divide. Without the mathematics of division, humankind cannot functionMarie Antoinette, Queen of France (infamously) said If people have no bread, let them eat cake, and while Ahmes - the scribe of the Rhind Mathematical Papyrus - dealt with loaves of bread, prosperous people in the twentieth century dealt with cake division, although bread is also uniformly available. You'll be surprised, but there are at least four books and over 200 scientific (not gastronomical!) papers on ca

Read more less

Book Synopsis- Part I Modelling Assets and Markets.- Introduction.- The Pricing of Financial Derivatives.- Part II Computational Pricing Methods in the Black-Scholes Framework.- Binomial Tree Methods.- Simulation I: Monte Carlo Methods.- Finite Difference Methods.- Part III Simulation Methods Beyond the Black-Scholes Framework.- Simulation II: Modelling Multivariate Financial Data.- Stochastic Models for Interest Rates.- Simulation III: Numerical Approximation of SDE Models.

Read more less

Book Synopsis

Read more less

Book SynopsisProbability is an area of mathematics of tremendous contemporary importance across all aspects of human endeavour. This book is a compact account of the basic features of probability and random processes at the level of first and second year mathematics undergraduates and Masters'' students in cognate fields. It is suitable for a first course in probability, plus a follow-up course in random processes including Markov chains.A special feature is the authors'' attention to rigorous mathematics: not everything is rigorous, but the need for rigour is explained at difficult junctures. The text is enriched by simple exercises, together with problems (with very brief hints) many of which are taken from final examinations at Cambridge and Oxford. The first eight chapters form a course in basic probability, being an account of events, random variables, and distributions - discrete and continuous random variables are treated separately - together with simple versions of the law of large numbersTable of ContentsPART A BASIC PROBABILITY; PART B FURTHER PROBABILITY

Read more less

Book Synopsis

Read more less

Book SynopsisSuitable for advanced undergraduate and beginning graduate students, this title introduces readers to the principal ideas and applications of game theory. It covers static and dynamic games, with complete and incomplete information and features a variety of examples, applications, and exercises.Trade Review"The book is enjoyable to read and truly an enrichment in game theory. It is widely well-structured and well-written and mathematically correct. The purpose is given perfectly. I recommend the book for researchers and graduate students who wants to get some insight in the area of game theory."--Sirma Zeynep, Zentralblatt MATH "The book aims to be precise and rigorous, yet accessible and reader-friendly, and, to a great extent, it does hit these apparently conflicting targets... The depth of the book is intermediate, with a conventional, yet clear, style of writing. It will please mainstream economists... It can help advanced undergraduates and also students at honors or master's levels. It can also be used by PhD students seeking a fast, not so mathematized introduction to the field."--Jose Rodriques-Neto, Economic RecordTable of ContentsPreface xi PART I Rational Decision Making Chapter 1 The Single-Person Decision Problem 3 *1.1 Actions, Outcomes, and Preferences 4 * 1.1.1 Preference Relations 5 * 1.1.2 Payoff Functions 7 *1.2 The Rational Choice Paradigm 9 *1.3 Summary 11 *1.4 Exercises 11 Chapter 2 Introducing Uncertainty and Time 14 *2.1 Risk, Nature, and Random Outcomes 14 2.1.1 Finite Outcomes and Simple Lotteries 15 2.1.2 Simple versus Compound Lotteries 16 2.1.3 Lotteries over Continuous Outcomes 17 *2.2 Evaluating Random Outcomes 18 2.2.1 Expected Payoff: The Finite Case 19 2.2.2 Expected Payoff: The Continuous Case 20 2.2.3 Caveat: It's Not Just the Order Anymore 21 2.2.4 Risk Attitudes 22 2.2.5 The St. Petersburg Paradox 23 *2.3 Rational Decision Making with Uncertainty 24 2.3.1 Rationality Revisited 24 2.3.2 Maximizing Expected Payoffs 24 *2.4 Decisions over Time 26 2.4.1 Backward Induction 26 2.4.2 Discounting Future Payoffs 28 *2.5 Applications 29 2.5.1 The Value of Information 29 2.5.2 Discounted Future Consumption 31 *2.6 Theory versus Practice 32 *2.7 Summary 33 *2.8 Exercises 33 PART II Static Games of Complete Information Chapter 3 Preliminaries 43 *3.1 Normal-Form Games with Pure Strategies 46 3.1.1 Example: The Prisoner's Dilemma 48 3.1.2 Example: Cournot Duopoly 49 3.1.3 Example: Voting on a New Agenda 49 *3.2 Matrix Representation: Two-Player Finite Game 50 3.2.1 Example: The Prisoner's Dilemma 51 3.2.2 Example: Rock-Paper-Scissors 52 *3.3 Solution Concepts 52 3.3.1 Assumptions and Setup 54 3.3.2 Evaluating Solution Concepts 55 3.3.3 Evaluating Outcomes 56 *3.4 Summary 57 *3.5 Exercises 58 Chapter 4 Rationality and Common Knowledge 59 *4.1 Dominance in Pure Strategies 59 4.1.1 Dominated Strategies 59 4.1.2 Dominant Strategy Equilibrium 61 4.1.3 Evaluating Dominant Strategy Equilibrium 62 *4.2 Iterated Elimination of Strictly Dominated Pure Strategies 63 4.2.1 Iterated Elimination and Common Knowledge of Rationality 63 4.2.2 Example: Cournot Duopoly 65 4.2.3 Evaluating IESDS 67 *4.3 Beliefs, Best Response, and Rationalizability 69 4.3.1 The Best Response 69 4.3.2 Beliefs and Best-Response Correspondences 71 4.3.3 Rationalizability 73 4.3.4 The Cournot Duopoly Revisited 73 4.3.5 The "p-Beauty Contest" 74 4.3.6 Evaluating Rationalizability 76 *4.4 Summary 76 *4.5 Exercises 76 Chapter 5 Pinning Down Beliefs: Nash Equilibrium 79 *5.1 Nash Equilibrium in Pure Strategies 80 5.1.1 Pure-Strategy Nash Equilibrium in a Matrix 81 5.1.2 Evaluating the Nash Equilibria Solution 83 *5.2 Nash Equilibrium: Some Classic Applications 83 5.2.1 Two Kinds of Societies 83 5.2.2 The Tragedy of the Commons 84 5.2.3 Cournot Duopoly 87 5.2.4 Bertrand Duopoly 88 5.2.5 Political Ideology and Electoral Competition 93 *5.3 Summary 95 *5.4 Exercises 95 Chapter 6 Mixed Strategies 101 *6.1 Strategies, Beliefs, and Expected Payoffs 102 6.1.1 Finite Strategy Sets 102 6.1.2 Continuous Strategy Sets 104 6.1.3 Beliefs and Mixed Strategies 105 6.1.4 Expected Payoffs 105 *6.2 Mixed-Strategy Nash Equilibrium 107 6.2.1 Example: Matching Pennies 108 6.2.2 Example: Rock-Paper-Scissors 111 6.2.3 Multiple Equilibria: Pure and Mixed 113 *6.3 IESDS and Rationalizability Revisited 114 *6.4 Nash's Existence Theorem 117 *6.5 Summary 123 *6.6 Exercises 123 PART III Dynamic Games of Complete Information Chapter 7 Preliminaries 129 *7.1 The Extensive-Form Game 130 7.1.1 Game Trees 132 7.1.2 Imperfect versus Perfect Information 136 *7.2 Strategies and Nash Equilibrium 137 7.2.1 Pure Strategies 137 7.2.2 Mixed versus Behavioral Strategies 139 7.2.3 Normal-Form Representation of Extensive-Form Games 143 *7.3 Nash Equilibrium and Paths of Play 145 *7.4 Summary 147 *7.5 Exercises 147 Chapter 8 Credibility and Sequential Rationality 151 *8.1 Sequential Rationality and Backward Induction 152 *8.2 Subgame-Perfect Nash Equilibrium: Concept 153 *8.3 Subgame-Perfect Nash Equilibrium: Examples 159 8.3.1 The Centipede Game 159 8.3.2 Stackelberg Competition 160 8.3.3 Mutually Assured Destruction 163 8.3.4 Time-Inconsistent Preferences 166 *8.4 Summary 169 *8.5 Exercises 170 Chapter 9 Multistage Games 175 *9.1 Preliminaries 176 *9.2 Payoffs 177 *9.3 Strategies and Conditional Play 178 *9.4 Subgame-Perfect Equilibria 180 *9.5 The One-Stage Deviation Principle 184 *9.6 Summary 186 *9.7 Exercises 186 Chapter 10 Repeated Games 190 *10.1 Finitely Repeated Games 190 *10.2 Infinitely Repeated Games 192 10.2.1 Payoffs 193 10.2.2 Strategies 195 *10.3 Subgame-Perfect Equilibria 196 *10.4 Application: Tacit Collusion 201 *10.5 Sequential Interaction and Reputation 204 10.5.1 Cooperation as Reputation 204 10.5.2 Third-Party Institutions as Reputation Mechanisms 205 10.5.3 Reputation Transfers without Third Parties 207 *10.6 The Folk Theorem: Almost Anything Goes 209 *10.7 Summary 214 *10.8 Exercises 215 Chapter 11 Strategic Bargaining 220 *11.1 One Round of Bargaining: The Ultimatum Game 222 *11.2 Finitely Many Rounds of Bargaining 224 *11.3 The Infinite-Horizon Game 228 *11.4 Application: Legislative Bargaining 229 11.4.1 Closed-Rule Bargaining 230 11.4.2 Open-Rule Bargaining 232 *11.5 Summary 235 *11.6 Exercises 236 PART IV Static Games of Incomplete Information Chapter 12 Bayesian Games 241 *12.1 Strategic Representation of Bayesian Games 246 12.1.1 Players, Actions, Information, and Preferences 246 12.1.2 Deriving Posteriors from a Common Prior: A Player's Beliefs 247 12.1.3 Strategies and Bayesian Nash Equilibrium 249 *12.2 Examples 252 12.2.1 Teenagers and the Game of Chicken 252 12.2.2 Study Groups 255 *12.3 Inefficient Trade and Adverse Selection 258 *12.4 Committee Voting 261 *12.5 Mixed Strategies Revisited: Harsanyi's Interpretation 264 *12.6 Summary 266 *12.7 Exercises 266 Chapter 13 Auctions and Competitive Bidding 270 *13.1 Independent Private Values 272 13.1.1 Second-Price Sealed-Bid Auctions 272 13.1.2 English Auctions 275 13.1.3 First-Price Sealed-Bid and Dutch Auctions 276 13.1.4 Revenue Equivalence 279 *13.2 Common Values and the Winner's Curse 282 *13.3 Summary 285 *13.4 Exercises 285 Chapter 14 Mechanism Design 288 *14.1 Setup: Mechanisms as Bayesian Games 288 14.1.1 The Players 288 14.1.2 The Mechanism Designer 289 14.1.3 The Mechanism Game 290 *14.2 The Revelation Principle 292 *14.3 Dominant Strategies and Vickrey-Clarke-Groves Mechanisms 295 14.3.1 Dominant Strategy Implementation 295 14.3.2 Vickrey-Clarke-Groves Mechanisms 295 *14.4 Summary 299 *14.5 Exercises 299 PART V Dynamic Games of Incomplete Information Chapter 15 Sequential Rationality with Incomplete Information 303 *15.1 The Problem with Subgame Perfection 303 *15.2 Perfect Bayesian Equilibrium 307 *15.3 Sequential Equilibrium 312 *15.4 Summary 314 *15.5 Exercises 314 Chapter 16 Signaling Games 318 *16.1 Education Signaling: The MBA Game 319 *16.2 Limit Pricing and Entry Deterrence 323 16.2.1 Separating Equilibria 324 16.2.2 Pooling Equilibria 330 *16.3 Refinements of Perfect Bayesian Equilibrium in Signaling Games 332 *16.4 Summary 335 *16.5 Exercises 335 Chapter 17 Building a Reputation 339 *17.1 Cooperation in a Finitely Repeated Prisoner's Dilemma 339 *17.2 Driving a Tough Bargain 342 *17.3 A Reputation for Being "Nice" 349 *17.4 Summary 354 *17.5 Exercises 354 Chapter 18 Information Transmission and Cheap Talk 357 *18.1 Information Transmission: A Finite Example 358 *18.2 Information Transmission: The Continuous Case 361 *18.3 Application: Information and Legislative Organization 365 *18.4 Summary 367 *18.5 Exercises 367 Chapter 19 Mathematical Appendix 369 *19.1 Sets and Sequences 369 19.1.1 Basic Definitions 369 19.1.2 Basic Set Operations 370 *19.2 Functions 371 19.2.1 Basic Definitions 371 19.2.2 Continuity 372 *19.3 Calculus and Optimization 373 19.3.1 Basic Definitions 373 19.3.2 Differentiation and Optimization 374 19.3.3 Integration 377 *19.4 Probability and Random Variables 378 19.4.1 Basic Definitions 378 19.4.2 Cumulative Distribution and Density Functions 379 19.4.3 Independence, Conditional Probability, and Bayes' Rule 380 19.4.4 Expected Values 382 References 385 Index 389

Read more less

Book SynopsisTrade Review"In this intriguing study, maths historian Eli Maor traces those echoes, along with the trajectories of the ‘scientists, inventors, composers, and occasional eccentrics’ behind them."---Barbara Kiser, Nature"The prolific author Eli Maor has released yet another very readable and enjoyable book on the history of mathematics from Princeton University Press. . . . As with all of Maor’s books, this one belongs in your library so that leading students can learn about unknowns like Joseph Sauveur in the fascinating story of how mathematics and music intersect."---Karl-Dieter Crisman, MAA Reviews"Maor is an experienced storyteller. His mixture of musical, mathematical, and physical history, enriched with personal experiences and some unexpected links and bridges are nice reading for anybody with a slight interest in music and science. No mathematical training required."---Adhemar Bultheel, European Mathematical Society"This is a fascinating study of the reciprocal relationship between music and mathematics in the West."---David Lorimer, Paradigm Explorer"For anyone who ponders the role mathematics has in music, this short and delightful book is a joy to read from cover to cover. It is full of anecdotes and interesting facts and, being by Eli Maor is intensely readable."---Phil Dyke, Leonardo Reviews"[Music by the Numbers] is enjoyable and readable"---Owen Toller, Mathematical Gazette

Read more less

Book SynopsisThird edition of popular undergraduate-level text offers historic overview, readable treatment of mathematics before Euclid, Euclid's Elements, non-Euclidean geometry, algebraic structure, formal axiomatics, sets, more. Problems, some with solutions. Bibliography.

Read more less

Book SynopsisDifferential equations and linear algebra are two central topics in the undergraduate mathematics curriculum. This innovative textbook allows the two subjects to be developed either separately or together, illuminating the connections between two fundamental topics, and giving increased flexibility to instructors. It can be used either as a semester-long course in differential equations, or as a one-year course in differential equations, linear algebra, and applications. Beginning with the basics of differential equations, it covers first and second order equations, graphical and numerical methods, and matrix equations. The book goes on to present the fundamentals of vector spaces, followed by eigenvalues and eigenvectors, positive definiteness, integral transform methods and applications to PDEs. The exposition illuminates the natural correspondence between solution methods for systems of equations in discrete and continuous settings. The topics draw on the physical sciences, engineer

Read more less

Book SynopsisFiguring: The Joy Of Numbers by Shakuntala Devi, is a book that teaches readers a series of computing shortcuts, which will not only reduce calculation time, but also help to develop an interest for the subject of mathematics.In Figuring: The Joy Of Numbers, renowned mathematician Shakuntala Devi, teaches readers about the wonders which can be sought by utilizing easy calculation methods. Devi''s book will help readers calculate faster and easier This book will teach readers how to proceed forward with different types of challenging calculations, with the aim of increasing precision as well as speed, without compromising the correctness of the result. In order to understand the techniques prescribed in the text, readers are required to have a basic knowledge of arithmetic. Devi states that initially the problems might seem too complicated or out of reach, but with time and practice readers will definitely acquire the skill to solve mathematic problems in an expedient and precise manner.

Read more less

Book Synopsis

Read more less

Book SynopsisStudy smarter and stay on top of your differential equations course with the bestselling Schaumâs Outlineânow with the NEW Schaumâs app and website! Schaumâs Outline of Differential Equations, Fifth Edition is the go-to study guide for all students of science who need to learn or refresh their knowledge of differential equations. With an outline format that facilitates quick and easy review and mirrors the course in scope and sequence, this book helps you understand basic concepts and get the extra practice you need to excel in the course. It supports the all major differential equations textbooks and is useful for study in Calculus (I, II, and III), Mathematical Modeling, Introductory Differential Equations and Differential Equations. Chapters include an Introduction to Modeling and Qualitative Methods, Classifications of First-Order Differential Equations, Linear Differential Equations, Variation of Parameters, Initial-Value Problems for Linear

Read more less

Book SynopsisMastering the basic concepts of mathematics is the key to understanding other subjects such as Economics, Finance, Statistics, and Accounting. Mathematics for Finance, Business and Economics is written informally for easy comprehension. Unlike traditional textbooks it provides a combination of explanations, exploration and real-life applications of major concepts. Mathematics for Finance, Business and Economics discusses elementary mathematical operations, linear and non-linear functions and equations, differentiation and optimization, economic functions, summation, percentages and interest, arithmetic and geometric series, present and future values of annuities, matrices and Markov chains. Aided by the discussion of real-world problems and solutions, students across the business and economics disciplines will find this textbook perfect for gaining an understanding of a core plank of their studies.Table of Contents1. Elementary Mathematical Concepts and Operations 2. Linear Equations 3. Non-Linear Functions and Equations 4. Functions and Differentiation 5. Economic Application of Functions and Differentiation 6. Summation, Percentages and Interest 7. Arithmetic and Geometric Series 8. Annuity and Amortization 9. Matrices and Markov Chains

Read more less

Book SynopsisEmphasizes a vectors approach and prepares students to make the transition from computational to theoretical mathematics. This book includes applications drawn from a variety of disciplines, which reinforce the fact that linear algebra is a valuable tool for modeling real-life problems.Table of Contents1. VECTORS. Introduction: The Racetrack Game. The Geometry and Algebra of Vectors. Length and Angle: The Dot Product. Exploration: Vectors and Geometry. Lines and Planes. Exploration: The Cross Product. Writing Project: Origins of the Dot Product and the Cross Product. Applications. 2. SYSTEMS OF LINEAR EQUATIONS. Introduction: Triviality. Introduction to Systems of Linear Equations. Direct Methods for Solving Linear Systems. Writing Project: A History of Gaussian Elimination. Explorations: Lies My Computer Told Me; Partial Pivoting; Counting Operations: An Introduction to the Analysis of Algorithms. Spanning Sets and Linear Independence. Applications. Vignette: The Global Positioning System. Iterative Methods for Solving Linear Systems. 3. MATRICES. Introduction: Matrices in Action. Matrix Operations. Matrix Algebra. The Inverse of a Matrix. The LU Factorization. Subspaces, Basis, Dimension, and Rank. Introduction to Linear Transformations. Vignette: Robotics. Applications. 4. EIGENVALUES AND EIGENVECTORS. Introduction: A Dynamical System on Graphs. Introduction to Eigenvalues and Eigenvectors. Determinants. Writing Project: Which Came First-the Matrix or the Determinant? Vignette: Lewis Carroll's Condensation Method. Exploration: Geometric Applications of Determinants. Eigenvalues and Eigenvectors of n x n Matrices. Writing Project: The History of Eigenvalues. Similarity and Diagonalization. Iterative Methods for Computing Eigenvalues. Applications and the Perron-Frobenius Theorem. Vignette: Ranking Sports Teams and Searching the Internet. 5. ORTHOGONALITY. Introduction: Shadows on a Wall. Orthogonality in Rn. Orthogonal Complements and Orthogonal Projections. The Gram-Schmidt Process and the QR Factorization. Explorations: The Modified QR Factorization; Approximating Eigenvalues with the QR Algorithm. Orthogonal Diagonalization of Symmetric Matrices. Applications. 6. VECTOR SPACES. Introduction: Fibonacci in (Vector) Space. Vector Spaces and Subspaces. Linear Independence, Basis, and Dimension. Writing Project: The Rise of Vector Spaces. Exploration: Magic Squares. Change of Basis. Linear Transformations. The Kernel and Range of a Linear Transformation. The Matrix of a Linear Transformation. Exploration: Tilings, Lattices and the Crystallographic Restriction. Applications. 7. DISTANCE AND APPROXIMATION. Introduction: Taxicab Geometry. Inner Product Spaces. Explorations: Vectors and Matrices with Complex Entries; Geometric Inequalities and Optimization Problems. Norms and Distance Functions. Least Squares Approximation. The Singular Value Decomposition. Vignette: Digital Image Compression. Applications. 8. CODES. (Online) Code Vectors. Vignette: The Codabar System. Error-Correcting Codes. Dual Codes. Linear Codes. The Minimum Distance of a Code. Appendix A: Mathematical Notation and Methods of Proof. Appendix B: Mathematical Induction. Appendix C: Complex Numbers. Appendix D: Polynomials.

Read more less

Book SynopsisThis textbook for advanced courses in group theory focuses on finite groups, with emphasis on the idea of group actions. Early chapters identify important themes and establish the notation used throughout the book, and subsequent chapters explore the normal and arithmetical structures of groups as well as applications. Includes 679 exercises. 1978 edition.

Read more less

Book SynopsisAn inclusive vision of mathematics—its beauty, its humanity, and its power to build virtues that help us all flourishTrade Review“Beautifully written, contains well-chosen and interesting mathematical puzzles, and offers an important viewpoint for mathematicians to consider. . . . The book is aimed at a broader audience and is also a call to being more inclusive, to recognising that there are many paths to success.”—Pamela Gorkin, Mathematical IntelligencerAwarded Book of the Year by Aleo ReviewWinner of the Euler Book Prize, sponsored by the Mathematical Association of AmericaSelected for the 2021 Phi Beta Kappa Award for Science Short List“The ancient Greeks argued that the best life was filled with beauty, truth, justice, play and love. The mathematician Francis Su knows just where to find them.”—Kevin Hartnett, Quanta Magazine “Please read this beautiful, compelling, galvanizing book if you care about mathematics, social justice, or humanity, which I hope is everyone.”—Eugenia Cheng, author of The Art of Logic in an Illogical World “The world desperately needs this all‑embracing and deeply human perspective on what mathematics is and why it matters. The key qualities developed by mathematical thinking are characteristics that we should all value and long for.”—Eddie Woo, author of It’s a Numberful World “I was mesmerized by this unusual, sublime book. Original insights and engaging puzzles made me feel young again, discovering a way to Zen and the Art of Mathematics.”—Nalini Joshi, University of Sydney “Francis Su believes that math can make us better humans—and he leads by example. Every page is a work of generosity and compassion. Plus, the puzzles will haunt you for weeks.”—Ben Orlin, author of Math with Bad Drawings “A celebration of mathematics and the human spirit. Learning mathematics enriches our lives, and Su wants everyone to have a seat at the banquet.”—Edward Scheinerman, author ofvThe Mathematics Lover’s Companion “A delightful mixture of philosophy, mathematical illustrations, and compassion.”—John Cook, Singular Value Consulting “Francis Su has written a lyrical meditation on the beauty of mathematics and how it connects to our common humanity.”—John Urschel, author of Mind and Matter: A Life in Math and Football “Su elegantly uncovers the beauty and power of mathematics as they relate to our desires to be loved, trusted, and accepted. A powerful narrative of mathematical beauty, this book is the antidote for a mathematically fixed mindset.”—Talithia Williams, author of Power in Numbers: The Rebel Women of Mathematics “This is perhaps the most important mathematics book of our time. Francis Su shows mathematics is an experience of the mind and, most important, of the heart.”—James Tanton, Global Math Project“The ancient Greeks argued that the best life was filled with beauty, truth, justice, play and love. The mathematician Francis Su knows just where to find them.”—Kevin Hartnett, Quanta Magazine

Read more less

Book Synopsis

Read more less

Book SynopsisGain a solid foundation in the principles of mathematical thinking with the algebra and trigonometry textbook that's written so you can understand it. ALGEBRA AND TRIGONOMETRY, 5th Edition by best-selling author team Stewart/Redlin/Watson explains concepts simply and clearly, helping you grasp the math that you need to succeed in this course. This edition provides updated guidelines on how to solve problems for each topic. New, helpful review and revised practice opportunities work with new content as the authors introduce problem solving and mathematical modeling early in the book and emphasize these principles throughout. Comprehensive and evenly paced, this edition introduces the function concept and guides you in using a graphing calculator as you develop insights into mathematical ideas. Online WebAssign resources are also available to provide interactive practice and assist you in mastering key principles.Table of ContentsPreface. To the Student. Prologue: Principles of Problem Solving. P. PREREQUISITES. Chapter Overview. P1. Modeling the Real-World with Algebra. P2. The Real Numbers. P3. Integer Exponents and Scientific Notation. P4. Rational Exponents and Radicals. P5. Algebraic Expressions. P6. Factoring. P7. Rational Expressions. P8. Solving Basic Equations. P9. Modeling with Equations. Chapter P Review. Chapter P Test. FOCUS ON MODELING: MAKING THE BEST DECISIONS. 1. EQUATIONS AND GRAPHS. Chapter Overview. 1.1 The Coordinate Plane. 1.2 Graphs of Equations in Two Variables; Circles. 1.3 Lines. 1.4 Solving Quadratic Equations. 1.5 Complex Numbers. 1.6 Solving Other Types of Equations. 1.7 Solving Inequalities. 1.8 Solving Absolute Value Equations and Inequalities. 1.9 Solving Equations and Inequalities Graphically. 1.10 Modeling Variations. Chapter 1 Review. Chapter 1 Test. FOCUS ON MODELING: Fitting Lines to Data. 2. FUNCTIONS. Chapter Overview. 2.1 Functions. 2.2 Graphs of Functions. 2.3 Getting Information from the Graph of a Function. 2.4 Average Rate of Change of a Function. 2.5 Linear Functions and Models. 2.6 Transformations of Functions. 2.7 Combining Functions. 2.8 One-to-One Functions and Their Inverses. Chapter 2 Review. Chapter 2 Test. FOCUS ON MODELING: MODELING WITH FUNCTIONS. 3. POLYNOMIAL AND RATIONAL FUNCTIONS. Chapter Overview. 3.1. Quadratic Functions and Models. 3.2 Polynomial Functions and Their Graphs. 3.3 Dividing Polynomials. 3.4 Real Zeros of Polynomials. 3.5 Complex Zeros and the Fundamental Theorem of Algebra. 3.6 Rational Functions. 3.7 Polynomial and Rational Inequalities. Chapter 3 Review. Chapter 3 Test. FOCUS ON MODELING: FITTING POLYNOMIAL CURVES TO DATA. 4. EXPONENTIAL AND LOGARITHMIC FUNCTIONS. Chapter Overview. 4.1 Exponential Functions. 4.2 The Natural Exponential Function. 4.3 Logarithmic Functions. 4.4 Laws of Logarithms. 4.5 Exponential and Logarithmic Equations. 4.6 Modeling with Exponential Functions. 4.7 Logarithmic Scales. Chapter 4 Review. Chapter 4 Test. FOCUS ON MODELING: FITTING EXPONENTIAL AND POWER CURVES TO DATA. 5. TRIGONOMETRIC FUNCTIONS: RIGHT TRIANGLE APPROACH. Chapter Overview. 5.1 Angle Measure. 5.2 Trigonometry of Right Triangles. 5.3 Trigonometric Functions of Angles. 5.4 Inverse Trigonometric Functions and Triangles. 5.5 The Law of Sines. 5.6 The Law of Cosines. Chapter 5 Review. Chapter 5 Test. FOCUS ON MODELING: SURVEYING. 6. TRIGONOMETRIC FUNCTIONS: UNIT CIRCLE APPROACH. Chapter Overview. 6.1 The Unit Circle. 6.2 Trigonometric Functions of Real Numbers. 6.3 Trigonometric Graphs. 6.4 More Trigonometric Graphs. 6.5 Inverse Trigonometric Functions and Their Graphs. 6.6 Modeling Harmonic Motion. Chapter 6 Review. Chapter 6 Test. FOCUS ON MODELING: FITTING SINUSOIDAL CURVES TO DATA. 7. CONIC SECTIONS. Chapter Overview. 7.1 Trigonometric Identities. 7.2 Addition and Subtraction Formulas. 7.3 Double-Angle, Half-Angle, and Sum-Product Formulas. 7.4 Basic Trigonometric Equations. 7.5 More Trigonometric Equations. Chapter 7 Review. Chapter 7 Test. FOCUS ON MODELING: TRAVELING AND STANDING WAVES. 8. POLAR COORDINATES, PARAMETRIC EQUATIONS, and VECTORS. Chapter Overview. 8.1 Polar Coordinates. 8.2 Graphs of Polar Equations. 8.3 Polar Form of Complex Numbers; DeMoivre's Theorem. 8.4 Plane Curves and Parametric Equations. 8.5 Vectors in Two Dimensions. 8.6 The Dot Product. Chapter 8 Review. Chapter 8 Test. FOCUS ON MODELING: THE PATH OF A PROJECTILE. 9. SYSTEMS OF EQUATIONS AND INEQUALITIES. Chapter Overview. 9.1 Systems of Linear Equations in Two Variables. 9.2 Systems of Linear Equations in Several Variables. 9.3 Partial Fractions. 9.4 Systems of Nonlinear Equations. 9.5 Systems of Inequalities. Chapter 9 Review. Chapter 9 Test. FOCUS ON MODELING: LINEAR PROGRAMMING. 10. MATRICES AND DETERMINANTS. Chapter Overview. 10.1 Matrices and Systems of Linear Equations. 10.2 The Algebra of Matrices. 10.3 Inverses of Matrices and Matrix Equations. 10.4 Determinants and Cramer's Rule. Chapter 10 Review. Chapter 10 Test. FOCUS ON MODELING: COMPUTER GRAPHICS. 11. CONIC SECTIONS. Chapter Overview. 11.1 Parabolas. 11.2 Ellipses. 11.3 Hyperbolas. 11.4 Shifted Conics. 11.5 Rotation of Axes. 11.6 Polar Equations of Conics. Chapter 11 Review. Chapter 11 Test. FOCUS ON MODELING: CONICS IN ARCHITECTURE. 12. SEQUENCES AND SERIES. Chapter Overview. 12.1 Sequences and Summation Notation. 12.2 Arithmetic Sequences. 12.3 Geometric Sequences. 12.4 Mathematical Induction. 12.5 The Binomial Theorem. Chapter 12 Review. Chapter 12 Test. FOCUS ON MODELING: MODELING WITH RECURSIVE SEQUENCES. 13. COUNTING AND PROBABILITY. Chapter Overview. 13.1 Counting. 13.2 Probability. 13.3 Binomial Probability. 13.4 Expected Value. Chapter 13 Review. Chapter 13 Test. FOCUS ON MODELING: THE MONTE CARLO METHOD. APPENDIX A: Geometry Review. APPENDIX B: Calculations and Significant Figures. APPENDIX C: Graphing with a Graphing Calculator. APPENDIX D: Using the TI-83/84 Graphing Calculator. Additional Topics Vectors in Three-Dimensions (available on website) Mathematics of Finance (available on website)

Read more less

Book SynopsisExam board: Cambridge Assessment International EducationLevel: A-levelSubject: MathematicsFirst teaching: September 2018First exams: Summer 2020Endorsed by Cambridge Assessment International Education to provide full support for Paper 5 of the syllabus for examination from 2020.Take mathematical understanding to the next level with this accessible series, written by experienced authors, examiners and teachers.- Improve confidence as a mathematician with clear explanations, worked examples, diverse activities and engaging discussion points. - Advance problem-solving, interpretation and communication skills through a wealth of questions that promote higher-order thinking. - Prepare for further study or life beyond the classroom by applying mathematics to other subjects and modelling real-world situations.- Reinforce learning with opportunities for digital practice via links to the Mathematics in Education and Industry's (MEI) Integral platform in the Boost eBook.**To have full access to the eBook and Integral resources you must be subscribed to both Boost and Integral. To trial our eBooks and/or subscribe to Boost, visit: www.hoddereducation.com/Boost; to view samples of the Integral resources and/or subscribe to Integral, visit integralmaths.org/internationalPlease note that the Integral resources have not been through the Cambridge International endorsement process. This book covers the syllabus content for Probability and Statistics 1, including representation of data, permutations and combinations, probability, discrete random variables and the normal distribution.

Read more less

Book SynopsisProbability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.Trade ReviewFrom the reviews: "This beautifully produced book is intended for advanced undergraduates, PhD students, and researchers and practitioners, primarily in the machine learning or allied areas...A strong feature is the use of geometric illustration and intuition...This is an impressive and interesting book that might form the basis of several advanced statistics courses. It would be a good choice for a reading group." John Maindonald for the Journal of Statistical Software "In this book, aimed at senior undergraduates or beginning graduate students, Bishop provides an authoritative presentation of many of the statistical techniques that have come to be considered part of ‘pattern recognition’ or ‘machine learning’. … This book will serve as an excellent reference. … With its coherent viewpoint, accurate and extensive coverage, and generally good explanations, Bishop’s book is a useful introduction … and a valuable reference for the principle techniques used in these fields." (Radford M. Neal, Technometrics, Vol. 49 (3), August, 2007) "This book appears in the Information Science and Statistics Series commissioned by the publishers. … The book appears to have been designed for course teaching, but obviously contains material that readers interested in self-study can use. It is certainly structured for easy use. … For course teachers there is ample backing which includes some 400 exercises. … it does contain important material which can be easily followed without the reader being confined to a pre-determined course of study." (W. R. Howard, Kybernetes, Vol. 36 (2), 2007) "Bishop (Microsoft Research, UK) has prepared a marvelous book that provides a comprehensive, 700-page introduction to the fields of pattern recognition and machine learning. Aimed at advanced undergraduates and first-year graduate students, as well as researchers and practitioners, the book assumes knowledge of multivariate calculus and linear algebra … . Summing Up: Highly recommended. Upper-division undergraduates through professionals." (C. Tappert, CHOICE, Vol. 44 (9), May, 2007) "The book is structured into 14 main parts and 5 appendices. … The book is aimed at PhD students, researchers and practitioners. It is well-suited for courses on machine learning, statistics, computer science, signal processing, computer vision, data mining, and bio-informatics. Extensive support is provided for course instructors, including more than 400 exercises, lecture slides and a great deal of additional material available at the book’s web site … ." (Ingmar Randvee, Zentralblatt MATH, Vol. 1107 (9), 2007) "This new textbook by C. M. Bishop is a brilliant extension of his former book ‘Neural Networks for Pattern Recognition’. It is written for graduate students or scientists doing interdisciplinary work in related fields. … In summary, this textbook is an excellent introduction to classical pattern recognition and machine learning (in the sense of parameter estimation). A large number of very instructive illustrations adds to this value." (H. G. Feichtinger, Monatshefte für Mathematik, Vol. 151 (3), 2007) "Author aims this text at advanced undergraduates, beginning graduate students, and researchers new to machine learning and pattern recognition. … Pattern Recognition and Machine Learning provides excellent intuitive descriptions and appropriate-level technical details on modern pattern recognition and machine learning. It can be used to teach a course or for self-study, as well as for a reference. … I strongly recommend it for the intended audience and note that Neal (2007) also has given this text a strong review to complement its strong sales record." (Thomas Burr, Journal of the American Statistical Association, Vol. 103 (482), June, 2008) "This accessible monograph seeks to provide a comprehensive introduction to the fields of pattern recognition and machine learning. It presents a unified treatment of well-known statistical pattern recognition techniques. … The book can be used by advanced undergraduates and graduate students … . The illustrative examples and exercises proposed at the end of each chapter are welcome … . The book, which provides several new views, developments and results, is appropriate for both researchers and students who work in machine learning … ." (L. State, ACM Computing Reviews, October, 2008) "Chris Bishop’s … technical exposition that is at once lucid and mathematically rigorous. … In more than 700 pages of clear, copiously illustrated text, he develops a common statistical framework that encompasses … machine learning. … it is a textbook, with a wide range of exercises, instructions to tutors on where to go for full solutions, and the color illustrations that have become obligatory in undergraduate texts. … its clarity and comprehensiveness will make it a favorite desktop companion for practicing data analysts." (H. Van Dyke Parunak, ACM Computing Reviews, Vol. 49 (3), March, 2008)Table of ContentsProbability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Read more less

Book SynopsisDrawing on primary source material and interviews with statisticians and other scientists, this book offers an account of Bayes' rule for general readers, It traces its discovery by an amateur mathematician in the 1740s through its development into roughly its modern form by French scientist Pierre Simon Laplace.Trade Review"If you're not thinking like a Bayesian, perhaps you should be."—John Allen Paulos, New York Times Book Review"A masterfully researched tale of human struggle and accomplishment . . . Renders perplexing mathematical debates digestible and vivid for even the most lay of audiences."—Michael Washburn, Boston Globe"[An] engrossing study. . . . Her book is a compelling and entertaining fusion of history, theory and biography."—Ian Critchley, Sunday Times"This account of how a once reviled theory, Baye’s rule, came to underpin modern life is both approachable and engrossing."—Sunday Times"Makes the theory come alive . . . enjoyable . . . densely packed and engaging . . . very accessible . . . an admirable job of giving a voice to the scores of famous and non-famous people and data who contributed, for good or for worse."—Significance Magazine"A very compelling documented account . . . very interesting reading."—José Bernardo, Valencia List Blog"McGrayne explains [it] beautifully. . . . Top holiday reading."—The Australian"Engaging . . . Readers will be amazed at the impact that Bayes' rule has had in diverse fields, as well as by its rejection by too many statisticians. . . . I was brought up, statistically speaking, as what is called a frequentist. . . . But reading McGrayne's book has made me determined to try, once again, to master the intricacies of Bayesian statistics. I am confident that other readers will feel the same."—The Lancet"The Theory That Would Not Die is a rollicking tale of the triumph of a powerful mathematical tool."—Andrew Robinson, Nature"The Theory That Would Not Die is the first popular science book to document the rocky story of Bayes’s rule. At times, her tale has everything you would expect of a modern-day thriller. . . . To have crafted a page-turner out of the history of statistics is an impressive feat. If only lectures at university had been this racy."—David Robson, New Scientist"The Theory That Would Not Die is an impressively researched, rollicking tale of the triumph of a powerful mathematical tool."—Andrew Robinson, Nature Vol. 475"McGrayne is such a good writer that she makes this obscure battle gripping for the general reader."—Engineering and Technology Magazine"Scientists and statisticians have fought over a deep philosophical divide about probability, which Sharon Bertsch McGrayne explores with great clarity and wit."—Christine Evans-Pughe, Engineering and Technology Magazine"McGrayne holds the hand of the general reader as she lays out the history of the theorem and how it is now used in just about every walk of life. . . . Science writing at its absolute peak."—The BooksellerEditor's Choice, New York Times Book Review"We now know how to think rationally about our uncertain world. This book describes in vivid prose, accessible to the lay person, the development of Bayes' rule over more than two hundred years from an idea to its widespread acceptance in practice."—Dennis Lindley, University College London"A book simply highlighting the astonishing 200 year controversy over Bayesian analysis would have been highly welcome. This book does so much more, however, uncovering the almost secret role of Bayesian analysis in a stunning series of the most important developments of the twentieth century. What a revelation and what a delightful read!"—James Berger, Arts & Sciences Professor of Statistics, Duke University, and member, National Academy of Sciences"Well known in statistical circles, Bayes’s Theorem was first given in a posthumous paper by the English clergyman Thomas Bayes in the mid-eighteenth century. McGrayne provides a fascinating account of the modern use of this result in matters as diverse as cryptography, assurance, the investigation of the connection between smoking and cancer, RAND, the identification of the author of certain papers in The Federalist, election forecasting and the search for a missing H-bomb. The general reader will enjoy her easy style and the way in which she has successfully illustrated the use of a result of prime importance in scientific work."—Andrew I. Dale, author of A History of Inverse Probability From Thomas Bayes to Karl Pearson and Most Honorable Remembrance: The Life and Work of Thomas Bayes"Compelling, fast-paced reading full of lively characters and anecdotes . . . A great story."—Robert E. Kass, Carnegie Mellon University"Fascinating . . . I truly admire [McGrayne’s] style of writing, and . . . ability to turn complex mathematical ideas into intriguing stories, centered around real people."—Judea Pearl, winner of the 2012 Turing Award

Read more less

Book SynopsisStudy smarter and stay on top of your probability course with the bestselling Schaumâs Outlineânow with the NEW Schaum's app and website!Schaumâs Outline of Probability, Third Edition is the go-to study guide for help in probability courses. It's ideal for undergrads, graduate students and professionals needing a tool for review. With an outline format that facilitates quick and easy review and mirrors the course in scope and sequence, this book helps you understand basic concepts and get the extra practice you need to excel in the course. Schaum's Outline of Probability, Third Edition supports the bestselling textbooks and is useful for a variety of classes, including Elementary Probability and Statistics, Data Analysis, Finite Mathematics, and many other courses.Youâll find coverage on finite and countable sets, binomial coefficients, axioms of probability, conditional probability, expectation of a finite random variable, Poisson distri

Read more less

Book SynopsisCONTEMPORARY ABSTRACT ALGEBRA, NINTH EDITION is primarily intended for an abstract algebra course whose main purpose is to enable students to do computations and write proofs. Gallian's text stresses the importance of obtaining a solid introduction to the traditional topics of abstract algebra, while at the same time presenting it as a contemporary and very much an active subject which is currently being used by working physicists, chemists, and computer scientists.Table of ContentsPART I: INTEGERS AND EQUIVALENCE RELATIONS. Preliminaries. Properties of Integers. Complex Numbers. Modular Arithmetic. Mathematical Induction. Equivalence Relations. Functions (Mappings). Exercises. PART I!: GROUPS. 1. Introduction to Groups. Symmetries of a Square. The Dihedral Groups. Exercises. Biography of Neils Abel 2. Groups. Definition and Examples of Groups. Elementary Properties of Groups. Historical Note. Exercises. 3. Finite Groups; Subgroups. Terminology and Notation. Subgroup Tests. Examples of Subgroups. Exercises. 4. Cyclic Groups. Properties of Cyclic Groups. Classification of Subgroups of Cyclic Groups. Exercises. Biography of J. J. Sylvester. Supplementary Exercises for Chapters 1-4. 5. Permutation Groups. Definition and Notation. Cycle Notation. Properties of Permutations. A Check-Digit Scheme Based on D5. Exercises. Biography of Augustin Cauchy. 6. Isomorphisms. Motivation. Definition and Examples. Cayley���s Theorem. Properties of Isomorphisms. Automorphisms. Exercises. Biography of Arthur Cayley. 7. Cosets and Lagrange���s Theorem. Properties of Cosets. Lagrange���s Theorem and Consequences. An Application of Cosets to Permutation Groups. The Rotation Group of a Cube and a Soccer Ball. Exercises. Biography of Joseph Lagrange. 8. External Direct Products. Definition and Examples. Properties of External Direct Products. The Group of Units Modulo n as an External Direct Product. Applications. Exercises. Biography of Leonard Adleman. Supplementary Exercises for Chapters 5-8 9. Normal Subgroups and Factor Groups. Normal Subgroups. Factor Groups. Applications of Factor Groups. Internal Direct Products. Exercises. Biography of ��variste Galois 10. Group Homomorphisms. Definition and Examples. Properties of Homomorphisms. The First Isomorphism Theorem. Exercises. Biography of Camille Jordan. 11. Fundamental Theorem of Finite Abelian Groups. The Fundamental Theorem. The Isomorphism Classes of Abelian Groups. Proof of the Fundamental Theorem. Exercises. Supplementary Exercises for Chapters 9-11. PART III: RINGS. 12. Introduction to Rings. Motivation and Definition. Examples of Rings. Properties of Rings. Subrings. Exercises. Biography of I. N. Herstein. 13. Integral Domains. Definition and Examples. Fields. Characteristic of a Ring. Exercises. Biography of Nathan Jacobson. 14. Ideals and Factor Rings. Ideals. Factor Rings. Prime Ideals and Maximal Ideals. Exercises. Biography of Richard Dedekind. Biography of Emmy Noether. Supplementary Exercises for Chapters 12-14. 15. Ring Homomorphisms. Definition and Examples. Properties of Ring Homomorphisms. The Field of Quotients. Exercises. 16. Polynomial Rings. Notation and Terminology. The Division Algorithm and Consequences. Exercises. Biography of Saunders Mac Lane. 17. Factorization of Polynomials. Reducibility Tests. Irreducibility Tests. Unique Factorization in Z[x]. Weird Dice: An Application of Unique Factorization. Exercises. Biography of Serge Lang. 18. Divisibility in Integral Domains. Irreducibles, Primes. Historical Discussion of Fermat���s Last Theorem. Unique Factorization Domains. Euclidean Domains. Exercises. Biography of Sophie Germain. Biography of Andrew Wiles. Supplementary Exercises for Chapters 15-18. PART IV: FIELDS. 19. Vector Spaces. Definition and Examples. Subspaces. Linear Independence. Exercises. Biography of Emil Artin. Biography of Olga Taussky-Todd. 20. Extension Fields. The Fundamental Theorem of Field Theory. Splitting Fields. Zeros of an Irreducible Polynomial. Exercises. Biography of Leopold Kronecker. 21. Algebraic Extensions. Characterization of Extensions. Finite Extensions. Properties of Algebraic Extensions Exercises. Biography of Irving Kaplansky. 22. Finite Fields. Classification of Finite Fields. Structure of Finite Fields. Subfields of a Finite Field. Exercises. Biography of L. E. Dickson. 23. Geometric Constructions. Historical Discussion of Geometric Constructions. Constructible Numbers. Angle-Trisectors and Circle-Squarers. Exercises. Supplementary Exercises for Chapters 19-23. PART V: SPECIAL TOPICS. 24. Sylow Theorems. Conjugacy Classes. The Class Equation. The Probability That Two Elements Commute. The Sylow Theorems. Applications of Sylow Theorems. Exercises. Biography of Ludvig Sylow. 25. Finite Simple Groups. Historical Background. Nonsimplicity Tests. The Simplicity of A5. The Fields Medal. The Cole Prize. Exercises. Biography of Michael Aschbacher. Biography of Daniel Gorenstein. Biography of John Thompson. 26. Generators and Relations. Motivation. Definitions and Notation. Free Group. Generators and Relations. Classification of Groups of Order up to 15. Characterization of Dihedral Groups. Realizing the Dihedral Groups with Mirrors. Exercises. Biography of Marshall Hall, Jr.. 27. Symmetry Groups. Isometries. Classification of Finite Plane Symmetry Groups. Classification of Finite Group of Rotations in R��. Exercises. 28. Frieze Groups and Crystallographic Groups. The Frieze Groups. The Crystallographic Groups. Identification of Plane Periodic Patterns. Exercises. Biography of M. C. Escher. Biography of George P��lya. Biography of John H. Conway. 29. Symmetry and Counting. Motivation. Burnside���s Theorem. Applications. Group Action. Exercises. Biography of William Burnside. 30. Cayley Digraphs of Groups. Motivation. The Cayley Digraph of a Group. Hamiltonian Circuits and Paths. Some Applications. Exercises. Biography of William-Rowan Hamilton. Biography of Paul Erd��s. 31. Introduction to Algebraic Coding Theory. Motivation. Linear Codes. Parity-Check Matrix Decoding. Coset Decoding. Historical Note: The Ubiquitous Reed-Solomon Codes. Exercises. Biography of Richard W. Hamming. Biography of Jessie MacWilliams. Biography of Vera Pless. 32. An Introduction to Galois Theory. Fundamental Theorem of Galois Theory. Solvability of Polynomials by. Radicals. Insolvability of a Quintic. Exercises. Biography of Philip Hall. 33. Cyclotomic Extensions. Motivation. Cyclotomic Polynomials. The Constructible Regular n-gons. Exercises. Biography of Carl Friedrich Gauss. Biography of Manjul Bhargava. Supplementary Exercises for Chapters 24-33.

Read more less

Book SynopsisThis new fourth edition of the acclaimed and bestselling Div, Grad, Curl, and All That has been carefully revised and now includes updated notations and seven new example exercises.

Read more less