Mathematics for the Liberal Arts

Inbunden, Engelska, 2012

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Beskrivning

Presents a clear bridge between mathematics and the liberal arts Mathematics for the Liberal Arts provides a comprehensible and precise introduction to modern mathematics intertwined with the history of mathematical discoveries. The book discusses mathematical ideas in the context of the unfolding story of human thought and highlights the application of mathematics in everyday life.Divided into two parts, Mathematics for the Liberal Arts first traces the history of mathematics from the ancient world to the Middle Ages, then moves on to the Renaissance and finishes with the development of modern mathematics. In the second part, the book explores major topics of calculus and number theory, including problem-solving techniques and real-world applications. This book emphasizes learning through doing, presents a practical approach, and features: A detailed explanation of why mathematical principles are true and how the mathematical processes workNumerous figures and diagrams as well as hundreds of worked examples and exercises, aiding readers to further visualize the presented conceptsVarious real-world practical applications of mathematics, including error-correcting codes and the space shuttle programVignette biographies of renowned mathematiciansAppendices with solutions to selected exercises and suggestions for further readingMathematics for the Liberal Arts is an excellent introduction to the history and concepts of mathematics for undergraduate liberal arts students and readers in non-scientific fields wishing to gain a better understanding of mathematics and mathematical problem-solving skills.

Produktinformation

Utgivningsdatum:2012-12-07
Mått:165 x 241 x 25 mm
Vikt:726 g
Format:Inbunden
Språk:Engelska
Antal sidor:424
Förlag:John Wiley & Sons Inc
ISBN:9781118352915

Utforska kategorier

Matematik inom Naturvetenskap och teknik

Mer om författaren

DONALD BINDNER, PhD, is Assistant Professor in the Department of Mathematics and Computer Science at Truman State University.MARTIN J. ERICKSON, PhD, is Professor of Mathematics in the Department of Computer Science at Truman State University and the author or coauthor of numerous books on mathematical topics.JOE HEMMETER, PhD, is a freelance software developer and a past professor of mathematics at both the University of Delaware and Truman State University.

Innehållsförteckning

Preface xiPART I MATHEMATICS IN HISTORY1 The Ancient Roots of Mathematics 31.1 Introduction 31.2 Ancient Mesopotamia and Egypt 71.3 Early Greek Mathematics: The First Theorists 201.4 The Apex: Third Century Hellenistic Mathematics 421.5 The Slow Decline 582 The Growth of Mathematics to 1600 732.1 China 742.2 India 892.3 Islam 1022.4 European Mathematics Awakens 1203 Modern Mathematics 1393.1 The 17th Century: Scientific Revolution 1403.2 The 18th Century: Consolidation 1563.3 The 19th Century: Expansion 1703.4 The 20th and 21st Centuries: Explosion 1933.5 The Future 217II TWO PILLARS OF MATHEMATICS4 Calculus 2214.1 What Is Calculus? 2214.2 Average and Instantaneous Velocity 2224.3 Tangent Line to a Curve 2264.4 The Derivative 2324.5 Formulas for Derivatives 2354.6 The Product Rule and Quotient Rule 2414.7 The Chain Rule 2484.8 Slopes and Optimization 2534.9 Applying Optimization Methods 2594.10 Differential Notation and Estimates 2664.11 Marginal Revenue, Cost, and Profit 2704.12 Exponential Growth 2764.13 Periodic Functions of Trigonometry 2874.14 The Fundamental Theorem of Calculus 2934.15 The Riemann Integral 2974.16 Signed Areas and Other Integrals 3014.17 Application: Rocket Science 3064.18 Infinite Sums 3114.19 Exponential Growth and Doubling Times 3174.20 Beyond Calculus 3215 Number Theory 3235.1 What Is Number Theory? 3235.2 Divisibility 3245.3 Irrational Numbers 3295.4 Greatest Common Divisors 3315.5 Primes 3365.6 Relatively Prime Integers 3395.7 Mersenne and Fermat Primes 3435.8 The Fundamental Theorem of Arithmetic 3455.9 Diophantine Equations 3505.10 Linear Diophantine Equations 3545.11 Pythagorean Triples 3585.12 An Introduction to Modular Arithmetic 3615.13 Congruence 3665.14 Arithmetic with Congruences 3705.15 Division with Congruences; Finite Fields 3745.16 Fermat’s Last Theorem 3815.17 Unfinished Business 383A Answers to Selected Exercises 385B Suggested Reading 401Index 405