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. Mathematics 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.

Table of Contents

• Preface
• Part I Mathematics In History
• 1 The Ancient Roots of Mathematics
• 1.1 Introduction
• 1.2 Ancient Mesopotamia and Egypt
• 1.3 Early Greek Mathematics: The First Theorists
• 1.4 The Apex: Third Century Hellenistic Mathematics
• 1.5 The Slow Decline
• 2 The Growth of Mathematics to 1600
• 2.1 China
• 2.2 India
• 2.3 Islam
• 2.4 European Mathematics Awakens
• 3 Modern Mathematics
• 3.1 The 17th Century: Scientific Revolution
• 3.2 The 18th Century: Consolidation
• 3.3 The 19th Century: Expansion
• 3.4 The 20th and 21st Centuries: Explosion
• 3.5 The Future
• Part II Two Pillars Of Mathematics
• 4 Calculus
• 4.1 What Is Calculus?
• 4.2 Average and Instantaneous Velocity
• 4.3 Tangent Line to a Curve
• 4.4 The Derivative
• 4.5 Formulas for Derivatives
• 4.6 The Product Rule and Quotient Rule
• 4.7 The Chain Rule
• 4.8 Slopes and Optimization
• 4.9 Applying Optimization Methods
• 4.10 Differential Notation and Estimates
• 4.11 Marginal Revenue, Cost, and Profit
• 4.12 Exponential Growth
• 4.13 Periodic Functions and Trigonometry
• 4.14 The Fundamental Theorem of Calculus
• 4.15 The Riemann Integral
• 4.16 Signed Areas and Other Integrals
• 4.17 Application: Rocket Science
• 4.18 Infinite Sums
• 4.19 Exponential Growth and Doubling Times
• 4.20 Beyond Calculus
• 5 Number Theory
• 5.1 What Is Number Theory?
• 5.2 Divisibility
• 5.3 Irrational Numbers
• 5.4 Greatest Common Divisors
• 5.5 Primes
• 5.6 Relatively Prime Integers
• 5.7 Mersenne and Fermat Primes
• 5.8 The Fundamental Theorem of Arithmetic
• 5.9 Diophantine Equations
• 5.10 Linear Diophantine Equations
• 5.11 Pythagorean Triples
• 5.12 An Introduction to Modular Arithmetic
• 5.13 Congruence
• 5.14 Arithmetic with Congruences
• 5.15 Division with Congruences; Finite Fields
• 5.16 Fermat's Last Theorem
• 5.17 Unfinished Business
• A Answers to Selected Exercises
• B Suggested Reading