The Development of Mathematics Throughout the Centuries: A Brief History in a Cultural Context

An introduction to major time periods and global cultures that have influenced the evolution of mathematics With a balanced blend of formal history with anecdotes and legends, The Development of Mathematics Throughout the Centuries: A Brief History in a Cultural Context takes readers on a journey throughout time in an effort to understand the patterns of quantity, structure, and dimensions found in the world. The author explores mathematics using a historical context and emphasizes that no single culture had a monopoly on mathematical advancements; rather, various groups influenced one another and developed simultaneously. The book begins with the earliest known records of human mathematics in Africa and continues on to ancient Egypt and Babylon. The journey moves into ancient Greece, China and India, and the Islamic world. Next, the mathematics of the pre–Columbian Americas, the dark period of mathematics in Europe after the fall of the Roman Empire, and the influence of Islamic mathematics on European thinking are presented. The European Renaissance through the 17 th , 18 th , and 19 th centuries are explored, and the 20 th century takes readers through Europe and to North America, which took the lead in mathematics after World War II. Finally, readers are provided with a modern review of mathematics in the 21 st century, along with the history of mathematics education and its development in the United States. The book also features: Interesting and enjoyable anecdotes and mathematical legends Examples of parallels between the historical development of mathematical methods and everyday problem solving Major mathematical findings and contributions by significant historical figures Highlights and contributions made by various world cultures including African, Egyptian, Babylonian, Chinese, Indian, Islamic, and pre–Columbian American A useful textbook for undergraduate courses on the history of mathematics, The Development of Mathematics Throughout the Centuries: A Brief History in a Cultural Context is also appropriate for elementary and secondary education majors. Presented in an easy–to–follow style, the book also serves as a resource for readers interested in the development of mathematics as a coherent discipline.

Introduction ix PART 1 MATHEMATICS IN AFRICA AND THE MEDITERRANEAN REGION 1 1 ANCIENT CIVILIZATION MATHEMATICS: AFRICA AS OUR BIRTHPLACE 3 2 ANCIENT EGYPTIAN MATHEMATICS: THE TIME OF THE PHARAOHS 7 3 BABYLONIAN MATHEMATICS: THE MESOPOTAMIAN CRADLE OF CIVILIZATION 17 4 GREEK MATHEMATICS: THE ARCHAIC PERIOD 25 5 GREEK MATHEMATICS: THE CLASSICAL PERIOD 37 6 GREEK MATHEMATICS: THE HELLENISTIC AND ROMAN/ BYZANTINE PERIODS 45 PART 2 MATHEMATICS IN ASIA AND PRE–COLUMBIAN AMERICA 59 7 CHINESE MATHEMATICS: ANCIENT TIMES TO THE MIDDLE AGES 61 8 INDIAN MATHEMATICS: ANCIENT TIMES TO THE MIDDLE AGES 75 9 ISLAMIC MATHEMATICS: PRESERVATION,INNOVATION, AND CONNECTION BETWEEN EAST AND WEST 87 10 PRE–COLUMBIAN AMERICAN MATHEMATICS: THE OLMEC, MAYA, AND INCA CIVILIZATIONS 97 PART 3 MATHEMATICS IN EUROPE 105 11 EUROPEAN MATHEMATICS: THE MIDDLE AGES AND THE RENAISSANCE 107 12 EUROPEAN MATHEMATICS: THE 17TH CENTURY 123 13 EUROPEAN MATHEMATICS: THE 18TH CENTURY 143 14 EUROPEAN MATHEMATICS: THE 19TH CENTURY 157 PART 4 MATHEMATICS IN THE 20TH AND 21ST CENTURIES 175 15 EUROPEAN, AMERICAN, AND GLOBAL MATHEMATICS: THE 20TH AND 21ST CENTURIES 177 16 EUROPEAN, AMERICAN, AND GLOBAL MATHEMATICS: A SHIFT IN THE 20TH CENTURY 199 17 AMERICAN MATHEMATICS EDUCATION: THE 20TH AND 21ST CENTURIES 207 Resources and Recommended Readings 219 Index 221

BRIAN R. EVANS is Department Chair and Associate Professor of Mathematics Education in the School of Education at Pace University in New York. He has authored over twenty–five publications and teaches pedagogical and content courses in mathematics including the history of mathematics. He is also managing editor for the peer reviewed Journal of the National Association for Alternative Certification.