History of Mathematics

Course Description

This one-credit course introduces students to a survey of the history of mathematics, including the background of famous mathematicians from ancient to modern times and their specific contributions to mathematics. The format and content of the course is conceptual rather than technical.

Topics and Objectives

The Earliest Use of Numbers

• Identify and discuss the conditions that gave rise to Neolithic man.
• Examine some of the human activities that stimulated the early concepts of numbers.
• Identify and discuss the independent mathematical achievements of the Minoan-Mycean, Maya, and Inca civilizations.

The Early Mathematics of the Egyptian and Babylonian Cultures

• Identify the Sumerian and Akkadan people, and discuss the events that gave rise to the Babylonian empire.
• Examine the mathematical motivations and accomplishments of the Egyptian and Babylonian cultures.

Classical Greek Mathematics

• Identify and discuss the conditions and events that gave rise to the classical Greek city-state.
• Analyze the nature of Greek mathematics, and discuss the ways in which it influenced the work of so many later cultures.
• Identify and discuss the work of the major figures in classical Greek mathematics.

Mathematics During Hellenistic and Roman Times

• Examine the circumstances and events that established Alexandria as the premier center of scholarship and training.
• Identify and discuss the work of the major Greek mathematical figures who studied and worked in Alexandria.
• Identify the "great works" we have from this time period, especially Euclid's Elements and Ptolemy's Almagest.

The Mathematical Achievements of the Chinese, Arabic, and Hindu Cultures

• Examine the major achievements of early Chinese and Hindu mathematics.
• Analyze and discuss the rise of Arabic and Islamic culture and their mathematical achievements.
• Discuss Arabic and Hindu preservation and enhancement of Greek mathematical knowledge and their role in the transmission of this knowledge to the West.

The Awakening in the West

• Identify the major mathematical figures during the Middle Ages and discuss their work.
• Discuss the mathematical contributions from scholastic philosophers during the Middle Ages.

The 17th Century

• Identify the major mathematical developments during this period.
• Examine the work, preceding Newton and Leibniz, during this period that continued to develop the ideas central to the development of calculus.
• Analyze the major works of Newton and Leibniz relating to their independent formalizations of what we now call calculus.

The 18th Century

• Identify and discuss the major European mathematical figures working at this time.
• Discuss the rapid development of calculus, including the important extensions of it resulting in the fields of the study of ordinary and partial differential equations as well as the calculus of variations.
• Identify the applications of the new tools of calculus; discuss the revolution in science and engineering that the new mathematics made possible.