The first half of a full-year survey of the history of mathematics, this course explores the ancient origins of numeracy up to the invention of Calculus. Starting from the premise that numeracy, like language, is a fundamental aspect of human activity, we explore the invention of numerals and counting systems in various global cultures and contexts, the beginnings of geometry and algebra, solutions to indeterminate equations, right triangle theory and trigonometry, expansions to the number concept, methods of proof and justification, birth of probability and invention of calculus.
Syllabus
- How Did Numeracy Begin?
- What Did the Ancients Know?
- The Ancient Greek Approach to Mathematics
- The Three Unsolved Problems of Antiquity
- Did Archimedes Do Calculus?
- Completing the Square with Al-Khwarizmi
- Solution to the Cubic Equation & Birth of Imaginary Numbers
- Zero as a Number
- Solving Systems of Linear Equations in Ancient China
- Solving Indeterminate Equations in China
- Optimization Before Calculus
- Quantifying Certainty: Pascal and Fermat Solve the Problem of Points
- The Cartesian Revolution
- Indivisibles and Infinitesimals
- Invention of Calculus
TRIUMPHS PROJECTS
For some learning in this course I drew upon curriculum materials created by a National Science Foundation funded project TRIUMPHS: Transforming Instruction in Undergraduate Mathematics via Primary Historical Sources.