The second half of a full-year survey of the history of mathematics, this course explores the growth and increasing abstraction of mathematics in the modern period. We explore how to think about the history of mathematics through the lens of philosophy while exploring invention of the function concept, infinite series, graph theory, complex numbers, geometry, set theory and computing. Other topics may include math education, mathematical recreations and games, ethics of algorithms, gender and diversity in STEM, open problems.
Syllabus
- Philosophies of Mathematics – Euler’s Polyhedral Formula
- Analysis of Distance – Maria Agnesi
- Analysis of Position – The Seven Bridges of Konigsberg
- Infinite Series – The Basel Problem
- The Function Concept
- Calculus Controversy
- The Real, The Imaginary, and the Complex
- Projective Geometry in Art and Mathematics
- Higher Dimensions in Math and Popular Culture
- Are The Revolutions in Mathematics?
- Infinity
- Lies, Damned Lies, and Statistics
- Data Visualization
- Mathematical Logic
- Tools and Ideas of Early Computation
- When Computers Were Human
- Computing and Cryptography
- Is Proof Inherently Human?
- Open Problems in Mathematics
TRIUMPHS PROJECTS
For some learning in this course I drew upon curriculum materials created by the NSF funded project TRIUMPHS: Transforming Instruction in Undergraduate Mathematics via Primary Historical Sources and from Learning Discrete Mathematics and Computer Science via Primary Historical Sources.