Course Outline and Seminars:
The following is a tentative outline for the classes, seminars, and required reading for the course.
| Seminar | Date | Topic | Reading |
|---|---|---|---|
| Module I · The Tyranny of Numbers | |||
| 1 | Jul 6 | Mathematics as a Human Endeavour | The Ishango Bone, 2 + 2 = 5, and Jaina Thoughts on Unity Not Being a Number |
| 2 | Jul 7 | The Place Value System | Development of Indian Numerals (Kim Plofker), The Major System, and A New Approach to Multiplication |
| 3 | Jul 9 | Committees and Course Policies | |
| 4 | Jul 10 | Fallacies and Proofs | W. V. O. Quine, “The Ways of Paradox” (1966) |
| Module II · The Syntax of Arithmetic | |||
| 5 | Jul 13 | Sets and Proofs | |
| 6 | Jul 14 | Peano Axioms | Paul Benacerraf, “What Numbers Could Not Be” (1965) |
| 7 | Jul 16 | The Principle of Mathematical Induction | |
| 8 | Jul 17 | Non-standard Arithmetic · Quiz | |
| Module III · Equivalences | |||
| 9 | Jul 20 | Invited Speaker: Ravi Chakraborty | |
| 10 | Jul 21 | Construction of Integers and Modular Arithmetic | |
| 11 | Jul 23 | Indeterminate Equations | |
| 12 | Jul 24 | Primitive Recursive Functions · Quiz | |
| Module IV · The View from Halfway Down | |||
| 13 | Jul 27 | Self-Reference and Paradoxes | |
| 14 | Jul 28 | The Arithmetization of Syntax | |
| 15 | Jul 30 | Gödel’s First Incompleteness Theorem | |
| 16 | Jul 31 | Invited Speaker: Shailaja Sharma | |
| Module V · Reasoning Without Certainty | |||
| 17 | Aug 3 | Eugenics · Quiz | Bernard Cohn, “The Census, Social Structure and Objectification in South Asia” (1987); Nicholas Dirks, Castes of Mind (2001) |
| 18 | Aug 4 | Rationality and Choice | |
| 19 | Aug 6 | Social Choice Theory | |
| 20 | Aug 7 | The Unreasonable Effectiveness of Broken Mathematics · Quiz | |
| Presentations and Final Exam | |||
| 21 | Aug 10 | Presentations | |
| 22 | Aug 11 | Presentations | |
| 23 | Aug 13 | Presentations | |
| 24 | Aug 14 | Final Exam | |