Discrete Mathematics, IIT Gandhinagar, 2025 (fall).
This is an archived teaching edition.
| Detail | Record |
|---|---|
| Institution or platform | IIT Gandhinagar |
| Year | 2025 |
| Term | fall |
| Course code | ES214 |
| Teaching role | instructor |
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Lecture schedule · second half of the 2025 offering
Find all notes from class here. Note: unedited and real-time, so expect these to be generally sloppy, illegible, and mostly useless, but hopefully also mostly harmless :)
| Date | Lecture |
|---|---|
| 06 Oct, 2025 | Explored some properties of kings in tournaments. · See this article on the The King Chicken Theorems by Stephen B. Maurer for more. |
| 07 Oct, 2025 | Birkhoff–von-Neumann Theorem · See the wikiedia entry on the topic for a proof. Slides from class. |
| 10 Oct, 2025 | Picture-Hanging Puzzles · See this paper for more context. |
| 13 Oct, 2025 | 100 Prisoners Puzzle · See this nice video by Veritasium and the wikipedia page. |
| 14 Oct, 2025 | Linear Algebra with Oddtown · See the first part of this document for the approach discussed in class, Theorem 1.1 here for a determinant-based argument for linear independence, and Theorem 2 here for a combinatorial argument |
| 17 Oct, 2025 | Nimbers – I · See this essay for a build up of the XOR strategy. |
| 20 Oct, 2025 | Nimbers – II · For further reading, check out transfinite Nim. |
| 24 Oct, 2025 | Counting Incomplete Cubes · Phenomenal tour of the problem by Paul Duncstep here. |
| 27 Oct, 2025 | Group Actions with Tic-Tac-Toe · Check out the Numberphile take on this problem. |
| 28 Oct, 2025 | Burnside with Colored Squares · We analyzed the number of squares whose edges have been colored with three colors (where not every color has to necessarily appear) discounting symmetries. |
| 31 Oct, 2025 | Permutation Puzzles · This material was inspired by this course. In particular, download the course book and look at section 5.2 for the questions discussed in class. · General challenge: can you figure out how Penn and Teller were fooled here? |
| 03 Nov, 2025 | Rubik Cube + Commutators · This class was a poor imitation of Ramprasad's amazing talk on the topic. You can find the cubing demos here. The material on solving equations was out of scope for our class, but you are welcome to explore it as further reading! |
| 04 Nov, 2025 | Commutators Continued · In this class we went over the commutator theorem. |
| 10 Nov, 2025 | Card Magic · Ternary and Binary · For practice with ternary representations, see the 27 card trick · For an application of binary representations, check out any card to any position using only perfect in and out shuffles. |
| 11 Nov, 2025 | Basic Number Theory · We mostly focused on the Fundamental Theorem of Arithmetic. · See the following essays by Gowers on the topic for additional reading: Why isn’t the fundamental theorem of arithmetic obvious? and Proving the fundamental theorem of arithmetic |
| 14 Nov, 2025 | Enigma · See Rejewski's 1980 paper and these notes. |
| 17 Nov, 2025 | Same-Size Intersections · We did another example of applying the linear algebraic method. · See the book Thirty-three Miniatures: Mathematical and Algorithmic Applications of Linear Algebra by Matoušek for more examples. What we discussed in class was based on Miniature #4. |