ES 214 | May-Jun 2025

ES214. Discrete Mathematics

May — June 2025

(co-instructor with Prof. Jyothi Krishnan.)

This is a first course in discrete mathematics and has a broad scope: we introduce elementary concepts in logic, set theory, combinatorics, graph theory, number theory, and probability. The course is designed to be accessible to students from all disciplines, and is a core course for the B.Tech. program at IITGN. We hope that students taking this course discover the beauty of mathematical methods and their applications.

You will find this course interesting if:

  • you think counting the number of ways in which you can complete your graduation requirements is a fun problem to think about,
  • you enjoy logic puzzles like this one or probability puzzles like this one, or
  • you like box-stacking challenges, or
  • you are enrolled in a program for which this course is in the core.

This course is self-contained and involves no pre-requisites.

  1. Discrete Mathematics and Its Applications by Kenneth Rosen
  2. Open Textbook on Discrete Mathematics
  3. Proofs: A Long-Form Mathematics Textbook by Jay Cummings
  4. Playing with Discrete Math by Kyle Burke and Craig Tennenhouse
  5. Online Course (with lecture videos): Math 4190, Summer I 2019
  • Venue: 7/101 and online via Zoom
  • If the Zoom link does not work, try to login with the meeting ID 955 8143 5196 and passcode erdos.
  • Lectures: as per the schedule below, 5PM to 7PM (with a 15-minute break in between)
  • There will be seven worksheets, each worth 10 points. Your top 5 scores from these worksheets account for 50% of the grade.
  • There will be one end-term exam with 21 problems, one from each theme. You can pick any five themes and answer the 15 questions corresponding to them. The end-term exam accounts for 30% of the total grade.
  • There is one assignment in math exposition. You will be required to pick a topics/themes and either prepare a video or write a blog about it. You will be expected to submit these to the Summer of Math Exposition. Although the SoME4 deadline is the end of Augsut, you would be expected to make your submissions by June 15th, 2025. You are strongly encouraged to discuss your topic with the instructors and TAs and get feedback as you develop your topic. This component accounts for 20% of your grade.
  • For IITGN students, (pre-)register through IMS as usual.
  • For discussions and announcements, please join the Zulip community here.
  • Information about how worksheets can be submitted will be shared soon.
  • If you are not from IITGN and are interested in taking up the course, then please send us an email.
Date Lecture Slides Notes Video
08 May, 2025 Foundations - 1
Place-value based number systems and introduction to logic.
Recommended watching: Matt Parker with 27 cards.
32 number trick · 27 card trick and reveal.
09 May, 2025 Foundations - 2
More logic with a variation of the Black Vienna game.
10 May, 2025 Foundations - 3
Hilbert's hotel (see this), Cantor's diagonalization arguments (see this).
Recommended watching: Videos by Veritasium: (1) and (2)
The questions we worked in class were hosted on Brilliant.
You can watch the recording to revisit them.
11 May, 2025 Tutorial 1
Download the worksheet here and submit your answers here.
14 May, 2025 Proofs - 1
Proofs and non-proofs by induction.
15 May, 2025 Proofs - 2
Proofs without words. The pictures in the slides are borrowed from the book on Proofs by Hamkins
16 May, 2025 Proofs - 3
Proofs based on invariance principles. Problems borrowed from the first chapter of Problem Solving Strategies by Arthur Engel.
See also: Timothy Gowers solving invariance-based problems on Youtube.
17 May, 2025 Tutorial 2
20 May, 2025 Counting - 1
Predicate Logic Continued
Introduction to the Game of SET
21 May, 2025 Counting Tutorial
Examples of Double Counting
Download the counting worksheet here.
22 May, 2025 Counting - 2
The Game of SET (continued)
23 May, 2025 Counting - 3
Capsets (reference: The Card Game Set by Benjamin L. Davis & Diane Maclagan, in Mathematical Entertainments, 2003)
Puzzle based on this Mathologer video
26 May, 2025 Uncertainity - 1
Probability, Random Variables, Expectation, Linearity of Expectation
27 May, 2025 Uncertainity - 2
The 100 prisoners puzzle. Find out more about the puzzle here.
Also see: video by Veritasium about the puzzle here.
28 May, 2025 Uncertainity - 3
Applications of probabilistic method to lower bounds on Ramsey numbers.
If you want to explore more applications of the probabilistic method see the notes here.
29 May, 2025 Tutorial 4
We wrap up some loose ends from the 100 prisoners puzzle and use the probabilistic method to construct a tournament with a lot of Hamiltonian paths.
Download the worksheet here and submit your answers here.
10 Jun, 2025 Structures - 1
Introduction to Groups and related structures through swap puzzles.
For extended further reading, this is a comprehensive book and course on the broad theme of permutation puzzles.
11 Jun, 2025 Structures - 2
Introduction to Linear Algebra through the Oddtown puzzle.
See Section 1.1 in this book or refer to these notes for more on oddtown and similar questions and approaches.
12 Jun, 2025 Structures - 3
Introduction to Matrices via the Lights Out Puzzle
Play Lights Out here.
More about the linear algebra solution in this article..
This was the demo we used in class, courtsey Lovable.
13 Jun, 2025 Tutorial 5
Introduction to groups with picture hanging puzzles. Find out more about picture hanging puzzles here.
Download the worksheet here and submit your answers here.
16 Jun, 2025 Project Discussion
Class participants pitched potential project ideas.
17 Jun, 2025 Numbers - 1
Introduction to number theory, Chinese Remainder Theorem.
Find out more about the card trick here.
The last card trick involving multiples of three can be found here.
20 Jun, 2025 Numbers - 2
The RSA cryptosystem. Notation borrowed from this video.
You can find out more about the perfect code based system here.
Download the worksheet here and submit your answers here.
21 Jun, 2025 Graphs
An introduction to graphs: we covered a puzzle involving a dinner party and a magic trick based on Euler Tours.
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