Organization

• Regular Classes: Monday & Wednesday at 2:15PM to 4:00PM

• Class Venue: Room 401 in the Library Building

• Discussion Hours with TAs: Tuesday 10:15am to 11:10am 

• Reading material and videos and exercises will be posted/uploaded regularly.

• Every 2/3 weeks a small online assignment will be posted. You will have to write up your solutions and submit a pdf (scanned or texed up) in the google classroom. 

• In you have any doubts or questions feel free to email the instructor or the TAs or post the question in classroom or ask the question during the class. 

• No cheating policy: If some student is caught cheating (in any of the exam or on the assignments) it would be reported to the dean. The dean will make the final decision on what action to be taken, but the instructor will insist on giving ZERO to the student in the whole course.

• Evaluation:  30% on midsem, 50% on endsem and 20% on Assignements

Study Materials

• Introductory material : Introduction, Sets, Relations, Functions [Part1 video, Part2 video, slides]

• Introductory material : Introduction to Propositional and Predicate Logic [Video, slides]

• Introductory material: Introduction to Graph Theory [Video, slides]

• Introduction to Elementary Number Theory and Proof techniques [Video, slides (4a), slides (4b)]

• Proof Techniques [Video, slides (5a), slides (5b)] 

• More on Proof Techniques [Video, slides (6a), slides (6b)] 

• More on Proof Techniques [Video, slides (7a), slides (7b)]

• Induction on Graphs [Video, slides8] 

• Nice write-up on induction 

• Nice write-up on generating function

• Nice write-up on recurrences

• Nice write-up on Binomial Coefficients

Topics covered in class

• Lecture 0: (6/1/25)  Introduction 

• Lecture 1: (8/1/25) Introduction to Graphs, Induction on graphs and set - AM-GM, Hamiltonian Path in Tournament (Not chekced Scribed Notes)

• Lecture 2: (13/1/25) Connectedness in graph, Sunflower Lemma, statement of Helly's theorem  (Not chekced Scribed Notes)

• Lecture 3: (15/1/25) Proof of Helly's Theorem  (Not chekced Scribed Notes)

• Lecture 4: (20/1/25) Introduction to Ramsey Theory  (Not chekced Scribed Notes)

• Lecture 5: (22/1/25) Asymptotic notations and recurrences  (Not chekced Scribed Notes)

• Lecture 6: (27/1/25) Applications of Helly's Theorem  (Not chekced Scribed Notes)

• Lecture 7: (29/1/25) Generating functions 1  (Not chekced Scribed Notes)

• Lecture 8: (10/2/25)  Generating functions 2

• Lecture 9: (11/2/25) Counting - Balls and Bins

• Lecture 10: (12/2/25) Counting using Recurrences

• Lecture 11: (17/2/25) Prufer code and solving recurrences using asymptotic notations 

• Lecture 12: (19/2/25) Introduction to algebraic techniques in combinatorics, spectral graph theory and  probabilistic methods 

• Midsem : (26/2/25) 

Assignments

Problem sets for Practice and useful links

• Link to previous years DMath course MTech 2022-23, MTech 2021-22, MTech2019-2020, MTech 2018-19. BStat 2023, BStat 2024

• Problem Set 0 on Introduction to Graph theory, Propositional and Predicate Logic and Proof Techniques

• Problem Set 1 for discussion on 21/1/25 tutorial class

• Problem Set 2 for discussion on 18/2/25 tutorial class