Regular Classes: Wednesday & Friday at 11:10AM to 12:55PM
Class Venue: Room 718 in the Library Building
Discussion Hours with TAs:
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
Instructor: Sourav Chakraborty (sourav@isical.ac.in)
TAs:
Soumi Nandi (nandisoumi1@gmail.com)
Avijeet Ghosh (avi.ghosh23@gmail.com)
Soura Sena Das (sourasenad@gmail.com )
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)]
Lecture 1: (11/1/23) Introduction
Lecture 2: (13/1/23) Introduction to graphs, induction of graphs, Handshake theorem, HP in tournaments.
Lecture 3: (18/1/23) Writing proofs in graphs theory. Eulerian Paths.
Lecture 4 (20/1/23) Counting using Recurrences, Ramsey Number, Sunflower Lemma.
Lecture 5 (25/1/23) Sunflower Lemma, Helly's Theorem
Lecture 6 (1/2/23) Formal Introduction to Propositional and Predicate Logic
Lecture 7 (3/2/23) Asymptotic notations and recurrences with asymptotic relations
Lecture 8 (8/2/23) Counting using generating functions
Lecture 9 (15/2/23) Solving recurrences using generating functions - Fibonacci sequence, Catalan Number
Lecture 10 (17/2/23) Counting the number of irreducible polynomials over F_p using generating functions
Lecture 11 (22/2/23) Revision on solving recurrences involving asymptotic relations
Lecture 12 (24/2/23) Revision of some of the topics
Midsem (3/3/23)
Lecture 13 (10/3/23) Matchings in graphs - Hall's Marriage THeorem
Lecture 14 (15/3/23) Connectivity in Graphs
Lecture 15 (16/3/23) Characterization of trees (Guest lecture by Krisnendu Mukhopadhyay)
Lecture 16 (22/3/23) Introduction to Planar Graphs
Lecture 17 (24/3/23) 5-coloring Theorem
Lecture 18 (29/3/23) Kurotowski's Theorem
Lectute 19 (31/3/23) Introduction to Network Flows
Lecture 20 (5/4/23) Max-flow Mincut Theorem
Lecture 21 (12/4/23) Introduction to Probabilistic Methods and Spectral Graph Theory
Lecture 22 (21/4/23) Revision of some of the topics
Assignment 3 - Solve the midsem paper
Link to previous years DMath course MTech 2022-23, MTech 2021-22, MTech2019-2020, MTech 2018-19
Problem Set on Introduction to Graph theory, Propositional and Predicate Logic and Proof Techniques
Problem Set on Asymptotic Relations and solving recurrences
Problem Set on Generating functions, Recurrences and Counting
Problem Set on everything to be covered till midsem
Problem Set on Planar Graphs