Organization

• Regular Classes: Monday 11:10AM to 12:55PM and Wednesday 9:15AM to  11:00AM 

• Class Venue: Room 705-06 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

Instructors and TAs

• Instructor: Sourav Chakraborty (sourav@isical.ac.in)

• TAs:  

1. Soumi Nandi (nandisoumi1@gmail.com)

2. Debarshi Chanda (debarshi.chanda.1997@gmail.com) 

3. Chandrima Kayal (chandrimakayal2012@gmail.com)

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 1: (8/1/24)  Introduction 

• Lecture 2: (15/1/24) Introduction to graphs, induction of graphs, Handshake theorem, HP in tournaments.

• Lecture 3: (18/1/24) More on induction on graphs, Ramsey Number, statement of Sunflower Lemma.

• Lecture 4: (24/1/24) Sunflower Lemma and Helly's Theorem

• Lecture 5: (29/1/24) Balls and bins counting and introduction to use of generating functions in counting and extended binomial theorem

• Lecture 6: (02/2/24) More on counting using generating functions, Counting family tree 

• Lecture 7: (05/2/24) Counting the number of spanning trees. Counting using recuruences

• Lecture 8: (09/2/24) Fibonacci sequence using generating functions and Introduction to Asymptotic Notations

• Lecture 9: (12/2/24) Solving recurrences using asympotic notations

• Lecture 10: (16/2/24) Connectivity in graphs

• Lecture 11: (19/2/24) Revision

• Lecture 12: (23/2/24) Revision

• Midsem

• Lecture 13: (4/3/24)  Planar Graphs and Euler's Theorem

• Lecture 14: (8/3/24) 5-color theorem

• Lecture 15: (11/3/24) Connectivity

• Lecture 16: (15/3/24) Kuratowski's Theorem

• Lecture 17: (18/3/24) Completion of Kuratowski's Theorem

• Lecture 18:(22/3/24) Network flows. Introduction to LP and its duality. 

• Lecture 19:(01/4/24) Max-flow Min-Cut Theorem

• Lecture 20: (05/4/24) Menger's Theorem and Hall Marriage Theorem using Max-flow Min-Cut Theorem 

Assignments

• Assignment 1

Problem sets for Practice and useful links

• Link to previous years DMath course BSTAT20023 MTech 2022-23, MTech 2021-22, MTech2019-2020, MTech 2018-19 

• Problem Set 1