Syllabus:
Logic and set theory. Introduction to proofs, axiomatic method, proof patterns. Well ordering principle. Logical formulas  propositional and predicate. Sets, relations, equivalences and partial orders. Induction. Recursive definitions. Infinite Sets: Cantorâ€™s theorem, diagonalization argument, halting problem. Logic of sets. [12 lectures + 4 tutorial sessions ]
Graph Theory. Graphs, degree. Common graphs. Walks, paths, connectivity, cycles, trees, forests. Cliques, Independent sets. Graph Isomorphism, bipartite graphs and matchings. Colouring. Planar graphs: Eulerâ€™s formula, 6colouring of planar graphs. Regular polyhedra. [8 lectures + 3 tutorial sessions]
Combinatorics. Product rule, division rule, counting subsets, sequences with repetitions  binomial and multinomial theorems. Pigeonhole principle. Inclusionexclusion. Combinatorial proofs. Twelvefold way. Recurrence relations  Fibonacci numbers and Towers of Hanoi puzzle. [8 lectures + 3 tutorial sessions]
Discrete Probability. Events and probability spaces, The four step method, birthday principle. Set theory and probability. Conditional probability, law of total probability. Independence. Probability versus confidence. Random variables: independence. distribution functions, expectations. Linearity of Expectation [14 lectures + 4 tutorial sessions]
Learning Outcomes

Use logical notation to define and reason about fundamental mathematical concepts such as sets, relations, functions, and integers.

Evaluate elementary mathematical arguments and identify fallacious reasoning (not just fallacious conclusions).

Synthesize new proofs based on standard proof patterns.

Apply graphtheoretic models to solve problems like job allocation, scheduling, connectivity etc.

Calculate numbers of possible outcomes of elementary combinatorial processes such as permutations and combinations.

Calculate probabilities and discrete distributions for simple combinatorial processes; calculate expectations.
Textbook
 Mathematics for Computer Science. Eric Lehman, F Thomson Leighton, Albert R Meyer. This book is available online under the terms of the Creative Commons Attribution ShareAlike 3.0 license. URL: https://courses.csail.mit.edu/6.042/spring18/mcs.pdf Printed version: 12th Media Services. ISBN13: 9781680921229.
Reference

Discrete Mathematics and Applications. Kenneth Rosen (7th Edition, 2012), McGrawHill Education (ISBN13: 9780073383095)

Invitation to Discrete Mathematics. JiÅ™Ã MatouÅ¡ek and Jaroslav NeÅ¡etÅ™il (2nd Edition) Oxford University Press (ISBN13: 9780198570424)

Discrete Mathematics: Elementary and Beyond. LÃ¡szlÃ³ LovÃ¡sz, JÃ³zsef PelikÃ¡n, Katalin Vesztergombi, Springer 2003, ISBN13: 9780387955858.
Popular Readings

Logicomix: An epic search for truth. Apostolos Doxiadis and Christos Papadimitriou. Bloomsbury USA. ISBN13: 9781596914520

What is the Name of This Book?: The Riddle of Dracula and Other Logical Puzzles. Raymond M. Smullyan. Dover Publications.
ISBN13: 9780486481982

Proofs from THE BOOK. Martin Aigner and GÃ¼nter M. Ziegler. Springer. ISBN13 : 9783642008559
 Combinatorics: A Very Short Introduction. Robin Wilson. Oxford University Press. ISBN13: 9780198723493
Notes
 This course is modelled along the Mathematics for Computer Science course (6.042J, Spring 2015) at MIT.
Past Offerings
(Note: Past offerings could be under a different course number.) Offered in AugNov, 2023 by Deepak Rajendraprasad
 Offered in JanMay, 2023 by Jasine Babu
 Offered in JanMay, 2022 by Satyadev Nandakumar
 Offered in JanMay, 2021 by Deepak, Krithika
 Offered in JanMay, 2020 by Jasine
 Offered in JanMay, 2019 by Deepak
Course Metadata
Item  Details 

Course Title  Discrete Mathematics 
Course Code  CS2020A 
Course Credits  3104 
Course Category  PMC 
Proposing Faculty  Krishnamoorthy Dinesh & Deepak Rajendraprasad 
Approved on  Senate 20 of IIT Palakkad 
Course status  NEW 
Course revision information  Revision of CS2020 Discrete Mathematics for Computer Science & CS2010 Logic for Computing 
Course prerevision code  CS2020 