Learning Objectives
The objective of this course is to introduce the students to various techniques in combinatorics by guiding them through a set of carefully chosen problems.
Learning Outcome
After successful completion of this course, a student will be able to

Analyse a given combinatorial problem with a view to solve it by applying one of the standard techniques they learned.

Slightly extend some of the techniques learned and apply the extended technique to solve harder problems.

Describe clearly a few open problems in the area and their current status.
Syllabus
Elementary techniques (to be reviewed)
Bijective proofs, mathematical induction, pigeonhole principle, double counting, parity arguments, and inclusionexclusion principle.
Advanced techniques (to be introduced)
Generating functions. Ordinary, exponential and other special generating functions, formal power series.
Probabilistic arguments. Positive probability based existence arguments, moment based arguments, alteration technique, Lovász local lemma.
Linear Algebraic arguments. Dimensionality arguments, orthogonality and rank arguments.
Problem selection
The problems to introduce and illustrate the power of the above techniques will be chosen from these areas: sets, partitions, sequences, permutations, graphs, partial orders, algorithms, geometry and number theory.
Textbooks

László Lovász, Combinatorial Problems and Exercises. (AMS Chelsea Publishing); 2nd edition. ISBN13: 9780821842621

Noga Alon and Joel H. Spencer, The Probabilistic Method WileyBlackwell; 4th revised edition ISBN13: 9781119061953

Herbert S. Wilf, Generating Functionology. A K Peters/CRC Press, 3rd edition ISBN13: 9781568812793

Stasys Jukna, Extremal Combinatorics: With Applications in Computer Science Springear; 2nd ed. ISBN13: 9783642173639
References

Richard Stanley, Enumerative Combinatorics: Volume 1. Cambridge University Press, 2nd edition. ISBN: 9781107015425

Richard Stanley, Enumerative Combinatorics: Volume 2. Cambridge University Press, 2nd edition. ISBN: 9780511609589

László Babai and Péter Frankl, Linear Algebra Methods in Combinatorics With Applications to Geometry and Computer Science. Preliminary Version 2 (September 1992).
Meta Data
 Proposing Faculty : Deepak Rajendraprasad
 Department / Centre : Computer Science and Engineering
 Programme : B.Tech
 Proposal Type: New Course
 Offerings: S5 and S7, AugDec 2018
Past Offerings
 Offered in JanMay, 2020 by Deepak
 Offered in JulyDec, 2018 by Deepak