Spring 2019, B. Stat II Year, Indian Statistical Institute

Textbook:

“Discrete Mathematics and Its Applications” by Kenneth Rosen, McGraw Hill Education, Seventh Edition, 2017.

Reference book:

“Applied Combinatorics” by Fred Roberts and Barry Tesman, Chapman and Hall/CRC, Second Edition, 2008.

Evaluation:

Total: 100.

Break up: Scribe: 20, Midsem: 30, Final: 50.

Scribe of Lectures:

Note that these scribes contain only a summary of what is discussed in class and do not necessarily cover all the points in detail.

1. Lecture 1: Sets, Relations, Functions
2. Lecture 2: Natural Numbers and Countability
3. Lecture 3: Well-ordering and Induction
4. Lecture 4: Mathematical Logic and Proof Techniques
5. Lecture 5: Basic Counting and Inclusion-Exclusion
6. Lecture 6: Recurrence Relations
7. Lecture 7: Order Notations
8. Lecture 8: Generating Functions
9. Lecture 9: Integer Partitions
10. Lecture 10: Pigeon Hole Principle
11. Lecture 11: Chains and Antichains
12. Lecture 12: Introduction to Graph Theory
13. Lecture 13: Ramsey Numbers
14. Lecture 14: Degree and Degree Sequence
15. Lecture 15: Paths, Components and Cycles
16. Lecture 16: Eulerian Tours and Hamiltonian Cycles
17. Lecture 17: Trees
18. Lecture 18: Planar Graphs
19. Lecture 19: More on Graph Coloring
20. Lecture 20: Graph Algorithms
21. Lecture 21: Flow Network
22. Lecture 22: Pólya Enumeration

Examination:

1. Mid-Semester Examination
2. Solution to Mid-Semester Examination