Discrete Mathematics

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: PĆ³lya Enumeration
Examination:
  1. Mid-Semester Examination
  2. Solution to Mid-Semester Examination