Spring 2019, B. Stat II Year, Indian Statistical Institute
“Discrete Mathematics and Its Applications” by Kenneth Rosen, McGraw Hill Education, Seventh Edition, 2017.
“Applied Combinatorics” by Fred Roberts and Barry Tesman, Chapman and Hall/CRC, Second Edition, 2008.
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.
- Lecture 1: Sets, Relations, Functions
- Lecture 2: Natural Numbers and Countability
- Lecture 3: Well-ordering and Induction
- Lecture 4: Mathematical Logic and Proof Techniques
- Lecture 5: Basic Counting and Inclusion-Exclusion
- Lecture 6: Recurrence Relations
- Lecture 7: Order Notations
- Lecture 8: Generating Functions
- Lecture 9: Integer Partitions
- Lecture 10: Pigeon Hole Principle
- Lecture 11: Chains and Antichains
- Lecture 12: Introduction to Graph Theory
- Lecture 13: Ramsey Numbers
- Lecture 14: Degree and Degree Sequence
- Lecture 15: Paths, Components and Cycles
- Lecture 16: Eulerian Tours and Hamiltonian Cycles
- Lecture 17: Trees
- Lecture 18: Planar Graphs
- Lecture 19: More on Graph Coloring
- Lecture 20: Graph Algorithms
- Lecture 21: Flow Network
- Lecture 22: Pólya Enumeration