Course Objectives:
1. Understand Fundamentals of Logic and Proofs: Learn propositional logic, predicates,
quantifiers, and various proof methods and strategies.
2. Apply Counting Techniques: Master basic counting principles, permutations,
combinations, and advanced techniques such as inclusion-exclusion and derangements.
3. Utilize Generating Functions and Recurrence Relations: Study generating functions,
their calculation techniques, and solve recurrence relations using various methods.
4. Apply Group Theory to Counting Problems: Understand group actions, the Orbit
Stabilizer Theorem, and apply Polya’s Counting Principle and Cycle Index Polynomial.
Course Outcomes:
Upon successful completion of this course, students will be able to:
1. Use propositional logic, predicates, quantifiers, and various proof methods to solve
problems and construct rigorous arguments.
2. Apply basic counting principles, permutations, combinations, and advanced methods like
inclusion-exclusion and derangements to solve complex counting problems.
3. Compute and apply generating functions, including exponential generating functions, and
use summation operators for problem-solving.
4. Solve first-order and second-order linear recurrence relations with constant coefficients,
including non-homogeneous cases, using generating functions.
5. Utilize group actions, the Orbit-Stabilizer Theorem, Polya’s Counting Principle, and Cycle
Index Polynomial to solve counting and enumeration problems.
- Teacher: Dr Chandru Hegde