Combinatorial Mathematics is a branch of Mathematics which deals with counting, arrangements, selection and operations of finite systems or discrete systems. It finds its applications in Computer Science, Cryptography, Communications networks, Computational molecular biology, simulation and so on. It has vide variety of applications in Probability and Statistics, Graph theory, logic, topology etc. Combinatorics is used in many optimization problems in operations research. Combinatorial Matematics play different roles in these fields. For example, in computer science, combinatorial problems arise in numerical analysis. Combinatorial techniques are used in the design of computers. Different divide and conquer algorithms and recurrence relations in Comb. Maths are used to handle big data. Combinatorial tools are used to the storage of information and its retrieval. This course will help the students to acquire a good knowledge in combinatorial mathematics which will also result a better understanding of the subjects where the combinatorial tools play lead roles.
Overview
Syllabus
Week 1 Day 1 Module 1 : Basic Counting Principles Day 2 Module 2 : Permutations - Part 1 Day 3 Module 3 : Permutations - Part 2 Day 4 Discussion Day 5 Assignments
Week 2 Day 1 Module 4 : COMBINATIONS WITHOUT REPETITIONS Day 2 Module 5 : COMBINATIONS WITHOUT REPETITIONS, COUNTING SUBSETS of a Set Day 3 Module 6 : COMBINATIONS WITH REPETITIONS Day 4 Discussion Day 5 Assignments
Week 3 Day 1 Module 7 : BINOMIAL THEOREM PART - 1 Day 2 Module 8 : BINOMIAL THEOREM PART - 2 Day 3 Module 9 : BINOMIAL THEOREM PART - 3 Day 4 Discussion Day 5 Assignments
Week 4 Day 1 Module 10 : Recurrence relations-Recurrence relation models Day 2 Module 11 : Solution of recurrence relations - Method of iteration Day 3 Module 12 : Solution of First and Second order Linear Difference Equations Day 4 Discussion Day 5 Assignments
Week 5 Day 1 Module 13 : Solution of Second-Order Homogeneous and Non
Homogeneous Linear Difference Equations Day 2 Module 14 : Divide and conquer relations Day 3 Module 15 : Principle of inclusion and exclusion Day 4 Discussion Day 5 Assignments
Week 6 Day 1 Module 16 : DERANGEMENTS AND INVERSION FORMULA Day 2 Module 17 : Algibra of Formal Power Series Day 3 Module 18 : Generating functions -Part I Day 4 Discussion Day 5 Assignments
Week 7 Day 1 Module 19 : Generating functions -Part 2 Day 2 Module 20 : Calculating generating functions Day 3 Module 21 : Exponential generating functions Day 4 Discussion Day 5 Assignments
Week 8 Day 1 Module 22 : Solutions of Recurrence Relations by Generating Functions – Part 1 Day 2 Module 23: Solutions of Recurrence Relations by Generating Functions – Part 2 Day 3 Module 24 : Set partitions part 1 Day 4 Discussion Day 5 Assignments
Week 9 Day 1 Module 25 : Set partitions part 2 Day 2 Module 26 : Stirling numbers Part 1 Day 3 Module 27: Stirling numbers Part 2 Day 4 Discussion Day 5 Assignments
Week 10 Day 1 Module 28 : Integer partitions 1 Day 2 Module 29 : Integer partitions 2 Day 3 Module 30 : Integer partitions 3 Day 4 Discussion Day 5 Assignments
Week 11 Day 1 Module 31 : Multinomial Theorem Day 2 Module 32 : Systems of Distinct Representatives - Part 1 Day 3 Module 33: Systems of Distinct Representatives - Part 2 Day 4 Discussion Day 5 Assignments
Week 12 Day 1 Module 34 : Latin Squares Part 1 Day 2 Module 35 : Latin Squares Part 2 Day 3 Module 36 : Hadamard Matrices Day 4 Discussion Day 5 Assignments
Week 13 Day 1 Module 37 : CYCLE INDEX - PART 1 Day 2 Module 38 : CYCLE INDEX - PART 2 Day 3 Module 39 : CYCLE INDEX - PART 3 Day 4 Discussion Day 5 Assignments
Week 14 Day 1 Module 40 : Burnside's Lemma Part 1 Day 2 Module 41 : Burnside's Lemma Part 2 Day 3 Module 42 : Burnside's Lemma Part 3 Day 4 Discussion Day 5 Assignments
Week 15 Day 1 Module 43 : POLYA'S THEOREM Day 2 Module 44 : APPLICATIONS OF POLYA'S THEOREM Day 3 Module 45 : Necklace Problem Day 4 Discussion Day 5 Assignments
Week 16 Day 1 Module 46 : Combinatorial Designs - t design Part 1 Day 2 Module 47 : Combinatorial Designs - t design Part 2 Day 3 Module 48 : Combinatorial Designs - BIBDs Day 4 Discussion Day 5 Assignments
Week 17 Day 1 Module 49 : Combinatorial Designs - SBIBDs Day 2 Module 50 : Some Special Combinatorial Design Day 3 Day 4 Discussion Day 5 Assignments
Week 2 Day 1 Module 4 : COMBINATIONS WITHOUT REPETITIONS Day 2 Module 5 : COMBINATIONS WITHOUT REPETITIONS, COUNTING SUBSETS of a Set Day 3 Module 6 : COMBINATIONS WITH REPETITIONS Day 4 Discussion Day 5 Assignments
Week 3 Day 1 Module 7 : BINOMIAL THEOREM PART - 1 Day 2 Module 8 : BINOMIAL THEOREM PART - 2 Day 3 Module 9 : BINOMIAL THEOREM PART - 3 Day 4 Discussion Day 5 Assignments
Week 4 Day 1 Module 10 : Recurrence relations-Recurrence relation models Day 2 Module 11 : Solution of recurrence relations - Method of iteration Day 3 Module 12 : Solution of First and Second order Linear Difference Equations Day 4 Discussion Day 5 Assignments
Week 5 Day 1 Module 13 : Solution of Second-Order Homogeneous and Non
Homogeneous Linear Difference Equations Day 2 Module 14 : Divide and conquer relations Day 3 Module 15 : Principle of inclusion and exclusion Day 4 Discussion Day 5 Assignments
Week 6 Day 1 Module 16 : DERANGEMENTS AND INVERSION FORMULA Day 2 Module 17 : Algibra of Formal Power Series Day 3 Module 18 : Generating functions -Part I Day 4 Discussion Day 5 Assignments
Week 7 Day 1 Module 19 : Generating functions -Part 2 Day 2 Module 20 : Calculating generating functions Day 3 Module 21 : Exponential generating functions Day 4 Discussion Day 5 Assignments
Week 8 Day 1 Module 22 : Solutions of Recurrence Relations by Generating Functions – Part 1 Day 2 Module 23: Solutions of Recurrence Relations by Generating Functions – Part 2 Day 3 Module 24 : Set partitions part 1 Day 4 Discussion Day 5 Assignments
Week 9 Day 1 Module 25 : Set partitions part 2 Day 2 Module 26 : Stirling numbers Part 1 Day 3 Module 27: Stirling numbers Part 2 Day 4 Discussion Day 5 Assignments
Week 10 Day 1 Module 28 : Integer partitions 1 Day 2 Module 29 : Integer partitions 2 Day 3 Module 30 : Integer partitions 3 Day 4 Discussion Day 5 Assignments
Week 11 Day 1 Module 31 : Multinomial Theorem Day 2 Module 32 : Systems of Distinct Representatives - Part 1 Day 3 Module 33: Systems of Distinct Representatives - Part 2 Day 4 Discussion Day 5 Assignments
Week 12 Day 1 Module 34 : Latin Squares Part 1 Day 2 Module 35 : Latin Squares Part 2 Day 3 Module 36 : Hadamard Matrices Day 4 Discussion Day 5 Assignments
Week 13 Day 1 Module 37 : CYCLE INDEX - PART 1 Day 2 Module 38 : CYCLE INDEX - PART 2 Day 3 Module 39 : CYCLE INDEX - PART 3 Day 4 Discussion Day 5 Assignments
Week 14 Day 1 Module 40 : Burnside's Lemma Part 1 Day 2 Module 41 : Burnside's Lemma Part 2 Day 3 Module 42 : Burnside's Lemma Part 3 Day 4 Discussion Day 5 Assignments
Week 15 Day 1 Module 43 : POLYA'S THEOREM Day 2 Module 44 : APPLICATIONS OF POLYA'S THEOREM Day 3 Module 45 : Necklace Problem Day 4 Discussion Day 5 Assignments
Week 16 Day 1 Module 46 : Combinatorial Designs - t design Part 1 Day 2 Module 47 : Combinatorial Designs - t design Part 2 Day 3 Module 48 : Combinatorial Designs - BIBDs Day 4 Discussion Day 5 Assignments
Week 17 Day 1 Module 49 : Combinatorial Designs - SBIBDs Day 2 Module 50 : Some Special Combinatorial Design Day 3 Day 4 Discussion Day 5 Assignments
Taught by
Dr. Resmi T
