Sets, Operations on sets, Cardinality of sets, inclusion-exclusion principle, pigeonhole principle, matrices, finding Eigen values and Eigen vectors.
Mathematical Logic
Propositional Logic, Applications of Propositional Logic, Propositional Equivalences Predicates and Quantifiers, Nested Quantifiers, Rules of Inference Introduction to Proofs
Relations
Relations and Their Properties, n-ary Relations and Their Application, Representing Relations, Closures of Relations,Equivalence Relations, Partial Orderings
Random variable and probability distribution
Concept of random variable, discrete probability distributions, continuous probability distributions, Mean, variance and co-variance and co-variance of random variables. Binomial and normal distribution, Exponential and normal distribution with mean and variables and problems
Graph Theory
Graphs and Graphs models, Graph Terminology and Special Types of Graphs, Representing Graphs and Graph Isomorphism, Connectivity, Euler and Hamilton Paths, Shortest-Path Problems, Planar Graphs, Graph Coloring
Question Paper Pattern:
• The Question paper will have TEN questions
• Each full question will be for 20 marks
• There will be 02 full questions (with maximum of four sub questions) from each module.
• Each full question will have sub questions covering all the topics under a module.
• The students will have to answer FIVE full questions, selecting one full question from each module.
Text book
1. Kenneth H Rosen, “Discrete Mathematics and its Applications”, McGraw Hill publications, 7th edition. (Chapters 2.1,2.2,2.5, 2.6,6.2,8.5,8.6,10.1 to 10.8)
2. Wolpole Myers Ye “Probability and Statistics for engineers and Scientist” Pearson Education, 8th edition.
References
1. 1.Richard A Johnson and C.B Gupta “Probability and statistics for engineers” Pearson Education.
2. 2.J.K Sharma “Discrete Mathematics”, Mac Millian Publishers India, 3rd edition,2011.
Course Outcomes:
At the end of the course student will be to
1. CO1: Apply the fundamentals of set theory and matrices for the given problem.
2. CO2: Apply the types of distribution, evaluate the mean and variance for the given case study/ problem.
3. CO3: solve the given problem by applying the Mathematical logic concepts
4. CO4: Model the given problem by applying the concepts of graph theory.
5. CO5: Design strategy using gaming theory concepts for the given problem.
6. CO6: Identify and list the different applications of discrete mathematical concepts in computer science.