MATHEMATICAL FOUNDATION OF COMPUTER SCIENCE By, A.Kousar Nikhath, Asst.Professor, CSE Dpt.

UNIT-I 1.1.Syllabus: Mathematical Logic: Statements and notations, Connectives, Well formed formulas, Truth Tables, tautology, equivalence implication, Normal forms. 1.2.Lesson Plan: Learn about the statements and the notations used to represent.1 hr Defining connectives and their usage.1 hr Defining rules for Well formed formulas.2 hr Defining truth tables and prove tautology and implication using them.1 hr Defining Conjunctive, Disjunctive Normal forms and PCNF, PCNF.2 hr Total Number of HRS 7 HRS

UNIT-II 2.1Syllabus: Predicates : Predicative logic, Free & Bound variables, Rules of inference, Consistency, proof of contradiction, Automatic Theorem Proving. 2.2 Lesson Plan: Understanding predictive logic.1 hr Defining free and bound variables with examples.1 hr Defining rules of inference.1 hr Implementing rules of inference with examples.1 hr Defining Consistency.1 hr Explain Proof of Contradiction with example. 1 hr Explain Automatic Theorem Proving with example.1 hr Total Number of HRS: 7 HRS

UNIT-III 3.1 Syllabus: Set Theory: Properties of binary Relations, equivalence, compatibility and partial ordering relations. Hasse diagram, Functions : Inverse Function,Composition of functions,recursive Functions,Lattice and its properties, Pigeon hole principles and its application. 3.2 Lesson Plan: Basics of relations and binary relations. 1 hr Equivalence and Partial Order Relation. 1 hr Hasse Diagrams for Relations—examples. 1 hr Functions and types of functions. 1 hr Lattice and its properties.1 hr Pigeon Hole Principles and its properties.1 hr Total Number of HRS: 6 HRS

UNIT-IV 4.1 Syllabus: Algebraic structures: Algebraic systems Examples and general properties, Semi groups and monoids, groups, subgroups homomorphism, Isomorphism. 4.2 Lesson Plan: Defining algebraic systems & properties with examples. 1 hr Define Groups and its properties.1 hr Define Semi groups and monoids & properties with examples. 1 hr Define Subgroup Homomorphism with examples.1 hr Define Subgroup Isomorphism with examples.1 hr Total Number of HRS: 5 HRS

UNIT-V 5.1Syllabus: Elementary Combinatorics: Basis of counting, Combinations & Permutations, with repetitions, Constrained repetitions, Binomial Coefficients, Binomial Multinomial theorems, the principles of Inclusion-Exclusion. Lesson Plan: 5.2 Concepts of Counting. Combinations –Problems on it. 1hr Permutations – Problems on it. 1hr Permutations with repetitions.1hr Permutations with constrained repetitions.1hr Binomial Coefficients with problems. 1hr Binomial Theorem with proof. 1hr Multinomial Theorem with proof.2hrs Principles of Inclusion and Exclusion. 1hr Total Number of HRS : 9 HRS

UNIT-VI 6.1Syllabus: Recurrence Relation: Generating Functions, Function of Sequences Calculating Coefficient of generating function, Recurrence relations, Solving recurrence relation by substitution and Generating functions. Characteristics roots solution of Inhomogeneous Recurrence Relation. 6.2 Lesson Plan: Generating functions.1hr Function of sequences.1hr Calculating coefficient of generating function.1hr Recurrence relations.1hr 1hr Solving recurrence relations by Substitution method.2hrs Solving recurrence relations by Generating functions.2hrs Characteristics roots --Inhomogeneous Recurrence relation.2hrs Total Number of HRS : 11 HRS

UNIT-VII 7.1 Syllabus: Graph Theory: Representation of Graph, DFS, BFS, Spanning Trees, planar Graphs. 7.2 Lesson Plan: Representing graph using different ways. 1hr Defining Depth First Search Algorithm.1hr Problems on Depth First Search Algorithm.1hr Defining Breadth First Search Algorithm. 1hr Problems on Breadth First Search Algorithm.1hr Defining Spanning trees.1hr Algorithms for constructing spanning trees.2hr Defining Planar Graphs. 1hr Problems on Planar graphs.1hr Total Number of HRS : 10 HRS

UNIT-VIII 8.1 Syllabus: Graph Theory and Applications: Basic Concepts Isomorphism and Sub graphs, Multi graphs and Euler circuits, Hamiltonian graphs, Chromatic Numbers. 8.2Lesson Plan: Basics of Subgraphs.1hr Isomorphism and problems related to it.2hrs Multigraphs and problems on it.1hr Euler and Hamiltonian graphs. 2hr Chromatic numbers and problems on it 1hr Total Number of HRS: 7HRS