Mathematical Foundation of Computer Science Notes JNTU – MFCS Notes JNTU of Total Complete Notes
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All the above units are covered according to the below units (JNTU)
MATHEMATICAL FOUNDATION OF COMPUTER SCIENCE
Mathematical Logic : Statements and notations, Connectives, Well formed formulas, Truth Tables, tautology, equivalence implication, Normal forms, Quantifiers, universal quantifiers.
Predicates : Predicative logic, Free & Bound variables, Rules of inference, Consistency, proof of contradiction, Automatic Theorem Proving.
Relations : Properties of binary Relations, equivalence, transitive closure,compatibility and partial ordering relations, Lattices, Hasse diagram. Functions: Inverse Function Compositions of functions, recursive Functions, Lattice and its Properties.
Algebraic structures : Algebraic systems Examples and general properties, Semi groups and monads, groups sub groups’ homomorphism, Isomorphism.
Elementary Combinatorics: Basis of counting, Combinations & Permutations, with repetitions, Constrained repetitions, Binomial Coefficients, Binomial Multinomial theorems, the principles of Inclusion – Exclusion.Pigeon hole principles and its applications.
Recurrence Relation : Generating Functions, Function of Sequences Calculating Coefficient of generating function, Recurrence relations, Solving recurrence relation by substitution and Generating funds. Characteristics roots solution of In homogeneous Recurrence Relation.
Graph Theory : Representation of Graph, DFS, BFS, Spanning Trees, planar Graphs
Graph Theory and Applications, Basic Concepts Isomorphism and Sub graphs, Multi graphs and Euler circuits, Hamiltonian graphs, Chromatic Numbers