**Mathematical Foundation of Computer Science Notes pdf – MFCS notes pdf file**

Mathematical Foundation of Computer Science Notes pdf – MFCS pdf notes – MFCS notes pdf file to download are listed below please check it –

**Link:Complete Notes**

**Link:Unit 1 Notes**

**Link:Unit 2 Notes**

**Link:Unit 3 Notes**

**Link:Unit 4 Notes**

**Link:Unit 5 Notes**

**Note :-** These notes are according to the R09 Syllabus book of JNTU.In R13 and R15,8-units of R09 syllabus are combined into 5-units in R13 and R15 syllabus. If you have any doubts please refer to the JNTU Syllabus Book.

**UNIT-I**

Mathematical Logic : Statements and notations, Connectives, Well formed formulas, Truth Tables, tautology, equivalence implication, Normal forms, Quantifiers, universal quantifiers.

**UNIT-II**

Predicates : Predicative logic, Free & Bound variables, Rules of inference, Consistency, proof of contradiction, Automatic Theorem Proving.

**UNIT-III**

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.

**UNIT-IV**

Algebraic structures : Algebraic systems Examples and general properties, Semi groups and monads, groups sub groups’ homomorphism, Isomorphism.

**UNIT-V**

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.

**UNIT-VI**

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.

**UNIT-VII**

Graph Theory : Representation of Graph, DFS, BFS, Spanning Trees, planar Graphs

**UNIT-VIII**

Graph Theory and Applications, Basic Concepts Isomorphism and Sub graphs, Multi graphs and Euler circuits, Hamiltonian graphs, Chromatic Numbers