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

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

**MFCS Latest Material Links**

**Download MFCS:Complete Notes**

**Download MFCS:Unit 1 Notes**

**Download MFCS:Unit 2 Notes**

**Download MFCS:Unit 3 Notes**

**Download MFCS:Unit 4 Notes**

**Download MFCS:Unit 5 Notes**

**MFCS Old Material Links**

**Download MFCS:Complete Notes**

**Download MFCS:Unit 1 Notes**

**Download MFCS:Unit 2 Notes**

**Download MFCS:Unit 3 Notes**

**Download MFCS:Unit 4 Notes**

**Download MFCS: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