JNTU Anantapur First Year MCA Syllabus 2009 |
Mathematical Foundations of Computer Science |
UNIT – I : |
Mathematical Logic : Statements and notations, Connectives, Well formed formulas, Truth Tables, tautology, equivalence implication, Normal forms, Quantifiers, universal quantifiers
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UNIT – II : |
Predicates : Predicative logic, Free & Bound variables, Rules of inference, Consistency, proof of contradiction, Automatic Theorem Proving.
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UNIT – III : |
Relations : Properties of Binary Relations, equivalence, transitive closure, compatibility and partial ordering relations, Lattices, Hasse diagram. Functions: Inverse Function, Composition of functions, recursive Functions, Lattice and its Properties.
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UNIT – IV : |
Algebraic structures: Algebraic systems examples and general properties, Semi groups and monads, groups, sub groups homomorphism, Isomorphism.
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UNIT – V : |
Elementary Combinatorics: Basis of counting, Enumerating Combinations & Permutations, with repetitions, Constrained repetitions, Binomial Coefficients, Binomial Multinomial theorems, the principles of Inclusion – Exclusion. Pigeon hole principles and its application
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UNIT – VI : |
Recurrence Relation: Generating Functions & Sequences , Calculating Coefficient of generating function, Recurrence relations, Solving Recurrence relation by substitution and Generating functions. Characteristic roots, solution of Inhomogeneous Recurrence Relation.
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UNIT – VII: |
Graph Theory: Representation of Graph, DFS, BFS, Spanning Trees, planar Graphs
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UNIT – VIII : |
Graph Theory Applications : Basic Concepts Isomorphism and Sub graphs, Multi graphs and Euler circuits, Hamiltonian graphs, Chromatic Numbers.
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REFERENCE |
TEXT BOOKS: |
1. Elements of Discrete Mathematics- A Computer Oriented Approach,C.L.Liu,
D.P. Mohapatra, 3/e,TMH.
2. Discrete Mathematics for Computer Scientists & Mathematicians, 2/e,
J.L.Mott, A. Kandel, T.P. Baker, PHI
3. Discrete Mathematical Structures with Application to Computer Science, Tremblay, Manohar
McGraw Hill Publication
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Reference Books |
1. Discrete and Combinatorial Mathematics- An Applied Introduction,Ralph. P.Grimaldi, 5/e,Pearson Education.
2. Discrete Mathematics and its applications, 6th edition, K.H.Rosen, TMH.
3. Discrete Mathematical Structures, Mallik and Sen, Cengage Learning.
4. Discrete Mathematical Structures, Bernand Kolman, Robert C. Busby, Sharon Cutler Ross, PHI/ Pearson Education.
5. Discrete Mathematics with Applications,Thomas Koshy,Elsevier.
6. Discrete Mathematics, Lovasz, Springer.
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