Discrete Structures & Optimization for NTA NET Computer Science & Applications
Mathematical Logic : Propositional and Predicate Logic, Propositional Equivalences, Normal Forms, Predicates and Quantifiers, Nested Quantifiers, Rules of Inference.
Sets and Relations : Set Operations, Representation and Properties of Relations, Equivalence Relations, Partially Ordering.
Counting, Mathematical Induction and Discrete Probability : Basics of Counting, Pigeonhole Principle, Permutations and Combinations, Inclusion- Exclusion Principle, Mathematical Induction, Probability, Bayes’ Theorem
Graph Theory : Simple Graph, Multi-graph, Weighted Graph, Paths and Circuits, Shortest Paths in Weighted Graphs, Eulerian Paths and Circuits, Hamiltonian Paths and Circuits, Planner graph, Graph Colouring, Bipartite Graphs, Trees and Rooted Trees, Prefix Codes, Tree Traversals, Spanning Trees and Cut-Sets.
Boolean Algebra : Boolean Functions and its Representation, Simplifications of Boolean Functions.
Optimization : Linear Programming – Mathematical Model, Graphical Solution, Simplex and Dual Simplex Method, Sensitive Analysis; Integer Programming, Transportation and Assignment Models, PERT-CPM: Diagram Representation, Critical Path Calculations, Resource Levelling, Cost Consideration in Project Scheduling.
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