UNIT 1:
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Propositional Logic
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Propositional equivalences
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Predicates and Quantifiers
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Nested Quantifiers
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Rules of inference
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Introduction to proofs
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Rules of inference
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Proof methods and strategy
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Proof methods and strategy
UNIT 2:
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Inclusion and exclusion principle and its applications.
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Mathematical induction
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Strong induction and well ordering
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The basics of counting – The pigeon hole principle
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Strong induction and well ordering
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Permutations and combinations
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Recurrence relations
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Solving linear recurrence relations
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Solving linear recurrence relations
UNIT 3:
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Graphs and graph models
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Graph terminology and special types of graphs
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Graph terminology and special types of graphs
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Matrix representation of graphs and graph isomorphism
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Matrix representation of graphs and graph isomorphism
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Matrix representation of graphs and graph isomorphism
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Connectivity
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Euler and Hamilton paths
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Euler and Hamilton paths
UNIT 4:
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Algebraic systems
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Semi groups and monoids
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Groups
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Groups
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Subgroups
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Homomorphism’s
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Normal subgroup and cosets
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Normal subgroup and cosets
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Lagrange’s theorem
UNIT 5:
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Boolean algebra
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Partial ordering – Posets
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Lattices as posets
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Properties of lattices
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Properties of lattices
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Lattices as algebraic systems
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Sub lattices
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Direct product and homomorphism
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Some special lattices
