Discrete Mathematics syllabus
UNIT I LOGIC AND PROOFS
Propositional Logic – Propositional equivalences – Predicates and Quantifiers – Nested Quantifiers -Rules of inference – Introduction to proofs – Proof methods and strategy.
UNIT II COMBINATORICS
Mathematical induction – Strong induction and well ordering – The basics of counting – The pigeon hole principle – Permutations and combinations – Recurrence relations – Solving linear recurrence relations – Generating functions – Inclusion and exclusion principle and its applications.
UNIT III GRAPHS
Graphs and graph models – Graph terminology and special types of graphs – Matrix representation of graphs and graph isomorphism – Connectivity – Euler and Hamilton paths.
UNIT IV ALGEBRAIC STRUCTURES
Algebraic systems – Semi groups and monoids – Groups – Subgroups – Homomorphism’s – Normal subgroup and cosets – Lagrange’s theorem – Definitions and examples of Rings and Fields.
UNIT V LATTICES AND BOOLEAN ALGEBRA
Partial ordering – Posets – Lattices as posets – Properties of lattices – Lattices as algebraic systems – Sub lattices – Direct product and homomorphism – Some special lattices – Boolean algebra.
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