MA8351 – NOTES & QP
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MA8351 – 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 pigeonhole 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.