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Discrete Mathematics
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Course Name
MCA (Master of Computer Application)
Subject Code MC0063 (Discrete Mathematics)
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PART - A
PART - B
PART - C
Discrete Mathematics Syllabus.
Part 1: Sets, Relations and Functions
Sets; Relations; Functions; Intervals; Functions of real variables;
Different functions.
Part 2: Mathematical Induction
Progressions; Principle of Mathematical Induction; Summation of series using
n, n2 and n3.; Arithmetico – Geometric series (A.G.P); Summation of series by
the Method of Differences and partial fractions.
Part 3: Combinatorics
Principles of Counting; Generating Function; Partitions and Compositions;
Orderings; Principle of Inclusion and Exclusion.
Part 4: Recurrences and Integer
Functions Recurrence Relation; Applications of Recurrences; Generating
Function; Integer Functions.
Part 5: Partially Ordered Sets and Lattices
Relation Matrices; Partial Ordered Sets; Lattices; Duality; Modular and
Distributive lattices.
Part 6: Semigroups, Monoids and Groups
Semigroups; Monoids; Groups; Permutation Groups.
Part 7: Rings, Fields and Vector Spaces
Rings and Integral domains; Fields; Vector Spaces.
Part 8: Propositional Calculus and Logical
Quantifiers
Logical Inference; Propositions and Tautologies; Predicates; Logical
Quantification of Propositions.
Part 9: Preliminaries
Sets; Functions; Equivalence Relations; Algebraic Systems; Algorithms.
Part 10: Theory of Numbers and Introduction
to Cryptography
Divisibility and Factorization; Congruence; Arithmetical Functions; Method
of Repeated Squares; Applications to Cryptography.
Part 11: Formal Languages
Grammars and Languages; Classification of Grammars; Backus – Naur Form (BNF);
Derivation Trees.
Part 12: Boolean Algebras and Logical
Circuits
Posets and Lattices; Boolean lattices and Boolean algebras; Uniqueness of
finite Boolean algebras; Boolean Expressions and Normal forms; Logical circuits
and applications.
Part 13: Finite – State Automata
Finite State Machine; Non – Determinants Finite State Automaton (NDFSA);
Languages accepted by an automation; Turing Machine.
Part 14: Algebraic Codes
Preliminaries; Hamming Distance; Linear Codes; Parity Check, Generator
Matrices.
Part 15: Fuzzy Sets and Fuzzy Logic
Fuzzy sets; Fuzzy Relations; Classical logic and Fuzzy logic; Linguistic
variable; Fuzzy Truth Qualifier.
Part 16: Graphs
Preliminary Definitions and Notations.
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