MA2265 Discrete Mathematics Hand Written Lecture Notes - Deepthi Edition

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    09-07-2015, 02:14 PM #1
       
    Discrete Mathematics (All Units) Handwritten Premium Lecture Notes, Prepared by Deepthi. Specially for Engineering Candidates. Syllabus Covered based on Anna University  B.Tech IT, R2008 and R2013 Regulation.

    CONTENT:

    UNIT-1 LOGIC AND PROOFS (No.of.pg:34)
    UNIT-2 COMBINATIONS (No. of Pg:20)
    UNIT-3 GRAPHS (No. of pg:34)
    UNIT-4 ALGEBRIC STRUCTURE (No. of. Pg: 25)
    UNIT-5 LATTICES AND BOOLEAN ALGRBRA (No .of .pg:20)

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    UNIT-1
    LOGIC AND PROOFS
    Definition: proposition
    Atomic IC statements
    Molecular statement
    Truth table
    Negation or not
    Conjuction
    Conditional statement
    Bi conditional statement
    Contrapositive
    Translating sentence into logical expression or symbolic form
    Tautology
    Contradiction
    Fallacy
    Duality
    Disjunction
    Conjunctive normal form
    Principle conjunction normal form
    Quantifiers
    Rules of inference
    Rules in quantifiers
    1. Universal specification
    2. Existential specification
    3. Existential specification
    4. Universal generalization
    Hypothesis
    Analisis
    Conclusion
    UNIT-2
    COMBINATIONS
    Principle of mathematical induction
    Strong induction
    Pigeonhole principle
    Generalization pigeonhole principle
    Extended pigeonhole principle
    Linear recurence relation
    Generating function
    Inclusion and exclusion
    UNIT-3
    GRAPHS
    Adjacent vertices
    Simple graph
    Parallel edges
    Multi graph
    Simple directed graph
    Directed graph
    Mixed graph
    Loop
    Weighed graph
    Underlying undirected graph
    Pseudo graphs
    In degree
    Out degree
    Complete graph
    N-cube
    Star graph
    Sub graph
    Union
    Representation graph and graph isomorphism
    Properties of adjacency matrix
    Connectivity
    Path
    Connected and disconnected graph
    Connectedness in D.G
    UNIT-4
    ALGEBRAIC STRUCTURE
    Binary operation
    General properties of algebraic structure
    1. Closure properties
    2. Associativity
    3. Commutativity
    4. Identity
    5. Element
    6. Distributivity
    7. Cancellation property
    Semi graph
    Monoid
    Semi graph homomorphism
    Monoid homomorphism
    Sub monoid
    Group
    Abelian group
    Properties of group
    Langrange’s thm
    Normal sub group
    Kernel of a homomorphism
    Isomorphism
    Cosets
    Integral domain

    UNIT-5
    LATTICES AND BOOLEAN ALGRBRA
    Partial order relation
    Poset
    Totally ordered set
    Well ordered
    Hasse diagram or partially ordered set diagram
    Lattice
    Greatest lower band and upper post
    Some properties of lattices
    Theorems
    Boolean algebra

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