Discrete Mathematics

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Number Systems : Natural Numbers, Integers, Rational Numbers, Real Numbers, Complex Numbers, Arithmetic Modulo a Positive Integer (Binary, Octal, Decimal and Hexadecimal Number Systems), Radix Representation of Integers, Representing Negative and Rational Numbers, Floating Point Notation.
Binary Arithmetic, 2‟s Complement Arithmetic, Conversion of Numbers from One of Binary / Octal / Decimal / Hexadecimal Number System to other Number System, Codes (Natural BCD, Excess-3, Gray, Octal, Hexadecimal, Alphanumeric – EBCDIC and ASCII), Error Codes.
Logic and Proofs : Proposition, Conjunction, Disjunction, Negation, Compound Proposition, Conditional Propositions (Hypothesis, Conclusion, Necessary and Sufficient Condition) and Logical Equivalence, De Morgan‟s Laws, Quantifiers, Universally Quantified Statement, Generalized De Morgan‟s Laws for Logic, Component of Mathematical System (Axiom, Definitions, Undefined Terms, Theorem, Leema and Corollary), Proofs (Direct Proofs, Indirect Proofs, Proof by Contra-Positive), Valid Argument, Deductive Reasoning, Modus Ponens (Rules of Inference), Universal Instantiation, Universal Generalization, Existential Instantiation, Universal Generalization Resolution, Principle of Mathematical Induction, Structural Induction.
Sets, Venn Diagrams, Ordered Pairs, Sequences and Strings, Relation (Reflexive, Symmetric, Anti-symmetric, Transitive, Partial Order), Inverse Relation (Injective, Subjective, bijective), Coposition of Functions, Restriction and Function Overriding, Function Spaces, Lambda Notation for functions, Lambda Calculus, Equivalence Relations, Interpretation using Digraphs. Cardinals, Countable and Uncountable Sets, Infinite Cardinal Numbers, Russell‟s Paradox, Operations on Cardinals, Laws of Cardinal Arithmetic.
Graph Theory, Undirected Graph, Digraph, Weighted Graph, Similarity Graphs, Paths and Cycles, Hamiltonian Cycles, Shortest Path Algorithm, Isomorphism of Graphs, Planar Graphs.
Trees, Characterization of Trees, Spanning Trees, Breadth First Search and Death First Search Method, Minimal Spanning Trees, Binary Trees, Tree Traversals, Decision Trees and the Minimum Time for Sorting, Isomorphism of Trees.

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