IIT Roorkee Course , Prof. Sugata Gangopadhyay

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IIT Roorkee Course , Prof. Sugata Gangopadhyay

Set Theory:Introduction to the theory of sets; combination of sets; power sets; finite and infinite sets; principle of inclusion and exclusion; selected problems from each topic;Logic:Proposition, predicate logic, logic operators, logic proposition and proof, method of proofs - Mathematical Induction Different forms of the principle of mathematical induction. selected problems on mathematical induction - Discrete Probability:Counting principles. Random experiment; sample space; events; axioms of probability; conditional probability. Theorem of total probability; Bayes' theorem. Application to information theory: information and mutual information;Graph theory:Path, cycles, handshaking theorem, bipartite graphs, sub-graphs, graph isomorphism, operations on graphs, Eulerian graphs and Hamiltonian graphs, planar graphs, Euler formula, traveling salesman problem, shortest path algorithms;Relations:Definitions and properties; Equivalence relations and equivalence classes. Representations of relations by binary matrices and digraphs; operations on relations. Closure of a relations; reflexive, symmetric and transitive closures. Warshall's algorithm to compute transitive closure of a relation;Partially Ordered Sets and Lattices - Partial order relations; POSETS; lattices - Boolean Algebra and Boolean Functions Introduction to Boolean algebra and Boolean functions. Different representations of Boolean functions. Application of Boolean functions to synthesis of circuits - Discrete Numeric Functions:Introduction of discrete numeric functions; asymptotic behaviour; generating functions;Recurrence Relations:Linear recurrence relations with constant coefficients (homogeneous case); discussion of all the three sub-cases. Linear recurrence relations with constant coefficients (non-homogeneous case); discussion of several special cases to obtain particular solutions. Solution of linear recurrence relations using generating functions

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Discrete Mathematics by Dr. Sugata Gangopadhyay & Dr. Aditi Gangopadhyay,Department of Mathematics,IIT Roorkee.For more details on NPTEL visit httpnptel.ac.in

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- 1.Introduction to the theory of sets
- 2.Set operation and laws of set operation
- 3.The principle of inclusion and exclusion
- 4.Application of the principle of inclusion and exclusion
- 5.Fundamentals of logic
- 6.Logical Inferences
- 7.Methods of proof of an implication
- 8.First order logic(1)
- 9.First order logic(2)
- 10.Rules of influence for quantified propositions
- 11.Mathematical Induction(1)
- 12.Mathematical Induction(2)
- 13.Sample space, events
- 14.Probability, conditional probability
- 15.Independent events, Bayes theorem
- 16.Information and mutual information
- 17.Basic definition
- 18.Isomorphism and sub graphs
- 19.Walks, paths and circuits operations on graphs
- 20.Euler graphs, Hamiltonian circuits
- 21.Shortest path problem
- 22.Planar graphs
- 23.Basic definition.
- 24.Properties of relations
- 25.Graph of relations
- 26.Matrix of relation
- 27.Closure of relaton(1)
- 28.Closure of relaton(2)
- 29.Warshalls algorithm
- 30.Partially ordered relation
- 31.Partially ordered sets
- 32.Lattices
- 33.Boolean algebra
- 34.Boolean function(1)
- 35.Boolean function(2)
- 36.Discrete numeric function
- 37.Generating function
- 38.Introduction to recurrence relations
- 39.Second order recurrence relation with constant coefficients(1)
- 40.Second order recurrence relation with constant coefficients(2)
- 41.Application of recurrence relation

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