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Discrete Mathematics - MTH202 - VU Video Lectures

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What is Discrete Mathematics?, Logic, Simple Statements, Compound Statements, Negation, Conjunction, Disjunction.
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Truth Tables, De morgan’S Laws, Tautology.
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Applying laws of logic, Conditional statements, Negation of conditional statement, Invers of conditional statement, Converse of conditional statement, Contrapositive of conditional statement.
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Biconditional, Laws of logic.
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Argument, Valid and Invalid argument.
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Switches in series, Switches in parallel, AND-gate, OR-gate, Combinational circuite, Determining output.
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Set, Tabular form, Descriptive form, Set builder form, Subset, Proper subset, Equal set, Null set, Universal set, Venn diagram, Finite and Infinite set.
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Union, Intersection, Difference, Complement.
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Set identities.
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Exercise, Partition of set, Power set.
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Ordered pair, Ordered n-tuple, Cartesian product, Binary relation, Domin and Range of relation, Graph of relation, Arrow diagram of relation, Matrix representation of relation.
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Reflexive relation, Directed graph of reflexive relation, Symmetric relation, Directed graph of Symmetric relation, Transitive relation, Directed graph of transitive relation, Equivalence relation.
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Irreflexive relation, Directed graph of irreflexive relation, Matrix representation of irreflexive relation, Antisymmetric relation, Directed graph of antisymmetric relation, Matrix representation of antisymmetric relation, Partial order relation.
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Inverse of relation, Arrow diagram of inverse relation, Matrix representation of inverse relation, Complementry relation, Composite relation.
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Relations and Functions, Function, Arrow diagram of function, Functions and Nonfunctions, Function not well defined, Image of set, Inverse image of set,Binary opration, Not-gate.
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One-to-One function (Injective function), Graph of one-to-one function, ONTO function (Surjective function), Graph of onto function, Bijective function(one-to-one correspondence), Graph of bijective function, Identity function, Constant function.
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Equality of functions, Inverse of functions, Composition of functions.
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Real-valued functions, Product of functions, quotient functions.
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Sequence, Arithmetic and Geometric sequence.
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Series, Arithmetic and Geometric series, Infinite geometric series.
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Recursion, Recursively defined function, Factorial function, Fibonacci sequence, Recurrence relation, Use of recursion.
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Recursively defined set, Recursive definition of Boolean expression, Parenthesis structure, Set of arithmetic expressions, Recursive definition of sum, Recursive definition of union of sets, Recursive definition of intersection of sets.
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Principal of mathematical induction.
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Mathematical induction for divisibility problems and inequality problems.
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Methods of proofs, Direct proof, Indirect proof, Proof by counter example.
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Proof by contradiction, proof by contraposition.
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Algorithm, Quotient-remainder theorem, Pre-conditions and Post-conditions, Loop invariants.
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Loop to compute product, Division algorithm, Euclidean algorithm.
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Combinatorics, Sum rule, product rule.
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factorial of positive integer, Counting formulas, Formula for k-sample, k-permutation, Formula for k-permutation,
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k-combination, Permutations and combinations, k-selections.
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K-selections, Ordered and unordered partition, Generalized permutation.
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Tree diagram, Inclusion and Exclusion principle.
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Inclusion and Exclusion principle for 3 and 4 sets, Pigeonhole principle.
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Introduction to probability.
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Addition law of probability, Probability of sub event.
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Conditional probability, Multiplication theorem, Independence.
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Random variable, Probability distribution,Expectation,Variance and Standard derivation of random variable.
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Introduction to graphs, Handshaking theorem.
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Paths and Circuites, Konigsberg bridges problem.
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Matrix representation of graphs.
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Isomorphism of graphs, Theorem of isomorphic invariant.
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Planar graph, Euler’s Formula, Graph coloring.
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Tree, Properties of tree, Rooted tree, Binary tree.
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Spanning trees, Kirchhoff's theorem Or Matrix-tree theorem, Prim's algorithm.