Discrete Mathematics and Its Applications, 6th edition
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Showing posts with label Discrete Mathematics. Show all posts
Showing posts with label Discrete Mathematics. Show all posts
Thursday, January 1, 2015
Wednesday, December 10, 2014
Discrete Mathematics(k.rosen)
Discrete Mathematics Lectures PPT
based on k.rosen
Click on the blue colored links to download the lectures.
Topics
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Lecture
Download
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Introduction: course policies; Overview, Logic, Propositions
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Tautologies, Logical Equivalences
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Predicates and Quantifiers: "there exists" and "for all"
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Sets:
curly brace notation, cardinality, containment, empty set {, power
set P(S), N-tuples and Cartesian product. Set Operations: set
operations union and disjoint union, intersection, difference,
complement, symmetric difference
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Functions:
domain, co-domain, range; image, pre-image; one-to-one, onto,
bijective, inverse; functional composition and exponentiation; ceiling
and floor. Sequences, Series, Countability: Arithmetic and geometric
sequences and sums, countable and uncountable sets, Cantor's
diagonilation argument.
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Big-Oh, Big-Omega, Big-Theta: Big-Oh/Omega/Theta notation, algorithms, pseudo-code, complexity.
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Integers:
Divisors Primality Fundamental Theorem of Arithmetic. Modulii:
Division Algorithm, Greatest common divisors/least common multiples,
Relative Primality, Modular arithmetic, Caesar Cipher,
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Number Theoretic Algorithms: Euclidean Algorithm for GCD; Number Systems: Decimal, binary numbers, others bases;
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RSA
Cryptography: General Method, Fast Exponentiation, Extended Euler
Algorithm, Modular Inverses, Exponential Inverses, Fermat's Little
Theorem, Chinese Remainder Theorem
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Proof Techniques.
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Induction Proofs: Simple induction, strong induction, program correctness
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Recursion: Recursive Definitions, Strings, Recursive Functions.
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Counting Fundamentals: Sum Rule, Product Rule, Inclusion-Exclusion, Pigeonhole Principle Permutations.
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r-permutations: P(n,r), r-combinations: C(n,r),
Anagrams, Cards and Poker; Discrete probability: NY State Lotto,
Random Variables, Expectation, Variance, Standard Deviation.
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Stars and Bars.
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Recurrence
Relations: linear recurrence relations with constant coefficients,
homogeneous and non-homogeneous, non-repeating and repeating roots;
Generelized Includsion-Exclusion: counting onto functions, counting
derangements
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Representing
Relations: Subsets of Cartesian products, Column/line diagrams,
Boolean matrix, Digraph; Operations on Relations: Boolean, Inverse,
Composition, Exponentiation, Projection, Join
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Graph
theory basics and definitions: Vertices/nodes, edges, adjacency,
incidence; Degree, in-degree, out-degree; Degree, in-degree,
out-degree; Subgraphs, unions, isomorphism; Adjacency matrices. Types
of Graphs: Trees; Undirected graphs; Simple graphs, Multigraphs,
Pseudographs; Digraphs, Directed multigraph; Bipartite; Complete
graphs, cycles, wheels, cubes, complete bipartite.
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Connectedness, Euler and Hamilton Paths
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Planar Graphs, Coloring
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Reading Period. Review session TBA.
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