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Combinatorics 1.1 The Rules of Sum and Product

Combinatorics 1.2 Permutations

Combinatorics 1.3 Combinations - The Binomial Theorem

Combinatorics 1.4 Combinations with Repetition

Combinatorics 4.1 The Well Ordering Principle - Mathematical Induction

Combinatorics 4.2 Recursive Definitions

Combinatorics 5.5 The Pigeonhole Principle

Combinatorics 8.1.1 The Principle of Inclusion and Exclusion

Combinatorics 8.1.2 Applications of The Principle of Inclusion and Exclusion

Combinatorics 8.2 Generalizations of The Principle - “Exactly” or “At Least”

Combinatorics 8.3 Derangements - Nothing Is In Its Right Place

Combinatorics 9.1 Generating Functions - Introductory Examples

Combinatorics 9.2.1 Generating Functions - Fundamental Identity

Combinatorics 9.2.2 Generating Functions - Finite Geometric Series

Combinatorics 9.2.3 Generating Functions - Binomial and Extended Binomial Theorem

Combinatorics 9.2.4 Generating Functions - Full Practice Questions

Combinatorics 9.3 Partitions of Integers

Combinatorics 10.1 First Order Linear Homogeneous Recurrence Relations

Combinatorics 10.2.1 Second Order Linear Homogeneous Recurrence Relations

Combinatorics 10.2.2 Higher Order Recurrence Relations and Word Problems

Combinatorics 10.4 Recurrence Relations - The Method of Generating Functions

Combinatorics 16.1 Group Theory - Definitions, Examples and Elementary Properties

Combinatorics 16.10 Counting and Equivalence - Burnside’s Theorem

Combinatorics 16.12 The Pattern Inventory - Polya’s Method of Enumeration

Combinatorics 11.1 Graph Theory - Definitions and Examples

Combinatorics 11.2 Subgraphs, Complements and Graph Isomorphisms

Combinatorics 11.3 Euler Trails and Circuits

Combinatorics 11.4 Planar Graphs and Euler's Theorem

Combinatorics 11.5 Hamilton Paths and Cycles

Combinatorics 11.6 Graph Coloring and Chromatic Polynomials

Combinatorics 12.1 Trees - Definitions, Properties and Examples

Combinatorics 12.2 Rooted Trees

Combinatorics 13.1 Dijkstra’s Shortest Path Algorithm

Combinatorics 13.2 Minimal Spanning Trees - The Algorithms of Kruskal and Prim

Description:

Explore advanced concepts in discrete mathematics and combinatorics through a comprehensive 12-hour course based on Grimaldi's "Discrete and Combinatorial Mathematics." Delve into fundamental principles like the Rules of Sum and Product, permutations, combinations, and the Binomial Theorem. Master mathematical induction, recursive definitions, and the Pigeonhole Principle. Study advanced topics including the Principle of Inclusion and Exclusion, derangements, generating functions, and partitions of integers. Investigate recurrence relations, group theory, and Burnside's Theorem. Examine graph theory concepts such as Euler trails, planar graphs, Hamilton paths, and graph coloring. Explore trees, rooted trees, and algorithms like Dijkstra's Shortest Path and minimal spanning trees. Gain a solid foundation in discrete mathematics and combinatorics applicable to various fields in computer science and mathematics.

Discrete Math II - Combinatorics

Kimberly Brehm

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#Mathematics #Discrete Mathematics #Combinatorics #Generating Functions #Permutations #Pigeonhole Principle #Mathematical Proofs #Mathematical Induction #Binomial Theorem

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