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    Combinatorics

    Combinatorics is a sub-discipline of Algebra which is concerned with the study of combination, enumeration and permutation of sets of elements. One of the main aspects of combinatorics is the study of combinatorial structures found in an algebraic context. It draws on principles from Group Theory and Representation Theory.

    Representation Theory is the study of abstract algebraic structures. It aims to represent their elements in the form of linear transformations of vector spaces; in essence, representation makes an abstract mathematical concept more concrete. Thus, it can be seen that this particular theory is especially prominent in the study of Combinatorics – as it hints at the appearance of enumerative methods in the area of algebraic geometry.

    Algebraic Combinatorial problems are not limited to the discipline of algebra, but rather they can extend into the realm of probability, geometry and topology. In fact, this study can go even further, as it has many applications in the fields of optimization, computer science and physics. Thus, understanding Combinatorics is crucial for the study of Algebra as well as other disciplines which examines combination, enumeration and permutation.

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    Logic and counting problems

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    Challenge problems in combinatorics theory

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    Challenge problems based on combinatorics theory.

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    Democrats and Republicans on Task Force

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    Permutations self study

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    Gaussian Elimination Count

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    Basic Permutation Example

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    Sets: Definitions and Examples

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    Permutations and Combinations-Single Row, Multiple Row Problems

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    Operations/Proofs with Sets

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    Combinations: Selecting members of committee

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    Discrete Math Counting

    How many permutations of the letters ABCDEFGH contain a. the string ED? b. the string CDE? c. the strings BA and FGH? d. the strings AB, DE and GH? e. the strings CAB and BED? f. the strings BCA and ABF? How many ways are there for eight men and five women to stand in a line so that no two women stand next to each other

    Dealing cards, counting bagels, permutations of a string

    How many ways are there to deal hands of seven cards to each of five players from a standard deck of 52 cards? A bagel show has onion, poppy seed, egg, salty, pumpernickel, sesame seed, raisin, and plain bagels. How many ways are there to choose: a) six bagels? b) a dozen bagels? c) two dozen bagels? d) a dozen bagels wi

    Permutations in Probability

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    Truth Tables of Seven Teachers and Three Children

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    Discrete math lists: MP3 player playlist, photos, rooks

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    Basics of Counting

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    Cryptography in RSA

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    Permutations and Combinations Results

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    find total number of combination

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    Cardinality, countability

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    Counting the number of different teams

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