Topics in a Discrete Mathematics Course
To learn more about a topic listed below, click the topic name to go to the
corresponding MathWorld classroom page.
General
| Algorithm |
An algorithm is a specific set of instructions for carrying out a procedure or solving a problem, usually with the requirement that the procedure terminate at some point. |
| Binary |
Binary refers to the "base 2" method of counting, in which only the digits 0 and 1 are used. |
| Discrete Mathematics |
Discrete mathematics is the branch of mathematics dealing with objects that can assume only distinct, separated values. |
| Logic |
Logic is the formal mathematical study of the methods, structure, and validity of mathematical deduction and proof. |
Combinatorics
| Binomial Coefficient: |
The binomial coefficient is a notation and function giving the number of ways of picking k unordered outcomes from n possibilities, also known as a combination or combinatorial number. |
| Binomial Theorem: |
The binomial theorem is a formula describing how to expand powers of a binomial (x+a)n using binomial coefficients. |
| Combinatorics: |
Combinatorica is the branch of mathematics studying the enumeration, combination, and permutation of sets of elements and the mathematical relations that characterize these properties. |
| Fibonacci Number: |
A member of the Fibonacci sequence. The Fibonacci sequence is generated by beginning with 1, 1, 2, 3 and continuing so that subsequent terms are the sum of the two previous numbers. |
| Generating Function: |
The generating function of a sequence of numbers is a formal power series whose coefficients are the members of that sequence. |
| Magic Square: |
A magic square is a square array of positive integers such that the sum of any row, column, or main diagonal equals that of any other. |
| Pascal's Triangle: |
Pascal's triangle is a triangular array of binomial coefficients that can visually illustrate several of their properties. |
| Permutation: |
In combinatorics, a permutation is a rearrangement of the elements in an ordered list S into a one-to-one correspondence with S itself. Combinatorics studies the number of possible ways of doing this under various conditions. |
| Recurrence Relation: |
A recurrence relation is a mathematical relationship expressing the members of a sequence as some combination of their predecessors. |
Graph Theory
| Chromatic Number: |
The chromatic number is the smallest number of colors necessary to color the vertices of a graph or the regions of a surface such that no two adjacent vertices or regions are the same color. |
| Complete Graph: |
A complete graph is a network in which every pair of vertices is connected by an edge. |
| Connected Graph: |
A connected graph is a network for which there is a path between any pair of vertices. |
| Cycle Graph: |
A cycle graph is a network containing a single cycle which passes through all its vertices. |
| Directed Graph: |
A directed graph is a network in which each edge is specified as going in a particular direction. |
| Graph: |
In graph theory, a graph, also called a network, is a collection of points together with lines that connect some subset of the points. |
| Graph Cycle: |
A graph cycle is any of a network's edge-set subsets that forms a path in which the first node is also the last. |
| Graph Theory: |
Graph theory is the study of formal mathematical structures called graphs (or networks), consisting of collections of points together with lines that connect some subset of the points. |
| Planar Graph: |
A planar graph is a network that can be drawn in a plane without any edges intersecting. |
| Polyhedral Graph: |
A polyhedral graph is a network made up of the vertices and edges of a polyhedron. Polyhedral graphs are always planar. |
| Tree: |
A tree is a network that contains no cycles. |
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TOPICS
