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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.


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.


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.