This page will attempt to list examples in mathematics. To qualify for inclusion, an article should be about a mathematical object with a fair amount of concreteness. Usually a definition of an abstract concept, a theorem, or a proof would not be an "example" as the term should be understood here (an elegant proof of an isolated but particularly striking fact, as opposed to a proof of a general theorem, could perhaps be considered an "example"). The discussion page for list of mathematical topics has some comments on this. Eventually this page may have its own discussion page. This page links to itself in order that edits to this page will be included among related changes when the user clicks on that button.

The concrete example within the article titled Rao-Blackwell theorem is perhaps one of the best ways for a probabilist

Probabilist

A probabilist is either:* A follower of probabilism * A mathematician who practices probability theory; see List of mathematical probabilists...

 ignorant of statistical inference to get a quick impression of the flavor of that subject.

Uncategorized examples, alphabetized

• Alexander horned sphere
  Alexander horned sphere
  The Alexander horned sphere is a wild embedding of a sphere into space, discovered by . It is the particular embedding of a sphere in 3-dimensional Euclidean space obtained by the following construction, starting with a standard torus:...
  
  
• All horses are the same color
• Cantor function
  Cantor function
  In mathematics, the Cantor function, named after Georg Cantor, is an example of a function that is continuous, but not absolutely continuous. It is also referred to as the Devil's staircase.-Definition:See figure...
  
  
• Cantor set
  Cantor set
  In mathematics, the Cantor set is a set of points lying on a single line segment that has a number of remarkable and deep properties. It was discovered in 1875 by Henry John Stephen Smith and introduced by German mathematician Georg Cantor in 1883....
  
  
• Checking if a coin is biased
• Concrete illustration of the central limit theorem
• Differential equations of mathematical physics
• Dirichlet function
• Discontinuous linear map
  Discontinuous linear map
  In mathematics, linear maps form an important class of "simple" functions which preserve the algebraic structure of linear spaces and are often used as approximations to more general functions . If the spaces involved are also topological spaces , then it makes sense to ask whether all linear maps...
  
  
• Efron's non-transitive dice
• Examples of contour integration
• Examples of differential equations
  Examples of differential equations
  Differential equations arise in many problems in physics, engineering, and other sciences. The following examples show how to solve differential equations in a few simple cases when an exact solution exists....
  
  
• Examples of generating functions
  Examples of generating functions
  The following examples are in the spirit of George Pólya, who advocated learning mathematics by doing and re-capitulating as many examples and proofs as possible...
  
  
• Examples of groups
  Examples of groups
  Some elementary examples of groups in mathematics are given on Group .Further examples are listed here.-Permutations of a set of three elements:Consider three colored blocks , initially placed in the order RGB...
  
  
  • List of the 230 crystallographic 3D space groups
• Examples of Markov chains
  Examples of Markov chains
  - Board games played with dice :A game of snakes and ladders or any other game whose moves are determined entirely by dice is a Markov chain, indeed, an absorbing Markov chain. This is in contrast to card games such as blackjack, where the cards represent a 'memory' of the past moves. To see the...
  
  
• Examples of vector spaces
  Examples of vector spaces
  This page lists some examples of vector spaces. See vector space for the definitions of terms used on this page. See also: dimension, basis.Notation. We will let F denote an arbitrary field such as the real numbers R or the complex numbers C...
  
  
• Fano plane
  Fano plane
  In finite geometry, the Fano plane is the finite projective plane with the smallest possible number of points and lines: 7 each.-Homogeneous coordinates:...
  
  
• Frieze group
  Frieze group
  A frieze group is a mathematical concept to classify designs on two-dimensional surfaces which are repetitive in one direction, based on the symmetries in the pattern. Such patterns occur frequently in architecture and decorative art...
  
  
• Gray graph
  Gray graph
  In the mathematical field of graph theory, the Gray graph is an undirected bipartite graph with 54 vertices and 81 edges. It is a cubic graph: every vertex touches exactly three edges. It was discovered by Marion C. Gray in 1932 , then discovered independently by Bouwer 1968 in reply to a question...
  
  
• Hall–Janko graph
• Higman–Sims graph
• Hilbert matrix
• Illustration of a low-discrepancy sequence
• Illustration of the central limit theorem
  Illustration of the central limit theorem
  This article gives two concrete illustrations of the central limit theorem. Both involve the sum of independent and identically-distributed random variables and show how the probability distribution of the sum approaches the normal distribution as the number of terms in the sum increases.The first...
  
  
• An infinitely differentiable function that is not analytic
• Leech lattice
  Leech lattice
  In mathematics, the Leech lattice is an even unimodular lattice Λ24 in 24-dimensional Euclidean space E24 found by .-History:Many of the cross-sections of the Leech lattice, including the Coxeter–Todd lattice and Barnes–Wall lattice, in 12 and 16 dimensions, were found much earlier than...
  
  
• Lewy's example
  Lewy's example
  In the mathematical study of partial differential equations, Lewy's example is a celebrated example, due to Hans Lewy, of a linear partial differential equation with no solutions...
  
   on PDEs
• List of finite simple groups
• Long line
  Long line (topology)
  In topology, the long line is a topological space somewhat similar to the real line, but in a certain way "longer". It behaves locally just like the real line, but has different large-scale properties. Therefore it serves as one of the basic counterexamples of topology...
  
  
• Normally distributed and uncorrelated does not imply independent
  Normally distributed and uncorrelated does not imply independent
  In probability theory, two random variables being uncorrelated does not imply their independence. In some contexts, uncorrelatedness implies at least pairwise independence ....
  
  
• Pairwise independence
  Pairwise independence
  In probability theory, a pairwise independent collection of random variables is a set of random variables any two of which are independent. Any collection of mutually independent random variables is pairwise independent, but some pairwise independent collections are not mutually independent...
  
   of random variables need not imply mutual independence.
• Petersen graph
  Petersen graph
  In the mathematical field of graph theory, the Petersen graph is an undirected graph with 10 vertices and 15 edges. It is a small graph that serves as a useful example and counterexample for many problems in graph theory. The Petersen graph is named for Julius Petersen, who in 1898 constructed it...
  
  
• Sierpinski space
  Sierpinski space
  In mathematics, the Sierpiński space is a finite topological space with two points, only one of which is closed.It is the smallest example of a topological space which is neither trivial nor discrete...
  
  
• Simple example of Azuma's inequality for coin flips
• Proof that 22/7 exceeds π
• Solenoid (mathematics)
  Solenoid (mathematics)
  In mathematics, a solenoid is a compact connected topological space that may be obtained as the inverse limit of an inverse system of topological groups and continuous homomorphisms...
  
  
• Sorgenfrey plane
• Stein's example
  Stein's example
  Stein's example , in decision theory and estimation theory, is the phenomenon that when three or more parameters are estimated simultaneously, there exist combined estimators more accurate on average than any method that handles the parameters separately...
  
  
• Three cards and a top hat
• Topologist's sine curve
  Topologist's sine curve
  In the branch of mathematics known as topology, the topologist's sine curve is a topological space with several interesting properties that make it an important textbook example....
  
  
• Tsirelson space
  Tsirelson space
  In mathematics, Tsirelson space T is an example of a reflexive Banach space in which neither an l p space nor a c0 space can be embedded.It was introduced by B. S. Tsirelson in 1974...
  
  
• Tutte eight cage
• Weierstrass function
  Weierstrass function
  In mathematics, the Weierstrass function is a pathological example of a real-valued function on the real line. The function has the property that it is continuous everywhere but differentiable nowhere...
  
  
• Wilkinson's polynomial
• Wallpaper group
  Wallpaper group
  A wallpaper group is a mathematical classification of a two-dimensional repetitive pattern, based on the symmetries in the pattern. Such patterns occur frequently in architecture and decorative art...
  
  
• Uses of trigonometry
  Uses of trigonometry
  Amongst the lay public of non-mathematicians and non-scientists, trigonometry is known chiefly for its application to measurement problems, yet is also often used in ways that are far more subtle, such as its place in the theory of music; still other uses are more technical, such as in number theory...
  
   (The "examples" in that article are not mathematical objects, i.e., numbers, functions, equations, sets, etc., but applications of trigonometry or scientific fields to which trigonometry is applied.)

Specialized lists of mathematical examples

• List of algebraic surfaces 
• List of curves 
• List of complexity classes 
• List of examples in general topology
• List of finite simple groups 
• List of Fourier-related transforms 
• List of mathematical functions 
• List of knots 
  • List of mathematical knots and links 
• List of manifolds 
• List of mathematical shapes 
• List of matrices 
• List of numbers 
• List of polygons, polyhedra and polytopes 
• List of prime numbers  —not merely a numerical table, but a list of various kinds of prime numbers, each with a table
• List of regular polytopes 
• List of surfaces 
• List of small groups 
• Table of Lie groups
  Table of Lie groups
  This article gives a table of some common Lie groups and their associated Lie algebras.The following are noted: the topological properties of the group , as well as on their algebraic properties .For more examples of Lie groups and other...
  
   

Sporadic groups

See also list of finite simple groups.

• Baby Monster group
  Baby Monster group
  In the mathematical field of group theory, the Baby Monster group B is a group of orderThe Baby Monster group is one of the sporadic groups, and has the second highest order of these, with the highest order being that of the Monster group...
  
  
• Conway group
  Conway group
  In mathematics, the Conway groups Co1, Co2, and Co3 are three sporadic groups discovered by John Horton Conway.The largest of the Conway groups, Co1, of order...
  
  
• Fischer group
  Fischer group
  In mathematics, the Fischer groups are the three sporadic simple groups Fi22, Fi23,Fi24' introduced by .- 3-transposition groups :...
  
  s
• Harada–Norton group
• Held group
  Held group
  In the mathematical field of group theory, the Held group He is one of the 26 sporadic simple groups, and has order...
  
  
• Higman–Sims group
• Janko group
  Janko group
  In mathematics, a Janko group is one of the four sporadic simple groups named for Zvonimir Janko. Janko constructed the first Janko group J1 in 1965. At the same time, Janko also predicted the existence of J2 and J3. In 1976, he suggested the existence of J4...
  
  s
• Lyons group
  Lyons group
  In the mathematical field of group theory, the Lyons group Ly , is a sporadic simple group of order...
  
  
• The Mathieu groups
• McLaughlin group
• Monster group
  Monster group
  In the mathematical field of group theory, the Monster group M or F1 is a group of finite order:...
  
  
• O'Nan group
  O'Nan group
  In the mathematical field of group theory, the O'Nan group O'N is a sporadic simple group of orderThe Schur multiplier has order 3, and its outer automorphism group has order 2...
  
  
• Rudvalis group
  Rudvalis group
  In the mathematical field of group theory, the Rudvalis group Ru is a sporadic simple group of order-Properties:The Rudvalis group acts as a rank 3 permutation group on 4060 points, with one point stabilizer the Ree group...
  
  
• Suzuki sporadic group
• Thompson group
  Thompson group (finite)
  In the mathematical field of group theory, the Thompson group Th, found by and constructed by , is a sporadic simple group of orderThe centralizer of an element of order 3 of type 3C in the Monster group is a product of the Thompson group and a group of order 3, as a result of which the Thompson...