65 relations: Absolute value, Arf invariant, Aromaticity, Bott periodicity theorem, Coding theory, Cohomology, Combinatorics, Compact space, Continued fraction, Cyclic compound, Darts, Degenerate bilinear form, Difference of two squares, Differentiable manifold, Divisibility rule, Divisor, Electron configuration, Euclid, Even code, Feit–Thompson theorem, Fermat's theorem on sums of two squares, Fibonacci Quarterly, Geometric topology, Group theory, Half-integer, Hückel's rule, Integer, Integer factorization, Irrational number, Irreducible fraction, L-theory, List of finite simple groups, List of representations of e, Localization of a ring, Mathematics, Multiplicative group of integers modulo n, Multiplicity (mathematics), Nicomachus, Non-abelian group, Number theory, Order (group theory), Organic chemistry, Orientability, P-adic number, P-adic order, Parallelizable manifold, Parity (mathematics), Parity of zero, Pi bond, PlanetMath, ..., Powerful number, Prime number, Pronic number, Proof by infinite descent, Quadratic form, Rational number, Reductio ad absurdum, Signature (topology), Skew-symmetric graph, Spin structure, Square root of 2, Surgery theory, Terezinha Nunes, Topological K-theory, Trigonometric functions. Expand index (15 more) » « Shrink index
In mathematics, the absolute value or modulus of a real number is the non-negative value of without regard to its sign.
In mathematics, the Arf invariant of a nonsingular quadratic form over a field of characteristic 2 was defined by Turkish mathematician when he started the systematic study of quadratic forms over arbitrary fields of characteristic 2.
In organic chemistry, the term aromaticity is used to describe a cyclic (ring-shaped), planar (flat) molecule with a ring of resonance bonds that exhibits more stability than other geometric or connective arrangements with the same set of atoms.
In mathematics, the Bott periodicity theorem describes a periodicity in the homotopy groups of classical groups, discovered by, which proved to be of foundational significance for much further research, in particular in K-theory of stable complex vector bundles, as well as the stable homotopy groups of spheres.
Christmas is an annual festival commemorating the birth of Jesus Christ,Martindale, Cyril Charles.
The Christmas season, also called the festive season, or the holiday season (mainly in the U.S. and Canada; often simply called the holidays),, is an annually recurring period recognized in many Western and Western-influenced countries that is generally considered to run from late November to early January.
Christmas Eve is the evening or entire day before Christmas Day, the festival commemorating the birth of Jesus.
Christmas traditions vary from country to country.
Coding theory is the study of the properties of codes and their respective fitness for specific applications.
In mathematics, specifically in homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups associated to a topological space, often defined from a cochain complex.
Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures.
In mathematics, and more specifically in general topology, compactness is a property that generalizes the notion of a subset of Euclidean space being closed (that is, containing all its limit points) and bounded (that is, having all its points lie within some fixed distance of each other).
In mathematics, a continued fraction is an expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number, then writing this other number as the sum of its integer part and another reciprocal, and so on.
A cyclic compound (ring compound) is a term for a compound in the field of chemistry in which one or more series of atoms in the compound is connected to form a ring.
Darts is a sport in which small missiles/torpedoes/arrows/darts are thrown at a circular dartboard fixed to a wall.
In mathematics, specifically linear algebra, a degenerate bilinear form on a vector space V is a bilinear form such that the map from V to V∗ (the dual space of V) given by is not an isomorphism.
In mathematics, the difference of two squares is a squared (multiplied by itself) number subtracted from another squared number.
In mathematics, a differentiable manifold (also differential manifold) is a type of manifold that is locally similar enough to a linear space to allow one to do calculus.
A divisibility rule is a shorthand way of determining whether a given integer is divisible by a fixed divisor without performing the division, usually by examining its digits.
In mathematics, a divisor of an integer n, also called a factor of n, is an integer m that may be multiplied by some integer to produce n. In this case, one also says that n is a multiple of m. An integer n is divisible by another integer m if m is a divisor of n; this implies dividing n by m leaves no remainder.
In atomic physics and quantum chemistry, the electron configuration is the distribution of electrons of an atom or molecule (or other physical structure) in atomic or molecular orbitals.
Euclid (Εὐκλείδης Eukleidēs; fl. 300 BC), sometimes given the name Euclid of Alexandria to distinguish him from Euclides of Megara, was a Greek mathematician, often referred to as the "founder of geometry" or the "father of geometry".
A binary code is called an even code if the Hamming weight of each of its codewords is even.
In mathematics, the Feit–Thompson theorem, or odd order theorem, states that every finite group of odd order is solvable.
In additive number theory, Fermat's theorem on sums of two squares states that an odd prime p can be expressed as: p.
The Fibonacci Quarterly is a scientific journal on mathematical topics related to the Fibonacci numbers, published four times per year.
In mathematics, geometric topology is the study of manifolds and maps between them, particularly embeddings of one manifold into another.
In mathematics and abstract algebra, group theory studies the algebraic structures known as groups.
In mathematics, a half-integer is a number of the form where n is an integer.
In organic chemistry, Hückel's rule estimates whether a planar ring molecule will have aromatic properties.
An integer (from the Latin ''integer'' meaning "whole")Integer 's first literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch").
In number theory, integer factorization is the decomposition of a composite number into a product of smaller integers.
In mathematics, the irrational numbers are all the real numbers which are not rational numbers, the latter being the numbers constructed from ratios (or fractions) of integers.
An irreducible fraction (or fraction in lowest terms or reduced fraction) is a fraction in which the numerator and denominator are integers that have no other common divisors than 1 (and -1, when negative numbers are considered).
In mathematics algebraic L-theory is the K-theory of quadratic forms; the term was coined by C. T. C. Wall, with L being used as the letter after K. Algebraic L-theory, also known as 'hermitian K-theory', is important in surgery theory.
In mathematics, the classification of finite simple groups states that every finite simple group is cyclic, or alternating, or in one of 16 families of groups of Lie type, or one of 26 sporadic groups.
The mathematical constant ''e'' can be represented in a variety of ways as a real number.
In commutative algebra, localization is a systematic method of adding multiplicative inverses to a ring.
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
In modular arithmetic, the integers coprime (relatively prime) to n from the set \ of n non-negative integers form a group under multiplication modulo n, called the multiplicative group of integers modulo n. Equivalently, the elements of this group can be thought of as the congruence classes, also known as residues modulo n, that are coprime to n. Hence another name is the group of primitive residue classes modulo n. In the theory of rings, a branch of abstract algebra, it is described as the group of units of the ring of integers modulo n. Here units refers to elements with a multiplicative inverse, which in this ring are exactly those coprime to n. This group, usually denoted (\mathbb/n\mathbb)^\times, is fundamental in number theory.
In mathematics, the multiplicity of a member of a multiset is the number of times it appears in the multiset.
New Year is the time or day at which a new calendar year begins and the calendar's year count increments by one.
New Year's Day, also called simply New Year's or New Year, is observed on January 1, the first day of the year on the modern Gregorian calendar as well as the Julian calendar.
In the Gregorian calendar, New Year's Eve (also known as Old Year's Day or Saint Sylvester's Day in many countries), the last day of the year, is on 31 December which is the seventh day of Christmastide.
Nicomachus of Gerasa (Νικόμαχος; c. 60 – c. 120 AD) was an important ancient mathematician best known for his works Introduction to Arithmetic and Manual of Harmonics in Greek.
In mathematics, and specifically in group theory, a non-abelian group, sometimes called a non-commutative group, is a group (G, ∗) in which there exists at least one pair of elements a and b of G, such that a ∗ b ≠ b ∗ a.
Number theory, or in older usage arithmetic, is a branch of pure mathematics devoted primarily to the study of the integers.
In group theory, a branch of mathematics, the term order is used in two unrelated senses.
Organic chemistry is a chemistry subdiscipline involving the scientific study of the structure, properties, and reactions of organic compounds and organic materials, i.e., matter in its various forms that contain carbon atoms.
In mathematics, orientability is a property of surfaces in Euclidean space that measures whether it is possible to make a consistent choice of surface normal vector at every point.
In mathematics, the -adic number system for any prime number extends the ordinary arithmetic of the rational numbers in a different way from the extension of the rational number system to the real and complex number systems.
In number theory, for a given prime number, the -adic order or -adic valuation of a non-zero integer is the highest exponent such that divides.
In mathematics, a differentiable manifold M of dimension n is called parallelizable if there exist smooth vector fields on the manifold, such that at any point p of M the tangent vectors provide a basis of the tangent space at p. Equivalently, the tangent bundle is a trivial bundle, so that the associated principal bundle of linear frames has a section on M. A particular choice of such a basis of vector fields on M is called a parallelization (or an absolute parallelism) of M.
In mathematics, parity is the property of an integer's inclusion in one of two categories: even or odd.
Zero is an even number.
In chemistry, pi bonds (π bonds) are covalent chemical bonds where two lobes of an orbital on one atom overlap two lobes of an orbital on another atom.
PlanetMath is a free, collaborative, online mathematics encyclopedia.
A powerful number is a positive integer m such that for every prime number p dividing m, p2 also divides m. Equivalently, a powerful number is the product of a square and a cube, that is, a number m of the form m.
A prime number (or a prime) is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers.
A pronic number is a number which is the product of two consecutive integers, that is, a number of the form.
In mathematics, a proof by infinite descent is a particular kind of proof by contradiction that relies on the least integer principle.
In mathematics, a quadratic form is a homogeneous polynomial of degree two in a number of variables.
In mathematics, a rational number is any number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator.
In logic, reductio ad absurdum ("reduction to absurdity"; also argumentum ad absurdum, "argument to absurdity") is a form of argument which attempts either to disprove a statement by showing it inevitably leads to a ridiculous, absurd, or impractical conclusion, or to prove one by showing that if it were not true, the result would be absurd or impossible.
In the mathematical field of topology, the signature is an integer invariant which is defined for an oriented manifold M of dimension d.
In graph theory, a branch of mathematics, a skew-symmetric graph is a directed graph that is isomorphic to its own transpose graph, the graph formed by reversing all of its edges, under an isomorphism that is an involution without any fixed points.
In differential geometry, a spin structure on an orientable Riemannian manifold allows one to define associated spinor bundles, giving rise to the notion of a spinor in differential geometry.
The square root of 2, or the (1/2)th power of 2, written in mathematics as or, is the positive algebraic number that, when multiplied by itself, gives the number 2.
In mathematics, specifically in geometric topology, surgery theory is a collection of techniques used to produce one finite-dimensional manifold from another in a 'controlled' way, introduced by.
Terezinha Nunes (born 3 October 1947) is a British-Brazilian clinical psychologist and academic, specialising in children's literacy and numeracy, and deaf children's learning.
In mathematics, topological -theory is a branch of algebraic topology.
In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are functions of an angle.
2018 has been designated as the third International Year of the Reef by the International Coral Reef Initiative.
2019 (MMXIX) will be a common year starting on Tuesday of the Gregorian calendar, the 2019th year of the Common Era (CE) and Anno Domini (AD) designations, the 19th year of the 3rd millennium, the 19th year of the 21st century, and the 10th and last year of the 2010s decade.
0 (mod 4), 2 (mod 4), 2 (modulo 4), 2 modulo 4, 2-adic order, 2-order, Divisible by 4, Divisible by four, Doubly Even Number, Doubly even, Doubly even number, Even times even, Even times odd, Multiple of 4, Singly even, Singly even number.