In mathematics, genus (pl.: genera) has a few different, but closely related, meanings. Intuitively, the genus is the number of "holes" of a surface....

Genus (mathematics), a classifying property of a mathematical object Genus of a multiplicative sequence Geometric genus In graph embedding, the genus...

In mathematics, the arithmetic genus of an algebraic variety is one of a few possible generalizations of the genus of an algebraic curve or Riemann surface...

birational, the definition is extended by birational invariance. Genus (mathematics) Arithmetic genus Invariants of surfaces Danilov & Shokurov (1998), p. 53 P...

In mathematics, a genus g surface (also known as a g-torus or g-holed torus) is a surface formed by the connected sum of g distinct tori: the interior...

In algebraic number theory, the genus field Γ(K) of an algebraic number field K is the maximal abelian extension of K which is obtained by composing an...

In number theory, a genus character of a quadratic number field K is a character of the genus group of K. In other words, it is a real character of the...

In mathematics, the spinor genus is a classification of quadratic forms and lattices over the ring of integers, introduced by Martin Eichler. It refines...

structure Scalar (physics) Linear algebra Matrix (mathematics) Row and column vectors Tensor Vector (mathematics and physics) Lay, David C. (2006). Linear Algebra...

Eccentricity (mathematics) Elliptic curve cryptography Envelope (mathematics) Fenchel's theorem Genus (mathematics) Geodesic Geometric genus Great-circle...

In mathematics, the genus is a classification of quadratic forms and lattices over the ring of integers. An integral quadratic form is a quadratic form...

articles about curves used in different fields: mathematics (including geometry, statistics, and applied mathematics), physics, engineering, economics, medicine...

(1977): Algebraic geometry, Springer, ISBN 0-387-90244-9. Kulikov, Viktor S. (2001) [1994], "Genus of a curve", Encyclopedia of Mathematics, EMS Press...

In mathematics, a genus of a multiplicative sequence is a ring homomorphism from the ring of smooth compact manifolds up to the equivalence of bounding...

In mathematics, homology is a general way of associating a sequence of algebraic objects, such as abelian groups or modules, with other mathematical objects...

Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer...

relationships of equality and inequality—are studied by mathematics. The essential part of mathematical quantities consists of having a collection of variables...

In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined and behave as the corresponding operations on...

example in the Riemann–Hurwitz formula for the effect of mappings on the genus. In a covering map the Euler–Poincaré characteristic should multiply by...

pattern 2-2-1-2-2-2-1 In mathematics, an abelian group is a group which is commutative. term: abelian group category: mathematical groups distinguishing...

In mathematics, an affine algebraic plane curve is the zero set of a polynomial in two variables. A projective algebraic plane curve is the zero set in...

absolute value of a real or complex number ( |a| ) Moduli space, in mathematics a geometric space whose points represent algebro-geometric objects Conformal...

achievements in mathematics. These include mathematical research, mathematics education,: xii  the history and philosophy of mathematics, public outreach...

In mathematics, a surface is a mathematical model of the common concept of a surface. It is a generalization of a plane, but, unlike a plane, it may be...

In mathematics, the slice genus of a smooth knot K in S3 (sometimes called its Murasugi genus or 4-ball genus) is the least integer g such that K is the...

Lehman, who instructed him in the classical languages and elements of mathematics. In 1816, the twelve-year-old Jacobi went to the Potsdam Gymnasium, where...

unambiguously qualifies what a mathematical term is and is not. Definitions and axioms form the basis on which all of modern mathematics is to be constructed....

Quandle Seifert surface Braids Braid theory Braid group Kirby calculus Genus (mathematics) Examples Positive Euler characteristic 2-disk Sphere Real projective...

Holly Krieger is a professor in mathematics at the University of Cambridge, where she is also the Corfield Fellow at Murray Edwards College. Her current...

In mathematics, a duality translates concepts, theorems or mathematical structures into other concepts, theorems or structures in a one-to-one fashion...