User:Richard Pinch

I am a professional mathematician, with research interests in number theory and combinatorics: my D.Phil (Oxford 1983) was in the arithmetic of elliptic curves and I have published about two dozen research papers and one book (Communication Theory). I held research and teaching posts at the University of Cambridge for 15 years and am now a civil servant. My Erdos number is 3.

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•  Absorbing element: An element whose behaviour with respect to an algebraic binary operation is like that of zero with respect to multiplication. ^[e]
•  Albert algebra: An exceptional Jordan algebra, consisting of 3×3 self-adjoint matrices over the octonions. ^[e]
•  Alternant code: A class of parameterised error-correcting codes which generalise the BCH codes. ^[e]
•  Altitude (geometry): In a triangle, a line from a vertex perpendicular to the opposite side. ^[e]
•  Arithmetic function: A function defined on the set of positive integers, usually with integer, real or complex values, studied in number theory. ^[e]
•  Artin-Schreier polynomial‎: A type of polynomial whose roots generate extensions of degree p in characteristic p. ^[e]
•  Associativity: A property of an algebraic operation such as multiplication: a(bc) = (ab)c. ^[e]
•  Automorphism: An isomorphism of an algebraic structure with itself: a permutation of the underlying set which respects all algebraic operations. ^[e]
•  Average order of an arithmetic function‎: A simple or well-known function, usually continuous and montonic, which on average takes the same or closely approximate values as a given arithmetic function. ^[e]
•  Baer-Specker group‎: An example of an infinite Abelian group which is a building block in the structure theory of such groups. ^[e]
•  Barycentre: The centre of mass of a body or system of particles, a weighted average where certain forces may be taken to act. ^[e]
•  Barycentric coordinates‎: The weights that would have to be assigned to a system of reference points to yield a given position as barycentre are used as coordinates. ^[e]
•  Binary operation: A function of two elements within a set, which assigns another value from among the elements of the set. ^[e]
•  Brun-Titchmarsh theorem: An upper bound on the distribution on primes in an arithmetic progression. ^[e]
•  Cameron-Erdos conjecture‎: Add brief definition or description
•  Cartesian product: The set of ordered pairs whose elements come from two given sets. ^[e]
•  Centraliser: The set of all group elements which commute with every element of a given subset. ^[e]
•  Centre of a group: The subgroup of a group consisting of all elements which commute with every element of the group. ^[e]
•  Cevian line: A line from the vertex of a triangle to some point on the opposite edge. ^[e]
•  Chain rule: A rule in calculus for differentiating a function of a function. ^[e]
•  Characteristic function: A function on a set which takes the value 1 on a given subset and 0 on its complement. ^[e]
• Circumcentre: The centre of the circle that goes through the vertices of a triangle or a cyclic polygon. ^[e]
•  Commutativity: A property of a binary operation (such as addition or multiplication), that the two operands may be interchanged without affecting the result. ^[e]
•  Commutator: A measure of how close two elements of a group are to commuting. ^[e]
•  Compactness axioms: Properties of a toplogical space related to compactness. ^[e]
•  Complement (linear algebra)‎: A pair of subspaces which form an (internal) direct sum. ^[e]
•  Complement (set theory)‎: The set containing those elements of a set (or "universal" set) which are not contained in a given set. ^[e]
•  Complex conjugation: The operation on complex numbers which changes the sign of the imaginary part, x+iy → x-iy ^[e]
•  Conductor of an abelian variety: A measure of the nature of the bad reduction at some prime. ^[e]
•  Congruent triangles: In Euclidean geometry, triangles which can be superposed by a rigid motion. ^[e]
•  Conjugation (group theory)‎: The elements of any group that may be partitioned into conjugacy classes. ^[e]
•  Content (algebra): The highest common factor of the coefficients of a polynomial. ^[e]
•  Continuant (mathematics): An algebraic expression which has applications in generalized continued fractions and as the determinant of a tridiagonal matrix. ^[e]
•  Coprime: Integers, or more generally elements of a ring, which have no non-trivial common factor. ^[e]
•  Cubic reciprocity: Various results connecting the solvability of two related cubic equations in modular arithmetic, generalising the concept of quadratic reciprocity. ^[e]
•  Cyclic group: A group consisting of the powers of a single element. ^[e]
•  Cyclic polygon: A polygon whose vertices lie on a single circle. ^[e]
•  Delta form: A modular form arising from the discriminant of an elliptic curve: a cusp form of weight 12 and level 1 for the full modular group and a Hecke eigenform. ^[e]
•  Different ideal: An invariant attached to an extension of algebraic number fields which encodes ramification data. ^[e]
•  Dirichlet series: An infinite series whose terms involve successive positive integers raised to powers of a variable, typically with integer, real or complex coefficients. ^[e]
•  Discrete metric: The metric on a space which assigns distance one to any distinct points, inducing the discrete topology. ^[e]
•  Disjoint union: A set containing a copy of each of a family of two or more sets, so that the copies do not overlap. ^[e]
•  Distributivity: A relation between two binary operations on a set generalising that of multiplication to addition: a(b+c)=ab+ac. ^[e]
•  Dowker space: A topological space that is T4 but not countably paracompact. ^[e]
• Empty set: In set theory, this is a set without elements, usually denoted $\{~\}$ or $\emptyset$. The empty set is a subset of any set. ^[e]
•  Equivalence relation: A reflexive symmetric transitive binary relation on a set. ^[e]
•  Erdos-Fuchs theorem: A statement about the number of ways that numbers can be represented as a sum of two elements of a given set. ^[e]
•  Essential subgroup: Add brief definition or description
•  Exact sequence: Add brief definition or description
•  Field automorphism: Add brief definition or description
•  Filter (mathematics)‎: Add brief definition or description
•  Frattini subgroup: Add brief definition or description
•  Free group: Add brief definition or description
•  Function composition: Add brief definition or description
•  Functional equation: Add brief definition or description
•  Genus field: Add brief definition or description
•  Group action: Add brief definition or description
•  Group homomorphism: Add brief definition or description
•  Group isomorphism problem: Add brief definition or description
•  Hall polynomial: Add brief definition or description
•  Hall-Littlewood polynomial‎: Add brief definition or description
•  Hutchinson operator: Add brief definition or description
•  Identity element: Add brief definition or description
•  Identity matrix: Add brief definition or description
•  Incentre: Add brief definition or description
•  Injective function: Add brief definition or description
•  Intersection: Add brief definition or description
•  Isolated singularity: Add brief definition or description
•  Jordan's totient function: Add brief definition or description
•  Justesen code: Add brief definition or description
•  KANT: Add brief definition or description
•  Kernel of a function: Add brief definition or description
•  Krull dimension: Add brief definition or description
•  Lambda function: Add brief definition or description
•  Lattice (geometry): Add brief definition or description
•  Limit point: Add brief definition or description
•  Littlewood polynomial: Add brief definition or description
•  Manin obstruction: Add brief definition or description
•  Median algebra: Add brief definition or description
•  Möbius function‎: Add brief definition or description
•  Modulus (algebraic number theory)‎: Add brief definition or description
•  Monogenic field: Add brief definition or description
•  Monoid: Add brief definition or description
•  Monotonic function: Add brief definition or description
•  Moore determinant: Add brief definition or description
•  Morita conjectures: Add brief definition or description
•  Neighbourhood: Add brief definition or description
• Nine-point centre: Add brief definition or description
•  Normal number: Add brief definition or description
•  Normal order of an arithmetic function‎: Add brief definition or description
•  Number Theory Foundation: Add brief definition or description
•  Order (group theory): Add brief definition or description
•  Order (relation): Add brief definition or description
•  Ordered field: Add brief definition or description
•  Ordered pair: Add brief definition or description
•  p-adic metric: Add brief definition or description
•  Pedal triangle: Add brief definition or description
•  Pole (complex analysis): Add brief definition or description
•  Power set: Add brief definition or description
•  Preparata code: Add brief definition or description
•  Primitive root: Add brief definition or description
•  Quadratic residue: Add brief definition or description
•  Removable singularity: Add brief definition or description
•  Residual property (mathematics): Add brief definition or description
•  Resolution (algebra): Add brief definition or description
•  Rigid motion: Add brief definition or description
•  S-unit: Add brief definition or description
•  Selberg sieve: Add brief definition or description
•  Semigroup: Add brief definition or description
•  Separation axioms: Add brief definition or description
•  Series (group theory): Add brief definition or description
•  Singleton set: Add brief definition or description
•  Srivastava code: Add brief definition or description
•  Stably free module: Add brief definition or description
•  Subgroup: Add brief definition or description
•  Sum-of-divisors function: Add brief definition or description
•  Surjective function: Add brief definition or description
•  Sylow subgroup: Add brief definition or description
•  Szpiro's conjecture: Add brief definition or description
•  Tau function: Add brief definition or description
•  Theta function: Add brief definition or description
•  Totient function: Add brief definition or description
•  Turan sieve: Add brief definition or description
•  Tutte matrix: Add brief definition or description