User:Richard Pinch
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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.
Working links
Articles I have started
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]
- Connected space: A topological space in which there is no non-trivial subset which is both open and closed. [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]
- Cyclotomic field: An algebraic number field generated over the rational numbers by roots of unity. [e]
- Cyclotomic polynomial: A polynomial whose roots are primitive roots of unity. [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]
- Diagonal matrix: A square matrix which has zero entries off the main diagonal. [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]
- Division (arithmetic): The process of determing how many copies of one quantity are required to make up another; repeated subtraction; the inverse operation to multiplication. [e]
- Divisor (algebraic geometry): Add brief definition or description
- Dowker space: Add brief definition or description
- Empty set: Add brief definition or description
- Equivalence relation: Add brief definition or description
- Erdos-Fuchs theorem: Add brief definition or description
- 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
- Frobenius map: 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 function: 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 of divisors 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 field: 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
- Symmetric difference: 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
- Zero matrix: Add brief definition or description
Redirects that might turn into articles
I have created various redirects which probably deserve their own articles.
- Antichain
- Artin's conjecture for primitive roots
- Artin-Schreier theorem
- Ascending chain condition
- Atom (order)
- Basis (topology)
- Boolean lattice
- Characteristic of a field
- Chief series
- Codomain
- Commutative monoid
- Complemented lattice
- Complete lattice
- Composition series
- Connected component
- Connectedness
- Coset
- Countably compact space
- Cyclic quadrilateral
- Derived group
- Derived set
- Descending chain condition
- Dilworth's theorem
- Distributive lattice
- Dirichlet convolution
- Effective divisor
- Exponent (group theory)
- Filter base
- First countable space
- Formal Dirichlet series
- Formal power series
- Formally real field
- Free monoid
- Free semigroup
- Fully invariant subgroup
- Group isomorphism
- Hausdorff space
- Index of a subgroup
- Infimum
- Inner automorphism
- Interval (order)
- Jordan-Dedekind chain condition
- Lagrange's Theorem
- Lattice (order)
- Lindelof space
- Mertens conjecture
- Metacompact space
- Möbius inversion formula
- Modular lattice
- Multiplicative function
- Normal series
- Normal space
- Orthocentre
- Orthocompact space
- Orthogonal matrix
- Paracompact space
- Path-connected space
- Perfect set
- Power associativity
- Projective dimension
- Ptolemy's theorem
- Quotient semigroup
- Ray class group
- Regular space
- Second countable space
- Separable space
- Sequentially compact space
- Sigma-compact space
- Square matrix
- Sub-basis (topology)
- Subnormal series
- Supremum
- Symmetric matrix
- Totally disconnected space
- Totally multiplicative function
- Ultrafilter
- Uniform base