Research & Development.

Pure Mathematics as a Human Culture

This culture has the dream or purpose to create or reinvent abstract concepts that develop accurate models for describing the real world.

Pure Mathematics - Subcultures

set-theory

Set Theory

in Pure Mathematics

The study of the properties of sets or well-defined collections of objects, which may or may not be of a mathematical nature, such as numbers or functions, for the definition of complex and sophisticated mathematical concepts.
universal-algebra

Universal Algebra

in Pure Mathematics

The study of algebraic structures themselves rather than the models of the structures.
stochastic-process

Stochastic Process

in Pure Mathematics

The study of probability theory, involving the operation of chance or random variables indexed against some other variable or set of variables.
combinatorics

Combinatorics

in Pure Mathematics

The study of the problems of selection, arrangement, and operation within a finite or discrete system, such as determining the number of possible configurations in graphs, designs, or arrays. Also called combinatorial mathematics.
functional-analysis

Functional Analysis

in Pure Mathematics

The study of the functions of functions, or of the spaces of functions and the formulation of properties of transformations of functions.
dynamical-systems

Dynamical Systems

in Pure Mathematics

The study of systems in which a function describes the time dependence of a point in a geometrical space, such as mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, and the number of fish each springtime in a lake.
theory-of-computation

Theory of Computation

in Pure Mathematics

The study of computer efficiency in problem solving, or the fundamental capabilities and limitations of computers.
intuitionistic-logic

Intuitionistic Logic

in Pure Mathematics

The study of the systems of symbolic logic, as they differ from the systems used for classical logic. Also called Constructive Logic.
representation-theory

Representation Theory

in Pure Mathematics

The study of representing the elements of abstract algebraic structures as linear transformations of vector spaces, to reduce problems in abstract algebra to linear algebra.
operations-research

Operations Research

in Pure Mathematics

The study of improving the management and administration of organized military, governmental, commercial, and industrial processes using scientific research data.
ring-theory

Ring Theory

in Pure Mathematics

The study of algebraic structures, their representations, modules, special classes, also an array of interesting properties both within the theory itself and for its applications.
numerical-analysis

Numerical Analysis

in Pure Mathematics

The study of creating, analyzing, and implementing algorithms for obtaining numerical solutions to problems involving continuous variables.
graph-theory

Graph Theory

in Pure Mathematics

The study of networks of points connected by lines, or structures used to model pairwise relations between objects.
geometry-topology

Geometry & Topology

in Pure Mathematics

The study of general frameworks that allow the uniform manipulation of the fields of geometry and topology.
proof-theory

Proof Theory

in Pure Mathematics

The study of representing inferred mathematical statements as formal mathematical objects, facilitating their analysis by mathematical techniques.
number-theory

Number Theory

in Pure Mathematics

The study of the properties of the positive integers (1, 2, 3 …) sometimes called higher arithmetic.
statistics

Statistics

in Pure Mathematics

The study of collecting, analyzing, interpreting, organizing, and presenting data.
probability-theory

Probability Theory

in Pure Mathematics

The study of random phenomena.
group-theory

Group Theory

in Pure Mathematics

The study of systems consisting of a set of elements and a binary operation that can be applied to two elements of the set, which together satisfy certain axioms.
differential-algebra

Differential Algebra

in Pure Mathematics

The study of rings, fields, and algebras equipped with finitely many derivations, which are unary functions that are linear and satisfy the Leibniz product rule.
model-theory

Model Theory

in Pure Mathematics

The study of creating sentences of mathematical logic that satisfy or interpret classes of mathematical structures such as groups, fields, and graphs.
associative-algebra

Associative Algebra

in Pure Mathematics

The study of algebraic structures such as groups, rings, fields, and lattices, which have compatible operations of addition, multiplication, and a scalar multiplication by elements in some fields.
harmonic-analysis

Harmonic Analysis

in Pure Mathematics

The study of describing and analyzing phenomena of a periodically recurrent nature, representing functions or signals as the superposition of basic waves.
k-theory

K-Theory

in Pure Mathematics

The study of a ring generated by vector bundles over a topological space or scheme, or study of certain kinds of invariants of large matrices.
modal-logic

Modal Logic

in Pure Mathematics

The study of extending classical propositional and predicate logic to include operators expressing modalities such as necessity, possibility, impossibility, contingency, strict implication, and certain other closely related concepts.

Pure Mathematics - Data Collection

As a Pure Mathematician, please Login and provide research data on any of the following topics.

1. Government Agencies.

In preparing the faculties of knowledge to function constitutionally as Arms of Government, please list as many government offices, agencies, ministries, institutions, or parastatals presently in your region you believe fall under the authority, leadership, jurisdiction, legislation, or administration of the faculty of Pure Mathematics.

 

2. Licensing Rights.

Products and services are the efforts of multiple faculties working collaboratively. However, in our new economic design, conflicts arise on which faculty should possess the rights of ownership. Example. CELLPHONES - Physics or Electrical Engineering. PLASTICS - Chemistry or Materials Science. PHARMACEUTICALS - Biology or Health Science. List as many services, gadgetries, products, creations, or inventions that pure mathematicians provide or offer presently in your region that you believe fall under the licensing rights of the faculty of Pure Mathematics.

 

3. The Future.

The faculty of Pure Mathematics has just been granted ample funding and unhindered federal powers. Suggest a new idea, course of action, strategy, dream, innovation, or next-generation agency that pure mathematicians could implement, establish, or research and develop towards achieving a utopia in your region.

Visit the Data Forums to contribute.