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

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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.
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.
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.
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.
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.
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.
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.
Proof Theory

Proof Theory

in Pure Mathematics

The study of representing inferred mathematical statements as formal mathematical objects, facilitating their analysis by mathematical techniques.
Probability Theory

Probability Theory

in Pure Mathematics

The study of random phenomena.
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.
Statistics

Statistics

in Pure Mathematics

The study of collecting, analyzing, interpreting, organizing, and presenting data.
Number Theory

Number Theory

in Pure Mathematics

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

Numerical Analysis

in Pure Mathematics

The study of creating, analyzing, and implementing algorithms for obtaining numerical solutions to problems involving continuous variables.
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.
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.
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.
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.
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.
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.
Geometry & Topology

Geometry & Topology

in Pure Mathematics

The study of general frameworks that allow the uniform manipulation of the fields of geometry and topology.
Universal Algebra

Universal Algebra

in Pure Mathematics

The study of algebraic structures themselves rather than the models of the structures.
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.
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.
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.

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 each faculty of knowledge to function constitutionally as an Arm of Government, we first need to specify or outline their boundaries. Please list as many offices, agencies, ministries, institutions, or parastatals presently in your region that you think fall under the authority, leadership, jurisdiction, legislation, or administration of the faculty of Pure Mathematics.

 

2. Licensing Rights.

The creation or invention of new products and services are the efforts of multiple faculties working collaboratively. However, in our new economic system design, conflicts arise as to which faculties should possess the rights of ownership to certain creations. For example. Should CELLPHONES fall under the licensing rights of Physics or Electrical Engineering? Should PLASTICS fall under the licensing rights of Chemistry or Materials Science? Should PHARMACEUTICALS fall under the licensing rights of Biology or Health Science? Please list as many services, gadgets, 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.

Assuming that the faculty of Pure Mathematics has just been granted ample funding and unhindered federal powers, please 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.

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