Geometric algebra (disambiguation)

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In mathematics, a geometric algebra is a specific algebraic structure. The term is also used as a blanket term for the theory of geometric algebras.

Geometric algebra may also refer to:

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Algebraic geometry Branch of mathematics

Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical problems about these sets of zeros.

Analytic geometry Study of geometry using a coordinate system

In classical mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts with synthetic geometry.

Discrete mathematics Study of discrete mathematical structures

Discrete mathematics is the study of mathematical structures that can be considered "discrete" rather than "continuous". Objects studied in discrete mathematics include integers, graphs, and statements in logic. By contrast, discrete mathematics excludes topics in "continuous mathematics" such as real numbers, calculus or Euclidean geometry. Discrete objects can often be enumerated by integers; more formally, discrete mathematics has been characterized as the branch of mathematics dealing with countable sets. However, there is no exact definition of the term "discrete mathematics".

Differential geometry Branch of mathematics dealing with functions and geometric structures on differentiable manifolds

Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra. The field has its origins in the study of spherical geometry as far back as antiquity. It also relates to astronomy, the geodesy of the Earth, and later the study of hyperbolic geometry by Lobachevsky. The simplest examples of smooth spaces are the plane and space curves and surfaces in the three-dimensional Euclidean space, and the study of these shapes formed the basis for development of modern differential geometry during the 18th and 19th centuries.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =. The word equation and its cognates in other languages may have subtly different meanings; for example, in French an équation is defined as containing one or more variables, while in English, any well-formed formula consisting of two expressions related with an equals sign is an equation.

Mathematics Field of study

Mathematics is an area of knowledge that includes such topics as numbers, formulas and related structures (algebra), shapes and the spaces in which they are contained (geometry), and quantities and their changes.

There have been several attempts in history to reach a unified theory of mathematics. Some of the most respected mathematicians in the academia have expressed views that the whole subject should be fitted into one theory.

Complex geometry Study of complex manifolds and several complex variables

In mathematics, complex geometry is the study of geometric structures and constructions arising out of, or described by, the complex numbers. In particular, complex geometry is concerned with the study of spaces such as complex manifolds and complex algebraic varieties, functions of several complex variables, and holomorphic constructions such as holomorphic vector bundles and coherent sheaves. Application of transcendental methods to algebraic geometry falls in this category, together with more geometric aspects of complex analysis.

<i>La Géométrie</i> Mathematical appendix to Descartes Discourse on Method, published in 1637

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Apollonius of Perga Ancient Greek geometer and astronomer noted for his writings on conic sections

Apollonius of Perga was an Ancient Greek geometer and astronomer known for his work on conic sections. Beginning from the contributions of Euclid and Archimedes on the topic, he brought them to the state prior to the invention of analytic geometry. His definitions of the terms ellipse, parabola, and hyperbola are the ones in use today. Gottfried Wilhelm Leibniz stated “He who understands Archimedes and Apollonius will admire less the achievements of the foremost men of later times.”

Synthetic geometry

Synthetic geometry is the study of geometry without the use of coordinates or formulae. It relies on the axiomatic method and the tools directly related to them, that is, compass and straightedge, to draw conclusions and solve problems.

Diophantine geometry Mathematics of varieties with integer coordinates

In mathematics, Diophantine geometry is the study of Diophantine equations by means of powerful methods in algebraic geometry. By the 20th century it became clear for some mathematicians that methods of algebraic geometry are ideal tools to study these equations.

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Algebra is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics.

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Ian Robertson Porteous was a Scottish mathematician at the University of Liverpool and an educator on Merseyside. He is best known for three books on geometry and modern algebra. In Liverpool he and Peter Giblin are known for their registered charity Mathematical Education on Merseyside which promotes enthusiasm for mathematics through sponsorship of an annual competition.

This glossary of areas of mathematics is a list of definitions of the terms and concepts that indicate or distinguish areas of study within mathematics. Mathematics is a broad subject with a vast history of topics identified as mathematical concerns. Concerns have been included in mathematical discourse of notable mathematicians, and some of those authors have explicitly defined areas of mathematics, conceptually encapsulating particular mathematical concerns, theorems and achievements. Other authors have categorised their concerns, theorems and achievements into areas of mathematics, by simply labelling their work with a title using terms implying an area of mathematics. To handle the dissimilarity in how areas of mathematics are identified, this glossary makes use of both extensional and intensional definitions. For a hierarchical organisation of topics of mathematics see mathematics subject classification. For a list of current mathematical concerns see list of unsolved problems in mathematics.

Foundations of Differential Geometry is an influential 2-volume mathematics book on differential geometry written by Shoshichi Kobayashi and Katsumi Nomizu. The first volume was published in 1963 and the second in 1969, by Interscience Publishers. Both were published again in 1996 as Wiley Classics Library.