Mathematics


Mathematics can be roughly divided into areas of mathematical foundations, arithmetic, algebra, analysis, geometry, and statistics.	Sapience Home Site Map About Sapience Culture Conceptual Culture Math Found Arithmetic Algebra Analysis Geometry Statistics

Mathematics can be roughly divided into areas of mathematical foundations, arithmetic, algebra, analysis, geometry, and statistics.

Foundations

Foundations includes areas of objects, set theory, mathematical structure, and symbolic logic.

Arithmetic

Arithmetic includes numeric arithmetic, approximate arithmetic, concrete arithmetic, and variant arithmetic.

Algebra

Algebra includes major divisions of real and complex algebra, linear algebra, and abstract algebra.

Analysis

Analysis includes areas of real and complex functions, infinite series, differential calculus, integral calculus, differential equations, and other more advanced areas.

Geometry

Geometry includes major divisions of Euclidean fundamentals, Euclidean plane geometry, Euclidean solid geometry, and non-euclidean geometry.

Statistics

Statistics incluces the major areas of probability theory, descriptive statistics, and inferential statistics.


A great deal of mathematics was developed in connection with science, which is a useful source of mathematical knowledge. Physics is particularly useful, but chemistry, astronomcy, earth science, and biology also have applications. Personal studies including he human body, psychology, and biography can be connected to mathematics. Anthropology including social foundations, demography, physical anthropology, human ecology, human geography, and particular groups can be connected.
There are also connections to material culture. There are also connections to language, graphics, literature, applied science, and philosophy. There are also connections to behavioral culture The connections of institutions will be examined further as the site is developed. This is somewhat connected to families, but better connected to education. Economics, government, and religion have also had some influence. Sociology Social structure and change inlcuding social structure, social types, and changes can be considered. Communities such as Tokyo, Seoul, Mexico City, and New York City will be useful in examining mathematics. Peoples of the world including Asiatic peoples African peoples can be considered. Particular nations such as India, Indonesia, Brazil, Pakistan, Bangladesh, and Russia will be useful in examining mathematics. Much development of mathematics has come through Western Civilization including the United States. There is some development of mathematics in Asiatic peoples including those of China. Rather less has come through American Indian peoples such as those of the United States. History The prehistory of mathematics is difficult to reconstruct, but it can be traced to antiquity without great difficulty. I know little of it in the 5th millennium BC or the 4th millennium BC, but it developed in the 3rd millennium BC, 2nd millennium BC, and early 1st millennium BC. It developed substantially in classical and medieval times. In Early classical times, mathematical foundations with the applications of logic was developed, and arithmetic also developed. In early classical times, the Greaks developed mathematics substantially. c. 300 BC Euclid compiles the "Elements", a treatise on geometry. c 250 - c. 211 BC. Archimedes does work in engineering, physics, and mathematics. In late classical times, there were few developments. In early medieval times, hindu-arabic numeration began to come into use, and by late medieval times, the rudeiments of algebra were developed by Islamic peoples. It has flourished substantially in modern times in close association with physical science, but has applications far beyond iit. Develoments of the 16th century, 17th century, 18th century, and 19th century can be examined. 1637 - 1649 Descartes publishes works on philosophy and mathematics. c. 1665-1704 Newton develops and publishes his theories of physics and astronomy, which have a profound influence on philosophy. 1727-1783. Euler becomes a prolific mathematician and introduces concepts and notation now fundamental in intermediate-level mathematics. It is also connected to the 20th century. including the early 20th century, early mid 20th century, mid 20th century, late mid 20th century, and late 20th century. The early 21st century including the early 2000s and lte 2000s can also be considered. Its future has not yet been examined.

A great deal of mathematics was developed in connection with science, which is a useful source of mathematical knowledge. Physics is particularly useful, but chemistry, astronomcy, earth science, and biology also have applications.

Personal studies including he human body, psychology, and biography can be connected to mathematics. Anthropology including social foundations, demography, physical anthropology, human ecology, human geography, and particular groups can be connected.

There are also connections to material culture.

There are also connections to language, graphics, literature, applied science, and philosophy.

There are also connections to behavioral culture

The connections of institutions will be examined further as the site is developed. This is somewhat connected to families, but better connected to education. Economics, government, and religion have also had some influence.

Sociology

Social structure and change inlcuding social structure, social types, and changes can be considered. Communities such as Tokyo, Seoul, Mexico City, and New York City will be useful in examining mathematics. Peoples of the world including Asiatic peoples African peoples can be considered. Particular nations such as India, Indonesia, Brazil, Pakistan, Bangladesh, and Russia will be useful in examining mathematics. Much development of mathematics has come through Western Civilization including the United States. There is some development of mathematics in Asiatic peoples including those of China. Rather less has come through American Indian peoples such as those of the United States.

History

The prehistory of mathematics is difficult to reconstruct, but it can be traced to antiquity without great difficulty. I know little of it in the 5th millennium BC or the 4th millennium BC, but it developed in the 3rd millennium BC, 2nd millennium BC, and early 1st millennium BC. It developed substantially in classical and medieval times. In Early classical times, mathematical foundations with the applications of logic was developed, and arithmetic also developed. In early classical times, the Greaks developed mathematics substantially.

c. 300 BC Euclid compiles the "Elements", a treatise on geometry.
c 250 - c. 211 BC. Archimedes does work in engineering, physics, and mathematics.

In late classical times, there were few developments. In early medieval times, hindu-arabic numeration began to come into use, and by late medieval times, the rudeiments of algebra were developed by Islamic peoples.

It has flourished substantially in modern times in close association with physical science, but has applications far beyond iit. Develoments of the 16th century, 17th century, 18th century, and 19th century can be examined.

1637 - 1649 Descartes publishes works on philosophy and mathematics.
c. 1665-1704 Newton develops and publishes his theories of physics and astronomy, which have a profound influence on philosophy.
1727-1783. Euler becomes a prolific mathematician and introduces concepts and notation now fundamental in intermediate-level mathematics.

It is also connected to the 20th century. including the early 20th century, early mid 20th century, mid 20th century, late mid 20th century, and late 20th century. The early 21st century including the early 2000s and lte 2000s can also be considered. Its future has not yet been examined.