Mathematics


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

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

Statistics

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

Geometry

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

Analysis

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

Algebra

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

Arithmetic

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

Foundations

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


History The development of mathematics in prehistory is difficult to reconstruct. In antiquity, the major branches of arithmetic and geometry can be recognized. In classical and medieval times, algebra and analysis were invented. In modern times, these were reformulated, and theories of mathematical foundations and statistics developed.
Prehistory The prehistory of mathematics is difficult to reconstruct. I have little information about early prehistory. including the Pliocene, early Pleistocene, early mid Pleistocene, late mid Pleistocene, or late Pleistocene. Middle prehistory including the 5th decamillennium BP, 4th decamillennium BP, 3rd decamillennium BP, 2nd decamillennium BP can be connected. Late prehistory including the early 8th millennium BC, late 8th millennium BC, early 7th cmillennium BC, late 7th millennium BC, early 6th millennium BC, and late 6th millennium BC can be connected. Antiquity The 5th millennium BC including the early 5th millennium BC, early mid 5th millennium BC, mid 5th millennium BC, late mid 5th millennium BC, and late 5th millennium BC can be connected. The 4th millennium BC including the early 4th millennium BC, early mid 4th millennium BC, mid 4th millennium BC, late mid 4th millennium BC, and late 4th millennium BC. The 3rd millennium BC including the early 3rd millennium BC, early mid 3rd millennium BC, mid 3rd millennium BC, late mid 3rd millennium BC, and late 3rd millennium BC can be connected. The 2nd millennium BC including the early 2nd millennium BC, early mid 2nd millennium BC, mid 2nd millennium BC, late mid 2nd millennium BC, and late 2nd millennium BC can be connected. The early 1st millennium BC including the 10th century BC, 9th century BC, 8th century BC, 7th century BC, and 6th century BC can be connected. Classical and medieval history In early classical times, the Greeks developed mathematics substantially. mathematical foundations with the applications of logic was developed, and arithmetic also developed. I do not yet have many details of the 5th century BC, 4th century BC, 3rd century BC, 2nd century BC, or 1st century BC. 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. I do not yet have details of the 1st century, 2nd century, 3rd century, 4th century, or 5th century. In early medieval times, hindu-arabic numeration began to come into use. I do not yet have details of the 6th century, 7th century, 8th century, 9th century, or 10th century. By late medieval times, the rudiments of algebra were developed by Islamic peoples. I do not yet have details of the 11th century, 12th century, 13th century, 14th century, or 15th century. Modern history Mathematics has flourished substantially in modern times in close association with physical science, but has applications far beyond it. Develoments of the 16th century including the early 16th century, early mid 16th century, mid 16th century, late mid 16th century, and late 16th century can be connected. The 17th century including the early 17th century, early mid 17th century, mid 17th century, late mid 17th century, and late 17th century can be connected. 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. The 18th century including the early 18th century, the early mid 18th century, the mid 18th century, the late mid 18th century, and the late 18th century can be connected. 1727-1783. Euler becomes a prolific mathematician and introduces concepts and notation now fundamental in intermediate-level mathematics. The 19th century including the early 19th century and early mid 19th century can be connected. The mid 19th century including the early 1840s, late 1840s, early 1850s, and late 1850s can be examined. The late mid 19th century including the early 1860s, late 1860s, erly 1870s, and late 1870s can be examined. The late 19th century including the early 1880s, late 1880s, early 1890s, and late 1890s can be connected. 20th century The early 20th century including the early 1900s, late 1900s, early 1910s, and late 1910s can be connected. The early mid 20th century including the early 1920s, late 1920s, early 1930s, and late 1930s can be connected. The mid 20th century including the early 1940s, late 1940s, early 1950s, and late 1950s can be connected. The late mid 20th century including the early 1960s, late 1960s, early 1970s, and late 1970s can be connected. The late 20th century including the early 1980s, late 1980s, early 1990s, and late 1990s can be connected. Early 21st century The early 2000s including 2001, 2002, 2003, 2004, and 2005 can be connected. The late 2000s including 2006, 2007, 2008, 2009, and 2010 can be connected. The early 2010s can be connected. 2011 can be connected. The first quarter 2011 including January 2011, February 2011, and March 2011 can be connected. The second quarter 2011 can be connected. Its future has not yet been examined. Sociology Peoples of the world including Asiatic peoples African peoples can be considered. Particular nations such as 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. India can be connected. Oriental peoples such as those of China can be connected. Rather less has come through American Indian peoples such as those of the United States. Communities such as Tokyo, Seoul, Mexico City, and New York City will be useful in examining mathematics. Social structure and change Social change including particular changes, social change processes, and social change factors can be connected. Social types including hunting and gathering societes, horticultural societies, agrarian societies, and industrial societies can be connected. Social structure including community and regional structure, class structure, institutional structure, cultural structure, and anthropological structure can be connected. Institutions Religion including religious organization, religious practice, and religious beliefs can be connected. Particular religions including Abrahamic religion, Asiatic religion, pagen religion, and secularism can be connected. Government including particular governments, government activity, government structure, and law can be connected. Economics including economic systems, industries, and economic activity can be connected. Education including schools, educational organization, cultural institutions, teaching, and research can be connected. Families including particular families, kinship, parenting, and marriage can be connected. Other culture There are also connections to behavioral culture including cultural events, recreation and entertainment, occupations, and customs. Other conceptual culture. There are also connections to language. Philosophy including philosophical schools and doctrines, special topics, aesthetics, ethics, metaphysics, epistemology, and logic can be connected. Applied science including applied social science, accounting, information science, medical science, navigation, engineering, and measurement depends heavily on pure mathematics and includes much of applied mathematics. Literature including literary works, types and genres, forms, and oral tradition can be connected. Graphic arts including animation, photography, printmaking, painting, and drawing can be connected. Material culture including miscellaneous artifacts, communication technology, transportation technology, clothing, foodstuffs, building technology, and industrial technology can be connected. Anthropology Particular groups can be connected. Human geography including European geography, Asian geography, African geography, North American geography, South American geography, and Oceanic geography can be connected. Human ecology including human effects on the environment, relations with other life, and environmental effects on people might be considered. Physical anthropology including human dispersion, racial variation, and human origins can be connected. Demography including population change, population size and structure, deaths, migration, and birth can be connected. Social foundations including social group behavior, social group types, social control, social interaction, and social presentation can be connected. Personal studies Biography is connected to mathematics. Psychology including social psychology, personality, mental disorders, developmental psychology, behavior patterns, mind, and behavioral elements can be connected. The human body including form and appearance, disease, the human life cycle, body functions, and body systems can be connected. Science A great deal of mathematics was developed in connection with physical and natural science which is a useful source of mathematical knowledge. Biology, earth science, astronomy, and chemistry have applications. Physics is particularly useful.

The development of mathematics in prehistory is difficult to reconstruct. In antiquity, the major branches of arithmetic and geometry can be recognized. In classical and medieval times, algebra and analysis were invented. In modern times, these were reformulated, and theories of mathematical foundations and statistics developed.

Prehistory

The prehistory of mathematics is difficult to reconstruct. I have little information about early prehistory. including the Pliocene, early Pleistocene, early mid Pleistocene, late mid Pleistocene, or late Pleistocene. Middle prehistory including the 5th decamillennium BP, 4th decamillennium BP, 3rd decamillennium BP, 2nd decamillennium BP can be connected. Late prehistory including the early 8th millennium BC, late 8th millennium BC, early 7th cmillennium BC, late 7th millennium BC, early 6th millennium BC, and late 6th millennium BC can be connected.

Antiquity

The 5th millennium BC including the early 5th millennium BC, early mid 5th millennium BC, mid 5th millennium BC, late mid 5th millennium BC, and late 5th millennium BC can be connected. The 4th millennium BC including the early 4th millennium BC, early mid 4th millennium BC, mid 4th millennium BC, late mid 4th millennium BC, and late 4th millennium BC. The 3rd millennium BC including the early 3rd millennium BC, early mid 3rd millennium BC, mid 3rd millennium BC, late mid 3rd millennium BC, and late 3rd millennium BC can be connected. The 2nd millennium BC including the early 2nd millennium BC, early mid 2nd millennium BC, mid 2nd millennium BC, late mid 2nd millennium BC, and late 2nd millennium BC can be connected. The early 1st millennium BC including the 10th century BC, 9th century BC, 8th century BC, 7th century BC, and 6th century BC can be connected.

Classical and medieval history

In early classical times, the Greeks developed mathematics substantially. mathematical foundations with the applications of logic was developed, and arithmetic also developed. I do not yet have many details of the 5th century BC, 4th century BC, 3rd century BC, 2nd century BC, or 1st century BC.

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. I do not yet have details of the 1st century, 2nd century, 3rd century, 4th century, or 5th century. In early medieval times, hindu-arabic numeration began to come into use. I do not yet have details of the 6th century, 7th century, 8th century, 9th century, or 10th century. By late medieval times, the rudiments of algebra were developed by Islamic peoples. I do not yet have details of the 11th century, 12th century, 13th century, 14th century, or 15th century.

Modern history

Mathematics has flourished substantially in modern times in close association with physical science, but has applications far beyond it.

Develoments of the 16th century including the early 16th century, early mid 16th century, mid 16th century, late mid 16th century, and late 16th century can be connected.

The 17th century including the early 17th century, early mid 17th century, mid 17th century, late mid 17th century, and late 17th century can be connected.

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.

The 18th century including the early 18th century, the early mid 18th century, the mid 18th century, the late mid 18th century, and the late 18th century can be connected.

1727-1783. Euler becomes a prolific mathematician and introduces concepts and notation now fundamental in intermediate-level mathematics.

The 19th century including the early 19th century and early mid 19th century can be connected. The mid 19th century including the early 1840s, late 1840s, early 1850s, and late 1850s can be examined. The late mid 19th century including the early 1860s, late 1860s, erly 1870s, and late 1870s can be examined. The late 19th century including the early 1880s, late 1880s, early 1890s, and late 1890s can be connected.

20th century

The early 20th century including the early 1900s, late 1900s, early 1910s, and late 1910s can be connected. The early mid 20th century including the early 1920s, late 1920s, early 1930s, and late 1930s can be connected. The mid 20th century including the early 1940s, late 1940s, early 1950s, and late 1950s can be connected. The late mid 20th century including the early 1960s, late 1960s, early 1970s, and late 1970s can be connected. The late 20th century including the early 1980s, late 1980s, early 1990s, and late 1990s can be connected.

Early 21st century

The early 2000s including 2001, 2002, 2003, 2004, and 2005 can be connected. The late 2000s including 2006, 2007, 2008, 2009, and 2010 can be connected. The early 2010s can be connected. 2011 can be connected. The first quarter 2011 including January 2011, February 2011, and March 2011 can be connected. The second quarter 2011 can be connected. Its future has not yet been examined.

Sociology

Peoples of the world including Asiatic peoples African peoples can be considered. Particular nations such as 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. India can be connected. Oriental peoples such as those of China can be connected. Rather less has come through American Indian peoples such as those of the United States.

Communities such as Tokyo, Seoul, Mexico City, and New York City will be useful in examining mathematics.

Social structure and change

Social change including particular changes, social change processes, and social change factors can be connected. Social types including hunting and gathering societes, horticultural societies, agrarian societies, and industrial societies can be connected. Social structure including community and regional structure, class structure, institutional structure, cultural structure, and anthropological structure can be connected.

Institutions

Religion including religious organization, religious practice, and religious beliefs can be connected. Particular religions including Abrahamic religion, Asiatic religion, pagen religion, and secularism can be connected.

Government including particular governments, government activity, government structure, and law can be connected. Economics including economic systems, industries, and economic activity can be connected. Education including schools, educational organization, cultural institutions, teaching, and research can be connected. Families including particular families, kinship, parenting, and marriage can be connected.

Other culture

There are also connections to behavioral culture including cultural events, recreation and entertainment, occupations, and customs.

Other conceptual culture. There are also connections to language. Philosophy including philosophical schools and doctrines, special topics, aesthetics, ethics, metaphysics, epistemology, and logic can be connected. Applied science including applied social science, accounting, information science, medical science, navigation, engineering, and measurement depends heavily on pure mathematics and includes much of applied mathematics. Literature including literary works, types and genres, forms, and oral tradition can be connected. Graphic arts including animation, photography, printmaking, painting, and drawing can be connected.

Material culture including miscellaneous artifacts, communication technology, transportation technology, clothing, foodstuffs, building technology, and industrial technology can be connected.

Anthropology

Particular groups can be connected. Human geography including European geography, Asian geography, African geography, North American geography, South American geography, and Oceanic geography can be connected. Human ecology including human effects on the environment, relations with other life, and environmental effects on people might be considered. Physical anthropology including human dispersion, racial variation, and human origins can be connected. Demography including population change, population size and structure, deaths, migration, and birth can be connected. Social foundations including social group behavior, social group types, social control, social interaction, and social presentation can be connected.

Personal studies

Biography is connected to mathematics. Psychology including social psychology, personality, mental disorders, developmental psychology, behavior patterns, mind, and behavioral elements can be connected. The human body including form and appearance, disease, the human life cycle, body functions, and body systems can be connected.

Science

A great deal of mathematics was developed in connection with physical and natural science which is a useful source of mathematical knowledge. Biology, earth science, astronomy, and chemistry have applications. Physics is particularly useful.