list of number theory topics

The aim of this page is to list all areas of modern mathematics, with a brief explanation about their scope and links to other parts of this encyclopedia, set out in a systematic way. The way research-level mathematics is internally organised is mostly determined by practitioners, and does change over time; this is in contrast with the apparently timeless syllabus divisions used in mathematics education, where calculus can seem to be much the same over a time scale of a century. Calculus itself does not appear as a major heading — m ...

Including:

• Areas of mathematics - Foundations / general
• Areas of mathematics - Algebra
• Areas of mathematics - Analysis
• Areas of mathematics - Geometry
• Areas of mathematics - Applied mathematics
• Areas of mathematics - Probability and statistics
• Areas of mathematics - Computational sciences
• Areas of mathematics - Physical sciences
• Areas of mathematics - Non-physical sciences

Read more here: » Areas of mathematics: Encyclopedia - Areas of mathematics

Number theory - Elementary number theory. In elementary number theory, integers are studied without use of techniques from other mathematical fields. Questions of divisibility, use of the Euclidean algorithm to compute greatest common divisors, factorization of integers into prime numbers, investigation of perfect numbers and congruences belong here. Several important discoveries of this field are Fermat's little theorem, Euler's theorem, the Chinese remainder theorem and the law of quadratic reciprocity. ...

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Number theory, Number theory - Fields, Number theory - Elementary number theory, Number theory - Analytic number theory, Number theory - Algebraic number theory, Number theory - Geometric number theory, Number theory - Combinatorial number theory, Number theory - Computational number theory, Number theory - History, Number theory - Early history, Number theory - Beginnings of a systematic theory, Number theory - Prime number theory, Number theory - Nineteenth-century developments, Number theory - Quotations

Read more here: » Number theory: Encyclopedia II - Number theory - Fields

Number theory - Elementary number theory. In elementary number theory, integers are studied without use of techniques from other mathematical fields. Questions of divisibility, use the Euclidean algorithm to compute greatest common divisors, factorization of integers into prime numbers, investigation of perfect numbers and congruences belong here. Several important discoveries of this field are Fermat's little theorem, Euler's theorem, the Chinese remainder theorem and the law of quadratic reciprocity. The ...

See also:

Number theory, Number theory - Fields, Number theory - Elementary number theory, Number theory - Analytic number theory, Number theory - Algebraic number theory, Number theory - Geometric number theory, Number theory - Combinatorial number theory, Number theory - Computational number theory, Number theory - History, Number theory - Early history, Number theory - Beginnings of a systematic theory, Number theory - Prime number theory, Number theory - Nineteenth-century developments, Number theory - Quotations

Read more here: » Number theory: Encyclopedia II - Number theory - Fields

The study of structure starting with numbers, first the familiar natural numbers and integers and their arithmetical operations, which are recorded in elementary algebra. The deeper properties of whole numbers are studied in number theory. The investigation of methods to solve equations leads to the field of abstract algebra, which, among other things, studies rings and fields, structures that generalize the properties possessed by everyday numbers. Long standing questions about ruler-and-compass constructions were finally settled by Galois ...

See also:

Areas of mathematics, Areas of mathematics - Foundations / general, Areas of mathematics - Algebra, Areas of mathematics - Analysis, Areas of mathematics - Geometry, Areas of mathematics - Applied mathematics, Areas of mathematics - Probability and statistics, Areas of mathematics - Computational sciences, Areas of mathematics - Physical sciences, Areas of mathematics - Non-physical sciences

Read more here: » Areas of mathematics: Encyclopedia II - Areas of mathematics - Algebra

Analysis is primarily concerned with change. Rates of change, accumulated change, multiple things changing relative to (or independently of) one another, etc. 26: Real functions, including derivatives and integrals 28: Measure and integration 30: Complex functions, including approximation theory in the complex domain 31: Potential theory 32: Several complex variables and analytic spaces 33: Special functions 34: Ordinary differential equations 35: Partial differentia ...

See also:

Areas of mathematics, Areas of mathematics - Foundations / general, Areas of mathematics - Algebra, Areas of mathematics - Analysis, Areas of mathematics - Geometry, Areas of mathematics - Applied mathematics, Areas of mathematics - Probability and statistics, Areas of mathematics - Computational sciences, Areas of mathematics - Physical sciences, Areas of mathematics - Non-physical sciences

Read more here: » Areas of mathematics: Encyclopedia II - Areas of mathematics - Analysis

Number theory - Early history. Number theory was a favorite study among the Ancient Greeks, who were aware of the Diophantine equation concept in numerous special cases. It revived in the sixteenth and seventeenth centuries, in Europe, with François Viète, Bachet de Meziriac, and especially Fermat, whose infinite descent method was the first general idea for dealing with diophantine questions. In the eighteenth century Euler and Lagrange made major contributions. Number theory - ...

See also:

Number theory, Number theory - Fields, Number theory - Elementary number theory, Number theory - Analytic number theory, Number theory - Algebraic number theory, Number theory - Geometric number theory, Number theory - Combinatorial number theory, Number theory - Computational number theory, Number theory - History, Number theory - Early history, Number theory - Beginnings of a systematic theory, Number theory - Prime number theory, Number theory - Nineteenth-century developments, Number theory - Quotations

Read more here: » Number theory: Encyclopedia II - Number theory - History