Mathematics

Major themes in mathematics

An alphabetical and subclassified list of mathematical topics is available. The following list of themes and links gives just one possible view. For a fuller treatment, see Areas of mathematics or the list of lists of mathematical topics.

Related Topics:
List of mathematical topics - Areas of mathematics - List of lists of mathematical topics

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Quantity

This starts from explicit measurements of sizes of numbers or sets, or ways to find such measurements.

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:Number – Natural number – Integers – Rational numbers – Real numbers – Complex numbers – Hypercomplex numbers – Quaternions – Octonions – Sedenions – Hyperreal numbers – Surreal numbers – Ordinal numbers – Cardinal numbers – p-adic numbers – Integer sequences – Mathematical constants – Number names – Infinity – Base

Related Topics:
Number - Natural number - Integer - Rational number - Real number - Complex number - Hypercomplex number - Quaternion - Octonion - Sedenion - Hyperreal number - Surreal number - Ordinal number - Cardinal number - ''p''-adic number - Integer sequence - Mathematical constant - Number names - Infinity - Base

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Change

:Ways to express and handle change in mathematical functions, and changes between numbers.

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:Arithmetic – Calculus – Vector calculus – Analysis – Differential equations – Dynamical systems – Chaos theory – List of functions

Related Topics:
Arithmetic - Calculus - Vector calculus - Analysis - Differential equation - Dynamical system - Chaos theory - List of functions

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Structure

:Pinning down ideas of size, symmetry, and mathematical structure.

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:Abstract algebra – Number theory – Algebraic geometry – Group theory – Monoids – Analysis – Topology – Linear algebra – Graph theory – Universal algebra – Category theory – Order theory – Measure theory

Related Topics:
Abstract algebra - Number theory - Algebraic geometry - Group theory - Monoid - Analysis - Topology - Linear algebra - Graph theory - Universal algebra - Category theory - Order theory - Measure theory

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Spatial relations

:A more visual approach to mathematics.

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:Topology – Geometry – Trigonometry – Algebraic geometry – Differential geometry – Differential topology – Algebraic topology – Linear algebra – Fractal geometry

Related Topics:
Topology - Geometry - Trigonometry - Algebraic geometry - Differential geometry - Differential topology - Algebraic topology - Linear algebra - Fractal geometry

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Discrete mathematics

:Discrete mathematics involves techniques that apply to objects that can only take on specific, separated values.

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:Combinatorics – Naive set theory – Theory of computation– Cryptography – Graph theory

Related Topics:
Combinatorics - Naive set theory - Theory of computation - Cryptography - Graph theory

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Applied mathematics

:Applied mathematics uses the full knowledge of mathematics to solve real-world problems.

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:Mathematical physics – Mechanics – Fluid mechanics – Numerical analysis – Optimization – Probability – Statistics – Financial mathematics – Game theory – Mathematical biology – Cryptography – Information theory

Related Topics:
Mathematical physics - Mechanics - Fluid mechanics - Numerical analysis - Optimization - Probability - Statistics - Financial mathematics - Game theory - Mathematical biology - Cryptography - Information theory

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Famous theorems and conjectures

:These theorems have interested mathematicians and non-mathematicians alike.

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:Pythagorean theorem – Fermat's last theorem – Goldbach's conjecture – Twin Prime Conjecture – Gödel's incompleteness theorems – Poincaré conjecture – Cantor's diagonal argument – Four color theorem – Zorn's lemma – Euler's identity – Church-Turing thesis – Collatz conjecture

Related Topics:
Pythagorean theorem - Fermat's last theorem - Goldbach's conjecture - Twin Prime Conjecture - Gödel's incompleteness theorem - Poincaré conjecture - Cantor's diagonal argument - Four color theorem - Zorn's lemma - Euler's identity - Church-Turing thesis - Collatz conjecture

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Important theorems and conjectures

See list of theorems, list of conjectures for more

Related Topics:
List of theorems - List of conjectures

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:These are theorems and conjectures that have changed the face of mathematics throughout history.

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:Riemann hypothesis – Continuum hypothesis – P=NP – Pythagorean theorem – Central limit theorem – Fundamental theorem of calculus – Fundamental theorem of algebra – Fundamental theorem of arithmetic – Fundamental theorem of projective geometry – classification theorems of surfaces – Gauss-Bonnet theorem

Related Topics:
Riemann hypothesis - Continuum hypothesis - P=NP - Pythagorean theorem - Central limit theorem - Fundamental theorem of calculus - Fundamental theorem of algebra - Fundamental theorem of arithmetic - Fundamental theorem of projective geometry - Classification theorems of surfaces - Gauss-Bonnet theorem

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Foundations and methods

:Approaches to understanding the nature of mathematics also influence the way mathematicians study their subject.

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:Philosophy of mathematics – Mathematical intuitionism – Mathematical constructivism – Foundations of mathematics – Set theory – Symbolic logic – Model theory – Category theory – Logic – Reverse Mathematics – Table of mathematical symbols

Related Topics:
Philosophy of mathematics - Mathematical intuitionism - Mathematical constructivism - Foundations of mathematics - Set theory - Symbolic logic - Model theory - Category theory - Logic - Reverse Mathematics - Table of mathematical symbols

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History and the world of mathematicians

See also list of mathematics history topics

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:History of mathematics – Timeline of mathematics – Mathematicians – Fields medal – Abel Prize – Millennium Prize Problems (Clay Math Prize) – International Mathematical Union – Mathematics competitions – Lateral thinking – Mathematical abilities and gender issues

Related Topics:
History of mathematics - Timeline of mathematics - Mathematicians - Fields medal - Abel Prize - Millennium Prize Problems (Clay Math Prize) - International Mathematical Union - Mathematics competitions - Lateral thinking - Mathematical abilities and gender issues

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Mathematics and other fields

:Mathematics and architecture – Mathematics and education – Mathematics of musical scales

Related Topics:
Mathematics and architecture - Mathematics and education - Mathematics of musical scales

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Mathematical coincidences

:List of mathematical coincidences

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