List of basic mathematics topics
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The Transhumanist
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'''[[Mathematics]]''' is the search for fundamental truths in pattern, quantity, and change. For more on the relationship between [[mathematics]] and [[science]], refer to the article on [[science#Mathematics and the scientific method|science]].
The following outline is provided as an overview of and introduction to '''mathematics''':
== Subjects of mathematics ==
=== Quantity ===
: ''Main article: [[Mathematics#Quantity|Quantity]]''
* [[Natural number]]s
* [[Integer]]s
* [[Rational number]]s
* [[Real number]]s
* [[Complex number]]s
=== Structure ===
: ''Main article: [[Mathematics#Structure|Structure]]''
* [[Number theory]]
* [[Abstract algebra]]
* [[Order theory]]
=== Space ===
: ''Main article: [[Mathematics#Space|Space]]''
*[[Geometry]]
* [[Trigonometry]]
* [[Differential geometry]]
* [[Topology]]
* [[Fractal geometry]]
=== Change ===
: ''Main article: [[Mathematics#Change|Change]]''
* [[Calculus]]
* [[Vector calculus]]
* [[Differential equation]]s
* [[Dynamical system]]s
* [[Chaos theory]]
=== Foundations and philosophy===
{{main|Foundations of mathematics}}
* [[Philosophy of mathematics]]
* [[Category theory]]
* [[Set theory]]
=== Mathematical logic ===
{{main|Mathematical logic}}
* [[Model theory]]
* [[Proof theory]]
* [[Recursion theory]]
* [[Set theory]]
=== Discrete mathematics ===
{{main|Discrete mathematics}}
* [[Combinatorics]]
* [[Theory of computation]]
* [[Cryptography]]
* [[Graph theory]]
=== Applied mathematics ===
{{main|Applied mathematics}}
* [[Mathematical physics]]
* [[Mechanics|Analytical mechanics]]
* [[Fluid mechanics|Mathematical fluid dynamics]]
* [[Numerical analysis]]
* [[Optimization (mathematics)|Optimization]]
* [[Probability]]
* [[Statistics]]
* [[Mathematical economics]]
* [[Financial mathematics]]
* [[Game theory]]
* [[Mathematical biology]]
* [[Cryptography]]
* [[Operations research]]
* [[Information theory]]
* [[Control theory]]
* [[Dynamical system]]s
== History of mathematics ==
: ''Main article: [[History of mathematics]]''
*[[Babylonian mathematics]]
*[[Egyptian mathematics]]
*[[Indian mathematics]]
*[[Greek mathematics]]
*[[Chinese mathematics]]
**[[Abacus]]
*[[History of the Hindu-Arabic numeral system]]
*[[Islamic mathematics]]
*[[Japanese mathematics]]
*[[History of algebra]]
*[[History of geometry]]
*[[History of mathematical notation]]
*[[History of trigonometry]]
*[[History of writing numbers]]
== Basic mathematics concepts ==
[[Algebra]] -- [[Mathematical analysis|Analysis]] -- [[area (geometry)|Area]] -- [[Arithmetic]] -- [[Calculus]] -- [[Category theory]] -- [[Combinatorics]] -- [[Complex number]] -- [[Computation]] -- [[Coordinate system]] -- [[Decimal]] -- [[Derivative]] -- [[Numerical digit|Digit]] -- [[Equation]] -- [[Fractal]] -- [[Function (mathematics)]] -- [[Geometry]] -- [[Infinity]] -- [[Integral]] -- [[Length]] -- [[Limit (mathematics)|Limit]] -- [[Logarithm]] -- [[Logic]] -- [[matrix (mathematics)|Matrix]] -- [[Number]] -- [[Numeral]] -- [[Pi]] -- [[Power (mathematics)|Power]] -- [[Prime number]] -- [[Mathematical proof|Proof]] -- [[Rational number]] -- [[Real number]] -- [[Series (mathematics)|Series]] -- [[Set]] -- [[Trigonometry]] -- [[Vector space]] -- [[Vector (spatial)]] -- [[Volume]]
== Influential mathematicians ==
{{main|List of mathematicians}}
*[[Bartel Leendert van der Waerden]]
*[[Leonhard Euler]]
*[[Pythagoras]]
*[[Fibonacci]]
== Mathematics lists ==
: ''Main article: [[Lists of mathematics topics]]''
==External links==
{{sisterlinks|Mathematics}}
<div class="references-small">
* Online [[Encyclopaedia of Mathematics]] [http://eom.springer.de] from Springer. Graduate-level reference work with over 8,000 entries, illuminating nearly 50,000 notions in mathematics.
* [http://www-math.mit.edu/daimp Some mathematics applets, at MIT]
* Rusin, Dave: [http://www.math-atlas.org/ ''The Mathematical Atlas'']. A guided tour through the various branches of modern mathematics. (Can also be found [http://www.math.niu.edu/~rusin/known-math/index/index.html here].)
* Stefanov, Alexandre: [http://us.geocities.com/alex_stef/mylist.html ''Textbooks in Mathematics'']. A list of free online textbooks and lecture notes in mathematics.
* Weisstein, Eric et al.: [http://www.mathworld.com/ ''MathWorld: World of Mathematics'']. An online encyclopedia of mathematics.
* Polyanin, Andrei: [http://eqworld.ipmnet.ru/ ''EqWorld: The World of Mathematical Equations'']. An online resource focusing on algebraic, ordinary differential, partial differential ([[mathematical physics]]), integral, and other mathematical equations.
* [http://planetmath.org/ ''Planet Math'']. An online mathematics encyclopedia under construction, focusing on modern mathematics. Uses the [[GNU Free Documentation License|GFDL]], allowing article exchange with Wikipedia. Uses [[TeX]] markup.
* [http://metamath.org/ ''Metamath'']. A site and a language, that formalize mathematics from its foundations.
* [http://www-history.mcs.st-and.ac.uk/~history/ Mathematician Biographies]. The [[MacTutor History of Mathematics archive]] Extensive history and quotes from all famous mathematicians.
* Cain, George: [http://www.math.gatech.edu/~cain/textbooks/onlinebooks.html Online Mathematics Textbooks] available free online.
* [http://etext.lib.virginia.edu/DicHist/analytic/anaVII.html Math & Logic: The history of formal mathematical, logical, linguistic and methodological ideas.] In ''The Dictionary of the History of Ideas.''
* [http://www.nrich.maths.org/public/index.php Nrich], a prize-winning site for students from age five from [[University of Cambridge|Cambridge University]]
* [http://www.freescience.info/mathematics.php 'FreeScience Library->Mathematics '] The mathematics section of FreeScience library
* [http://garden.irmacs.sfu.ca Open Problem Garden], a [[wiki]] of open problems in mathematics
* [http://www.mathmotivation.com/all-applications.html Applications of High School Algebra]
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