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Mathematics includes many practical results concerning quantity and measure, such as calculations involving numbers, financial accounting, geometric construction of building, astronomical calculations, calendar dating, telling time, engineering, physics, chemistry, etc. but also more abstract issues such as establishing the conditions under which certain kinds of equations and formulas have solutions.
Mathematics includes many practical results concerning quantity and measure, such as calculations involving numbers, financial accounting, geometric construction of building, astronomical calculations, calendar dating, telling time, engineering, physics, chemistry, etc. but also more abstract issues such as establishing the conditions under which certain kinds of equations and formulas have solutions.
== Numeracy ==
''See also:'' [[Numeracy]]
[[Numeracy]] is the ability to understand, interpret, and use numbers effectively in everyday life. It goes beyond basic arithmetic, encompassing logical reasoning, problem-solving, and the ability to apply mathematical concepts to real-world situations. Whether managing personal finances, interpreting data, or making informed decisions, numeracy is a fundamental skill for modern living.
==Symbols, Equations, and Theories==
==Symbols, Equations, and Theories==
A mathematical theory is expressed as a set of sentences, called [[axiom]]s. These axioms should be self-consistent, that is, they must not contradict with each other. From these axioms, new results can be derived adhering strictly to mathematical logic. These derived results are called [[theorem]]s. It is important to note that, according to the [[Godel's Incompleteness Theorems]], it is impossible to state a self-consistent set of axioms from which the whole mathematics can be derived.
A mathematical theory is expressed as a set of sentences, called [[axiom]]s. These axioms should be self-consistent, that is, they must not contradict with each other. From these axioms, new results can be derived adhering strictly to mathematical logic. These derived results are called [[theorem]]s. It is important to note that, according to the [[Godel's Incompleteness Theorems]], it is impossible to state a self-consistent set of axioms from which the whole mathematics can be derived.
==Pure and Applied Mathematics==
==Pure and Applied Mathematics==
====[[Analysis]]====
====[[Analysis]]====
Analysis is concerned with limits and other infinite processes. This subject includes the theory of limits of sequences and series and all forms of [[statistics]], and [[calculus]], including the calculus of several variables, vector calculus and tensor calculus. Also included is numerical analysis, the study of error propagation in [[algorithm]]s carried out to finite precision. Additional topics in analysis include [[real analysis]] and [[complex analysis]].
Analysis is concerned with limits and other infinite processes. This subject includes the theory of limits of sequences and series and all forms of [[statistics]], and [[calculus]], including the calculus of several variables, vector calculus and tensor calculus. Also included is numerical analysis, the study of error propagation in [[algorithm]]s carried out to finite precision. Additional topics in analysis include [[real analysis]] and [[complex analysis]].
==== [[Calculus]] ====
[[Calculus]] is the mathematical subject that studies rates of change of functions. There are two main branches of calculus: [[Derivative (calculus)|differential]] calculus, and [[integral]] calculus. There are subfields of these: single [[variable]] calculus, [[exterior calculus]], and multi [[variable]] calculus.
====Chaos Theory====
====Chaos Theory====
The study of discrete structures, such as graphs, Latin squares, and block designs. Discrete mathematics can be studied from a pure, theoretical standpoint, or by studying its applications, such as those to theoretical computer science and combinatorial optimization.
The study of discrete structures, such as graphs, Latin squares, and block designs. Discrete mathematics can be studied from a pure, theoretical standpoint, or by studying its applications, such as those to theoretical computer science and combinatorial optimization.
[[Image:Von.jpg|thumb|right|200px|The mathematician [[John von Neumann]] helped develop [[game theory]]. ]]
====[[Combinatorics]]====
====[[Combinatorics]]====
Combinatorics is the study of situations in which elements of a set or sets are combined or permuted in various ways. An example of a combinatorics problem would be "in a group of six men and four women, how many possible ways are there to choose three men and two women?" Derangements are another concept in combinatorics. A derangement is a re-ordering of a set so that no element ends up where it was originally; a derangement problem typically asks how many arrangements are possible for a given set, meeting given conditions.
Combinatorics is the study of situations in which elements of a set or sets are combined or permuted in various ways. An example of a combinatorics problem would be "in a group of six men and four women, how many possible ways are there to choose three men and two women?" Derangements are another concept in combinatorics. A derangement is a re-ordering of a set so that no element ends up where it was originally; a derangement problem typically asks how many arrangements are possible for a given set, meeting given conditions.
====[[Game Theory]]====
====[[Game Theory]]====
== See also ==
== See also ==
*[[Quantitative reasoning]]
*[[Data literacy]]
*[[Mathematical modeling]]
*[[Critical numeracy]]
*[[Additive property of equality]]
*[[Additive property of equality]]
*[[Amédée Mannheim]]
*[[Amédée Mannheim]]