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{{anchor|Formal science}}'''[[Outline of formal science|Formal science]]''' – branches of knowledge that are concerned with formal systems. Unlike other sciences, the formal sciences are not concerned with the validity of theories based on observations in the real world, but instead with the properties of formal systems based on definitions and rules.
*'''[[Outline of mathematics|Mathematics]]''' – study of quantity, structure, space, and change. Mathematicians seek out patterns, and formulate new conjectures. (See also: [[Lists of mathematics topics]])
** [[Outline of arithmetic|Arithmetic]] – the oldest and most elementary branch of mathematics, involving the study of quantity, especially as the result of combining numbers. The simplest arithmetical operations include addition, subtraction, multiplication and division.
** [[Outline of algebra|Algebra]] – the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures.
*** [[Outline of linear algebra|Linear algebra]] – the branch of mathematics concerning linear equations and linear maps and their representations in vector spaces and through matrices.
*** [[List of abstract algebra topics|Abstract algebra]] – the branch of mathematics concerning algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras.
**** [[List of commutative algebra topics|Commutative algebra]] – branch of abstract algebra that studies commutative rings, their ideals, and modules over such rings.
*** [[List of algebraic coding theory topics|Algebraic coding theory]] – aka ''coding theory'', is the study of the properties of codes and their respective fitness for specific applications.
*** [[List of Boolean algebra topics|Boolean algebra]] – branch of algebra in which the values of the variables are the truth values true and false, usually denoted 1 and 0, respectively. It is used for describing logical operations.
** [[Outline of calculus|Analysis/Calculus]] – the branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. Calculus is the study of change, in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations.
** [[Outline of category theory|Category theory]] – the branch of mathematics examining the properties of mathematical structures in terms of collections of objects and arrows
** [[Outline of discrete mathematics|Discrete mathematics]] – the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics – such as integers, graphs, and statements in logic – do not vary smoothly in this way, but have distinct, separated values.
*** [[Outline of combinatorics|Combinatorics]] – the branch of mathematics concerning the study of finite or countable discrete structures.
** [[Outline of geometry|Geometry]] – this is one of the oldest branches of mathematics, it is concerned with questions of shape, size, relative position of figures, and the properties of space.
*** [[List of algebraic geometry topics|Algebraic geometry]] – study of zeros of multivariate polynomials.
**** [[List of convexity topics|Convexity]] –
*** [[List of circle topics|Circles]] – geometric shapes consisting of all points in a plane that are at a given distance from a given point, the center.
*** [[List of combinatorial computational geometry topics|Combinatorial computational geometry]] – states problems in terms of geometric objects as discrete entities and hence the methods of their solution are mostly theories and algorithms of combinatorial character.
*** [[List of computer graphics and descriptive geometry topics|Computer graphics and descriptive geometry]] –
*** [[List of differential geometry topics|Differential geometry]] – geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds.
*** [[List_of_topology_topics|Topology]] – developed from geometry, it looks at those properties that do not change even when the figures are deformed by stretching and bending, like dimension.
**** [[List of algebraic topology topics|Algebraic topology]] – uses tools from abstract algebra to study topological spaces.
**** [[List of general topology topics|General topology]] – also known as point-set topology, it deals with the basic set-theoretic definitions and constructions used in topology. It is the foundation for most of the other branches of topology.
**** [[List of geometric topology topics|Geometric topology]] – study of manifolds and maps between them, particularly embeddings of one manifold into another.
** [[List of mathematical logic topics|Mathematical logic]] – study of formal logic within mathematics.
*** [[List of set theory topics|Set theory]] – studies sets, which can be informally described as collections of objects.
**** [[Outline_of_algebraic_structures|Algebraic structure]] – the sum total of all properties that arise from the inclusion of one or more operations on a set.
** [[Outline of trigonometry|Trigonometry]] – branch of mathematics that studies triangles and the relationships between their sides and the angles between these sides. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclical phenomena, such as waves.
*** [[List of triangle topics|Triangles]] – type of polygon, with three edges and three vertices. The triangle is one of the basic shapes in geometry.

* '''[[Outline of logic|Logic]]''' – formal systematic study of the principles of valid inference and correct reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science.

* '''Other mathematical sciences''' – academic disciplines that are primarily mathematical in nature but may not be universally considered subfields of mathematics proper.
** [[Outline of statistics|Statistics]] – study of the collection, organization, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments.
*** [[Outline of regression analysis|Regression analysis]] – techniques for modeling and analyzing several variables, when the focus is on the relationship between a dependent variable and one or more independent variables. More specifically, regression analysis helps one understand how the typical value of the dependent variable changes when any one of the independent variables is varied, while the other independent variables are held fixed.
** [[Outline of probability|Probability]] – way of expressing knowledge or belief that an event will occur or has occurred. The concept has an exact mathematical meaning in probability theory, which is used extensively in such areas of study as mathematics, statistics, finance, gambling, science, artificial intelligence/machine learning and philosophy to draw conclusions about the likelihood of potential events and the underlying mechanics of complex systems.
** [[Theoretical computer science]] – a division or subset of general computer science and mathematics that focuses on more abstract or mathematical aspects of computing and includes the theory of computation.

Wiki143:Contents/Outlines/Mathematics and logic - Revision history

imported>Erregea5: removed duplicate triangle