Mathematics is the study of representing and reasoning about abstract objects (such as numbers, points, spaces, sets, structures, and games). Mathematics is used throughout the world as an essential tool in many fields, including natural science, engineering, medicine, and the social sciences. Applied mathematics, the branch of mathematics concerned with application of mathematical knowledge to other fields, inspires and makes use of new mathematical discoveries and sometimes leads to the development of entirely new mathematical disciplines, such as statistics and game theory. Mathematicians also engage in pure mathematics, or mathematics for its own sake, without having any application in mind. There is no clear line separating pure and applied mathematics, and practical applications for what began as pure mathematics are often discovered. ( Full article...)
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Fourteen ways of triangulating a hexagon Image credit: User:Dmharvey |
The Catalan numbers, named for the Belgian mathematician Eugène Charles Catalan, are a sequence of natural numbers that are important in combinatorial mathematics. The sequence begins:
The Catalan numbers are solutions to numerous counting problems which often have a recursive flavour. In fact, one author lists over 60 different possible interpretations of these numbers. For example, the nth Catalan number is the number of full binary trees with n internal nodes, or n+1 leaves. It is also the number of ways of associating n applications of a binary operator as well as the number of ways that a convex polygon with n + 2 sides can be cut into triangles by connecting vertices with straight lines. ( Full article...)
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Mathematics is the study of representing and reasoning about abstract objects (such as numbers, points, spaces, sets, structures, and games). Mathematics is used throughout the world as an essential tool in many fields, including natural science, engineering, medicine, and the social sciences. Applied mathematics, the branch of mathematics concerned with application of mathematical knowledge to other fields, inspires and makes use of new mathematical discoveries and sometimes leads to the development of entirely new mathematical disciplines, such as statistics and game theory. Mathematicians also engage in pure mathematics, or mathematics for its own sake, without having any application in mind. There is no clear line separating pure and applied mathematics, and practical applications for what began as pure mathematics are often discovered. ( Full article...)
![]() |
Fourteen ways of triangulating a hexagon Image credit: User:Dmharvey |
The Catalan numbers, named for the Belgian mathematician Eugène Charles Catalan, are a sequence of natural numbers that are important in combinatorial mathematics. The sequence begins:
The Catalan numbers are solutions to numerous counting problems which often have a recursive flavour. In fact, one author lists over 60 different possible interpretations of these numbers. For example, the nth Catalan number is the number of full binary trees with n internal nodes, or n+1 leaves. It is also the number of ways of associating n applications of a binary operator as well as the number of ways that a convex polygon with n + 2 sides can be cut into triangles by connecting vertices with straight lines. ( Full article...)
View all selected articles |
Algebra | Arithmetic | Analysis | Complex analysis | Applied mathematics | Calculus | Category theory | Chaos theory | Combinatorics | Dynamical systems | Fractals | Game theory | Geometry | Algebraic geometry | Graph theory | Group theory | Linear algebra | Mathematical logic | Model theory | Multi-dimensional geometry | Number theory | Numerical analysis | Optimization | Order theory | Probability and statistics | Set theory | Statistics | Topology | Algebraic topology | Trigonometry | Linear programming
Mathematics | History of mathematics | Mathematicians | Awards | Education | Literature | Notation | Organizations | Theorems | Proofs | Unsolved problems
General | Foundations | Number theory | Discrete mathematics |
---|---|---|---|
| |||
Algebra | Analysis | Geometry and topology | Applied mathematics |
ARTICLE INDEX: | |
MATHEMATICIANS: |
The
Mathematics WikiProject is the center for mathematics-related editing on Wikipedia. Join the discussion on the project's
talk page.
The following Wikimedia Foundation sister projects provide more on this subject: