Portal:Mathematics
The Mathematics Portal
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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- ... that although the problem of squaring the circle with compass and straightedge goes back to Greek mathematics, it was not proven impossible until 1882?
- ... that multiple mathematics competitions have made use of Sophie Germain's identity?
- ... that despite published scholarship to the contrary, Andrew Planta neither received a doctorate nor taught mathematics at Erlangen?
- ... that the music of math rock band Jyocho has been alternatively described as akin to "madness" or "contemplative and melancholy"?
- ... that after Archimedes first defined convex curves, mathematicians lost interest in their analysis until the 19th century, more than two millennia later?
- ... that in 1940 Xu Ruiyun became the first Chinese woman to receive a PhD in mathematics?
- ... that Latvian-Soviet artist Karlis Johansons exhibited a skeletal tensegrity form of the Schönhardt polyhedron seven years before Erich Schönhardt's 1928 paper on its mathematics?
- ... that the word algebra is derived from an Arabic term for the surgical treatment of bonesetting?
More did you know –
- ...that people are significantly slower to identify the parity of zero than other whole numbers, regardless of age, language spoken, or whether the symbol or word for zero is used?
- ...that Auction theory was successfully used in 1994 to sell FCC airwave spectrum, in a financial application of game theory?
- ...properties of Pascal's triangle have application in many fields of mathematics including combinatorics, algebra, calculus and geometry?
- ...work in artificial intelligence makes use of swarm intelligence, which has foundations in the behavioral examples found in nature of ants, birds, bees, and fish among others?
- ...that statistical properties dictated by Benford's Law are used in auditing of financial accounts as one means of detecting fraud?
- ...that modular arithmetic has application in at least ten different fields of study, including the arts, computer science, and chemistry in addition to mathematics?
- ... that according to Kawasaki's theorem, an origami crease pattern with one vertex may be folded flat if and only if the sum of every other angle between consecutive creases is 180º?
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A labeled graph on 6 vertices and 7 edges Image credit: User:Booyabazooka |
Informally speaking, a graph is a set of objects called points, nodes, or vertices connected by links called lines or edges. In a proper graph, which is by default undirected, a line from point A to point B is considered to be the same thing as a line from point B to point A. In a digraph, short for directed graph, the two directions are counted as being distinct arcs or directed edges. Typically, a graph is depicted in diagrammatic form as a set of dots (for the points, vertices, or nodes), joined by curves (for the lines or edges). Graphs have applications in both mathematics and computer science, and form the basic object of study in graph theory.
Applications of graph theory are generally concerned with labeled graphs and various specializations of these. Many problems of practical interest can be represented by graphs. The link structure of a website could be represented by a directed graph: the vertices are the web pages available at the website and a directed edge from page A to page B exists if and only if A contains a link to B. A graph structure can be extended by assigning a weight to each edge of the graph. Graphs with weights, or weighted graphs, are used to represent structures in which pairwise connections have some numerical values. For example if a graph represents a road network, the weights could represent the length of each road. A digraph with weighted edges in the context of graph theory is called a network. Networks have many uses in the practical side of graph theory, network analysis (for example, to model and analyze traffic networks). (Full article...)
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