Mathematics is the study of numbers, quantity, space, structure, and change. 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.
Selected article  Selected picture  Did you know...  Topics in mathematics
Categories  WikiProjects  Things you can do  Index  Related portals
There are approximately 31,444 mathematics articles in Wikipedia.
The four charts each map part of the circle to an open interval, and together cover the whole circle. Image cr: User:KSmrq 
A manifold is an abstract mathematical space in which every point has a neighborhood which resembles Euclidean space, but in which the global structure may be more complicated. In discussing manifolds, the idea of dimension is important. For example, lines are onedimensional, and planes twodimensional.
In a onedimensional manifold (or onemanifold), every point has a neighborhood that looks like a segment of a line. Examples of onemanifolds include a line, a circle, and two separate circles. In a twomanifold, every point has a neighborhood that looks like a disk. Examples include a plane, the surface of a sphere, and the surface of a torus.
Manifolds are important objects in mathematics and physics because they allow more complicated structures to be expressed and understood in terms of the relatively wellunderstood properties of simpler spaces.
View all selected articles  Read More... 
Simpson's paradox (also known as the Yule–Simpson effect) states that an observed association between two variables can reverse when considered at separate levels of a third variable (or, conversely, that the association can reverse when separate groups are combined). Shown here is an illustration of the paradox for quantitative data. In the graph the overall association between X and Y is negative (as X increases, Y tends to decrease when all of the data is considered, as indicated by the negative slope of the dashed line); but when the blue and red points are considered separately (two levels of a third variable, color), the association between X and Y appears to be positive in each subgroup (positive slopes on the blue and red lines — note that the effect in realworld data is rarely this extreme). Named after British statistician Edward H. Simpson, who first described the paradox in 1951 (in the context of qualitative data), similar effects had been mentioned by Karl Pearson (and coauthors) in 1899, and by Udny Yule in 1903. One famous reallife instance of Simpson's paradox occurred in the UC Berkeley genderbias case of the 1970s, in which the university was sued for gender discrimination because it had a higher admission rate for male applicants to its graduate schools than for female applicants (and the effect was statistically significant). The effect was reversed, however, when the data was split by department: most departments showed a small but significant bias in favor of women. The explanation was that women tended to apply to competitive departments with low rates of admission even among qualified applicants, whereas men tended to apply to lesscompetitive departments with high rates of admission among qualified applicants. (Note that splitting by department was a more appropriate way of looking at the data since it is individual departments, not the university as a whole, that admit graduate students.)
The Mathematics WikiProject is the center for mathematicsrelated ing on Wikipedia. Join the discussion on the project's talk page.
Project pages
Essays
Subprojects
Related projects
Algebra  Arithmetic  Analysis  Complex analysis  Applied mathematics  Calculus  Category theory  Chaos theory  Combinatorics  Dynamic systems  Fractals  Game theory  Geometry  Algebraic geometry  Graph theory  Group theory  Linear algebra  Mathematical logic  Model theory  Multidimensional geometry  Number theory  Numerical analysis  Optimization  Order theory  Probability and statistics  Set theory  Statistics  Topology  Algebraic topology  Trigonometry  Linear programming
Mathematics (books)  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:  A B C D E F G H I J K L M N O P Q R S T U V W X Y Z (0–9) 
MATHEMATICIANS:  A B C D E F G H I J K L M N O P Q R S T U V W X Y Z 
Algebra  Analysis  Category theory 
Computer science 
Cryptography  Discrete mathematics 
Geometry 
Logic  Mathematics  Number theory 
Physics  Science  Set theory  Statistics  Topology 