This page uses content from Wikipedia and is licensed under CC BYSA.
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.
A number is an abstract entity that represents a count or measurement. A symbol for a number is called a numeral. The arithmetical operations of numbers, such as addition, subtraction, multiplication and division, are generalized in the branch of mathematics called abstract algebra, the study of abstract number systems such as groups, rings and fields.
Numbers can be classified into sets called number systems. The most familiar numbers are the natural numbers, which to some mean the nonnegative integers and to others mean the positive integers. In everyday parlance the nonnegative integers are commonly referred to as whole numbers, the positive integers as counting numbers, symbolised by . Mathematics is used in many classes throughout the course of one's education.
The integers consist of the natural numbers (positive whole numbers and zero) combined with the negative whole numbers, which are symbolised by (from the German Zahl, meaning "number").
A rational number is a number that can be expressed as a fraction with an integer numerator and a nonzero natural number denominator. Fractions can be positive, negative, or zero. The set of all fractions includes the integers, since every integer can be written as a fraction with denominator 1. The symbol for the rational numbers is a bold face (for quotient).
View all selected articles  Read More... 
This is a graph of a portion of the complexvalued Riemann zeta function along the critical line (the set of complex numbers having real part equal to 1/2). More specifically, it is a graph of Im ζ(1/2 + it) versus Re ζ(1/2 + it) (the imaginary part vs. the real part) for values of the real variable t running from 0 to 34 (the curve starts at its leftmost point, with real part approximately −1.46 and imaginary part 0). The first five zeros along the critical line are visible in this graph as the five times the curve passes through the origin (which occur at t ≈ 14.13, 21.02, 25.01, 30.42, and 32.93 — for a different perspective, see a graph of the real and imaginary parts of this function plotted separately over a wider range of values). In 1914, G. H. Hardy proved that ζ(1/2 + it) has infinitely many zeros. According to the Riemann hypothesis, zeros of this form constitute the only nontrivial zeros of the full zeta function, ζ(s), where s varies over all complex numbers. Riemann's zeta function grew out of Leonhard Euler's study of realvalued infinite series in the early 18th century. In a famous 1859 paper called "On the Number of Primes Less Than a Given Magnitude", Bernhard Riemann extended Euler's results to the complex plane and established a relation between the zeros of his zeta function and the distribution of prime numbers. The paper also contained the previously mentioned Riemann hypothesis, which is considered by many mathematicians to be the most important unsolved problem in pure mathematics. The Riemann zeta function plays a pivotal role in analytic number theory and has applications in physics, probability theory, and applied statistics.
The Mathematics WikiProject is the center for mathematicsrelated editing 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 