This category is for sites about university departments doing scientific research and providing scientific educational programs in mathematics.

Algebra is a branch of mathematics that uses letters or other symbols to represent unknown quantities, called variables. These variables and number values are combined to form equations. The rules of these equations follow the exact same rules as arithmetic, such as the commutative and associative laws for addition and multiplication. Functions are a special type of equation, where one variable can be uniquely defined in terms of the other. Another part of this topic is graphing of equations and functions using the Cartesian coordinate graph or polar coordinates. Also, covered in this topic is set theory or what constitutes a grouping of numbers.

Applications of mathematics, other than mathematical physics.

MSC 2000classes

• 62Pxx Applications
• 91-XX Game theory, economics, social and behavioral sciences
• 92-XX Biology and other natural sciences
• 93-XX Systems theory; control
• 94-XX Information and communication, circuits

Calculators are devices that perform numerical operations, typically including the basic operations of addition, multiplication, subtraction and division, but possibly going further to include evaluation of more advanced functions and even the ability to draw graphs. Calculators are distinguished from computers by the fact that their abilities are limited to a certain set of operations. But this line is becoming blurred as more advanced scientific calculators can perform computer algebra and can execute programs written in with own programming language.

Calculus is a branch of mathematics concerned with two types of functions: derivatives and integrals.

The derivative calculates the rate of change of the function at a point on a curved line. This formula also works for a straight line, as well. A derivative of a function is written by adding a apostrophe like this: f'(x). One of the applications of derivatives is to determine velocity and acceleration of an object in motion.

Integrals measure the area under a curved line graph, such as a half circle. The integral symbol looks like a flattened S.

Derivatives and integrals are related in that they are inverse functions of each other. That means the operations will cancel each other out, such as taking the square root of a squared number will give you the original number.

Applications of integrals include calculating areas of plane regions or surfaces, as well as calculating volumes of solids.

Both derivatives and integrals are defined by using the concept of a limit. An example of a limit is where you have the equation 1/x. If you take x to be very large, then 1/x gets closer to 0.

A fractal is a chaotic mathematic object which can be divided into parts, each of which is similar to the original object. Fractals are said to possess infinite detail, and are generally self-similar and independent of scale. In many cases a fractal can be generated by a repeating pattern, typically a recursive or iterative process. The term fractal was coined in 1975 by Benoît Mandelbrot, from the Latin fractus or "broken"/"fraction". Chaos theory, in mathematics and physics, deals with the behavior of certain nonlinear dynamical systems that (under certain conditions) exhibit the phenomenon known as chaos, most famously characterised by sensitivity to initial conditions. Systems that exhibit mathematical chaos are deterministic and thus orderly in some sense; this technical use of the word chaos is at odds with common parlance, which suggests complete disorder.

Contains mailing lists, newsgroups, forums, message boards, and chat rooms which are designed to discuss a spectrum of mathematics topics.

Combinatorics studies problems involving finite sets of objects that are defined by certain specified properties. For example, the objects in question may themselves be sets, numbers, graphs or other geometrical configurations. Enumerative combinatorics is concerned with counting the number of objects of a certain kind. Extremal combinatorics is concerned with finding the optimal objects of a certain kind. Topological methods, algebraic methods and even probabilistic methods have been used to solve combinatorial problems. Computer algorithms have also been used to solve some seemingly intractable combinatorial problems. Conversely, combinatorial methods have been used successfully to solve problems in many areas of mathematics and computer science. Here is a sample problem that would use combinatorics: Strangers and Acquaintances (F.P. Ramsey 1930): What is the least number of people that you need to have in a room so that there is always a group of three mutual strangers or a group of three mutual acquaintances? The answer is six.

Differential equations relate functions of several variables to derivatives of the functions. Such equations are often used in the sciences to relate a quantity to its rate of change.

Link collections, especially annotated ones regarding math, math research, math education, and so on.

Science/Math/Education is for educational web sites of interest to educators, parents, students and professionals emphasizing the teaching or learning of various aspects of math or math topics.

The best sites will try to teach or instruct about math, though clear, easy-to-follow explanations of topics are useful as well.

Careers advice and employment information in Mathematics.

Conferences, courses, meetings, seminars,workshops and other events in Mathematics generally.

This category is about mathematical logic and foundations of mathematics. (So it roughly corresponds to category 03-XX in the 1991 Mathematical Sciences Classification.) Major related subjects outside mathematics are computer science at one end, and philosophical logic at the other. If you are looking for basic, non-technical information on logic, you may want to look at the subcategories Encylopedia Articles and Educational Resources. If you think your site or one that you have come across fits here: please submit it. If not sure give it to us anyway ... we will do our best to find where it belongs.

Biography and personal web pages of math professionals and enthusiasts, living and dead.

Number theory addresses problems about integer and rational numbers. It includes congruences, divisibility, primes, and Fermat's Last Theorem.

A branch of mathematics that studies the use of repeated discrete operations to find approximate solutions to continuous equations.

The study of operations research (OR) is concerned with mathematical methods and tools for solving problems relating to the allocation of scarce resources subject to constraints. Frequently these problems have to do with determining the least cost or greatest profit possible for a cost or profit function subject to constraints such as capacities and required amounts over a very large number of variables. Important problems within this space include minimum cost routing problems, network maximum flow or minimum cost flow problems, and machine scheduling problems. The growing trends in OR increasingly utilize applications of more than one technique and involve individuals from other disciplines. Moreover, they involve a blend of "hard" and "soft" as well as a mixing of different "hard" or "soft" techniques with the increasing use of multiple methods within one piece of analysis. A creative thinking must look in detail at how those from disciplines outside of OR can come to work in the organizations on multi-disciplinary studies. Those who have come from such backgrounds, clearly share their perspectives and experiences. The field of OR is always changing. Its changes are driven by the technology it uses and that it extends, and the applications that it affects.

Sites of professional mathematics organizations, including national and international organizations.

Lists, tables, dictionaries and similar reference material in Mathematics.

A weblog (often shortened just to blog) is a user-generated website where entries are made in journal style and displayed in a reverse chronological order. This category is for blogs about breaking news in mathematics or personal views on general mathematical topics.