LIST OF MATHEMATICS

• Algebra:

• Algebra includes the study of algebraic structures, which are sets and operations defined on these sets satisfying certain axioms. The field of algebra is further divided according to which structure is studied; for instance, group theory concerns an algebraic structure called group.

• Calculus and analysis:
• Calculus studies the computation of limits, derivatives, and integrals of functions of real numbers, and in particular studies instantaneous rates of change. Analysis evolved from calculus.

• Geometry and topology.:
• Geometry is initially the study of spatial figures like circles and cubes, though it has been generalized considerably. Topologydeveloped from geometry; it looks at those properties that do not change even when the figures are deformed by stretching and bending, like dimension

• Combinatorics:

• Combinatorics concerns the study of discrete (and usually finite) objects. Aspects include "counting" the objects satisfying certain criteria (enumerative combinatorics), deciding when the criteria can be met, and constructing and analyzing objects meeting the criteria (as in combinatorial designs and matroid theory), finding "largest", "smallest", or "optimal" objects (extremal combinatorics and combinatorial optimization), and finding algebraic structures these objects may have (algebraic combinatorics).

• Logic:
• Logic is the foundation which underlies mathematical logic and the rest of mathematics. It tries to formalize valid reasoning. In particular, it attempts to define what constitutes a proof.

• Number theorY:
• Number theory studies the natural, or whole, numbers. One of the central concepts in number theory is that of the prime number, and there are many questions about primes that appear simple but whose resolution continues to elude mathematicians.

• Dynamical systems and differential equations:
• A differential equation is an equation involving an unknown function and its derivatives.
  In a dynamical system, a fixed rule describes the time dependence of a point in a geometrical space. The mathematical models used to describe the swinging of a clock pendulum, the flow of water in a pipe, or the number of fish each spring in a lake are examples of dynamical systems.

• Mathematical physics:
• Mathematical physics is concerned with "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories"

CONCEPTS OF MATHS

1) The Pythagorean Theorem : This theorem is foundational to our understanding of geometry. It describes the relationship between the sides of a right triangle on a flat plane: square the lengths of the short sides, a and b, add those together, and you get the square of the length of the long side, c.

This relationship, in some ways, actually distinguishes our normal, flat, Euclidean geometry from curved, non-Euclidean geometry. For example, a right triangle drawn on the surface of a sphere need not follow the Pythagorean theorem.

2) Logarithms : Logarithms are the inverses, or opposites, of exponential functions. A logarithm for a particular base tells you what power you need to raise that base to to get a number. For example, the base 10 logarithm of 1 is log(1) = 0, since 1 = 10 0 ; log(10) = 1, since 10 = 10 1 ; and log(100) = 2, since 100 = 10 2 .

The equation in the graphic, log(ab) = log(a) + log(b), shows one of the most useful applications of logarithms: they turn multiplication into addition.

Until the development of the digital computer, this was the most common way to quickly multiply together large numbers, greatly speeding up calculations in physics, astronomy, and engineering.

3) Calculus : The formula given here is the definition of the derivative in calculus. The derivative measures the rate at which a quantity is changing. For example, we can think of velocity, or speed, as being the derivative of position - if you are walking at 3 miles per hour, then every hour, you have changed your position by 3 miles.

Naturally, much of science is interested in understanding how things change, and the derivative and the integral - the other foundation of calculus - sit at the heart of how mathematicians and scientists understand change.

SOME EXAMPLES OF MATHS

Specialized lists of mathematical examples[edit]

• List of algebraic surfaces
• List of curves
• List of complexity classes
• List of examples in general topology
• List of finite simple groups
• List of Fourier-related transforms
• List of mathematical functions
• List of knots
  • List of mathematical knots and links
• List of manifolds
• List of mathematical shapes
• List of matrices
• List of numbers
• List of polygons, polyhedra and polytopes
• List of prime numbers —not merely a numerical table, but a list of various kinds of prime numbers, each with a table
• List of regular polytopes
• List of surfaces
• List of small groups
• Table of Lie groups

Sporadic groups[edit]

See also list of finite simple groups.

• Baby Monster group
• Conway group
• Fischer groups
• Harada–Norton group
• Held group
• Higman–Sims group
• Janko groups
• Lyons group
• The Mathieu groups
• McLaughlin group
• Monster group
• O'Nan group
• Rudvalis group
• Suzuki sporadic group
• Thompson group
• Example Link