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ALGEBRAIC GEOMETRY

JUST A SNIPPET

THE SOUL THEOREM

THROUGH THE EYES OF A TOPOLOGIST

ORDINARY DIFFERENTIAL EQUATION

An ordinary differential equation is a differential equation containing one or more functions of one independent variable and the derivatives of those functions.

 

 

 

INTEGRAL TRANSFORMS

 

In mathematics, an integral transform maps a function from its original function space into another function space via integration, where some of the properties of the original function might be more easily characterized and manipulated than in the original function space.

 

 

LOGIC

 

Logic is the discipline that deals with the methods of reasoning. On an elementary level, logic provides rules and techniques for determining whether a given argument is valid. Logical reasoning is used in mathematics to prove theorems, and in computer science to verify the correctness of programs.

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FOURIER SERIES

 

Fourier series is an expansion of a periodic function f(x) in terms of an infinite sum of sines and cosines. Fourier series make use of the orthogonality relationships of the sine and cosine functions.

 

 

JACOBI ELLIPTIC FUNCTIONS

 

Jacobi elliptic functions are found in the description of the motion of a pendulum, as well as in the design of electronic elliptic filters. While trigonometric functions are defined with reference to a circle, the Jacobi elliptic functions are a generalization that refers to other conic sections, the ellipse in particular.

 

 

LAGRANGE’S EQUATION

 

As long as algebra and geometry have been separated, their progress have been slow and their uses limited; but when these two sciences have been united, they have lent each mutual forces, and have marched together towards perfection.

Joseph-Louis Lagrange

 

 

THE HEAT EQUATION

 

The heat equation is among the most widely studied topics in pure mathematics, and its analysis is regarded as fundamental to the broader field of partial differential equations. Solutions to the heat equation are sometimes known as caloric functions.

 

 

GROUP THEORY

 

Poetically speaking,

“Group Theory is the branch of Mathematics that answers the question ‘ What is symmetry?’ “- Nathan C. Carter

Definition 1.1– A group ‘G’ is a set with two operations or functions, one called multiplication (or addition in some cases) m : G X G → G and the other called the inverse i: G → G.

 

 

HANKEL TRANSFORM

 

Just as the Fourier transform for an infinite interval is related to the Fourier series over a finite interval, so the Hankel transform over an infinite interval is related to the Fourier–Bessel series over a finite interval.

 

 

SURFACES

 

In mathematics, a surface is a geometrical shape that resembles a deformed plane. The most familiar examples arise as boundaries of solid objects in ordinary three-dimensional Euclidean space R3, such as spheres.

 

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People who are mathematically inclined, there is often a definite aesthetic aspect to much of mathematics. Many mathematicians talk about the elegance of mathematics, its intrinsic aesthetics and inner beauty.
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SOUL OF MATHEMATICS
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