Fourier theory is pretty complicated mathematically. But there are some beautifully simple holistic concepts behind Fourier theory which are relatively easy to explain intuitively. There are other sites on the web that can give you the mathematical formulation of the Fourier transform. I will present only the basic intuitive insights here, as applied to spatial imagery.
"I protest against the use of infinite magnitude as something completed, which is never permissible in mathematics. Infinity is merely a way of speaking, the true meaning being a limit which certain ratios approach indefinitely close, while others are permitted to increase without restriction." (Gauss)
"I don't know what predominates in Cantor's theory - philosophy or theology, but I am sure that there is no mathematics there." (Kronecker)
"...classical logic was abstracted from the mathematics of finite sets and their subsets...Forgetful of this limited origin, one afterwards mistook that logic for something above and prior to all mathematics, and finally applied it, without justification, to the mathematics of infinite sets. This is the Fall and original sin of [Cantor's] set theory ..." (Weyl)
Chapters: Compound Statements,
Sets and counting problems,
Probability theory,
Vectors and matrices,
Computer programming,
Statistics,
Linear programming and the theory of games,
Applications to the behavioral and managerial sciences
Welcome to the UC Davis front end for the mathematics arXiv, maintained at Cornell University. The arXiv has 48123+6083 mathematics articles (primary+secondary) as of April 20, 2006.