CD-ROM consists of four directories: parametric plots, fractals, etc; nonlinear differential equations; fuzzy logics; and graphics files.

The Cantor Diagonal Argument (CDA) is the quintessential result in Cantor's infinite set theory. This is one procedure that almost everyone who studies this subject finds astounding. However, mathematicians maintain that the CDA is absolutely correct and that the "countless" people trying to repudiate the CDA are not only wrong but are seemingly "irrational" enough to challenge such a widely accepted result.This book outlines all the different issues with the CDA. And, there are many.This book does not attempt to disprove the CDA by finding fault with it. Since the mathematical community has not bought into any of the tens of counterarguments it likely will ignore yet one more.Instead, assuming the CDA is correct, we create a situation where the CDA produces results when it really shouldn't and use the CDA itself to discredit the CDA.Cantor's infinite set theory is largely based on arbitrary rules, confounding axioms, and logic that defies intuition and common sense. Our previous books explain exactly what is wrong and why. The theory is hopelessly flawed because the starting assumption - the axiom of infinity - is wrong. There is no such thing as an infinite set. But mathematicians stubbornly stick to their belief that everything is correct.Hopefully this is the straw that breaks the camel's back!

Winner of a CHOICE Outstanding Academic Title Award for 2011!This book offers an introduction to modern ideas about infinity and their implications for mathematics. It unifies ideas from set theory and mathematical logic, and traces their effects on mainstream mathematical topics of today, such as number theory and combinatorics. The treatment is h

Infinity is an intriguing topic, with connections to religion, philosophy, metaphysics, logic, and physics as well as mathematics. Its history goes back to ancient times, with especially important contributions from Euclid, Aristotle, Eudoxus, and Archimedes. The infinitely large (infinite) isintimately related to the infinitely small (infinitesimal). Cosmologists consider sweeping questions about whether space and time are infinite. Philosophers and mathematicians ranging from Zeno to Russell have posed numerous paradoxes about infinity and infinitesimals. Many vital areas ofmathematics rest upon some version of infinity. The most obvious, and the first context in which major new techniques depended on formulating infinite processes, is calculus. But there are many others, for example Fourier analysis and fractals.In this Very Short Introduction, Ian Stewart discusses infinity in mathematics while also drawing in the various other aspects of infinity and explaining some of the major problems and insights arising from this concept. He argues that working with infinity is not just an abstract, intellectualexercise but that it is instead a concept with important practical everyday applications, and considers how mathematicians use infinity and infinitesimals to answer questions or supply techniques that do not appear to involve the infinite.ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, andenthusiasm to make interesting and challenging topics highly readable.

Conceived by the author as an introduction to "why the calculus works," this volume offers a 4-part treatment: an overview; a detailed examination of the infinite processes arising in the realm of numbers; an exploration of the extent to which familiar geometric notions depend on infinite processes; and the evolution of the concept of functions. 1982 edition.

This work contains detailed descriptions of developments in the combinatorics of the space of diagonal harmonics, a topic at the forefront of current research in algebraic combinatorics. These developments have led in turn to some surprising discoveries in the combinatorics of Macdonald polynomials.