Finite Mathematics And Its Applications

Finite Mathematics and Its Applications

A Beginner’s Guide to Finite Mathematics

When elementary courses in discrete and combinatorial mathematics first became popular, they usually covered a broad spectrumofpure and applied topics. Most of the students were in Mathematics and Computer Science, with a handful ofbrave souls from other disciplines. Those other students usually found the courses quite difficult. However, the applications were useful in a numberofareas. The teaching of discrete topics has evolved into two streams. The more math ematical parts are studied in courses called Discrete Mathematics, and more ad vanced, more rigorous courses called Combinatorics, or named for specific areas (Graph Theory, Combinatorial Designs, Cryptography, and so on). Introductions to those areas of applicable discrete mathematics used by students in business, management and the social sciences are usually called Finite Mathematics, and e1ementary courses on this material are now standard at many colleges and uni versities.These courses are typically offered at the freshman level although many students take them later in their careers.

Finite Mathematics as the Foundation of Classical Mathematics and Quantum Theory

This book delves into finite mathematics and its application in physics, particularly quantum theory. It is shown that quantum theory based on finite mathematics is more general than standard quantum theory, whilst finite mathematics is itself more general than standard mathematics.As a consequence, the mathematics describing nature at the most fundamental level involves only a finite number of numbers while the notions of limit, infinite/infinitesimal and continuity are needed only in calculations that describe nature approximately. It is also shown that the concepts of particle and antiparticle are likewise approximate notions, valid only in special situations, and that the electric charge and baryon- and lepton quantum numbers can be only approximately conserved.