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A Mathematical Analysis
1st Edition - January 28, 1989
9 7 8 - 0 - 3 2 3 - 1 6 0 3 8 - 4
Spontaneous Phenomena: A Mathematical Analysis covers certain aspects in the teaching of mathematics, including historical perspective, model-building, and the inner nature of… Read more
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Spontaneous Phenomena: A Mathematical Analysis covers certain aspects in the teaching of mathematics, including historical perspective, model-building, and the inner nature of mathematics. This book is organized into 12 chapters beginning with the development of the relevant mathematics and physics. This topic is followed by considerable chapters on the theoretical and statistical principles of mathematical analysis, with an emphasis on a model for a radioactive decay. Other chapters discuss various phenomena within biology, medicine, statistics of medicine, determination of age, traffic analysis, and other fields. The concluding chapters present the fundamentals of the Poisson approximation to the binomial distribution and the chi-square test for goodness of fit. This book is an ideal source for mathematics and physics pre-college and early college students.
Preface and Introduction
List of Symbols
1. The Problem
2. Thoughts on Model Building
3. On Stochastic Models
4. Time Invariance
6. Intermezzo on the Binomial Distribution
7. On the Physical Background to the Assumptions
8. The Intensity
9. Mathematics, at last!
10. Confrontation with Reality
11. Critique of the Mathematics
12. Critique of the Physics
13. Other Applications of the Model
14. The Poisson Approximation to the Binomial Distribution
15. Spatially Uniform Distribution, Point Processes