Spontaneous Phenomena

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

5. Independence

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

16. A Detailed Analysis of Actual Observations

17. The chi-square Test for Goodness of Fit

18. The Historical Perspective

Exercises

Examples for Further Investigation

Programs

References

Index