پدیده‌های خودجوش: یک تحلیل ریاضی

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. Content: Front Matter , Page iii Copyright , Page iv PREFACE AND INTRODUCTION , Pages vii-x List of Symbols , Page xi 1 - The Problem , Pages 1-3 2 - Thoughts on Model Building , Pages 5-7 3 - On Stochastic Models , Pages 9-16 4 - Time Invariance , Pages 17-20 5 - Independence , Pages 21-22 6 - Intermezzo on the Binomial Distribution , Pages 23-25 7 - On the Physical Background to the Assumptions , Pages 27-28 8 - The Intensity , Pages 29-30 9 - Mathematics, at last! , Pages 31-37 10 - Confrontation with Reality , Pages 39-41 11 - Critique of the Mathematics , Pages 43-46 12 - Critique of the Physics , Pages 47-50 13 - Other Applications of the Model , Pages 51-52 14 - The Poisson Approximation to the Binomial Distribution , Pages 53-57 15 - Spatially Uniform Distribution, Point Processes , Pages 59-63 16 - A Detailed Analysis of Actual Observations , Pages 65-80 17 - The chi—square Test for Goodness of Fit , Pages 81-91 18 - The Historical Perspective , Pages 93-111 Exercises , Pages 113-140 Examples for Further Investigation , Pages 141-159 Programs , Pages 161-175 REFERENCES , Page 177 Index , Pages 179-182