Fundamentals of Calculus and Probability

About the Book

"Fundamentals of Calculus and Probability" is a book intended for students that have already had a course or two in Calculus, but perhaps not recently. The book is an assortment of topics related to basic mathematical and statistical analysis. It starts with a discussion of the real number system and some set theory, which includes a discussion of countable and uncountable infinity, which is an important and relevant part of advanced mathematics. From there, the book contains a chapter that provides a review of some of the key concepts of single-variable calculus. Then the book discusses a bit of so-called "measure" and how this relates to the integers, rationals, irrational, and real number systems. Finally, the book discusses probability, important probability distributions, and a good introduction to the basic concepts of statistical estimation and statistical inference (hypothesis testing). Along the way, the author interjects some of his own speculations about certain mathematical topics, and some comments about probability distributions, and in addition some topics involving space and time. It is not a textbook with exercises, but it has an abundance of examples throughout to explain the essential concepts and ideas. The book should appeal to students returning to school for graduate study, in a field such as statistics, that would benefit from an overview of many important topics in mathematics and statistics, which they will encounter in their advanced studies.

About the Author

My name is Timothy Clayton Kearns. I was born in Arlington, Va. USA, and except for my college years, I have lived in northern Virginia all my life. I have spent the last 35 years studying formally and informally the subjects of statistics, mathematics, elementary physics, the history of science, and many other subjects to various degrees. In June 1983, in Blacksburg, Va, I graduated (cum laude) from Virginia Polytechnic Institute and State University, with a Bachelor of Science degree in statistics and a strong minor in mathematics. I have also completed some graduate level study in mathematics and statistics at George Mason University in Fairfax, Va, from 1985 to 1989. I have taught calculus as a graduate assistant at GMU and have spent the last 11 years as a self­employed math tutor in the northern Va. area, tutoring students from the middle school level to the PhD level. This book is a serious attempt to satisfy some desire within me to help others appreciate and understand some important parts of mathematics and statistics, which has given me much pleasure over the years.