The Strength in Numbers: The Fundamentals of Mathematics and Statistics

This book is an excellent compilation, review, and summary of the fundamentals of mathematics and statistics for prospective teachers, graduate students that are returning to school in technical disciplines, talented high school students planning to go on to college, and for anybody that needs to, wants to, or just enjoys reading about math, statistics, and its many applications. The book is organized into three main parts: Math Fundamentals, Probability Fundamentals, and Statistics Fundamentals. In the math part, there are chapters on logic, set and number theory, algebra and geometry, and the fundamentals of trigonometry and the single variable calculus. In the probability part, there are chapters on combinatorics and probability, random variables, probability distributions and their parameters. In the statistics part, there are chapters on simple random samples and some common statistics, the law of large numbers, many common probability distributions, the normal distribution and its relation to the Central Limit Theorem, the basics of small and large sample statistical inference involving hypothesis testing and confidence interval estimation, and an introduction to linear regression and the associated idea of correlation. The reader has been supplied with many exercises, along with the answers in an appendix. These should help to reinforce the basic ideas for the reader as they proceed through the book. It should be noted that there is a significant amount of the book devoted to the single variable calculus, since it is so important for many students of technical subjects. However, the last two parts of the book devoted to probability and statistics are presented in an entirely algebraic way and do not involve calculus. This should not lessen the books usefulness for most readers.