Undergraduate Probability: A Brief Introduction

Probability is a beautiful mathematical theory in its own right, but it also is a theory that can be very widely applied. Quantum mechanics and statistical mechanics are vitally informed by it, and its methods of analysis are frequently encountered in just about every field of knowledge or endeavor that uses quantitative methods: economics, business, psychology, sociology, meteorology, biology, chemistry---the list goes on. Consequently, it is the goal of Undergraduate Probability to enable its readers to see how the mathematical formalisms of probability theory are naturally relevant to various real-world phenomena. Some of the application topics that are discussed in this text include velocities and pressures in ideal gases, climate data correlations, randomness and consciousness, and of course also a number of elementary random experiments involving coin flips or darts or rolls of a die. Moreover and more specifically, the great importance of the normal distribution and the Central Limit Theorem is consistently emphasized and thoroughly explored.