This is a book of elementary probability theory that includes a chapter on algorithmic randomness. It rigorously presents definitions and theorems in computation theory, and explains the meanings of the theorems by comparing them with mechanisms of the computer, which is very effective in the current computer age.
Random number topics have not been treated by any books on probability theory, only some books on computation theory. However, the notion of random number is necessary for understanding the essential relation between probability and randomness. The field of probability has changed very much, thus this book will make and leave a big impact even to expert probabilists.
Readers from applied sciences will benefit from this book because it presents a very proper foundation of the Monte Carlo method with practical solutions, keeping the technical level no higher than 1st year university calculus.
Sample Chapter(s)
Chapter 1: Mathematics of coin tossing (996 KB)
- Mathematics of Coin Tossing
- Random Number:
- Recursive Function
- Kolmogorov Complexity and Random Number
- Limit Theorem:
- Bernoulli's Theorem
- Law of Large Numbers
- De Moivre — Laplace's Theorem
- Central Limit Theorem
- Mathematical Statistics
- Monte Carlo Method:
- Monte Carlo Method as Gambling
- Pseudorandom Generator
- Monte Carlo Integration
- From the Viewpoint of Mathematical Statistics
- Appendix
Readership: First year university students to professionals.
