Grinstead and Snell's Introduction to Probability

by Charles M. Grinstead

This is an introductory probability textbook, published by the American Mathematical Society. It is designed for an introductory probability course taken by mathematics, the physical and social sciences, engineering, and computer science students. The text can be used in a variety of course lengths, levels, and areas of emphasis. For use in a standard one-term course, in which both discrete and continuous probability is covered, students should have taken as a prerequisite two terms of calculus, including an introduction to multiple integrals. In order to cover Chapter 11, which contains material on Markov chains, some knowledge of matrix theory is necessary. The text can also be used in a discrete probability course. For use in a discrete probability course, students should have taken one term of calculus as a prerequisite. All of the computer programs that are used in the text have been written in each of the languages TrueBASIC, Maple, and Mathematica. Contents: 1) Discrete Probability Distributions. 2) Continuous Probability Densities. 3) Combinatorics. 4) Conditional Probability. 5) Distributions and Densities. 6) Expected Value and Variance. 7) Sums of Random Variables. 8) Law of Large Numbers. 9) Central Limit Theorem. 10) Generating Functions. 11) Markov Chains. 12) Random Walks. The text is best used in conjunction with software and exercises available online at http: //www.dartmouth.edu/ chance/teaching_aids/books_articles/probability_book/book.htm

Genres: Mathematics, Textbooks, Science, Ebooks

518 pages, Paperback

First published July 1, 1997

Reviews

[Lukasz Pruski · Rating 5 out of 5]

"One may summarize these results by stating that one should not get drunk in more than two dimensions."

The above is the most extraordinary sentence one can find in a university textbook on advanced mathematics! Charles M. Grinstead's and J. Laurie Snell's Introduction to Probability (Second Edition, 1997) is indeed a most remarkable textbook, by far the best text that I have ever used in my almost 40 years of teaching undergraduate mathematics and computer science. Probability was my favorite field of mathematics during my own studies in the early 1970s, but I somehow avoided teaching it, most likely because I had not found a textbook that I really liked. Until Grinstead and Snell.

Standard textbooks heavily focus on the combinatorial aspects of probability, which do not interest me too much. When I teach the upper-division probability course I love to emphasize the calculus-based approach, particularly when it involves multidimensional calculus and its applications to joint probability distributions. Grinstead and Snell's approach is virtually tailor-made for my probability course.

The second factor that makes me love the textbook is the emphasis on random numbers and pseudo-random variables generation. Having worked in the field of mathematical modeling and simulation for over 40 years I believe this is a natural approach to ground the probability course in. Grinstead and Snell's geometry-based problems that use the cumulative distribution functions to find the densities are a wonderful teaching tool: the students can also appreciate the applications of calculus: many of my students seemed to like discovering the connections.

Yet another great feature of the textbook is its emphasis on the moment generating function. Naturally, it is used to prove the Central Limit Theorem, the fundamental theorem of probability and the foundation of statistics. I follow the mathematical argument in class every time I teach the course so that math majors can appreciate a little more elaborate proof than the usual toy ones.

I also love the inclusion of a chapter of random walks (from which the epigraph is taken). When teaching partial differential equations (another of my favorite fields in math) I often discuss the Tour du Wino method of numerically solving the Laplace equation, which uses the random walks approach. The authors provide the famous proof by Pólya, which shows that a random walk must eventually return to the origin in one or two dimensions, but not necessarily for higher dimensions.

Of many other nice features of the textbook I should mention the authors' clear treatment of the Bayes' Theorem and the fascinating Historical Remarks that accompany many chapters. A truly wonderful book! The best textbook I have ever used!

Five stars.

[Leo Walsh · Rating 5 out of 5]

This is an excellent -- and free -- introduction to probability theory. Grinstead and Snell do a great job filling in the gaps left by most statistics classes. And leads the diligent reader to think, and relaibly answer the question "well, what are the odds?"

The text covers not only classical, discrete probability, but also looks at continuous probability density functions. If you've had basic calculus, you can follow the examples relatively easily. But even if you haven't, its great to see a text that will help you understand probability. Alsmost like a gambler would conceive of it.

For example, LeBron James shoots 90% freethrows, what are his odds of making two-in-a-row? They are only 81%. And his odds of making three-in-a-row only 78%...

Enjoy. From one math geek to another...

[David Shuster · Rating 3 out of 5]

3-star = "I liked it."
Used for self-study.
Pros:
- for the most part, fun motivations and helpful examples
- I don't have much reference, but as far as I can tell, it covers a nice variety of introductory topics at a substantive depth; I generally like the organization and topics chosen, etc.
- Generally enjoyed the historical remarks sections, as well as the lighter forays into niche areas

Cons:
- some portions, I felt I've seen explained in better intuition elsewhere
- also, some parts, the language is a little vague/confusing. Some places go into rabbit holes that could ideally be marked "optional" or something, to be honest.

Overall: nice book but probably more useful for a class than for beginning self-study. But I don't have much context, because I haven't really surveyed the options :P

[Aniket Patil · Rating 2 out of 5]

Introduction made me think of not going ahead with this one. Still I was patient enough to go through all the book. I think its not the introduction/introductory book for the newbie.