Introductory Probability/Combinatorics

Question

What's a good introductory book on probability? The ones I can find are all too advanced. I'm looking for something that doesn't have too much linear algebra, as I haven't read anything about it.

Thank you.

Answer 1

I like Hogg's and Tanis's Probability and Statistical Inference (Amazon link)

I both taught and learned from this book and find it very reasonable with good intuitive explanations but with mathematical precision as well.

This is calculus-based but no linear algebra as you are asking.

PS This is expensive but you can get older editions much cheaper, Amazon sells 6th edition for under $20.

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For combinatorics, Laszlo Lovasz has a nice-looking book called Discrete Mathematics (Amazon link), which is still #13 on Amazon Combinatorics sales list and the first book on the best-sellers that has to do with elementary combinatorics and probability that is slightly more sophisticated than just counting. Also covers topics from Graph Theory.

Answer 2

I like Sheldon Ross, A first course in Probability (Amazon link)

I was taught from this book in my first year and I really liked it. Pretty precise and lots of good examples.

Answer 3

For some time now, my favorite probability text has been "A First Course in Probability" by Sheldon Ross, because of its excellent set of examples and exercises. But lately I've been reading "Understanding Probability" by Henk Tijms, and I think I may like it even better than Ross. Like Ross, Tijms's book has excellent examples and exercises, but Tijms also has an emphasis on simulation, which I like, and there are more real-world examples. Tijms's book has an unusual organization in that it is divided into two parts, the first being an intuitive approach and the second part more formal. There are some matrices in the second part of the book, in particular with regard to the multivariate normal distribution and Markov chains, where matrices are pretty much unavoidable, but most of the book does not use matrices. Ross manages to discuss the multivariate normal without matrices, but he does use matrices in his discussion of Markov chains.

Anyway, Ross or Tijms, you can't go wrong with either one. Ross's book has been around longer (there are eight editions so far), but Tijms deserves consideration.