What Probability book suits me better?

[Pallatinus]

I found those books in my library and I want to know which suits better for me. (Want to learn rigorous Probability AND applies it to statistical mechanics) Previous knowledge: Calculus 1 and 2, Introductory Statistics and Combinatorics.

Books:
Probability Theory: The Logic of Science - E.T. Jaynes
Introduction to Probability - Charles M. Grinstead and J. Laurie Snell
Probability with a View Toward Statistics - Volume I and II - J. Hoffmann-Jorgensen
Probability for Applications - Paul E. Pfeiffer
Probability - Jim Pitman
Probability and Measure - Patrick Billingsley
Any other book...

 

[vanhees71]

You should, perhaps, just read a statistics textbooks. Since you seem to be more on the mathematical side, maybe one using the infromation-theoretic approach is good (I favorize this approach very much compared to the more oldfashioned handwavy way to introduce entropy, and it's by far the most comprehensive way to introduce this key issue). My favorite book for both classical and quantum statistical physics using the information-theoretical approach is

Katz, Amnon: Principles of Statistical Mechanics, W. H. Freeman and Company, 1967

 

[Pallatinus]

You should, perhaps, just read a statistics textbooks. Since you seem to be more on the mathematical side, maybe one using the infromation-theoretic approach is good (I favorize this approach very much compared to the more oldfashioned handwavy way to introduce entropy, and it's by far the most comprehensive way to introduce this key issue). My favorite book for both classical and quantum statistical physics using the information-theoretical approach is

Katz, Amnon: Principles of Statistical Mechanics, W. H. Freeman and Company, 1967

Thanks for the help! Information-theoretical approach is exactly what I'm looking for, but do you know if any of these books I mentioned will be a good complement? or I just don't need any?

 

[vanhees71]

I don't know any of these books. So I can't say anything about them.

 

[jasonRF]

I'm familiar with two of the books:

Billingsley is a measure-theoretic book aimed at graduate students in math or statistics. With only two calculus courses under your belt it is likely much too advanced.

Jaynes is book different from any other I have seen. He treats probability as an extension of logic. I don't recommend learning the basics from it at all, but after you are comfortable with probability and statistics it is worth borrowing from your library to see if it is your cup of tea. Jaynes was a physicist that did a lot of work in statistical physics, information theory, probabilility and statistics. He strongly favors bayesian and entropy based approaches, and wrote a couple of well-known papers in the 1950s on information theory and statistical mechanics. You can find them linked int he references here:
https://en.wikipedia.org/wiki/Maximum_entropy_thermodynamics

I find his book to be fascinating, but it rambles and has a bunch of passages that read almost like he is replaying old arguments he has had with colleagues.

Good luck,

Jason

EDIT: I should have let you know that Jaynes' book does not really spend any time on statistical physics, it is almost all on probability and statistical inference. His papers are the place to look for that treatment. He does have one chapter on repeatable experiments like coin flipping, where he discusses the relationship between the deterministic laws of physics and the "random" nature of coins, dice, etc.

 

[micromass]

A very nice book https://www.amazon.com/dp/052100618X/?tag=pfamazon01-20
It's choice of topics is really impressive. Its treatment is not that rigorous that it requires very advanced mathematics, but it's not handwaving either. It's one of the best books I've seen, I wish I could have used this when I learned probability. (I learned it from Billingsley which is still my favorite book on probability and one of my favorite books of all time, but I wish I started with something easier).

 

[Hercuflea]

If you want to learn "rigorous" probability, you will need to know measure theory (real analysis) first...then you can read Paul Halmos' measure theory book.

 

[micromass]

If you want to learn "rigorous" probability, you will need to know measure theory (real analysis) first...then you can read Paul Halmos' measure theory book.

Correct, but I do not recommend learning rigorous probability without a good knowledge of how non-measure theoretic probability works. And perhaps measure theory is not needed for the OP, he should look into in what extend it is useful for him.

 

[Hercuflea]

He said he wants to learn rigorous probability and how it applies to statistical mechanics. I agree he should take an undergrad probability and statistics course first, but statistical mechanics is still an active area of research in probability and if he is interested in that in the future maybe he should move towards that by starting with real analysis.

edit* he has had an undergrad statistics course already.

 

[micromass]

He said he wants to learn rigorous probability and how it applies to statistical mechanics. I agree he should take an undergrad probability and statistics course first, but statistical mechanics is still an active area of research in probability and if he is interested in that in the future maybe he should move towards that by starting with real analysis.

edit* he has had an undergrad statistics course already.

Sure he says he wants to learn rigorous probability. But perhaps he doesn't know what rigorous probability entails precisely and whether it would be useful. The measure theoretic approach is not useful for most.

 

[Pallatinus]

I appreciate for all the help, I reach the conclusion that I should first use Weighing and Odds, It seems that is well fit for me in the moment and use Jaynes as supplement. I pretend to take a real analysis course next year and maybe use a measure theory book.

 

[MidgetDwarf]

A very nice book https://www.amazon.com/dp/052100618X/?tag=pfamazon01-20
It's choice of topics is really impressive. Its treatment is not that rigorous that it requires very advanced mathematics, but it's not handwaving either. It's one of the best books I've seen, I wish I could have used this when I learned probability. (I learned it from Billingsley which is still my favorite book on probability and one of my favorite books of all time, but I wish I started with something easier).

Looking to get into probability. The goal is to atleast be able to get through and understand Kolmogorov's book on probability.

Is this at the same level of Ross: A first Course Of Probability?

 

[micromass]

Looking to get into probability. The goal is to atleast be able to get through and understand Kolmogorov's book on probability.

Is this at the same level of Ross: A first Course Of Probability?

Yes, it is at the same level of Ross. But I think the book I quoted contains much more exciting material. A downside is that it really really lacks problems. Ross does have a lot of problems, but very few seem really mathematically interesting in the sense that most are applications of the theory and are plug and chug. Such problems are important, but I since you're into math, you should also want more theoretical problems.
Did Morin's book come out yet? He will likely have very nice problems.

 

[MidgetDwarf]

Yes, it is at the same level of Ross. But I think the book I quoted contains much more exciting material. A downside is that it really really lacks problems. Ross does have a lot of problems, but very few seem really mathematically interesting in the sense that most are applications of the theory and are plug and chug. Such problems are important, but I since you're into math, you should also want more theoretical problems.
Did Morin's book come out yet? He will likely have very nice problems.

I believe Morin's book came out yet. Here is the link https://www.amazon.com/dp/1523318678/?tag=pfamazon01-20
not sure if this is the book you are referring to.

Hmm. I may order both since they are inexpensive. I never got a stinker book recommendation from you.

Do you know of any good problem books for Geometry, Calculus, and probability?

 

[micromass]

I believe Morin's book came out yet. Here is the link https://www.amazon.com/dp/1523318678/?tag=pfamazon01-20
not sure if this is the book you are referring to.

Hmm. I may order both since they are inexpensive. I never got a stinker book recommendation from you.

Oh wow, the Morin book looks really nice. Too bad I couldn't see any of the problems in the book, but knowing Morin I think they'll be rather challenging. Seriously thinking of buying the book even though I know everything in there.

Do you know of any good problem books for Geometry, Calculus, and probability?

You mean books with only problems? No, sorry, I don't really look at such books.

 

[MidgetDwarf]

Oh wow, the Morin book looks really nice. Too bad I couldn't see any of the problems in the book, but knowing Morin I think they'll be rather challenging. Seriously thinking of buying the book even though I know everything in there.
You mean books with only problems? No, sorry, I don't really look at such books.

Thank you. I went ahead and ordered both books. I won't be able to go through them until 2 months from now. Have to review some older math topics for work.
I read the pages on available on Amazon, and the writing for Morin's book seems crystal clear, fun, and engaging.