I am currently a junior undergraduate student taking an Introductory Course on Probability Theory. I have been struggling with the subject for the last few weeks because mathematics can be challenging and I haven't built up enough intuition to train my mind to think probabilistically enough.
That being said, I'm between a few choices for a book for supplementary study. I've found the PDFs by Hoel, Port and Stone as well as Hossein-Pishro Nik's online text and Feller Volume 1. I was wondering, which of these books present the material in the most intuitive manner?
I often have a difficult time with Combinatorial Analysis as well, so I'm looking for a book that presents the material intuitively and yet rigorously enough so that I can truly gain a better understanding and grasp of the subject. I am open to any and all recommendations.
Best Answer
My two personal favorites for introductory probability are A First Course in Probability by Ross (there are several editions) and Understanding Probability by Tijms. Neither one uses measure theory. Ross's book is distinguished by its wealth of fully-worked out, interesting examples. Tijms's book strikes me as slightly more modern, with an emphasis on simulation and an unusual structure; the book is in two parts, with the first part an intuitive approach with lots of examples of applications, and the second part more formal.
I like Feller's book, but I don't think it is a good choice for a first introduction. Compared to Ross and Tjims, Feller Volume I is more advanced and doesn't have much discussion of continuous distributions. I can't comment on your other two books because I haven't read them.