I was taught undergraduate probability theory by one of the best. Williams’s book Probability with Martingales is a popular introduction to advanced probability theory, and was the text I used to learn about the formal theoretical framework that holds probability together (I highly recommend going through all the exercises at the back of the book).

But what is the best way to teach probability theory? I remember having a discussion with a PhD colleague on whether it is however really necessary to go through all the sigma-algebra part before getting into the interesting measure theory story.

My view has been that advanced probability theory can be taught in a different way, and I always thought that we should put more emphasis on the intuition behind the measure-theory aspects and on how clever the notation is. As an effort to back up my claims, a few years ago I started to write my own Introduction to Probability.

I got about 20 pages down. Uncompleted later chapters were given titles and show the direction I was heading. If I get interesting feedback on what’s there so far I’ll put in the effort to finish this off.

Mathematician (PhD in Probability Theory).
Art lover (spent one excellent year studying painting and ceramics at Batley Art College).
Ex investment banker (2yrs of fixed-income exotics trading, 5 yrs of quantitative research, 2 yrs of inflation structuring).
Now busy as a quantitative software developer.
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9 thoughts on “A fast-moving introduction to advanced probability theory”

Like the doc, I had never gotten past the sigma algebra part of measure theory and this finally gave me the intuition for it.

Robert hi, I think you do a good job with this blog, pdf very straightforward. I hope you will continue to blog regularly, its a pleasure to follow you. Kind regards

Hi Robert!
“If I get interesting feedback on what’s there so far I’ll put in the effort to finish this off.” — please do so! What you have done so far is really nice (thank you!), and it would be great to have a condensed/fast-moving intro to probability!

Like the doc, I had never gotten past the sigma algebra part of measure theory and this finally gave me the intuition for it.

That’s great to hear! Thanks for the comment.

Robert hi, I think you do a good job with this blog, pdf very straightforward. I hope you will continue to blog regularly, its a pleasure to follow you. Kind regards

I fully intend to keep blogging regularly, glad you enjoy reading!

Hi Robert!

“If I get interesting feedback on what’s there so far I’ll put in the effort to finish this off.” — please do so! What you have done so far is really nice (thank you!), and it would be great to have a condensed/fast-moving intro to probability!

Thank you very much Robert! I join the cause and I would gently ask you to add more chapters!!!

Hi Robert,

You are doing a wonderful job through this blog. Would love to read your book.

Thanks.

hi, did you ever finish this off? they’re really nice notes!

Unfortunately I did not write any more of this article.