Here is a link to a PDF doc I wrote a few years back: My fast-moving introduction to Advanced Probability Theory.

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.

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Tags: sigma algebra, measure theory, change of measure

This entry was posted on November 30, 2011 at 3:45 pm and is filed under Mathematics, Probability Theory. You can follow any responses to this entry through the RSS 2.0 feed.
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January 20, 2012 at 8:44 pm |

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

January 20, 2012 at 9:32 pm |

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

January 27, 2012 at 9:38 am |

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

January 27, 2012 at 6:33 pm |

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

June 20, 2012 at 4:26 pm |

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!

May 22, 2013 at 6:12 pm |

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