Coursera Probability Course and Recommended Probability Book

Just completed the Coursera Probability Course by UPenn (University of Pennsylvania), lectured by Professor Santosh S. Venkatesh who is the author of the highly recommended book: The Theory of Probability: Explorations and Applications.

Coursera Review

The course isn’t very hard, it is very suitable for undergraduates and even high school students should be able to understand majority of the content. It actually overlaps with the A level syllabus in Singapore, and hence I would say that a 17-18 year old student would be able to grasp most of the concepts in this course.

The lecturer is very good at words, and his lectures are full of imagery and vivid descriptions. The homework is a little tricky, and hence would require some thought, even though the concepts tested are elementary (elementary in the sense that it doesn’t require calculus).

A sample of a tricky question is the “Six Saucer Question”: Six cups and saucers come in pairs: there are two cups and saucers that are red, white, and blue. If the cups are placed randomly onto the saucers (one each), find the probability that no cup is upon a saucer of the same color.

It is very tricky and to get it correct on the first try is a major accomplishment.

Overall, this Coursera Course is highly recommended, and students should try to take it the next time it comes out!

Coursera Course Review: An Introduction to Functional Analysis

Recently, I completed an excellent Coursera Course: An Introduction to Functional
Analysis, offered by École Centrale Paris.

Although challenging, it was a fun and interesting course, thanks to the effort by Professors John Cagnol and Anna Rozanova-Pierrat. Functional Analysis is a pretty difficult topic, and it was great to have two good professors explain it.

This course is actually more suitable for students who have some mathematical background, especially in mathematical analysis. New students may find it too hard to follow it from scratch. It is excellent as a review course for students who have taken functional analysis a few years ago but have forgotten some of it.

Featured Book:

Introductory Functional Analysis with Applications