3 out of 5 stars.
A little disjointed and need to be faster
Date: April 25, 2010
"Although this course has some interesting insights and examples, I only give it a three star rating.
Here are some insights and examples from the course that I found interesting:
1. Fibonacci patterns in nature: Pineapples, cone flower and daisy.
2. The existence of 5 platonic solids (and no more than 5).
3. The representation of fourth dimension in the third dimension.
4. Probability trivia: Door number 2 or 3 --> contemplating extreme value & how our intuition may not be accurate.
5. Non-transitive dice.
6. St Peterburg's paradox - how an infinite expected value may not mean that it's a good idea to bet any large $ amount.
7. Experiment with 2 decks of cards - withdrawing each card simultaneously and figuring out the probability we find the exact same card in the same sequence, and
8. The birthday probability trivia.
But why the three star rating? Several reasons:
a. Too slow & not enough insights per lecture: I define whether a course is good or not from how many new, insightful ideas I can learn from each lecture. This one here doesn't provide as many new, insightful ideas as it could have. In comparison, the course "The Art and Craft of Mathematical Problem Solving" by Prof Paul Zeits (which I have also reviewed) have many new insightful ('AHA') ideas packed (too heavily in fact! - I had to 'pause' a lot) into each lecture. I recommend faster delivery for most of the lectures in this course.
b. The lectures are somewhat disjointed / too random: e.g., talking about Mobius Band and Klein Bottle --> so what? how does it link to the rest of the lectures? or how does it link to the 'geometry' section? what's the implication to the real world?
c. Some typo (typing error): For e.g., in the DVD in lecture 20, the probability of winning the car by switching the first guess (in a 1 billion door example) is written on the DVD as 1 / 999,999,999 --> this is wrong! (the lecturer said it correctly - but it was written wrongly).
d. I feel Prof Ed Burger is better than Prof Michael Starbird in explaining the lectures' examples, although both are enthusiastic.
e. Awkward camera perspectives/angles - for instance, when Prof Michael Starbird was explaining the cones and ellipses, the camera moved from the schematics to the closed-up real example (i.e., cone held by Prof Starbird) too much that it confused me. I figured out the insight myself through my own experimentation but this could have been explained clearer by just having the camera sticking to the schematics only.
f. Not enough mathematics. For instance, in lecture 22 (on randomness), Prof Ed Burger noted that the probability that the needle in Buffon's needle will cross a line is exactly equal to 2 / pi. But how was this answer arrived at?? Prof Paul Zeits, in contrast, will go through this in detail.
Another example is: In lecture 23, there's a very interesting probability problem where Prof Ed Burger talked about two decks of cards and withdrawing the cards simultaneously. He said that the probability of flipping over two of the exact same cards at the same time = two thirds (66.7%). But how did he arrive at this conclusion? Out of curiosity, I googled it and couldn't find it. So I calculated this myself and found that the answer is actually 63.9% (but I could be wrong). I wish Prof Burger explained this more!
g. Need answers to the questions at the back.
h. Advice/life lessons too vague and basic, and most can be grouped together."
