My latest review: "The Art and Craft of Mathematical Problem Solving" (from The Teaching Company)

Here is my latest review of the course: "The Art and Craft of Mathematical Problem Solving" by Professor Paul Zeits from The Teaching Course. I have posted my review here as well:http://www.teach12.com/ttcx/coursedesclong2.aspx?cid=1483

Here it is below:

Fantastic topics and presentation
Date: April 10, 2010

"Around two lectures into this course, I couldn't help but saying to myself "WOW". This course is fantastic for several reasons:

1. It uses plenty of pictures, animations and graphs. This really helped the understandings of the problems and their solutions. This is my fifth or sixth TTC course, and I really love the presentation of this course (through the use of the animations, pictures etc.) compared to the DVD versions of the other courses I have seen (which relied too much on the lecturers' verbal commentaries).


2. Every lecture always has at least one problem to be solved - i.e., practical.


3. Prof Zeits also almost always explains WHY the problems are solved in such ways, rather than just the HOWs.


4. Some of the mathematical problems are very interesting and fun.

Overall though, most parts of this course are quite (mathematically) hard-core and require mastery of at least most of high school geometry, algebra, trigonometry and calculus to fully appreciate the courses' nuances. I have loved maths from a very young age, and there were around 3 - 5% of the problems/examples i did not fully get.

One recommendation I would like to make to Prof Zeits and TTC is that I noticed small / a few typos in the notes as well as in the written texts on the DVD, which occurred (I noticed) around where the problem's climax is at! (which could get annoying). But these are very minor in frequency. For instance, on page 27 of the course guidebook, point I.B.3 should end with "8Tn + 1" instead of "8Tn".

Personally, I loved the following problems (& the strategies and tactics to solve them) - not in any order:

• The pill problem (in lecture 1).


• "Determine, with proof, the largest number that is the product of positive integers whose sum is 1976" - using 2s and 3s - amazing! (and the importance of e) (in lecture 16).


• The pigeonhole (and intermediate pigeonhole) tactics (in lecture 14). I think it has great applications - for instance, problem 2 on page 60 of guidebook.


• Handshake problem (in lecture 10) - contemplate extreme values.


• Wythoff's Nim or "puppies and kittens" problem (in lecture 9) - solved by plotting positions and contemplating symmetries.


• And lastly, the problem in lecture 20: "What is the probability that a randomly chosen number in Pascal's triangle is even?" I love the process of answering this and the final patterns and answer!

Overall, this is a superb superb course and I highly recommend it, but only for the hard-core math enthusiasts."