Math Blog from the Other Coast

An excellent mathematics-based blog has come across my (virtual) desk:

What's new

The diarist, Terence Tao, a professor in the Mathematics Department at UCLA, explores mostly his research and related issues, so some of the posts may be stratospheric and out of the reach of many math enthusiasts. But there are also posts with good air-pressure, and some excellent advice on math-related careers and writing techniques, as well as mathematical constructs and such. For instance, his latest post on the nature of "proof-by-contradiction" makes for excellent reading. Give it a try!

Mathematics Study Tips - Banking practice problems

In the recent post Mathematics Study Tips - Scrimmaging, I talked about a method for studying for a mathematics exam by mimicking, as best as you can, the exam environment. Sounds obvious, right? One doesn't create a soldier by watching war movies. The idea of practicing for an exam by doing new problems in a timed environment works to gauge your understanding of the material while reducing the stress of an exam by acclimating yourself to the climate within the exam. Here is another idea, mentioned in that last post:

In an actual exam, there usually will NOT be a marker on each problem telling you, for example, that "this problem is from Section 3.2 on the Mean Value Theorem". Instead, all you will see is the statement of the problem (and an implicit promise by the Instructor that the problem falls within the scope of the course). Without the context of which section the problem came from, can you still manage to do the problem? One way to help you to be sure is to take your problems out of the context they are in. Try this:

After each section of a text has been discussed in lecture and you have completed the homework problems for submission, take some time to re-write some of the other section exercises (ones that are "like" the ones in your homework set) in a common place later in your notebook. Add other problems when other sections are completed. Rewrite these problems verbatim from the text, but do not write the section or problem number. Don't DO these problems, just bank them for later.

Now when the exam approaches, and you are looking for items to focus on, go to this section of your notebook, grab 5 or 6 of these "banked" problems, go to a quiet, distraction-less place, and time yourself doing these problems without notes, text, or any other aid. If you can do the problems with ease, you are ready for these types of problems on the exam. If you cannot, however, or if some of them prove difficult, then simply re-orient these problem problems with their original sections and note these sections as ones you still need to focus on. Out of context, these problems are much closer to what you will see on an exam.

Another way to do this is to work with someone else, who can grab a problem from the text without telling you which section it comes from. While this is easier and requires little prior planning, it does involve more than one person. But then again, talking mathematics with others is really how one learns, right?

Again, in bocca al lupo!