Comment on Open Thread: January 2010

Fri, 08 Jan 2010 01:42:19 GMT

I don't understand why/how anyone would learn equations without understanding them.

I agree that wikipedia is not a good substitute for textbooks in general, neither does it replace actual practice by problem solving. You can still learn a lot of math (even complete proofs) from it: get good first impressions on whole areas. It even contains high quality introductory material on certain important topics and facts.

However I completely agree with you: the most important thing in math is to think about problems. Undergraduate Springer books (yellow series) typically contain a lot of problems alongside actual text. My method is the following:

1) Read one chapter and write up the statement of every theorem.

2) Go through all statements and reproduce the proof without rereading the material

3) Iterate 1)-2) if your are stuck with any of the proofs

4) Proceed with the problem section and try to solve all problems. Omit problems only if they are marked as hard and if you are stuck after an hour of thinking.

The most topics books to start with are linear algebra and calculus. Working through the undergraduate material in the above way takes a long time, but you will build a firm base for further studies.

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