Jun 8, 2009

How to Read Mathematics


Mathematics says a lot with a little.  The reader must participate.  At every stage, he/she must decide whether or not the idea being presented is clear.  Ask yourself these questions:

·            Why is this idea true? 

·            Do I really believe it? 

·            Could I convince someone else that it is true? 

·            Why didn't the author use a different argument? 

·            Do I have a better argument or method of explaining the idea? 

·            Why didn't the author explain it the way that I understand it? 

·            Is my way wrong? 

·            Do I really get the idea? 

·            Am I missing some subtlety? 

·            Did this author miss a subtlety? 

·            If I can't understand the point, perhaps I can understand a similar but simpler idea?

·            Which simpler idea? 

·            Is it really necessary to understand this idea? 

·            Can I accept this point without understanding the details of why it is true? 

·            Will my understanding of the whole story suffer from not understanding why the point is true?

Putting too little effort into this participation is like reading a novel without concentrating.  After half an hour, you wake up to realize the pages have turned, but you have been daydreaming and don’t remember a thing you read.

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