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        riddles >> general problem-solving / chatting / whatever >> How can I think outside the box? 
        
(Message started by: Mugwump101 on Apr 12^th, 2005, 8:18pm)

Title: How can I think outside the box?
Post by Mugwump101 on Apr 12^th, 2005, 8:18pm

I've been coming here a few times before in the past and it's been a great joy even though I understand a only a margin of what you are talking about.

High school math is interesting but I am very eager to learn more about pure math than implied math at school.

Can anyone recommend me Mathemathics books that require thought and effort as well as they give me information and new sort of knowledge they don't teach in school? How do I become like you guys that solve relatively difficult problems so easily? It's simply amazing how much everyone here knows about mathemathics and the wisdom outside school to be able to grasp thought and think up a solution for the math problems.

I am behind in Math dearly, I'm taking Mathemathics A Semester 2 0f 3 for a freshman at High school but I'm so curious and willed to study more about real and pure math than implied math!

Title: Re: How can I think outside the box?
Post by Barukh on Apr 13^th, 2005, 2:32am

Mugwump101, have you read "What is Mathematics?" by Courrant and Robinson? It's an easy reading book, but so profound it teaches you a lot.

Also, George Polya's books "How to Solve It?" and "Mathematics and Plausible Reasoning".

Title: Re: How can I think outside the box?
Post by rmsgrey on Apr 13^th, 2005, 4:06am

On the recreational side, Martin Gardner's collections of Scientific American columns (book titles usually Mathematical ______), Ian Stewart's books and Raymond Smullyan's books on logic are also accessible, and also can lead to some very deep waters.

I haven't really surveyed the field, so I can't say whether there are other authors that meet or exceed the same standards, but those three shouldn't disappoint.

All three are focussed more on exploring specific topics and having the maths arise naturally rather than on picking an aspect of maths and explaining it, so they're not ideal for learning about maths per se, but they played a large part in my developing the sense of wonder and curiosity and the habit of (more or less) logical thought that are very useful for studying mathematics, and, I suspect, are common to a number of the uberpuzzlers here.