Especially if you are looking to -suppliment- an education system that is based on "here is a TYPE X problem... you solve it this way with this algorithm..."
I suggest books such as Proofs from THE BOOK. Firstly it deals with topics outside the -regular curriculum- but whose problems are easily explained to (and understood by) just about anyone. "Graph Theory"... simply put "connect-the-dots". "Combinatorics", well that's just "counting things".
This book is particularly good as it offers, in many cases, more than one proof for a given problem, looking at problems in different creative ways to find elegant solutions. Feynman was a huge advocate of this (see the "Cargo Cult Science" chapter in his book Surely you're joking Mr. Feynman!
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Especially if you are looking to -suppliment- an education system that is based on "here is a TYPE X problem ... you solve it this way with this algorithm ..."
... simply put "connect-the-dots". "Combinatorics", well that's just "counting things".
I suggest books such as Proofs from THE BOOK. Firstly it deals with topics outside the -regular curriculum- but whose problems are easily explained to (and understood by) just about anyone. "Graph Theory"
This book is particularly good as it offers, in many cases, more than one proof for a given problem, looking at problems in different creative ways to find elegant solutions. Feynman was a huge advocate of this (see the "Cargo Cult Science" chapter in his book Surely you're joking Mr. Feynman!