The art and craft of problem solvingThis text on mathematical problem solving provides a comprehensive outline of "problemsolvingology," concentrating on strategy and tactics. It discusses a number of standard mathematical subjects such as combinatorics and calculus from a problem solver's perspective. 
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Review: The Art and Craft of Problem Solving
User Review  Krollo  GoodreadsI'm a bit new to Olympiad maths, but this book has given me a decent overview. I especially liked the combinatorics but all of it was pretty good. We'll see how I'll do in BMO1, but it's not fair to blame my failures on this book! Fnarr fnarr... Read full review
Review: The Art and Craft of Problem Solving
User Review  GoodreadsI'm a bit new to Olympiad maths, but this book has given me a decent overview. I especially liked the combinatorics but all of it was pretty good. We'll see how I'll do in BMO1, but it's not fair to blame my failures on this book! Fnarr fnarr... Read full review
Contents
Chapter  7 
Strategies for Investigating Problems  15 
Fundamental Tactics for Solving Problems  68 
Copyright  
11 other sections not shown
Common terms and phrases
algebra algorithm AMGM AMGM inequality argument assume cards circle coefﬁcients color complex numbers compute conjecture Consider contains contradiction converges count crux move deﬁne deﬁnition degree denote difﬁculty divisor easy edges equal equation Eulerian path exactly example extreme principle factor ﬁgure ﬁnd ﬁnite ﬁrst ﬁxed formula function geometric series graph greatest common divisor Hamiltonian paths ideas inequality inﬁnite integer coefﬁcients lattice points leam least element locker look mathematical mean value theorem modulo monic monic polynomial multiple nonnegative notation Notice number theory pairs parity partitions path pattem penultimate step perfect square permutation pigeonhole principle pigeons plane polygon polynomial positive integer possible prime problem solving Problems and Exercises proof Prove Putnam real numbers rectangle reﬂection rooks roots of unity satisﬁes sequence Show simple Solution speciﬁc strategy subsets symmetry tactic theorem tool triangle true USAMO variables vector vertex vertices words zero