The art and craft of problem solving
This text on mathematical problem solving provides a comprehensive outline of "problemsolving-ology," 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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Strategies for Investigating Problems
Fundamental Tactics for Solving Problems
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algebra algorithm AM-GM AM-GM 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 non-negative 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