Problem Solving Through Problems

She does fantastic work in our courses, and was easily among the very top students in the class she took with me, and yet she still occasionally hits problems that she can’t solve.Moreover, she has access to an excellent math teacher in her school who sometimes can’t help her get past these problems, either.I think a lot of what we do at Ao PS is preparing students for challenges well outside mathematics.

The purpose of this book is to isolate and draw attention to the most important problem-solving techniques typically encountered in undergradu ate mathematics and to illustrate their use by interesting examples and problems not easily found in other sources.

Each section features a single idea, the power and versatility of which is demonstrated in the examples and reinforc The purpose of this book is to isolate and draw attention to the most important problem-solving techniques typically encountered in undergradu ate mathematics and to illustrate their use by interesting examples and problems not easily found in other sources.

Don't be afraid to play with the numbers for a good while…

simple number patterns (especially the triangular numbers) have a part in a surprising proportion of the solutions but if you haven't extrapolated numerically this can be difficult if not impossible to see.2.

I recommend extensively trying it; among other things, getting good at being stuck is an immensely valuable part of learning to problem solve.

I still generally only get half marks on BMO/IMO papers if I work to the time limit so you can't take this as gospel but if I was just starting out on this style of paper these are two bits of advice I'd want (beyond the mathematics staple of 'if in doubt, sketch it out').1.

(This is no slight to him—I have students bring me problems I can’t solve, too! ” We ask hard questions because so many of the problems worth solving in life are hard.

If they were easy, someone else would have solved them before you got to them.

The book is both an anthology of problems and a manual of instruction.

It contains over 700 problems, over one-third of which are worked in detail.

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