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I was wondering what resources people new to mathematics competitions could use for preparing for the William Lowell Putnam Competition(or just the Putnam).

My background in mathematics is limited. I have recently started doing the book Abstract Algebra by Dummit and Foote and I am enjoying that book. I am yet to get a taste of real analysis though I have done single variable calculus rigorously .

1) How much mathematics does one need to learn before sitting for the Putnam?
2) What are the resources/books one could use?

I may never even study in the USA but I wish to convince myself that I can solve the Putnam problems too!

Thanks in advance!

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General advice is for high-school students NOT to do the Putham exam. –  GEdgar Oct 14 '12 at 17:21
    
Mind explaining why? –  Richard Nash Oct 14 '12 at 17:24
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Regulations say a student may take the Putnam at most 4 times, and must not have a bachelors degree. For most people, the best four scores will be the last four years before the bachelors degree. Someone who took it as a high-school student may therefore be ineligible in a later year when he/she is most likely to get a top score. –  GEdgar Oct 14 '12 at 23:27
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1 Answer

up vote 5 down vote accepted

You might start with this list of links.

You will get a large number of useful hits if you Google Putnam practice problems. I particularly like the problem selection from the Berkeley course H90 that used to be run by Professor William Kahan. There are a number of other courses and training programs with a web presence. While it is not possible to duplicate the atmosphere of a course if you are working by yourself, they are the nearest one can get.

One can do well on the Putnam with background that does not go beyond first or second year material (plus considerable problem solving experience). Many first year students have done very well.

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I am now actually considering sitting for the olympiads!I am still in high school. –  Richard Nash Oct 14 '12 at 17:02
    
Great! Most national Olympiads are invitational, but there is usually a clear path to an invitation, the various lower level competitions. –  André Nicolas Oct 14 '12 at 17:06
    
Is there 1 book that covers most of the Olympiad stuff needed for olympiads like the USAMO? –  Richard Nash Oct 14 '12 at 18:20
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The book Problem solving Strategies by Engel is quite good good. The books by Andreescu have nice material. I expect you are familiar with the web site Art of Problem Solving. Too many resources, too little time! –  André Nicolas Oct 14 '12 at 19:46
    
Well, it seems I have some unfinished business with the olympiads left. Thanks a ton! –  Richard Nash Oct 15 '12 at 4:00
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