Putnam Math: Know What You Need

[bor0000]

Putnam- what math??

please tell me what math knowledge is needed to solve any of the problems listed there. i.e. prob x1 requires no previous math knowledge. probx2 requires linear algebra course. and so on.

i would not be surprised if most of those problems required analysis or algebra. but i have no idea what is 'number theory,graph theory, combinatorics'-and i'd like to know to which problems those courses apply. thanks.

http://www.unl.edu/amc/a-activities/a7-problems/putnam/-pdf/1995.pdf

 

[philosophking]

Hahaha. I'm not laughing at you, just at how I'm about to answer. I had a similar reaction the first time I saw Putnam problems.

The Putnam prides itself on saying that all that is absolutely necessary to solve its problems are calc 1,2,3 and maybe a linear algebra course.

That's all. No analysis, algebra, combinatorics, number theory are inherently necessary. haha!

Have you ever heard of the IMO? USAMO? AIME? These are extremely difficult (IMO) or somewhat difficult (AIME) high school math tests that pride themselves on the fact that the only prerequisite mathematical knowledge is up through precalculus, even though some USAMOE and most IMO problems are extremely difficult for even professional mathematicians. I suggest you look those up as well to get a clearer idea.

 

[bor0000]

thanks, but I am not interested in those(i know about aime though), as I am a college student.

actually to better phrase my questions:
what courses help you in solving question # whatever? i.e. i only skimmed through those questions, and i noticed that A-5 requires a course in linear algebra, but nothing more really.. on the other hand B-3 requires number theory?

 

[bor0000]

also I am interested if i could get any benefit if i were got 'honorable mention' on such a test(i.e. in gradschool or medschool admissions)? i see that honorable mention requires about 4-5 problems/ 12 solved. i think that is far from impossible if i properly prepared. on the other hand anything more, i wouldn't even try.

 

[bor0000]

i actually skimmed through this 1995 test, and numbers A-1 and B-5 are too easy. A-1 is supposed to be easy, but I am surprised about B-5, it seems to mimic a chess -pawn endgame where you have a choice to move your king diagonally or vertically in order to cause the other person run out of moves(and you also can have a few moves with pawns to help that). it doesn't involve much strategy as even a 6yo can do it... Also it seems that A-4 can be proved by induction, but i only saw proofs by induction recently, and so far i can't do it. Also A-5 seems very doable.

On the other hand in the year 2000 version of the exam, none of the questions are giveaways like these! i believe there are 1 or 2 that could be proved by induction(again if i knew how to do that), but most are completely foreign to me. on the other hand if they had such an easy B-5 question, it seems to suggest that as long as you have the proper math knowledge(like all those questions on differentials or integrals require analysis), then the problems can't be too hard.

 

[Moose352]

From what some of my friends who have done USAMO, putnam, etc. say, the tests may pride themselves on not needing much mathematical knowledge, but the fact of the matter is that they do require a lot of knowledge, and learning a lot of math certainly helps a lot.