America's Hardest Mathematics Exam

Let's look at one of the world's hardest mathematics exam: the Putnam Competition!

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[praematura]

This brought back memories... mostly good, I promise! 😄 I participated in Putnam 1988 as a freshman representing Rensselaer Polytechnic Institute, which apparently was one of the "easier" years. I believe there were 7 or 8 of us that took it that year. I don't recall my exact score, but I do recall it was in the high 20s, and that I scored the 2nd highest at RPI that year, behind one of the seniors, which really floored me. It was a very cool experience, and one I wish I'd experienced more than once! (Only once as I left RPI my sophomore year for personal reasons.) Thank you for bringing this very difficult but fascinating competition to a wider audience!

[jamiewalker]

With the trig problem, you could realise that 1/2f "(0) is the coefficient of x^2 in the maclaurin series. Expanding all the cosines up until second order term, we just need the x^2 term of (1 - 1/2 x^2)(1 - 1/2 (2x)^2)....(1 - 1/2 (nx)^2). To get x^2 terms, we must take the "1" term in n-1 brackets, and the x^2 term of the remaining bracket. This yields - 1/2 (1^2 +2^2 + 3^2 + .... n^2) as required. (*Also, you could just realise the function is even, so it's derivative must be zero at x = 0 in your analysis)

[alberteinstein]

I took this exam and was able to solve both questions A1 and B2. It wasn’t easy though, it took me 2 hours of thinking and writing to get to each of those answers. It’s definitely nothing to sneeze at

[satyamvaishnav]

I am a competitive programmer And you really is my inspiration 🥹
Because of you I started studying mathematics again and I am becoming more logical and better programmer..!

[superman]

I took the Putnam exam twice and surprisingly one of the hardest things about it was not being allowed a calculator. Even if you get a question mostly correct, which is rare, it would take me a lot of the allowed time to get to the final answer as a number. For example, A1 2023, which you did in the video, was one of the more manageable problems I have encountered on the practice papers and the two I took. But it took me longer to find the cutoff of 17/18 than to get to the final stage of the cubic inequality 😅

[michaelb]

I took the Putnam as a physics major, and at the time had very little idea of how to do formal mathematical proofs. The results were predictable, though to be fair to myself, I think only one student at my (relatively small) university got even a single answer correct. Oddly, I don't remember the test being long (though I know it was indeed six hours), but I definitely remember the free donuts 😂 In retrospect, I'm happy I took the chance to at least attempt it.

[mukutchatterjee]

For Q1 an alternative way, first we can ln both sides converts to log series then differentiate first gets f' then similarly f"

[HarshRaj-pxse]

23:11 I know I am sounding foolish, but why don't we just put n=1 and then bob would just chose odd no 1, which would result in him getting k=1 that is odd which he selected.

[sidnath]

This is very STEP-like-esque + interview. Nice video 👍🏽

[hakerfamily]

For the first one, it seems you could think of multiplying the Taylor series for cos(kx) together. You would only need to care about the x^2 terms in the product. It’s immediate then.

[mirakoop]

I just got my first 10/10 on a Putnam problem and have been beaming all day (I found out this morning), so glad you’ve made a video about it!

[basinstreetdesign]

I took this exam in grade 13 when there was a grade 13 in Ontario. I won a gold pin. There was no fanfare just my teacher dropping it off at my desk as if to say "By the way, this is for you!" I wish I still had it because it was real gold.

[pranavtubehd]

For the first question my first thought was taking the natural log on both sides for the function then differentiating it once and finding f'(0) then differentiating again to find f''(0).this seems pretty straight forwards and I'm questioning myself if it is working out.could you help out if there is any error in the method

[gjop-zkwi]

The first equation, in the solution to the conundrum is reimansum n goes to i =1, i . 1+2+3...n = n(n+1)/2

[mrmajestical]

25:02 in the last case its 1 and not 0

[markomak]

Please do a video on the entrance exam to ENS Paris (the school that has the most Fields medalists among its alumni)

[virais]

I'm an engineering student, but I think that with the knowledge I have, I can't solve any question in this exam 😂😂😂, with the training I have so far. Apart from the fact that in an exam you have to solve this question in a maximum of 5 minutes, your explanations are great, although it is still challenging for me, but I am familiar with the rules of derivation and integration as well as summations and their properties, however I am not a mathematician . I'm really excited to get to your level, or at least evolve with your teachings. ❤👍

[parthtehlan]

for the first question, you could multiply and divide the function by sinx, and use the double angle formula for sin repeatedly. this would result in sin(2^n.x)/[(2^n)sinx] and then take the derivative of this twice. would be simpler

[yu]

to differentiate in the first question
we can take log on both sides it simplifies things easily..

[ZyroZoro]

I took the Putnam three times. The first two times I got a 0. The third time I got a 10 having solved exactly one problem. I'm really happy with that lol.