(This is a bit of a follow-up to the solution reading post last month. Spoiler warnings: USAMO 2014/6, USAMO 2012/2, TSTST 2016/4, and hints for ELMO 2013/1, IMO 2016/2.) I want to say a little about the process which I use to design my olympiad handouts and classes these days (and thus by extension the… Continue reading Some Thoughts on Olympiad Material Design
Tag: olympiad
Formal vs Functional Series (OR: Generating Function Voodoo Magic)
Epistemic status: highly dubious. I found almost no literature doing anything quite like what follows, which unsettles me because it makes it likely that I'm overcomplicating things significantly. 1. Synopsis Recently I was working on an elegant problem which was the original problem 6 for the 2015 International Math Olympiad, which reads as follows: Problem… Continue reading Formal vs Functional Series (OR: Generating Function Voodoo Magic)
New algebra handouts on my website
For olympiad students: I have now published some new algebra handouts. They are: Introduction to Functional Equations, which cover the basic techniques and theory for FE's typically appearing on olympiads like USA(J)MO. Monsters, an advanced handout which covers functional equations that have pathological solutions. It covers in detail the solutions to Cauchy functional equation. Summation,… Continue reading New algebra handouts on my website
Against the “Research vs. Olympiads” Mantra
There's a Mantra that you often hear in math contest discussions: "math olympiads are very different from math research". (For known instances, see O'Neil, Tao, and more. More neutral stances: Monks, Xu.) It's true. And I wish people would stop saying it. Every time I've heard the Mantra, it set off a little red siren… Continue reading Against the “Research vs. Olympiads” Mantra
Stop Paying Me Per Hour
Occasionally I am approached by parents who ask me if I am available to teach their child in olympiad math. This is flattering enough that I've even said yes a few times, but I'm always confused why the question is "can you tutor my child?" instead of "do you think tutoring would help, and if… Continue reading Stop Paying Me Per Hour
Some Advice for Olympiad Geometry
I know some friends who are fantastic at synthetic geometry. I can give them any problem and they'll come up with an incredibly impressive synthetic solution. I also have some friends who are very bad at synthetic geometry, but have such good fortitude at computations that they can get away with using Cartesian coordinates for… Continue reading Some Advice for Olympiad Geometry
Writing Olympiad Geometry Problems
You can use a wide range of wild, cultivated or supermarket greens in this recipe. Consider nettles, beet tops, turnip tops, spinach, or watercress in place of chard. The combination is also up to you so choose the ones you like most. --- Y. Ottolenghi. Plenty More In this post I'll describe how I come… Continue reading Writing Olympiad Geometry Problems
Putnam 2015 Aftermath
(EDIT: These solutions earned me a slot in N1, top 16.) I solved eight problems on the Putnam last Saturday. Here were the solutions I found during the exam, plus my repaired solution to B3 (the solution to B3 I submitted originally had a mistake). Some comments about the test. I thought that the A… Continue reading Putnam 2015 Aftermath
Cauchy’s Functional Equation and Zorn’s Lemma
This is a draft of an appendix chapter for my Napkin project. In the world of olympiad math, there's a famous functional equation that goes as follows: $latex \displaystyle f : {\mathbb R} \rightarrow {\mathbb R} \qquad f(x+y) = f(x) + f(y). &fg=000000$ Everyone knows what its solutions are! There's an obvious family of solutions… Continue reading Cauchy’s Functional Equation and Zorn’s Lemma
Teaching A* USAMO Camp
In the last week of December I got a position as the morning instructor for the A* USAMO winter camp. Having long lost interest in coaching for short-answer contests, I'd been looking forward to an opportunity to teach an olympiad class for ages, and so I was absolutely psyched for that week. In this post… Continue reading Teaching A* USAMO Camp
Power Overwhelming 