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The most interesting math exam of my life was my qualifying exam for my PhD. It was an oral exam, and I prepared a syllabus and gave it to my three examiners ah

The most interesting math exam of my life was my qualifying exam for my PhD. It was an oral exam, and I prepared a syllabus and gave it to my three examiners ahead of time. At the actual exam, we all showed up and they took turns asking me their questions that they had prepared relating to my syllabus. I was expected to solve the problems at the board. They didn't necessarily expect me to solve them immediately, but they wanted to hear me think out loud and communicate my ideas. There were around 5-10 questions total over the course of I think a few hours, ranging in complexity from trivia (i.e. memorized facts) to computations to proofs. Some of them I found solutions for and some of them I didn't, and they assigned me some to solve later as "homework" (though they did pass me without it being conditioned on the homework). In hindsight, it was very similar to white-board coding interviews, but I didn't know anything about coding interviews at the time. I can't really think of any other place such a format would be appropriate as a math exam. When else would a paper math exam not be sufficient.

sdenton4 3y ago
Yes, my math grad student time ws an excellent preparation for coding interviews. In addition to the oral exams, I found TA'ing was also an excellent preparation. Students show up with lots of questions, which you get to solve on your toes at a board... Classes and competitions also generally have an allowed 'bag of tricks' from which you build your solutions. White-board coding interviews are the same. If you want to do well, you get to know what the 'atomic' operations are in your bag of tricks, how they combine into useful tools, and how to spot when they might be useful in the 'wild.' Restating/reworking a problem into a form where some tricks are more obviously applicable is also a useful skill. These are general problem solving skills, which are pretty independent of what's actually in the bag of tricks... Draw a picture, try a concrete example, identify the pen-ultimate step, etc. When I give whiteboard interviews, I have a favorite question with about four reasonable stopping points. My general approach is to work with the candidate until they get stuck, and then see how handle being stuck and getting un-stuck. So, even if you have trouble with the 'easiest' part of the problem, I can still get a good read on the general problem solving skills. (And if you sail through to the hardest level solution without getting stuck, you're probably worth hiring anyway...)
- selecsosi 3y ago
  Your experience matches my own with TA'ing being a fertile training ground for solving problems from a variety of perspectives on your toes. I also appreciate your resultant interview approach with which I've also found great success. The point for me that is most revealing is the adaptation to the sticking point, as the questions are engineered to zig, when a candidate zags more than from solving any particular software problem.
paulpauper 3y ago
Why not a written part too? I heard it's both usually.
bitwize 3y ago
This sounds amazing, like the many scenes from science-themed movies that feature two scientists, often an elder and a younger. The younger is scrawling out the solution to some near-intractable problem on the blackboard, while the elder guides and goads, perhaps pointing out a flaw in the proof or an overlooked detail. I believe Good Will Hunting and Theory of Everything had scenes like this. Regrettably I've squandered my youth and it's too late for my chance at the blackboard, solving something really hard under the eye of a judging but patient mentor. So now I code webshit for a living. Congrats on that doctorate, man.
wodenokoto 3y ago
This is similar to oral math exams in Danish high school. The main differences being that the teacher submits the curriculum, and the student draws 1 topic on the day of the exam and is given something like 20 minutes to prepare between drawing and presentation. All submitted topics are known to the student, through the submitted curriculum, which has all been taught throughout the year(s). Grade is dependent on how well you do the proof related to the topic and how well you manage to reference related topics in the curriculum.

sdenton4 3y ago

Yes, my math grad student time ws an excellent preparation for coding interviews. In addition to the oral exams, I found TA'ing was also an excellent preparation. Students show up with lots of questions, which you get to solve on your toes at a board... Classes and competitions also generally have an allowed 'bag of tricks' from which you build your solutions. White-board coding interviews are the same. If you want to do well, you get to know what the 'atomic' operations are in your bag of tricks, how they combine into useful tools, and how to spot when they might be useful in the 'wild.' Restating/reworking a problem into a form where some tricks are more obviously applicable is also a useful skill. These are general problem solving skills, which are pretty independent of what's actually in the bag of tricks... Draw a picture, try a concrete example, identify the pen-ultimate step, etc. When I give whiteboard interviews, I have a favorite question with about four reasonable stopping points. My general approach is to work with the candidate until they get stuck, and then see how handle being stuck and getting un-stuck. So, even if you have trouble with the 'easiest' part of the problem, I can still get a good read on the general problem solving skills. (And if you sail through to the hardest level solution without getting stuck, you're probably worth hiring anyway...)

selecsosi 3y ago
Your experience matches my own with TA'ing being a fertile training ground for solving problems from a variety of perspectives on your toes. I also appreciate your resultant interview approach with which I've also found great success. The point for me that is most revealing is the adaptation to the sticking point, as the questions are engineered to zig, when a candidate zags more than from solving any particular software problem.

paulpauper 3y ago

Why not a written part too? I heard it's both usually.

bitwize 3y ago

This sounds amazing, like the many scenes from science-themed movies that feature two scientists, often an elder and a younger. The younger is scrawling out the solution to some near-intractable problem on the blackboard, while the elder guides and goads, perhaps pointing out a flaw in the proof or an overlooked detail. I believe Good Will Hunting and Theory of Everything had scenes like this. Regrettably I've squandered my youth and it's too late for my chance at the blackboard, solving something really hard under the eye of a judging but patient mentor. So now I code webshit for a living. Congrats on that doctorate, man.

wodenokoto 3y ago

This is similar to oral math exams in Danish high school. The main differences being that the teacher submits the curriculum, and the student draws 1 topic on the day of the exam and is given something like 20 minutes to prepare between drawing and presentation. All submitted topics are known to the student, through the submitted curriculum, which has all been taught throughout the year(s). Grade is dependent on how well you do the proof related to the topic and how well you manage to reference related topics in the curriculum.