9 ms·

Can you give an example or two of the more complex issues you deal with? I honestly have no idea.

murbard2 12y ago
Can't be too specific, but I often need to solve differential equations, find closed form solutions to some integrals (mathematica helps but is often not sufficient), build models which strike a good balance between realism and tractability. Find which properties are important to preserve in models and which aren't, etc. chollida1's comment is spot on and I oscillate between 1 and 2.
- FD3SA 12y ago
  None of these have any similarity to brainteasers. In fact, these are all excellent subjects on their own that could be tested directly. For example: "Give me an overview of a numerical method used to solve differential equations." The more time you spend asking brainteasers, the less time you have to devote to your actual skills of interest. You may even find that quizzing someone on mathematics may help refresh and solidify your own understanding.
  - murbard2 12y ago
    Do you have experience interviewing candidates? Many candidates will answer this question correctly and yet be totally unable to do anything when they're confronted with a non textbook case. To be clear the brain teasers I ask are mathematical problems, not the type of brain teasers used in consulting interviews. For instance: We play a game where we each draw a secret random number uniformly between 0 and 1. We each may re-throw if dissatisfied with our first throw, or me may keep it. We do not know whether or not the other has chosen to re-throw. We then compare our results and he who holds largest number wins $1. What is the best strategy to follow? That's the type of brainteaser I'd ask. It's accessible to a good high school student. I interviewed a PhD candidate in applied mathematics from a top Ivy league university who: - wouldn't believe that maximizing the expected value of the number obtained wasn't optimal until shown an explicit counterexample - was unable to write the equations properly or model the problem - was unable to solve the equations after I handed them out to them He was however able to talk about his thesis work. Your questions wouldn't have caught that at all. His thesis work was in game theory.
    - foldr 12y ago
      There's two ways of interpreting that result, though. Maybe it shows that mathematical brain teasers aren't a good way of testing for mathematical ability.
    - upquark 12y ago
      I wouldn't describe this as a brainteaser. It's a well-defined math problem, not some BS question about manhole covers or barbers in Chicago.
      - murbard2 12y ago
        I suppose it depends on the industry then... These are what we tend to call brainteasers in quant finance, and they're the type of problems you'll find in the book "Heard on the street" recommended above.
    - thecage411 12y ago
      I haven't read up on game theory in a long time, does "best strategy to follow" mean "the strategy that maximizes my expected payoff for all the strategies my opponent could employ"? So, an explicit counterexample would be my opponent picking a strategy of only re-throwing above .25. His expectation is then .25 * (0 + .25)/2 + .75 * (0 + 1)/2 ~= .40, so I should not rethrow if I get above .40 and below .50, even though it would raise my own expectation. Am I thinking about that correctly?
      - murbard2 12y ago
        Don't focus on expectation, focus on probability of winning.
    - blahblah3 12y ago
      hey murbard is the answer to this 1-goldenratio? (.618...) to get this I computed the function f(x,y) which is my expected value if I reroll if roll <= x and my opponent re-rerolls if roll <= y. let p be the optimal value. by symmetry f(p,p) = 0.5 so there must be a local minimum around that point. solving by taking a one sided derivative gives me (sqrt(5)-1)/2

Can't be too specific, but I often need to solve differential equations, find closed form solutions to some integrals (mathematica helps but is often not sufficient), build models which strike a good balance between realism and tractability. Find which properties are important to preserve in models and which aren't, etc. chollida1's comment is spot on and I oscillate between 1 and 2.

FD3SA 12y ago
None of these have any similarity to brainteasers. In fact, these are all excellent subjects on their own that could be tested directly. For example: "Give me an overview of a numerical method used to solve differential equations." The more time you spend asking brainteasers, the less time you have to devote to your actual skills of interest. You may even find that quizzing someone on mathematics may help refresh and solidify your own understanding.
- murbard2 12y ago
  Do you have experience interviewing candidates? Many candidates will answer this question correctly and yet be totally unable to do anything when they're confronted with a non textbook case. To be clear the brain teasers I ask are mathematical problems, not the type of brain teasers used in consulting interviews. For instance: We play a game where we each draw a secret random number uniformly between 0 and 1. We each may re-throw if dissatisfied with our first throw, or me may keep it. We do not know whether or not the other has chosen to re-throw. We then compare our results and he who holds largest number wins $1. What is the best strategy to follow? That's the type of brainteaser I'd ask. It's accessible to a good high school student. I interviewed a PhD candidate in applied mathematics from a top Ivy league university who: - wouldn't believe that maximizing the expected value of the number obtained wasn't optimal until shown an explicit counterexample - was unable to write the equations properly or model the problem - was unable to solve the equations after I handed them out to them He was however able to talk about his thesis work. Your questions wouldn't have caught that at all. His thesis work was in game theory.
  - foldr 12y ago
    There's two ways of interpreting that result, though. Maybe it shows that mathematical brain teasers aren't a good way of testing for mathematical ability.
  - upquark 12y ago
    I wouldn't describe this as a brainteaser. It's a well-defined math problem, not some BS question about manhole covers or barbers in Chicago.
    - murbard2 12y ago
      I suppose it depends on the industry then... These are what we tend to call brainteasers in quant finance, and they're the type of problems you'll find in the book "Heard on the street" recommended above.
  - thecage411 12y ago
    I haven't read up on game theory in a long time, does "best strategy to follow" mean "the strategy that maximizes my expected payoff for all the strategies my opponent could employ"? So, an explicit counterexample would be my opponent picking a strategy of only re-throwing above .25. His expectation is then .25 * (0 + .25)/2 + .75 * (0 + 1)/2 ~= .40, so I should not rethrow if I get above .40 and below .50, even though it would raise my own expectation. Am I thinking about that correctly?
    - murbard2 12y ago
      Don't focus on expectation, focus on probability of winning.
  - blahblah3 12y ago
    hey murbard is the answer to this 1-goldenratio? (.618...) to get this I computed the function f(x,y) which is my expected value if I reroll if roll <= x and my opponent re-rerolls if roll <= y. let p be the optimal value. by symmetry f(p,p) = 0.5 so there must be a local minimum around that point. solving by taking a one sided derivative gives me (sqrt(5)-1)/2