On this page you will find random musings on various aspects of mathematics. There is not set schedule
for these thoughts. Keep coming back here often. I hope that you find it interesting.
As graduation season is upon us I have been thinking about two matters.
* What should you know now that you have a math major?
* What are employers who are seeking mathematically talented applicants asking?
I have had a wonderful book on my bookshelf:
Heard on the Street: Quantitative Questions from Qall Stree Job Interviews
The book is now in it's 9
^{th} edition and is a wonderfull compendium of actual questions asked in interviews. From
conversations with people who have recently been on the job market, these types of questions are not specific to Wall Street. Here
is a sample:
- Consider the following game. The player tosses a die once only. The payoff is $1 for each "dot" on the upturned face.
Assuming a fair die, at what level should you set the ticket price for this game?
- Please prove that the following relationship holds:
\[\int_{-\infty}^{+\infty} e^{-x^2} dx = \sqrt{\pi}\]
- You are given eith balls. They appear identical but one is heavier than the rest. How do you find the heavy ball.
Note: A scale can determine which of two items is the heavier but not the weight of a particular item.
- Solve the following differential equation:
\[ u'' + u' + u = 1 \]
- A, B, C, D, E, F, G, H, and I are the nine integers from one to nine (not necessarily in order). They satisfy
the following constraints:
A + B + C + D |
= |
20 |
B + C + D + E + F |
= |
20 |
D + E + F + G + H |
= |
20, and |
F + G + H + I |
= |
20. |
What are the values of each A to I.
- A small boat is floating in a swimming pool. The boat contains a very small by very heavy rock. If the rock is
tossed out of the boat into the pool, what happens to the water level in the pool?
Is this what you expect in your coming job interviews?
For What should you know ..., stay tuned.