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W00T! I just won a $25 000 scholarship! (pg. 5)
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| DJ_Elyot |
First of all, thank you to everyone for all of your wonderful comments.
I wrote day 2 of the USAMO today... I totally owned it, got all 3 problems, and I'm so happy.
I'd love to come to the vault tomorrow to celebrate, but all my math studying has left me with a bunch of due dates that are all piling up... I'll likely be up until 4am tomorrow writing an essay for English. BAH!
I don't intend to pursue pure math though. I want to do computer science and applied math or combinatorics and optimization or something. Just pure math would be a little bit boring.
With respect to the whole actuarial sciences thing, I really have some issues with insurance companies... how they market themselves, how they end up controlling the policies of public institutions, etc. I really just couldn't see myself working in statistics or working for an insurance company. I also do have a lot of other examples where corporate externalities to minimize costs have hurt a lot of people. I've done some research. I'm sure there are some good jobs out there in Actuarial Sciences, but the number of bad things I've heard is enough to deter me. You should read "The Corporation" by Joel Bacon, which is a very enlightening, quick, and fairly unbiased way of examining the impacts of publicly traded corporations on the economical and social world.
Thanks for your advice though... I hope my comments didn't offend you too much. It's never the individuals; it's just the institution. I don't like the way it works, so I don't want to be a part of it. That doesn't mean that I've got anything against those who are. Kudos to you for making it through all the exams and stuff too. I know it's not easy.
I didn't know the example I used was from Fight Club though... never seen that movie.
I've always found financial math pretty boring, and in all honesty, I'm likely going to end up doing research/professorship/etc for the rest of my life. With a good CS background, there will be some programming/development jobs available too. For example, last summer I programmed at Maplesoft, a company that creates mathematical software. Most of the people there had PhDs in mathematics or CS, many of them in pure math. I've done my research and there will be good jobs out there.
To the mathematically-inclined TAs... got any favourite problems?
Thanks for the comments! |
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| Durafei |
| quote: | | To the mathematically-inclined TAs... got any favourite problems? |
A few nice problems(all three problems are from job interviews).
1) How can three people find out their average salary if they don't want to disclose their salary to each other.
2) How can two people find out if they earn the same salary(salary is an integer number) if they don't want to disclose their salary to each other. Note. I'm actually not too sure whether the salary has to be an integer. The solution that I have requires that condition. There might be a better solution that relaxes this requirement.
3) A submarine is travelling along an infinite integer line at a constant speed(ie. locations: 5, 7, 9, 11 etc) At any time unit, you can "ping" a number on that line to check whether the submarine is at that point. If it is, you caught the submarine. If it's not, you can ping another number(or same number if you wish) at the next time unit. Is there a strategy such that you will eventually catch the submarine ? |
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| girllovingtvibe |
| huge congrats :) |
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| JRinger |
| quote: | Originally posted by DJ_Elyot
With respect to the whole actuarial sciences thing, I really have some issues with insurance companies... how they market themselves, how they end up controlling the policies of public institutions, etc. I really just couldn't see myself working in statistics or working for an insurance company. I also do have a lot of other examples where corporate externalities to minimize costs have hurt a lot of people. I've done some research. I'm sure there are some good jobs out there in Actuarial Sciences, but the number of bad things I've heard is enough to deter me. You should read "The Corporation" by Joel Bacon, which is a very enlightening, quick, and fairly unbiased way of examining the impacts of publicly traded corporations on the economical and social world.
Thanks for your advice though... I hope my comments didn't offend you too much. It's never the individuals; it's just the institution. I don't like the way it works, so I don't want to be a part of it. That doesn't mean that I've got anything against those who are. Kudos to you for making it through all the exams and stuff too. I know it's not easy. |
I still think you're uninformed about the profession (which sure isn't unusual - most of my friends and family have no clue what it is I do all day). You're discounting a career in actuarial science b/c you have an issue with insurance companies? Insurance companies are not the only employer of actuaries. The market for consulting actuaries (which is what I do) is almost as large as the one for insurance actuaries (at least in North America). There are also plenty of actuaries working in the reinsurance sector (which isn't the same as working for an insurance company), working in the investment sector, working for the government, and working in-house at large corporate entities or for public-sector agencies (e.g., HOOPP, OMERS, OTPP, etc.)
You're also equating some issues you have with institutions and corporations with the work of actuaries, which as someone in the profession, I take big issue with. I really think you're uninformed on this matter.
I'm not trying to "sell" the profession by any means. But I am trying to clear up some glaring misconceptions you seem to have about it. |
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| DJ_Elyot |
| quote: | Originally posted by JRinger
I still think you're uninformed about the profession (which sure isn't unusual - most of my friends and family have no clue what it is I do all day). You're discounting a career in actuarial science b/c you have an issue with insurance companies? Insurance companies are not the only employer of actuaries. The market for consulting actuaries (which is what I do) is almost as large as the one for insurance actuaries (at least in North America). There are also plenty of actuaries working in the reinsurance sector (which isn't the same as working for an insurance company), working in the investment sector, working for the government, and working in-house at large corporate entities or for public-sector agencies (e.g., HOOPP, OMERS, OTPP, etc.)
You're also equating some issues you have with institutions and corporations with the work of actuaries, which as someone in the profession, I take big issue with. I really think you're uninformed on this matter.
I'm not trying to "sell" the profession by any means. But I am trying to clear up some glaring misconceptions you seem to have about it. |
I'm not necessarily equating the institutions with the individuals... I just don't want to springboard myself into a career where most of the time I'll be working with business people, and for corporations.
Many years ago I decided not to ever go into business or politics because of the amount of problems there, and working in reinsurance, financing, or investing just fuels the fire IMO. I'm quite content on doing research and/or teaching. |
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| DJ_Elyot |
| quote: | Originally posted by jenna_rae
btw isn't The Corporation a documentary too? |
I think so... |
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| trancechaos |
| congrats man, after some of that confusing you said in the why why why??? thread you really deserve it. respect for having such a high love for mathematics. scholarships are sooo key to have, i dont know where i would be today without mine. |
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| DJ_Elyot |
| quote: | Originally posted by Durafei
A few nice problems(all three problems are from job interviews).
1) How can three people find out their average salary if they don't want to disclose their salary to each other.
2) How can two people find out if they earn the same salary(salary is an integer number) if they don't want to disclose their salary to each other. Note. I'm actually not too sure whether the salary has to be an integer. The solution that I have requires that condition. There might be a better solution that relaxes this requirement.
3) A submarine is travelling along an infinite integer line at a constant speed(ie. locations: 5, 7, 9, 11 etc) At any time unit, you can "ping" a number on that line to check whether the submarine is at that point. If it is, you caught the submarine. If it's not, you can ping another number(or same number if you wish) at the next time unit. Is there a strategy such that you will eventually catch the submarine ? |
Solutions to problems here! Do not read unless you want to!
3) I'll start with this one cuz I really like it. This actually took me a few minutes until I realized what it was...
Let an ordered pair (a,b) represent the submarine's start location and speed. The cardinality of the set of all possible (a,b) is the same as the cardinality of the rational numbers a/b, where a and b are integers, b not zero. Since the cardinality of the rational numbers is aleph zero (ie is countably infinite), then you can eventually catch the sub if you try locations corresponding to teach and every possible a&b. Therefore, a strategy exists.
If you want me to also find a strategy as well as prove that one exists, then you can do the following: to try to see if a given (a,b) is correct, you would want to ping a+(t*b), where t is the time unit. You would start with (a,b) = (0,1) then (0,-1) (ie all combinations such that abs(a) + abs(b) = 1), then try the next set of combinations where abs(a) + abs(b) = 2, which means to try (0,2),(1,1),(-1,1),(0,-2),(-1,-1),(1,-1), etc. This is the same as the method by which you count integer points on a cartesian plane, except we're not going to count points on the x-axis, since I think we can assume speed is non-zero (it's not like it would be difficult to modify the method if speed could be zero anyway...)
2)One reveals the even digits of his salary to the other, and one reveals the odd digits of his salary to the other. If they both match, then both salaries are equal, but neither man will know the other's salary. I don't see why this wouldn't work for rational salaries too, if each wrote their salary in reduced form and the same thing was done for both the numerator and denominator. I don't know about irrational though... that could get tricky. Then again, who the hell makes an irrational salary?
1)Here's my solution:
lets call the 3 people Alphonse, Beryl, and Colleen, with salaries A, B, and C.
They each express their salaries as a sum (or difference) of 2 numbers... ie they find a1,a2,b1,b2,c1,c2 such that A = a1+a2, B=b1+b2, and C=c1+c2.
Then A gives a1 to B and a2 to C. B gives b1 to A and b2 to C. C give c1 to A and c2 to B.
Then each person adds up the two numbers they've been given (ie A calculates t1, where t1=c1+b1; B calculates t2, where t2=a1+c2; and C calculates t3, where t3=a2+b2).
After that, they all present their respective totals to the group and add them up, giving the grand total T.
Since T=t1+t2+t3, we have T=a1+a2+b1+b2+c1+c2.
Thus T=A+B+C.
Then you simply divide T by 3 to find their average salary. |
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| zoogla |
| My God I have a headache and I'm going to bed...please no alternative solutions!! LOL!!! |
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| DJ_Elyot |
Here's a really simple but neat math problem...
A square is inscribed in a circle. Another square is inscribed in a semicircle of the same radius as the circle. What is the ratio of the areas of the two squares? |
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| 404 Science |
| you're a smart guy Elyot:cool: |
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| Shaya007 |
Congrats.. I think this is the car you were reffering to;
Fiero... |
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