Math Occupations

I copied this from the University of Northern British Columbia website. I'm claiming ignorance as to copy write laws, but I'm giving them credit, so i think I'm fine. This seems like a good list. I edited this down just a bit. The full page is at http://www.unbc.ca/math-statistics/careers-mathematics

Careers with a Mathematics Degree

Aside from being useful to becoming a High School teacher, a degree in Mathematics is quite useful in the following job areas (where people with a Mathematics degree have been hired).

1. It prepares you for an MBA (Masters of Business Administration) degree and become, for example, an Accounting Manager or a Certified Public Accountant.
2. Can work as a computer scientist at the National Institute of Standards and Technology.
3. Can work as a mathematician in places like Rockwell International Corporation.
4. With a degree in mathematics you can go to Law School.
5. Can work as a project manager in a company like Hewlett-Packard.
6. You can go on to an engineering school and become an industrial engineer or work in companies like Westinghouse Wireless Solutions.
7. Informations Systems Consultant.
8. Manager at a place like Advanced Research Computing Services.
9. Can work as an actuary for a life insurance company.
10. Senior software engineer (e.g. at Harris Scientific Calculations).
11. With a MSc in Mathematics one can work as an aerospace mathematician in space centers like the NASA Goddard Space Flight Center.
12. Can be a mathematics editor for a publisher (e.g. Simon & Schuster, Inc.).
13. A computer systems specialist for a chemical company.
14. A professional relations representative for a health care company.
15. Educational markets manager for companies like Texas Instruments.
16. Operations research analyst (e.g. for FedEx or any courier company).
17. Director for inventory control.
18. Can work in companies like Exxon Production as a research specialist.
19. A statistician at a health research laboratory.
20. Can work at a Boeing company as instructor and/or consultant on quality control.
21. An environmental mathematician for an engineering company.
22. With a double major with economics you can become an economist for an oceanographic company.
23. Some national laboratories hire mathematicians to analyze problems numerically (Numerical analysis).
24. A statistician in a census bureau.
25. Telephone companies are known to hire mathematicians, even ones with only a BSc degree.
26. Financial analyst.

Rating Baseball Players

I stumbled onto something called Elo Rater. It is a way of rating former or current baseball players if they were to face off in a head to head match up. It was developed by Arpad Elo. He was born in what was at that time Austria-Hungary in 1903 and passed away in 1992. Arpad was a physics professor at Marquette University and was an avid chess player. He developed his rating system originally to rank chess players.

Frankly, I don't completely understand every bit of this. There are original point values for the players. I'm not sure how those are determined. And I don't know who decides how it is determined that one player goes against another. It looks like maybe people can go to the website and pick a couple players and they play each other. Since he was a college professor, I'm going to assume he knew what he was doing. Also his ratings seem pretty accurate. His top five hitters of all time are:

1. Babe Ruth
2. Stan Musial
3. Ty Cobb
4. Lou Gehrig
5. Mike Schmidt

You can check out his full lists at http://www.baseball-reference.com/friv/elo.cgi

Here is an example used on the site.

RA is the rating for Player A and RB is the rating for Player B. Working out the probability that Player B wins where RA =  2450 and RB = 2500:

P(B wins) = 1 / (1 + 10^((RA - RB) / 400)) 

= 1 / (1 + 10^((-50) / 400)) 

= 1 / (1 + 10^(-0.125)) = 

= 0.571

To analyse how these come out means looking at fraction exponents and negative exponents. You can find the details of the process at http://www.baseball-reference.com/about/elo.shtml

Hawking's Imaginaries

Stephen Hawking wrote the bestselling book, "A Brief history of Time. In it he spoke of how imaginary numbers are used in relativity theory. It's not totally satisfying as a high school mathematics application. To do it justice mathematically would probably make it incomprehensible. And to tone it down is to miss the application.

Since there aren't a lot of imaginary number applications to share in a high school class, I thought I might quote from the book. At least students can see that there is a reason for their existence.

"We don't yet have a complete and consistent theory that combines quantum mechanics and gravity. However, we are fairly certain of some features that such a unified theory should have. One is that it should incorporate [physicist Richard] Feynman's proposal to formulate quantum theory in terms of a sum over histories. In this approach, a particle does not have just a single history, as it would in a classical theory. Instead, it is supposed to follow every possible path in space-time, and with each of these histories there are associated a couple of numbers, one representing the size of a wave and the other representing its position in the cycle (its phase). The probability that the particle, say passes through some particular point is found by adding up the waves associated with every possible history that passes through that point. When one actually tries to perform these sums, however, one runs into severe technical problems. The only way around these is the following peculiar prescription: one must add the waves for particle histories that are not in the"real" time that you and I experience but take place in what is called imaginary time... (For those that don't know there is an interlude of a brief and undoubtedly insufficient explanation of what imaginary numbers are) ... To avoid Feynman's sum over histories, one must use imaginary time. That is to say, for the purposes of the calculation one must measure time using imaginary numbers, rather than real one. This has an interesting effect on space-time: the distinction between time and space disappears completely. A space-time in which events have imaginary values of the time coordinate is said to be Euclidean...In Euclidean space-time there is no difference between the time direction and directions in space. On the other hand, in real space-time, in which events are labeled by ordinary, real values of the time coordinate, it is easy to tell the difference - the time direction at all points lies within the light cone, and space directions lie outside. In any case, as far as every day quantum mechanics is concerned, we may regard our use of imaginary time and Euclidean space-time as merely a mathematical device (or trick) to calculate answers about real space-time."