The Math Major

CSU Fresno Mathematics Department

September 16, 1996

Vol 1. No. 2

Editor: Dr. Larry Cusick

The Single Subject Credential Program

(From Dr. Tuska) In 1992, the Commission on Teacher Credentialing for the state of California put into place new standards for subject matter preparation programs. The CSU Fresno math department's program was approved in the summer of 1996.

How does this effect a math major? If you are seeking a single subject credential in mathematics (for California) you must demonstrate your competency in one of two ways: (1) complete the requirements of an approved subject matter preparation program (like ours) or (2) pass the mathematics parts of the PRAXIS exam.

The current mathematics courses in our subject matter preparation program are:

and also The above program is nearly identical with the current math major requirements. The credential program requires one more math course than the major. Students already in the program can finish it under the ``old" requirements they were admitted under. However, beginning January 1 of 1998 only students satisfying the currently approved program requirements can get admitted to the credential program. The credential program has its own admission procedure--see pages 258-261 in the current catalog. If you plan to be a mathematics teacher, or you have any question about the credential program, see one of the two credential advisors Dr. Tuska (PB 351) or Dr. Woo (PB 355).

Math Club

Math major Tina Attashian is interested working with other math majors to form a math club. She can be contacted via e-mail at ta100@csufresno.edu. (Or you might see her in PB428.) To get an idea of what other math clubs are up to, visit some web pages--like Cal Poly SLO or CSU Northridge.

Actuary Exam

If you are interested in taking the Actuary Exam, please be aware that the registration deadline for the November exam is September 20. Contact Dr. Helmers (PB 353) for more information.

Web Watch--Big Primes

Prime numbers are both simple and complicated. Euclid proved there were an infinite number of primes, while Eratosthenes gave an algorithm (the sieve of Eratosthenes) for enumerating them. Modern mathematicians compete to find the largest known prime. The latest record is 2^(1257787) - 1, a 378, 632 digit number, which was announced at the beginning of this month by David Slowinsky and Paul Gage (both at Cray Research). Are there an infinite number of twin primes? No one knows. (Twin primes are pairs of primes that differ by 2.) All of this, and more, can be found at Chris Caldwell's Largest Known Primes Page at http://www.utm.edu/research/primes/largest.html. Check it out.

Fresno Problem Solving Group?

Only one student has contacted me about a problem solving group for this semester. Last year we had seven participating students in the group. As a math major you face difficult math problems almost every day--and perhaps you feel that you have no more time to spend on extra problems. But, time spent on solving problems is not a waste. The best way to sharpen your problem solving skills is to work on problems. If interested contact Dr. Cusick (PB 358 or email at larry_cusick@csufresno.edu.

Math Joke (A Moldy Oldie)

An engineer, a physicist and a mathematician were enjoying the pastoral view of a field full of black cows. The engineer said, "There seem to be only black cows in this pasture." The physicist replied, "Well, actually only the cows we have seen are black." Whereupon the mathematician thoughtfully said , "To be correct, we can only say that the cows we have seen appear to be black on one side."

Problem Corner

Problem 1.1: A ten story building is being refurbished. All ten floors need to be painted. There are two possible colors, white and blue. Each floor is to be painted one color, but no two blue floors can be on top of one another. In how many ways can this be done?

Solution to Problem 1.1: It is easier if we generalize the problem to n floors. Let p9n) be the number of ways to paint the building. Then p(n) = w(n) + b(n) where b(n) is the number of ways to paint the building with a blue top floor and w(n) is the number of ways wih a white top floor. Now, it should be clear that w(n) = p(n-1) (since if the top floor is white, w(n) counts the number of ways to paint all but the top floor) and b(n) = p(n-2) (since, if the top floor is blue, the next to top must be white, and the remaining can be painted p(n-2) ways. This gives us the Fibonacci recurrence relation p(n) = p(n-1) + p(n-2). Clearly p(1) = 2 and p(2) = 3, which gives us p(10) = 144.

Correct solutions were received from Sherry Lutes (and son), Patrick Villa and David Yoshihara.

New Problem

Problem 1.2: Is there a set S of positive integers such that a number is in S if and only if it is a sum of two distinct members of S or a sum of two distinct positive integers not in S

Solutions may be delivered to the math department office (for Dr. Cusick) or by e-mail at larry_cusick@csufresno.edu. no later than Thursday September 26, 4pm. There is a $75 dollar first prize and a $50 second prize to be awarded at the end of the semester to the student(s) who submit the most correct solutions.

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