The Math Major Vol. 2, No. 10

The Math Major

CSU Fresno Mathematics Department

Vol 2. No. 10

Math Club Film Series

The Math Club sponsors a video film showing every other tuesday. Everyone is cordially invited to attend.

Date: Tuesday, March 10, 5 pm
Film: "The Man Who Loved Numbers"
Location: PB 428
Description:

Sirivasa Ramanujan (1887-1920) was one of India's greatest mathematical geniuses. Even though he was self taught in higher mathematics, he made significant contributions to the theory of numbers, elliptic functions, continued fractions, and infinite series.

Math Field Day Coming

(From Dr. Della Duncan) Looking forward to Spring? Remember that the Annual Math Field Day will once again be held during Vintage Days at CSU-Fresno. On Sat. April 18th high schools throughout the valley will send more that 200 students to participate in this traditional event.

This year students will have the opportunity to compete in three different contests. Two problem solving events allow students to compete as individuals or as pairs. There is also a team event which includes a presentation on this year's topic "Public Key Cryptography".

A highlight for this year is the agreement with Wolfram Research to provide their Math Mobile at this event. They will be offering demonstrations of the latest version of Mathematica.

We will be needing volunteers to help with this project. If you are interested please contact Della Duncan 278-4999 or email.

The Graduate Program at CSUF

(From Dr. Hugo Sun) The math department offers a Master of Arts degree in Mathematics. The Master's degree program is for those students who wish to continue their study of mathematics beyound the undergraduate program. Why should you pursue a Master's degree?

It is fun. The modern attitude is "If it's not fun, why do it?" There is a world of knowledge for everybody with curiosity.
To confirm that the mathematics you learned as an undergraduate is sound. We learn elementary algebra and geometry in a calculus class, and we learn calculus in a real or complex analysis class, etc. So if we don't take a graduate level class, how do we learn abstract and linear algebra or real and complex ananlysis?
To prepare for a career. Most people with graduate training are better equipped for a career or equipped for a better career.
To advance in the present position. Most of our graduate students have a full or part-time job. By going through graduate study, they either find a better position or have their salary increased.

For more information on our graduate program, contact the math graduate program advisor Dr. Hugo Sun (Ed.).

Problem Corner

Problem 2.9: The ancient Babylonians used the formula K = (a+c)(b+d)/4 for the area enclosed by a quadrilateral with consecutive side lengths a, b, c, d. Prove that the formula is valid only if the quadrilateral is a rectangle.

Solution to Problem 2.9: (Solution by John Jamison)

Areas are as follows:

C = (1/2) cd sin Z

A = (1/2) ab sin X

B = (1/2) bc sin Y

D = (1/2) ad sin W

So the area of the quadrilateral would be

T = (A+B+C+D)/2

= (ab sin X + bc sin Y + cd sin Z + ad sin W)/4

< (ab + bc + cd + ad)/4

= ((a+c)(b+d))/4,

if any of X, Y, Z, W are less than 90 degrees. Since any non-convex quadrilateral can be replaced by a convex quadrilateral (with larger area) with the same side lengths, the proof is complete.

John Jamison submitted the only correct solution.

New Problem

Problem 2.10: (Due Thursday March 12 by 4 pm) We can write 1 = 1/2 + 1/3 + 1/6. Write 2 as the sum of no more than twelve distinct (no two the same) fractions in the form 1/N where N can be any whole number larger than 1 but less than 30.

Solutions may be delivered to the math department office (for Dr. Cusick) or by e-mail at larryc@csufresno.edu. 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.