The Math Major

CSU Fresno Mathematics Department

Vol 1. No. 13 (Last Issue for Spring Semester)

Math Department Colloquium Schedule

This colloquium was originally scheduled for March 17, but was postponed.

Date & Time: March 17, 4:10-5pm
Speaker: Dr. Joel Hass, UC Davis
Title of Talk: Double Bubbles Minimize
Location: S 145
Abstract: Dr. Hass will be speaking about the mathematical models of soap films and bubbles, which are modeled by minimal surfaces and constant mean curvature surfaces respectively. Dr. Hass, with his collaborator Roger Schlafly, proved last year the "Double Bubble Conjecture" which answered a question that had been first asked 2000 years ago and had been studied by many great mathematicians throughout history. He will be speaking about some of the innovative techniques used in this important work and will have some computer graphics as well as soap bubbles to illustrate the ideas.

Sixteenth CSU, Fresno Math Field Day: A Success

On Saturday April 19, the CSUF math department hosted the Math Field Day for high schools. There were 11 high schools represented by approximately 200 students. Students competed in mathematical competitions that required problem solving skills to tackle difficult math problems. Edison high school received the top award. Second place was Dinuba high school. The department would like to thank the CSU Fresno student volunteers and the staff of the math department office who helped make the event possible.

Education Loans

(From Dr. Tuska) Applications for the Assumption Program of Loans for Education (APLE) are currently available in Room 100 of the Education Building. If selected for this program, students will have up to $8,000 in student loans repaid by the California Student Aid Commission. These applications must be returned to Room 100 no later than Friday, May 2, 1997 by 5:00p.m. Contact the School of Education for more information and the minimum requirements.

Web Watch--The MAA Student's Page

The Mathematical Association of America (MAA) sponsors a Student's Web Page. A few things you will see there are:

Links to other university student math clubs,
career profiles of working mathematicians,
links to other sites that would be of interest to math students and
some job related links such as Teach for America, Employment Resources Guide, the Online Career Center and Job Hunt.

Problem Corner

Problem 1.12: Draw a planar grid that is 31 squares wide and 17 squares high. How many non-trivial rectangles can be drawn, using the lines of the grid to determine the boundaries? (Here ``non-trivial" means that the rectangle has positive width and positive height.)

Solution to Problem 1.12: Label the rows and columns (j, k). Consider the rectangles with lower left hand corner at (j, k). There are (31 - j) possible widths and (17-k) possible heights. Thus, all together there are (31 - j)\times(17-k) rectangles with lower left hand corner at (j, k). Thus, the total number of rectangles S = \sum_{j=0}^{30}\sum_{k=0}^{16} (31 - j)(17-k). Expand, regroup and use the standard formulas for linear and quadratic sums to get S = 75888.

The only correct solution received was from Anar Ahmedov. There were two incorrect solutions received.

New Problem

Problem 1.13: Prove that every integer can be written in the form x^2 + y^2 - 5 z^2 where x, y and z are integers.

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 Thursday May 1, 3pm. 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.

CSU Fresno Math Department Home Page

California State University, Fresno