The Math Major Vol. 2, No. 7

The Math Major

CSU Fresno Mathematics Department

Vol 2. No. 7

Editor: Dr. Larry Cusick.

Math Department Colloquium Schedule

The Math Department Colloquia are a series of talks intended for a general audience. Everyone is encouraged to attend and the talks are directed at people who have a reasonable comprehension of the topics in undergraduate mathematics. Come meet our undergraduates, graduate students and faculty as well as our distinguished guest speakers. The updated colloquia schedule can be found on the math departments web page. For more information contact Dr. Sean Cleary.

Math Talk at Physics Colloquium

Math department faculty member Dr. Elinore Velasquez will present a talk to the Physics department colloquium on Friday, 12 December at 3:10 p.m. McLane 162. The title of the talk will be "Integrable Models, Theta Functions, and Riemann surfaces". According to Dr. Velasquez: In this talk, I will give a brief introduction to Riemann surfaces and then construct theta functions related to these surfaces. In the latter part of the talk, I shall indicate how the theta functions help describe a set of solutions for a particular type of nonlinear partial differential equation. Time permitting, I will speak about some my investigations in this area.

Students Receive MAA and AWM Memberships

Congratulations to students Matthew Bourez, David Hieb, Clarence Hopper, Lina Obeid, Bryan Sheldon and Elaine Wagner. Each was nominated by the department to receive an honorary membership to the MAA (Mathematical Association of America). Also congratulations to Sandra Atkins, Tina Attashian and Joy Bjerke who were nominated for honorary memberships to the AWM (Association of Women in Mathematics).

Four Brave Math Students Face the Putnam Exam

Anar Ahmedov, Matthew Bourez, David Horn and Bryan Sheldon will participate (along with a couple of thousand other mathies from around the country) in the William Lowell Putnam Mathematical Competition on Saturday December 6. The national winner receives a full paid scholarship to Harvard. The exam lasts from 8 AM to 4PM, with a 2 hour break in the middle, and is very difficult, with typically half of the competitors receiving a zero score. The four will be competing for a $100 first prize and $75 second prize for CSU Fresno participants. We wish our intrepid students well.

Graduate Assistants

Applications for Graduate Assistantships (for Spring semester) are due in the Math department office before the end of this semester.

Grades by Star

Final grades will be available to students via STAR on January 8 from 8:00 am to 8:00 pm.

Web Watch--Knot Plot

The web site of merit today is The Knot Plot Site From the site description: The images here were created with KnotPlot, a fairly elaborate program to visualize and manipulate mathematical knots in three and four dimensions. The knot pictures are varied and fun to look at.

Problem Corner

Problem 2.6: There are several values for a prime, p, with the property that any five digit multiple, m, of p remains a multiple of p under every cyclic permutation of the digits of m. One such value is p = 41 (for example, 50635 is a multiple of 41, so are 55063, 35506, 63550 and [0]6355). Another such value of p is 3. Compute the value of p that is greater than 41.

Solution to Problem 2.6: Let n = 10000a + 1000 b +100 c + 10 d + e be a five digit multiple of p. Then p must also divide n' = eabcd, and (since p is greater than 10) p divides 10 n' = 100000e + 10000 a + 1000 b + 100 c + 10 d = 99999e + n. Thus p divides 99999e, so it must divide 99999 = 32 x 41 x 271. Thus p must be 271.

Correct solutions were received from Anar Ahmedov and John Jamison.

New Problem

Problem 2.7: (Due no later than Thursday December 11, 4pm) Consider the equation

100 ... 00b + 100... 00b+1 = 100... 00b+2,

where each term contains exactly n zeros and each subscript b, b+1, b+2 is the base in which the term is written. For how many values of n, n >=2, will a solution (i.e., a positive integer value of b) exist for the equation?

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.