The Math Major Vol. 2, No. 7
The Math Major
CSU Fresno Mathematics Department
Vol 2. No. 7
Editor: Dr. Larry Cusick.
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.
- Date:
Thursday, December 4th
- Speaker: Dr. Steve Chiappari, Santa Clara University Department of Mathematics
- Title: "Dividing Polygons by Lines"
- Time: 3:10-4pm
- Location: San Ramon 6, Room 6
- Abstract: Given a polygon, one may divide its interior into subregions
by line segments emanating from vertices and passing through a point
interior to a side. In this talk we discuss two related problems
concerning the maximal number of such subregions possible under
various conditions. In each case we produce a polygon with the
maximal number of subregions.
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.