FULLERTON
COLLEGE
PACIFIC SUMMER UNSOLVED
MATHEMATICS SEMINAR
2010
(Unfunded project that was organized by Dr. Dana Clahane)

PSUMS was initiated by Dr. Clahane
in the Summer of 2010 at Fullerton College as an experiment designed to spark
summer interest in mathematics, student talks, and student papers and to foster
summer mathematical interactions between community college students interested
in unknown mathematics, mathematicians, scientists, graduate students, and other
college/university students on the Pacific Coast. This project was unfunded during Summer 2010.
SCHEDULE
Date

Time

Room

Speaker

Affiliation

Title of Talk

Th 6/17 (6 students and 1 faculty member participated) 
34:30pm 
611C 
Fullerton College 
Completely continuous composition operators 

Th 6/24 (7 students and 3 faculty members participated) 
34:30pm 
611C 
UC Riverside 
The Continuum Hypothesis 

M 6/28 and T 6/29 

611 
Wilson Lee Colleen Nelson (student assistants) Dr. Dana Clahane Dr. Scot Childress 
Fullerton College 
Mathematical mysteries of the universe (Introduction to the American
Math Competitions, the Putnam Competion and
unsolved problems postermaking in mathematics, designed by Dr. Clahane and Dr. Childress for 120 7th to 11th grade high
school students as part of the Project
GPS2 STEM Minicamp Program) Click here to see
pictures (which can be zoomed in
on/enlarged) of the posters created by these
students! 
Th 7/1 (21 students and 2 faculty members participated) 
34:30pm 
611C 
Wilson Lee 
Fullerton College and Cerritos High School Mentor: 
HardyWeinberg Equilibrium Conditions with Fstatistics
and de Finetti's Diagram 
Th 7/8 (15 students and one faculty member participated) 
34:30pm 
611C 
Derek Taylor (accepted “with distinction” in Fall 2010 as a math major at CSU Fullerton) 
Fullerton College Mentor: 
Dimension four 



Fullerton College 
The Hadamard conjecture: Is
there a Hadamard matrix of order 4k for every
positive integer k? 

Th 7/15 (17 students and 1 faculty member participated) 
34:30pm 
611C 
Mustafa Khafateh 
Fullerton College '10 Cal Poly San Luis Obispo Mentor: 
An introduction to the mathematics of computerized
tomography 



Fullerton College 
1. Suppose that d is a
semimetric on a set X with the property that whenever d(x_{n},y_{n}) and d(y_{n},z_{n})
tend to 0 as n tends to ∞, d(x_{n},y_{n})
tends to 0. Does the fact that for
some x in X, d(x_{n},x) tends to 0 as n
tends to ∞,
imply that d(x_{n},y)
tends to d(x,y) for all y in X? 2. Can we answer this
question even with the additional assumption that whenever for some x in X,
d(x_{n},x) and d(y_{n},x)
tend to 0 as n tends to ∞, we have that d(x_{n},y_{n})
tends to 0 as n tends to ∞ ? For a recent paper by Arendelovic and Petrovic on
this subject, click here 

Th 7/22 (26 students and 2 faculty members participated) 
34:30pm 
611C 
Matthew Maldonado (now a statistics/math major at UC Riverside) 
Fullerton College '10 Mentor: 
The problem of finding the smallest knots that can be surjectively colored by the quandles
induced by nth roots of unity for various n's 
Th 7/29 (14 students and 2 faculty members participated, school not in session) 
34:30pm 
611C 
UC Irvine 
The
Riemann Hypothesis and the Prime Number Theorem (click on the title above to download/view a .pdf file containing Dr. Russo’s lecture notes
[approximately 8MB]) Click here
for more details from Dr. Russo’s 2005 Freshman Seminar on this subject) 

Th 8/5 (8 students and 2 faculty members participated, school not in session) 
34:30pm 
611C 
Fullerton College 
If 1) a subset W of
ndimensional complex space is an increasing union of compact polynomially convex sets, and 2) p(W) is an
open set in the complex plane for every polynomial p in n complex variables, then is W open? 

Th 8/12 (10 students, 2 Math faculty members, 1 Chemistry faculty member, and 2 Special Programs Office staff members participated) (school not in session) 
33:30pm 
611C 
David Salazar 
National Community College Aerospace Scholars & Fullerton College Mentor: 
The mathematics of planning missions to Mars, part I 

3:454:30pm 
611C 
Fullerton College 
Solution to a recent College Mathematics Journal Problem:
Prove that for every positive integer n that is at least 3, there are n
distinct positive integers such that each of these integers divides the sum
of the others. 
BACK TO THE FC MATH
EVENTS WEBPAGE
There is risk, but there is also reward.
This webpage was established in June 2010 Webpage visual design by: Ivan Luna (student) and Dr. Dana Clahane Project GPS2 Poster photos by Anne Wolfe, Project GPS2
Staff member Webpage conceptual design, content, and page maintenance
by: (all rights/copyrights reserved) MATHEMATICS & COMPUTER SCIENCE DIVISION FULLERTON COLLEGE 321 E. Chapman Ave. Fullerton, CA 92832 7149927041
