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)

3-4:30pm

611C

Dr. Dana Clahane*

 Fullerton College

Completely continuous composition operators

Th 6/24

 

(7 students and 3 faculty members participated)

3-4:30pm

611C

Dr. Scot Childress

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 poster-making 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 Mini-camp 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)

3-4:30pm

611C

Wilson Lee

Fullerton College and Cerritos High School

 

Mentor:

Dr. Dana Clahane

Hardy-Weinberg Equilibrium Conditions with F-statistics and de Finetti's Diagram

Th 7/8

 

(15 students and one faculty member participated)

3-4:30pm

611C

Derek Taylor

 

(accepted “with distinction” in Fall 2010 as a math major at CSU Fullerton)

Fullerton College

 

Mentor:

Dr. Dana Clahane

Dimension four

 

 

 

Dr. Dana Clahane*

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)

3-4:30pm

611C

Mustafa Khafateh

Fullerton College '10

 

Cal Poly San Luis Obispo

 

Mentor:

Dr. Dana Clahane

An introduction to the mathematics of computerized tomography

 

 

 

Dr. Dana Clahane*

Fullerton College

1. Suppose that d is a semi-metric on a set X with the property that whenever d(xn,yn) and d(yn,zn) tend to 0 as n tends to ∞, d(xn,yn) tends to 0.  Does the fact that for some x in X, d(xn,x) tends to 0 as n tends to , imply that  d(xn,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(xn,x) and d(yn,x) tend to 0 as n tends to ∞, we have that d(xn,yn) 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)

3-4:30pm

611C

Matthew Maldonado

 

(now a statistics/math major at UC Riverside)

Fullerton College '10

 

Mentor:

Dr. Dana Clahane

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)

3-4:30pm

611C

Dr. Bernard Russo

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)

3-4:30pm

611C

Dr. Dana Clahane*

Fullerton College

If

 

1)    a subset W of n-dimensional 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)

3-3:30pm

611C

David Salazar

National Community College Aerospace Scholars

&

Fullerton College

 

Mentor:

Dr. Dana Clahane

The mathematics of planning missions to Mars, part I

 

3:45-4:30pm

611C

Dr. Bill Cowieson

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:

Dr. Dana Clahane

(all rights/copyrights reserved)

 

MATHEMATICS & COMPUTER SCIENCE DIVISION

FULLERTON COLLEGE

321 E. Chapman Ave. Fullerton, CA 92832

714-992-7041