FULLERTON COLLEGE

Math Colloquium and Association Calendar

Fall 2010 (ad hoc, unfunded)

Archived calendar of events, including abstracts and presentations

 

Co-organizers:

Dr. Dana Clahane and Dr. Bill Cowieson

**

 

Date

Time

Room

Speaker

Institutional Affiliation

Title of Talk

(Abstracts, flyers, and power point presentations available for some talks)

T 8/17

 

(27 students and 2 faculty members participated)

4:15-5:30pm

3010

Dr. Dana Clahane*

Fullerton College

Are there infinitely many prime quadruplets?

 

 

 

 

 

Organizational meeting - students who would like to get experience giving a colloquium talk or mini-talk are encouraged to attend this meeting, but even if you miss this meeting, don't hesitate to ask Dr. Clahane or Dr. Cowieson to schedule you as a speaker on any topic that these two faculty members are scheduled to talk on (see below).

T 8/24

 

(24 students and 5 faculty members participated)

4:15-5:30pm

3010

Dr. Bill Cowieson*

Fullerton College

The Polignac Conjecture and a more general conjecture of Hardy-Littlewood on the asymptotic behavior of the number of prime gaps of fixed size n, prior to x, as x goes to infinity

 

 

 

Wilson Lee

Fullerton College and Cerritos High School

A solution to Problem 929, College Math Journal

 

 

 

 

 

Organizational items - students who would like to volunteer to give a talk sometime this year are encouraged to attend this meeting, although it is not required for voluntering later.

T 8/31

 

36 students and 9 faculty participated

4:15-5:30pm

3010

Dr. Sam Nelson

Claremont-McKenna College

The algebra of knots

 

Abstract here

Flier here

Click here to view a power point/beamer presentation of Dr. Nelson's fantastic talk

T 9/7

 

24 students and 2 faculty members participated

4:15-5:30pm

3010

Dr. Dana Clahane*

Fullerton College

Fortune's conjecture

 

 

 

Wilson Lee

Fullerton College

(one of Dr. Clahane's Math 299 students)

and

Cerritos High School

The question of whether or not the sum, difference, product or exponentiation of π and e are irrational; proofs of the irrationality of π and e

 

Abstract here

W 9/8

4:15-5:30pm

The Claremont Center for the  Mathematical Sciences Colloqium

 

On the north side of 6th St. just east of College Ave. in Claremont, zip code 91711

 

Millikan 134

Pomona College

 

Refreshments served

3:45-4:15pm, Millikan 209

Dr. Dana

Clahane

Fullerton College

An introduction to problems in bicomplex analysis

 

Flier here

F 9/10

 

23 students and 3 faculty members participated

11am-2pm

615

Dr. Dana Clahane

 

Dr. Bill Cowieson

 

Paul Sjoberg

 

(Coaches)

Fullerton College

AMATYC Student Math League Practice Session #1

T 9/14

 

38 students and 6 faculty members participated

4:15-5:30pm

3010

Dr. Bernard Russo

UC Irvine

The Riemann Hypothesis and the Prime Obsession

 

Click on the title above to view a (2MB) .pdf file of Professor Russo’s lecture slides for this talk

 

Abstract here

 

(Click here to see Dr. Russo’s Summer entertainment 2010 PSUMS lecture notes on the relationship between the Prime Number Theorem and the Riemann Hypothesis)

F 9/17

 

(approximately 15 students participated)

11am-2pm

615

Dr. Dana Clahane

 

Dr. Bill Cowieson

 

Paul Sjoberg

 

(Coaches)

Fullerton College

AMATYC Student Math League Practice Session #2

T 9/21

 

(21 students and 2 faculty members participated)

4:15-5:30pm

3010

Nicole Gillum

Fullerton College

 

(one of Dr. Clahane's Math 299 students)

Is every Mersenne number square free?

 

To view a pretty poster that Ms. Gillum made regarding this problem, click here

 

To view Ms. Gillum's great power point presentation given during part of her talk, click here.

 

 

 

Dr. Bill Cowieson

Fullerton College

A solution to Problem 930, College Math Journal

 

 

 

Dr. Dana Clahane*

Fullerton College

If S is a subset of points in the plane, not including the origin, on the right side of the graph of a parabola, such that the distance between any two points in S is rational, how large can S be?

F 9/24

 

(8 students and 2 faculty members participated)

11am-2pm

615

Dr. Dana Clahane

 

Dr. Bill Cowieson

 

(Coaches)

Fullerton College

AMATYC Student Math League Practice Session #3

M 9/27

 

(Special colloquium)

 

(21 students and 4 faculty members participated)

4:15-5:30pm

229 (College Center)

 

NOTE THE DIFFERENT LOCATION THAN OUR USUAL

John Huerta

UC Riverside

The quaternions

 

Click on the title above for a slide presentation of Mr. (soon to be Dr.) Huerta’s excellent talk

 

Click here for an abstract

T 9/28

 

(15 students and 2 faculty members participated)

4:15-5:30pm

3010

Dr. Bill Cowieson*

Fullerton College

The Cullen prime conjecture

 

 

 

Wilson Lee

Fullerton College

(one of Dr. Clahane's Math 299 students)

and

Cerritos High School

Continued fractions, simple continued fractions, and their computations

 

Abstract here

F 10/1

 

(THIS PRACTICE SESSION WAS CANCELLED DUE TO A CAMPUS CLOSURE - LIGHTNING STORM/POWER OUTAGE)

11am-2pm

615

Dr. Dana Clahane

 

Dr. Bill Cowieson

 

Paul Sjoberg

 

(Coaches)

Fullerton College

AMATYC Student Math League Practice Session #4

S 10/2

9am-noon

Exhibit Hall B

Anaheim Convention Center

800 West Katella Avenue

Anaheim, CA 92802

parking: $12

-

-

SACNAS Community Day

T 10/5

 

(16 students and 2 faculty members participated)

4:15-5:30pm

3010

Wilson Lee

Fullerton College

(one of Dr. Clahane's Math 299 students)

and

Cerritos High School

Products and sums of simple continued fractions

 

Abstract here

 

 

 

Dr. Dana Clahane*

Fullerton College

Gilbreath’s conjecture

F 10/8

 

(14 students participated)

11am-2pm

615

Dr. Dana Clahane

 

Dr. Bill Cowieson

 

Paul Sjoberg

 

(Coaches)

Fullerton College

AMATYC Student Math League Practice Session #5

T 10/12

 

(16 students and 2 faculty members participated)

4:15-5:30pm

3010

Dr. Bill Cowieson*

Fullerton College

The abc conjecture

 

 

 

Dr. Dana Clahane*

Fullerton College

Terminology pre-lecture in preparation for Dr. Kakihara’s 10/19 Colloquium:

 

We will attempt to clearly define as many of the following terms as possible, to give participants a boost in understanding Dr. Kakihara's lecture next week (all of these terms are crucial in graduate school, it turns out, so students will benefit by seeing these things - no previous knowledge will be assumed other than knowledge of what a function is - see wikipedia, for example, for anything below that we don't get to:

1. sigma-algebras (also called sigma-fields), and generated sigma-fields, as well as tensor product sigma-fields

2. measurable spaces

3. measures and measure spaces

4. probability measures

5. measurable transformations and measurable, real-valued functions

6. indicator (characteristic functions)

7. simple functions

8. suprema

8. integration with respect to a measure on the line

9. Linear spaces and norms

10. Cauchy sequences

11. Complete normed spaces

12. Bounded functions and continuous ones

13. The supremum norm on such functions over a closed finite real interval

14. Convex subsets of a set of measures and extreme points of these sets

15. absolute continuity of a measure with respect to another

F 10/15

 

(10 students participated)

11am-2pm

615

Dr. Dana Clahane

 

Dr. Bill Cowieson

 

Paul Sjoberg

 

(Coaches)

Fullerton College

AMATYC Student Math League Practice Session #6

T 10/19

 

(18 students, 5 faculty members, and 1 staff member participated)

4:15-5:30pm

3010

Dr. Yuichiro Kakihara

CSU San Bernadino

Information channels to channel operators

 

Abstract here

 

Click here to view a .pdf file of Dr. Kakihara's beautiful lecture notes for this talk

F 10/22

 

(10 students participated)

11am-2pm

615

Dr. Dana Clahane

 

Paul Sjoberg

 

(Coaches)

Fullerton College

AMATYC Student Math League Practice Session #7

 

(FINAL PRACTICE SESSION)

T 10/26

 

(10 students and 2 faculty members participated)

4:15-5:30pm

3010

Dr. Bill Cowieson*

Fullerton College

The Fermat-Catalan Conjecture

 

 

 

Wilson Lee

Fullerton College (one of Dr. Clahane's Math 299 students) and Cerritos High School ('11)

Sums and products of continued fractions, after Vuillemin

 

Abstract here

F 10/29

 

(61 students participated)

10am-noon

 

(Arrive prior to 11am in order to be eligible - no sign up necessary)

615 (Tentative)

Dr. Dana Clahane

 

Dr. Bill Cowieson

 

Paul Sjoberg

 

(Coaches)

-

American Mathematical Association of Two Year Colleges (AMATYC) Annual Math Competition

 

(All students strongly encouraged to participate!)

 

CONGRATULATIONS TO THE FULLERTON COLLEGE TOP 5 SCORERS, RANKING FULLERTON COLLEGE AS 9TH IN THE NATION IN ROUND ONE OF THIS COMPETITION!!!!!

T 11/2

 

(6 students and 2 faculty members participated)

 

4:15-5:30pm

3010

Kevin Oskar Negron

Fullerton College

(one of Dr. Clahane's Math 299 students)

and

CSU Fullerton

Introduction to the visualization of function behavior involving iteration (dynamics) using Mathematica, for example

 

 

 

Dr. Dana Clahane*

Fullerton College

Lehmer's Mahler measure conjecture

T 11/9

 

(17 students and 2 faculty participated)

4:15-5:30pm

3010

Brandon Sim

 

(postponed due to illness)

Diamond Bar High School

('11)

The equivalence of the Riemann Hypothesis to Lagarias' elementary statement that

d(n) < H(n) + eH(n) ln H(n) for positive integers n >1 and equality holds for n=1, where d(n) is the sum of the divisors of n and H(n) is the sum of the reciprocals of the first n positive integers.

 

 

 

Dr. Bill Cowieson*

Fullerton College

Pre-lecture in preparation for Dr. Emerson's 11/16 Colloquium lecture:

 

1.  Dynamics of complex polynomials, especially z^2+c, and their relation to the well-known Mandelbrot set

2.  Iterates and closest return times of self-maps of the complex plane

3.  Fibonacci, tribonacci, and r-bonacci numbers

4.  The asymptotic relationship between the ratios of consecutive Fibonacci numbers and the Golden ratio

T 11/16

 

29 students and 4 faculty members participated

4:15-5:30pm

3010

Dr. Nathaniel Emerson

USC

Dynamics of polynomials and meta-Fibonacci numbers

 

Abstract here

 

Click here to view a .pdf file containing Dr. Emerson’s intriguing lecture notes on this topic

F 11/19

 

(16 students and 2 faculty members participated)

11am-2pm

615

Dr. Dana Clahane

 

Dr. Bill Cowieson

 

(co-coaches)

Fullerton College

Putnam Competition Practice and Strategy Session #1

 

 

 

 

 

Gary Ramirez (one of Dr. Clahane's Math 150B students)

Fullerton College

Solution to Problem B2, 1993 William Lowell Putnam Competition

 

 

 

Saroush Roufee

(one of Dr. Clahane’s Math 150B students)

Fullerton College

Solution (Version 1) to Problem A1, 2009 William Lowell Putnam Competition

 

 

 

Jonathan Wolfe

Fullerton College

Solution (Version 2) to Problem A1, 2009 William Lowell Putnam Competition

T 11/23

 

(14 students and 3 faculty members participated)

4:15-5:30pm

3010

Gary Ramirez

Fullerton College

(one of Dr. Clahane’s Math 150B students)

If p is a prime number that is greater than 3, then the square of p is 24n+1 for some positive integer n.

 

 

 

Dr. Dana Clahane*

Fullerton College

The equivalence, due to J. Lagarias, of the Riemann Hypothesis and an easy-to-state inequality involving the divisor function and harmonic numbers

T 11/30

 

(16 students and 2 faculty members participated)

4:15-5:30pm

3010

Wilson Lee

Fullerton College (one of Dr. Clahane's Math 299 students) and Cerritos High School ('11)

The spectrum of a weighted composition operator on weighted Hardy spaces of the ball, after Zhou/Yuan, part I

 

 

 

Dr. Bill Cowieson*

Fullerton College

Erdös' conjecture on arithmetic progressions

F 12/3

 

(20 students and 2 faculty members participated)

11am-2pm

615

Dr. Dana Clahane

(Presented Problem B1 from the 2009 Putnam competition, after the outline provided in the MAA Putnam archive)

 

Dr. Bill Cowieson

(Presented Problem A3 from the same exam)

Fullerton College

Putnam Competition Practice and Strategy Session #2

 

(Even if you missed Session #1, come anyway – it will not be assumed that anyone was at the first session.)

S 12/4

 

(22 students participated – this may be a U.S. community college record)

8:00am-4:00pm

 

(two three hour exam parts and a two hour break from 11am-1pm)

621

Dr. Dana Clahane

 

Dr. Bill Cowieson

 

Faculty supervisors

 

2010 WILLIAM LOWELL PUTNAM COMPETITION

Students who want to compete should sign up at the FC Putnam webpage NO LATER THAN OCTOBER 10! 

 

Click here to register as a contestant and view the FC Putnam competition webpage.

 

FC Record holder:

Mustafa Khafateh (2009)

10 points out of 120

 

Goal for FC this year: At least two scorers, one of which scores higher than ten, and at least one female scorer

T 12/7

4:15-5:30pm

3010

Dr. Mark Kozek

Whittier College

Covering systems: Number theory in the spirit of Paul Erdös

 

Click on the above title to view Dr. Kozek’s very nice slide presentation for this great talk.

 

Abstract here

S 12/11

 

(11 students and 3 faculty members participated)

2:30-6pm

Fullerton College

 

Room 615

 

Matt Maldonado

(FC & UCR)

“The reflection and other quandles

 

 

Colleen Nelson

(FC)

“Group theory and one of the Putnam exam problems last week”

 

Reza Nikoopor

(FC)

“Maxwell’s charge-location potential equilibrium problem”

 

Gary Ramirez

(FC)

“Forms of powers of odd numbers”

 

Anonymous student

(Paul Sjoberg’s Math 250A student)

(FC)

An introduction to tropical mathematics

 

Brandon Sim

(FC & Diamond Bar High School, recently accepted to Harvard University and Columbia University)

“Two recent alternative versions of the Riemann Hypothesis”

 

 

 

 

Indicated under each student’s name

ß

 

 

 

 

 

 

Southern California Community College Student Math Mini-Conference

 

Organized by Dr. Dana Clahane

 

 

**

BACK TO THE MAIN MATH COLLOQUIUM/ASSOCIATION PAGE

 

-There is risk, but there is also reward.-

This website was established in June 2010

Webpage conceptual design, content, and page maintenance by:

Dr. Dana Clahane and Dr. Bill Cowieson (all rights/copyrights reserved)

Abstracts by Dr. Dana Clahane

11/16 abstract by Dr. Bill Cowieson

 8/31 Colloqium flier by:

Leo Postovoit, courtesy of the Office of Special Programs

 

MATHEMATICS & COMPUTER SCIENCE DIVISION

FULLERTON COLLEGE

321 E. Chapman Ave. Fullerton, CA 92832

714-992-7041