| Date |
Location |
Speaker |
Topic |
| Thurs 2/3 @ 4:30pm |
FN2 |
Mickey
McDonald |
APOS and Infinity:
An Example of Research in Undergraduate Mathematics Education.
Drawing from my on-going research on how individuals might
construct their understanding of various aspects of infinity,
I will describe: (1) one type of research in undergraduate
mathematics education, (2) APOS Theory, the specific research
framework my colleagues and I use in our work, and (3) some
results of our work and some ideas for future research. |
| Thurs 2/10 @ 4:30pm |
Johnson 205 |
Nicholas
Biller |
Senior Comps:
"Some Variations on the Tennis Ball Problem"
We look at Catalan and Motzkin numbers.
Using interpretations such as Catalan and Motzkin paths
and the "Balls on the Lawn" problem, we examine
certain interesting properties of the number sequences.
We also investigate a formula for counting Motzkin
paths with flaws in terms of Motzkin numbers.
A straight forward combinatorial proof of Motzkin paths
with 2 and 3 flaws will be given. |
| Thurs 2/17 @ 4:30pm |
Johnson 205 |
Sara Blaski |
Senior Comps:
"Fractal Image Compression" Have
you ever agonized over digital images that take up too much
space on your computer’s hard drive? To deal with this problem, a technology called fractal image
compression is in development.
This technology combines mathematics and computers to
bring about a more efficient way of storing and sending images across the
internet. A
fractal is an object that displays self-similarity at all
magnifications, meaning
the object must retain
the same structure at every scale.
Fractal image compression applies fractal geometry by
using systems of equations known as affine transformations to
scale, rotate, or translate a digital image in order to fit in
just a small fraction of a computer’s hard drive. Wouldn’t you rather store images as efficiently as that? |
| Thurs 2/24 @ 4:30pm |
Johnson 205 |
Tae Youn |
Senior
Comps: "The RSA Cryptosystem" The
first and one of the most popular public-key
cryptosystem is RSA cryptosystem, created by Rivest, Shamir,
and Adleman in 1978. It has been close to three
decades, yet it still withstands any attack that tries to
break the system. However, there are cases where RSA
cryptosystem can be broken. One of such cases is when
the secret exponent is too small. This error will be
exploited to discover the secret key by continued fraction
algorithm. |
| Marie Smith |
Senior
Comps: "Is There a Chicken King?" Even
in a barnyard flock of chickens, there exists a social
hierarchy. The term pecking-order is even derived from a barnyard.
A chicken will demonstrate its dominance over a weaker
chicken by pecking him in the neck or head.
Each chicken in a flock will either peck or be pecked
by every other chicken. So,
if a chicken is a king, then it must peck every chicken in its
flock, either directly or through another chicken.
It would appear that every flock should then have a
definable king. But
does it? Does a king chicken necessarily exist? |
| Thurs 3/3 @ 4:30pm |
Johnson 205 |
Joe Salazar |
Senior Comps:
"Traffic Flow Modeling"
How
is it that traffic congestion can be alleviated by stopping
traffic with a red light signal? Why does an accident back
traffic up for miles? An instantaneous interruption in traffic
flow may be mathematically modeled using shock waves. Some
interruptions are due to accidents, while others are
strategically placed to regulate traffic flow. After
understanding the underlying wave theory of traffic flow, one
may understand that the light didn’t turn red to cause you
to be late, but rather, it turned red to improve your chances
of getting there on time. |
| Sandra
Fuentes |
Senior Comps:
"Capture-Recapture
Method: Maximum
Likelihood Estimation"
I
will discuss in detail the capture-recapture method by means
of direct sampling and inverse sampling and will show the
improvement of the maximum likelihood estimate through its
properties. The
properties that I will discuss in this paper are biasness,
unbiasedness, and relative error of each estimate. |
Fri 3/4 @ 12:30
@ 11:30 |
Johnson 208
Fowler North 4 |
Helmer
Aslaksen, National
University of Singapore |
The Mathematics of
the Chinese, Indian, Islamic and Gregorian Calendars.
Have you always wondered why Chinese New Year, the end of
Ramadan, Deepavali and Easter Sunday fall on different days
each year? Then this is the talk for you! I will give an
overview of the Chinese, Islamic and Indian calendars and
compare them with the Gregorian calendar. The Gregorian
calendar is fairly simple, while the three other involves deep
mathematical problems. However, there are simple rules of
thumb that allow you to predict the date of Chinese New Year,
the end of Ramadan and Deepavali with an error of at most one
day. I will also discuss the relationship between the
mathematics and astronomy and various historical and cultural
aspects of the calendars. I hope that this talk will
make you more conscious of the mathematics of the world around
you, and give you knowledge that you will enjoy sharing with
others for the rest of your life. |
| Fri 3/11 @ 12:30 |
Young Dining Room, JSC |
Arpi
Madirossian,
USC |
An informal lunch with
an Oxy alum. (Line lunch provided) |
| Fri 3/25 @ 12:30 |
Weingart 117 |
Olga
Radko, UCLA |
The Mathematics of
Musical Scales. Why do some musical intervals sound
pleasant, while other do not? Why do we have exactly 12
notes in an octave of a piano? Why aren't distances
between frets on a flute or a guitar equal to each other?
The answers, surprisingly, involve deep mathematical analysis
and topics such as continued fractions, the problem of
doubling the cube, and rational approximations. |
Fri 4/1 @ 12:30 |
Weingart 117 |
Sharon
Clarke,
Pepperdine University |
CANCELLED |
Fri 4/8 @ 12:30 |
Weingart 117 |
Kendra
Killpatrick,
Pepperdine University |
CANCELLED |
| Fri 4/8 @ 12:30 |
Weingart 117 |
Nina Gilberte,
Occidental College |
This presentation is about the natural and
cultural riches of Madagascar. Because there are fewer
than 1000 Malagasy people in the United States, accurate first
hand accounts of the challenges and experiences of living in
this evolutional oasis are scarce. My account of Malagasy life
is the result of my voyage back to my home land in (Northern
Hemisphere) Summer of 2003. This short film and presentation
is meant to raise awareness of the difficulties facing third
world nations where environmental treasures compete with the
desire for a better standard of living.
Nina Gilberte is from a small village in the
central highlands of Madagascar. She lived there for 26
years before coming to Southern California where she is
currently a Junior in the Math department at Occidental
College. |
| Fri 4/22 @ 12:30 |
Weingart 117 |
Erika
Camacho,
Loyola Marymount Univeristy |
Photoreceptors,
evolutionary games, and differential equations. In
this talk, I will present three applications of nonlinear
differential equations and give some results. The first
two applications deal with the photoreceptors of the eye. In
one case we model the interaction between the eyes by
considering their respective melatonin levels. This work is
based on experimental results obtained which gave evidence of
circadian rhythms in the eyes. In the second case we model the
interaction between photoreceptors and their trophic
pool. This approach is motivated by observed phenomena
in the eye disease retinitis pigmentosa. The third application
examines the generalized version of the Rock-Paper-Scissors
game under reinforced learning as introduced by Sato, Akiyama,
and Farmer in 2002. The replicator equations, which are also
fundamental in describing population dynamics, govern the
dynamics of this game and give rise to interesting behavior. |
