Current Directions in Mathematical Research

In this research course, we will examine some of the latest developments
in pure and applied mathematics. We will study topics from recent
publications by the Mathematical Association of America (MAA) and the American
Mathematical Society (AMS). In this context, we will consider what
research in mathematics involves, strategies for success in this field,
public perceptions, and applications to daily tasks. Investigations will
include developments in mathematical biology, relationships between geometry
and music, the Poincare conjecture, the debate about Lawrence Summers'
comments about the
innate ability of women in mathematics, whether we still need to learn
multiplication tables, representations of math and mathematicians on
television/in the media, aspects of American competitiveness, and influences
on the global economy. Students will research a topic of their choosing,
with approval and guidance of the instructor, complete a paper of the
caliber of journal submission, and present their
findings at the final research symposium. (Dr. Sarah Greenwald & staff)

July 3-12 and 16-20, 1-3:30 or 3:45 in Sanford 304

July 23-27, 8:30-3:30 in the library

Research Symposium July 28, 8:30 Location CAP 110

Research Facilitator:
Dr. Sarah J. Greenwald

Research Assistant: Sharareh Nikbakht

**Tuesday July 3**
Andrew Wiles and Fermat's Last Theorem.

**Homework** see the bottom of
Andrew Wiles.
Read through the
online research project guidelines
(Living Mathematician
Research Project Presentation and
Media Research Project
Presentation) and write down any questions you have.
Begin reading the New York Times Science Times and prepare to share something
you found interesting.
**Wednesday July 4**
Research at the NSA.

**Homework** Search the web for
a quote about mathematics. Write down your quote and the
person. One person will share their quote each day - if your quote
has been taken, you must find another.
**Thur July 5**
AMS Math Moments. Library research.

**Homework** Work on the
Living Mathematician
Research Project Presentation
**Fri July 6**
MAA Math Horizons. Chose one article in your issue to read carefully.
In addition, conduct additional research on your article and create a
written review in the style of MathSciNet math reviews.
The review should be completed by 3:40 and emailed to Dr. Sarah at
greenwaldsj@appstate.edu. Dr. Sarah's copies of the magazine must be
returned. If time remains, work on the
Living Mathematician
Research Project Presentation
**Mon July 9**
Data Analysis
**Tues July 10**
Carolyn Gordon and time to work on the
Living Mathematician
Research Project Presentation
**Wed July 11** Living Mathematician
Research Project Presentation due. Presentations.
**Thur July 12** Research in Statistics with a presentation by
Dr. Thomley.

**Homework for Monday**: Complete the Mid-Seminar Evaluation
for Dr. Sarah's
Research Seminar.
**Mon July 16** While Dr. Sarah
has mini-conferences with individuals, the rest of the class
researches current topics in mathematics related to
mathematical biology, geometry and music, the Poincare conjecture,
Lawrence Summers, and American Competitiveness and mathematics,
and then works on
projects. Class shares what they found and then
Dr. Sarah answers questions about herself.
**Tuesday July 17**
Work on the media project or the research project.
At the one hour and two hour mark, do a self reflection:
what did you do during the last hour; how effectively did you use your time;
what could have been improved?
**Wed July 18** Media Research
Project Presentation due. Work on selecting a topic for the research
project - think about whether you enjoy learning new (to you)
material and reporting
on it, whether you are interested in thinking about designing an experiment,
or instead collecting and analyzing data. Also think about
topics you are interested in. Topics must be
pre-approved by Dr. Sarah. This is to be an individual project unless you
can demonstrate good reason why you should work with someone else and how each
person will write their own paper and separately contribute to the project.
Walk to the mathematics department for a tour and to look at books in
Dr. Sarah's office for possible research topics.
**Thur July 19** Work on research projects. Talk by Dr. Salinas on
mathematical biology. **Homework** Work on selecting a research topic
if you have not already done so.
**Fri July 20** Fieldtrip.
Meet in front of Katherine Harper Hall (formerly Kerr Scott Hall - it is
across the street from the Steam Plant and ATM and next to the parking
garage - see a campus map) at 12:30 for a trip to Beech Mountain to
tour the wind energy
farm and look at the physics and mathematics
of electricity generation and power transmission.
Safety and crowd management are
paramount for this privilege and the privelege of attending future fieldtrips.
We will only go if the weather there is going to be
good, so I will keep you informed when we meet at Harper Hall.
Students need to take a jacket and a water bottle is recommended. It will
be cold up on Beech.
If we have time we will visit a gift shop up on Beech.
**Mon July 23** Meet in the Sanford classroom.
Discuss instructions for the library, including
a reflection to turn in before lunch:

1) What did you get done related to your project?

2) What else did you do (coffee break, etc)?

3) How do you feel your research time went? Explain.

Walk to the library to work on research. Meet back in the atrium
and collect reflections. Break for lunch.
After lunch return to the Sanford classroom. Those who wish to
watch *A Beautiful Mind* can stay in the classroom to do so with
Ms. Sherry. Others return to the library with Dr. Sarah. For those watching
the film:
Take notes on five items to turn in:

1) the positive representations of mathematics

2) the negative representations of mathematics

3) the positive representations of mathematicians

4) the negative representations of mathematicians

5) any questions you have
**Tues July 24** Research in the classroom and then the library.
At 4pm meet for a fieldtrip at East Hall - cookout and campfire.
**Wed July 25** Research in the library. After lunch, print out a
draft of your paper for Ms. Sherry and Dr. Sarah to read. Hand back
paper drafts.
**Thur July 26**
Look at presentation guidelines.
Research in the library and revise the paper based on Ms. Sherry and Dr.
Sarah's comments. By the end of the day,
turn in an electronic abstract and talk title and information on how
you want me to introduce you. If you want Dr. Sarah
to read your next paper draft, turn in a printed version.
**Fri July 27** Presentation practice and feedback in CAP 110.
Each person evaluates:

What did you like?

What improvements do you suggest?

What questions might a parent ask or do you have?

Students are called from index cards to share their feelings on this.
**Sat July 28**
Research Symposium Presentations in CAP 110. Final
electronic version of the paper is due to Dr. Sarah. She will bring her
laptop so that you can turn it in on a pen drive.

### Quote of the Day

Tuesday July 3 - **Dr. Sarah**:
This universality of application [of mathematics] can
be traced back to the fact that all aspects of Nature and areas of life are
governed by the same principles of order and intelligence that have been
discovered subjectively by mathematicians by referring back to the principles
of intelligence in their own consciousness. (by Maharishi Mahesh Yogi)

Wednesday July 4 - **Ms. Sharareh**:
The mathematical rules of the universe re visible to men in the form of
beauty. (by John Michel)

Thursday July 5 - **Eric**:
Life is too short for long division (anonymous)

Friday July 6 - **Ricky**:
In mathematics you don't understand things. You just get used to them.
(by Johann van Neumann)

Monday July 9 - **Miranda**:
Mathematics is like love- it's a simple idea but sometimes
it can get complicated. (by Albert Einstein)

Tuesday July 10 - **Quan**:
Old theorems never die; they turn into definitions (by E. Hewitt)

Wednesday July 11 - **Mary**:
The essences of mathematics is not to make simple things complicated, but
to make complicated things simple. (by S. Gudder)

Thur July 12 - **Laurel**: Pure mathematics is, in its way, the poetry
of logical ideas. (by Albert Einstein)

Mon July 16 - **Kyle**: If equations are trains threading the
landscape of numbers, then no train stops at pi. (by Richard Preston)

Tues July 17 - **Julian**: Math is good. (by Julian Pinheiro)

Wed July 18 - **Miranda**: Arithmetic is being able to count up to
twenty without taking off your shoes. (by Plato)

Thur July 19 - **Jennifer**:
If people do not believe that mathematics is simple, it is only
because they do not realize how complicated life is. (by John Louis von
Neumann)

Fri July 20 - **Milan**: Go down deep enough into anything and you
will find mathematics. (by Dean Schlicter)

Mon July 23 - **Wisun**: I see it, but I don't believe it. (by George
Cantor)

Tues July 24 - **Hannah**: As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality. (by Albert Einstein, Sidelights on Relativity)

Wed July 25 - **Patrick**:
Perfect numbers like perfect men are very rare (by Descartes)