Math Majors Magazine - MITweb.mit.edu/uma/www/mmm/mmm0202.pdf · Vol. 2 Issue 2 Math Majors...
Transcript of Math Majors Magazine - MITweb.mit.edu/uma/www/mmm/mmm0202.pdf · Vol. 2 Issue 2 Math Majors...
[M3]
Spring 2009-10
Vol. 2 Issue 2
Math Majors Magazine
Brought to you by:
Undergraduate Mathematics Association
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The [m3] Editorial Team
Basant V Sagar ‘11
Christopher Policastro’11
Nicole Fong’13
Frank Li’13
[m3] Faculty Advisor
Prof. Ju-Lee Kim
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Editorial
We are pleased to release the Spring issue of [m3] – the Math Majors Magazine. With
this issue [m3] completes two years of publication. The [m
3] team will keep bringing
you a whole lot of features, interviews and articles to make your life as a math major
easier and fun.
This year MIT won the William Lowell Putnam contest. Congratulations to all the
winners and participants! MIT has always been one of the best-performing schools at
the contest and this year we bested their metric of determining the winning team as
well.
Speaking of having fun at math contests, our friends at HMMT (Harvard-MIT Math
Tournament) decided to host a contest of their own one fine Spring weekend. Maria
Monks’10 describes the thrill of having a local undergraduate math contest in an article
in this issue.
This issue also carries an interview with Prof. Jonathan Kelner, who talks about teaching,
research and a colleague’s prowess at soccer.
The limited print version of this issue will be available at UMA events and in the Math
Majors Lounge. The electronic version is available on the UMA website.
Let us know what you like best about the magazine. Also, if you want to join the fun that
interviewing, editing and writing about math is, email us at [email protected].
The [m3] Team
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In This Issue
Editorial 2
An Interview with Prof. Kelner 4
MIT’s Putnam Victory Report 9
The HMMT Masters Round 11
Awesome Quotes 13
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An Interview with Prof. Kelner
Interviewed by Nicole Fong’13
Prof. Jonathan A. Kelner is an Assistant Professor of Applied Mathematics and a member of the Computer Science and Artificial Intelligence
Laboratory (CSAIL) at MIT. He is teaching 18.440 (Probability and Statistics) this spring. His research focuses on fundamental mathematical problems related to algorithms and complexity theory.
Your undergraduate degree is in math, and your master’s degree and
PhD are in computer science. What made you change your focus?
It is not as much change as you think. In the field of theoretical computer
science, there are many interesting math questions. My research interests
are related to the intersection
between math and computer science.
So it is kind of bouncing between
math and CS.
You are currently working on
something like quantum money and
cryptography. Can you tell us why you
are interested in those fields?
About quantum money, it was a
question brought up by my coauthor
when we were working on some
quantum things. Most people hear
about it from the field of cryptography.
Some things which are totally impossible in classical cryptography can be
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done using quantum computers. Understanding what can be done with
quantum computing and what can be done with regular computing is a
very interesting question. That is how quantum money came about. In
looking at this problem, my coauthor found out that quantum money is
related to questions asked about a decade ago in classical and theoretical
computer science. .
Can you tell us why you chose to work at MIT instead of other colleges?
It is really a fantastic place. There are so many things going on related to
my field. At other colleges, there are people who are really strong in one
field, but that’s it. When you are working at MIT, there are so many
people from different departments working on my research field –
algorithms. They can be people from physics, EE, theoretical computer
science, RLE, Sloan and math, of course. There are so many people at MIT
that are working in areas tightly related to my field which provides a good
research environment.
You are teaching 18.440 for the third time. How do you feel about the
class and why do you want to continue teaching it?
The first time I taught the class there were some kinks. But whenever I
teach it , I learn from my previous experiences and improve all the things
that I didn’t do well . There are advantages of teaching the same class
more than once because you get to see what most students at first don’t
understand, and also what they either love or hate. You can do a better
job when you teach a class more than once; you can flip things a little bit
and fix the flaws – 18.440 is a great chance for that.
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If you ask the same question to the old faculty members, they will say
that the quality of your class will go up to a certain point, but then turn
down a little bit when you teach it again and again, because you get tired
of it. Right now I am not at that point, and every time I teach the class, I
get better.
What about your students? Do their questions ever make you stressed
out?
I am not stressed about their questions because I know the materials
really well. It is more interesting for students to ask questions that I don’t
know than I do know. Since probability is something that is connected to
my work, I don’t worry that much about getting these sorts of questions. I
have taught some graduate classes though, and the questions in those
classes are more stressful. For such questions, sometimes the answer is
“Yes”, sometimes the answer is “I don’t know”, and sometimes the
answer is “Nobody knows”.
How do you balance teaching with research?
It is kind of interesting when people do research and teach at the same
time. You can interact with students while answering their questions and
you can come up with some ideas that you have never thought about
before. Thus you can manage both jobs well together.
Can you tell us your hobbies (besides math)?
I like watching baseball, and I play tennis. That is the only sport that I can
actually play well. I think my hobbies are pretty much similar to those of
other people. I don’t invest myself too much though in tennis.
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I’m also interested in soccer. Prof. John Bush is a fantastic soccer player. .
John is not only good, he is actually at the national championship level in
terms of 40-year-olds. The team he is playing with has something like
three or four players from the Brazilian national soccer team. But I am not
quite there.
So how do you manage your time between sports, teaching and
research?
It is a general question that everyone has, from undergraduates to faculty.
At MIT it is just when you can get back and sleep.
Do you get enough sleep after becoming a professor?
That might be a better question to ask you. One thing you learn as an
undergraduate is balancing. Sometimes you cannot get your work done if
you sit there working for hours. If you drop off a little bit and spend some
time networking, it may make you more efficient.
Sometimes you need to make time not to work.
Do you feel that your life in graduate school was more difficult than as
an undergraduate ?
Those are totally different experiences. As an undergraduate, you are
taking classes and your main job is to finish your problem sets. But in
graduate school, you are learning how to do research and coming up with
new contributions to your field. You are learning different skills. Also, in
college, when you are doing a problem set, you know that someone has
already figured out the answers. They are hard, but not too hard.
Whereas for graduate school, you are working on interesting questions
but no one has figured out the answers. Some answers of mathematical
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problems are very simple and clean, but it can take years for a
mathematician to find and develop them. I think one of the main goals
and challenges in graduate school is to deal with structured and
unstructured time, i.e. being able to accomplish anything in a week, and
knowing that your main goal can be accomplished in four years.
Do you think if math majors should pursue graduate school or is it
enough to go to industry after graduation?
I don’t think there is a general answer. I think students should go to
graduate school if being mathematicians is something they enjoy. It is
four very difficult years, so you need to have enough passion in math. But
I think if you are very interested, you should consider going.
I am glad that I went to graduate school. It was a good choice for me, and
now I can do something that I really enjoy.
Can you give any suggestions or opinions to math majors and
undergraduate students?
Something that you can learn from math is how to understand difficult
and abstract concepts. Taking theoretical math classes is great even when
you don’t want to be a mathematician, because when learning theoretical
math, you will learn different skills. Like what to prove, how to prove it,
what you want to argue for, how to come up with the structure of things,
why certain fact are true, and figuring out the right logical arguments for
them. Those skills are really useful for those who want to be lawyers or
historians. I totally support 18.100. I think every student should take that
class.
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For math majors, make sure that you understand your foundations. Many
college students are trying to take the hardest classes that they can find. I
remember that I took some graduate classes in my freshman year. It was
great, and I enjoyed it, but I made sure that I understood all the
foundational work. When you understand all the concepts really well, you
will understand the things that build on them. Make sure that you
understand the building blocks of your field really well before taking
graduate classes, otherwise you will regret it.
What do you think about the prospects of math and computer science?
The world is moving towards numbers. I think the interface between
math and computer science is really good. Computer science is a
relatively young field, more so than other sciences People are starting to
handle interesting math questions using it. I believe that for theoretical
computer scientists, we have to answer the questions that we come up
with in the future.
The 1800s and 1900s were eras for formulas, like Maxwell’s equations,
Newton’s laws. I think what is coming up in 21st century is the dominance
of data.
Thank you for your interview!
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MIT’s Putnam Victory Report
Frank Li‟13
On the morning of December 5th, 2009,
a number of MIT students could be
found concentrating intensely and
writing furiously in the Walker
Memorial Center, a common location
for tests taking at MIT. You might think
this is for some class, but you‟d be
wrong. It‟s a Saturday. So what could so
many students be laboring over? These
MIT students are competing in the 70th
William Lowell Putnam Mathematical
Competition.
The prestigious Putnam Competition is the premier undergraduate math
contest in the United States. It‟s a lengthy
six hour, 12 problems written test taken
individually. A school can also designate
three team participants, with the sum of
their ranks being the team score (and the
teams with the lowest score wins).
Although the exam does not require any
mathematics beyond calculus and
linear algebra, clever ideas are need to solve
the problems. To the top performances,
recognition and even cash is at the end of the
road. MIT has been an active participator with, according to MIT‟s Putnam
wiki, over 100 students competing ever year.
Contestants of Putnam’09
Putnam Exam in Walker Memorial
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MIT has always been one of the top performers in the Putnam, but this year, it
claimed victory as the winning team, ending a four year drought. The team
consisted of seniors Qingchun Ren, Bohua Zhan, and Yufei Zhao. MIT also
performed amongst the best individually, although this is nothing new. “Well
regardless of the team results, I think
everyone knows that MIT performs the best
overall on the Putnam,” said Jacob
Steinhardt „11, one of MIT‟s top performers.
According to MIT‟s Putnam wiki, “MIT
students represented over 50% of those
ranked among the top 25 participants, and
over 30% of those ranked Honorable
Mention or above (approximately the top 75
participants).”
This year, Qingchun Ren „10 and Yufei Zhao
„10 earned the Putnam Fellow distinction by
finishing top 5 in the competition. This was
the third time Yufei Zhao became the Putnam fellow, while for Ren it was the
second time on the Putnam fellow list. Bohua Zhan „11, Jacob Steinhardt ‟11,
Panupong Pasupat ‟12, Colin Sandon „12 and Sergei Bernstein „13 placed in
the top 15. MIT competitors also claimed 20 of the 50 honorable mentions.
Finishing behind team champion MIT came Harvard, Caltech, Stanford, and
then Princeton.
Congratulations to MIT as team champions and to all of MIT‟s participants!
Winning team members (L to R)-
Bohua Zhan, Yufei Zhao and
Qingchun Ren
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The HMMT Masters Round:
A new math contest for undergraduates and beyond
Maria Monks’10
On Saturday, April 3, twenty-five contestants gathered in Harvard's
Science Center to compete in the first annual HMMT (Harvard-MIT Math
Tournament) Masters Round. A four-hour contest featuring ten questions
of varying difficulty, the Masters Round is designed to bring the art and
spirit of problem solving into higher mathematics. The problems test
mastery of the topics found in introductory courses at MIT and Harvard in
algebra, topology, real and complex analysis, combinatorics, and number
theory.
Results
Among the 25 competitors, 15 were undergraduates at MIT, 6 were
undergraduates at Harvard, and 4 were either graduate students or
former undergraduate math majors. The undergraduates competed in a
separate division from the graduates, and individual awards were given in
both divisions.
Arnav Tripathy, a senior at Harvard, was first overall, scoring 39 out of a
possible 50 points.
In close second was Daniel Kane, a graduate student at Harvard, scoring
an impressive 37 points, despite having to leave the test after only two of
the four hours. Yi Sun, also a senior at Harvard, rounded out the top
three with 36 points.
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Despite Harvard's impressive showing in the individual rankings, MIT's
depth earned them the undergraduate team award, led by Alex
Zamorzaev, Bohua Zhan, and Shaunak Kishore, each of whom scored 24
points. (A school's team score is the sum of the ranks of the top 5
individuals from that school, after all non-team participants are removed
from the results. Ties are broken by the 6th place individuals from the
respective schools.)
Four Graders' Choice Awards were also given to particularly inventive or
elegant proofs, nominated and chosen by the graders. Sergei Bernstein,
Anders Kaseorg, Bohua Zhan, and Alex Zamorzaev were all awarded
Graders' Choice Awards.
For full results, problems, and solutions, see:
http://hmmt.mit.edu/masters.
How you can get involved
First and foremost, you can take the exam next year! The contest is free
and open to all undergraduates, and if you are not an undergraduate you
may compete in our open division.
Moreover, you may help with the grading afterwards.
We also need two directors for next year. The tournament director is in
charge of logistics, and the problem czar is in charge of writing the test.
If you wish to get involved with either the Masters Round or with
HMMT's contests for high school students, send us an email to hmmt-
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Awesome Quotes
Compiled by Nicole Fong’13
“Only two things are infinite, the universe and human stupidity, and I'm not sure
about the former.”
(Albert Einstein)
“Do not worry about your problems with mathematics. I assure you mine are far
greater.”
(Albert Einstein)
“A topologist is a person who doesn't know the difference between a coffee cup
and a doughnut.”
(Anonymous)
“There is no Royal Road to Geometry.”
(Euclid)
“Mathematics consists in proving the most obvious thing in the least obvious
way.”