[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 mmm-exec@mit.edu.

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-

request@mit.edu.

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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.”

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(George Polya)

“The theory of probabilities is at bottom nothing but common sense reduced to

calculus.”

(Laplace)

“You know we all became mathematicians for the same reason: we were lazy”

(Max Rosenlicht)

“Mathematics is as old as Man.”

(Stefan Banach)