undergrad_research_talk

8/7/2019 Undergrad_Research_Talk

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Intro Specific Programs Our Experiences El Fin

Undergraduate Research

Jessica Lin and Karol Koziol

January 21st, 2009



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Outline

General overview of undergrad research

Program Specifics:REUSURESummer Schools/Expository Programs

Our Personal Experiences



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General Overview

Many institutions provide undergrads with the opportunity toconduct research in serious (but fun!) areas of mathematics.



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General Overview

Many institutions provide undergrads with the opportunity toconduct research in serious (but fun!) areas of mathematics.Programs center on a wide variety of topics, so you can find one

that suits your particular interests. In most cases, previous researchexperience is not expected, and background knowledge in thespecific topic is picked up as you go.



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General Overview

Many institutions provide undergrads with the opportunity toconduct research in serious (but fun!) areas of mathematics.Programs center on a wide variety of topics, so you can find one

that suits your particular interests. In most cases, previous researchexperience is not expected, and background knowledge in thespecific topic is picked up as you go. Regardless of which programyou choose to participate in, it will give you great experience, and

give you an idea of what research is like. In addition, you will learnA TON of math.



S O

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Programs

REUs



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REUs

REU - Research Experience for Undergraduates

Funded by National Science Foundation (NSF)Sites located all over the United States

Not just in math - physics, biology, compsci, etc.

Meant to encourage research in a friendly setting

Fantastic opportunity to study in a different academic setting,and learn from different professors and peers.



I t S ifi P O E i El Fi

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Many topics center around more “discrete” topics: graph theory,knot theory, combinatorics, and algebra. These topics require less

background, and can be picked up fairly quickly. There are alsoREUs in PDEs, differential geometry, ergodic theory, etc.




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Many topics center around more “discrete” topics: graph theory,knot theory, combinatorics, and algebra. These topics require less

background, and can be picked up fairly quickly. There are alsoREUs in PDEs, differential geometry, ergodic theory, etc. Mostsites admit 10 to 20 students, and divide them into groups of 4 to5 based on interest. The groups work closely on the topic theiradvisor has chosen. Some projects have been ongoing for several

years, and some are new.




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Requirements

Requirements:

2 letters of recommendation

Personal Statement

Transcript

No specific course requirements, but the more, the better

Most of those admitted are rising seniors (and some rising juniors, but this is not a blanket statement!)

Deadlines are quickly approaching!!! (most are dueFebruary/March)




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WARNING: ABOUT REUS

In this present day, most people look favorably upon students whopartcipate in REUs. However, there has been a tradition in thepast that some graduate schools claim they do not think REUs areworthwhile. You must understand the following:

Not all REUs are doing original research. Many REUs studymore expository projects, which is great, but this is not thesame as being a research scientist.

Many times we do research that is not always successful. DONOT WORRY! It is very hard to do meaningful research atthe undergraduate level, so don’t be discouraged if your workdoes not result in publications or anything. This is just foryour experience .




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Programs

SURE




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SURE

SURE is the summer research program funded by the NYU MathDepartment.Program Description:

Pays for roughly 8 weeks of work.

You and a faculty member at NYU decide upon a project towork on.

At the end of the summer, you write a report of your work(samples of these are available online through the math

department website)In the Fall, you give a 10 minute presentation on your summerwork open to all of Courant.




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How to Apply for SURE

It’s Easy!!You will need:

Faculty Advisor (this is not absolutely required, but to behonest, you probably will not get accepted unless you have afaculty member agreeing to work with you)

Fill out a form (takes 5 minutes) with your courses andgrades. (These will be available in March!)

THAT’S IT!!




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How is SURE different from an REU??

Participating in either SURE or REU counts as your thesisrequirement for honors students*

It is possible to work other jobs as well as doing research inSURE. (i.e. Tutoring and Grading)

Projects in SURE can begin/continue into the school year asIndependent Studies, which can count for credit.

Participating in SURE gives you the opportunity to get closer

to a faculty member here!




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Programs

Summer Schools/Expository Programs




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Just for Girls!

There are several summer schools that are only open to women.These include:

Princeton/IAS: Women and Mathematics–A 2 week(supported) summer school at Princeton University (in earlyJune). This year’s topic is GEOMETRIC PDE

George Washington University: Summer Program for Womenin Mathematics–A 5-week (supported) summer school. MUSTBE A CURRENT JUNIOR (or have junior standing). You getPAID to go!! (End of June to Early August)

Carleton College: Summer Mathematics Program forWomen–A 4-week (supported) summer school. MUST BE ACURRENT FRESHMAN OR SOPHOMORE, and have takenlinear algebra in the past year. You get PAID to go! (End of June to End of July)




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Summer Program in Princeton

Spend 3 weeks at Princeton studying like a graduate student!

Designed for current juniors, seniors, and first year graduate

students.

Typical topics include special topics in analysis and geometry,although they have not been announced yet for 2009.

Fully supported, but no stipend.




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Park City

Study number theory at Park City Mathematics Institute

Located in lovely Utah

Focus on elliptic curves, modular forms, L-functions (numbertheory-ish things)

Funding available

Deadline: January 28th




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CUNY/Columbia/NYU

Research in number theory at CUNY Graduate Center

In NYC

Focus on algebraic number theory and analytic number theory

Prereqs: Algebra I and Complex Analysis (respectively)

Stipend available

Deadline: March 15th




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Pros and Cons of Research

Pros

1 Get really good at LATEX

2 Learn a lot of math

3 Meet some great people

4 Chance to travel (Mathfest, JMM)

5 YOU GET PAID!!

Jessica Lin and Karol KoziolUndergraduate Research


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Pros and Cons of Research

Pros

1 Get really good at LATEX

2 Learn a lot of math

3 Meet some great people

4 Chance to travel (Mathfest, JMM)

5 YOU GET PAID!!

Cons

1 None.



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Our Experiences

Our Experiences



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NYU SURE

Jessica’s Summer: 2007

Topic: A Theory of Induced Dynamics for Infinite-DimensionalDynamical Systems

Advisor: William Ott (NOTE: Will was a postdoc at the time,

and it is absolutely fine, if not better, to have a postdoc foran advisor.)Met with advisor several times a week, worked independently.Worked for about 3 months, although was only paid for 2.

Simultaneously worked as a tutor for the math department.Received DURF grant for additional stipend, expenses forbooks, and travel to conference.Attended Mathfest 2007, Winner of SIAM Award forOutstanding Talk in Applied Math



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NSF SMALL Program at Williams College

Jessica’s REU, Summer 2008

Located at Williams College, in Williamstown, MA, deep inthe Berkshires.

Lasted 9 weeks.

24 students: 6 groups: Algebraic Number Theory, Geometry,Discrete Geometry, Hyperbolic Geometry, Knot Theory,Ergodic Theory

Topic: Measurable Time-Restricted SensitivityWeekly Colloquia, daily meetings with advisor and group,daily athletic and social events (tea, outings, girls lunch, etc.),Mathfest 2008.



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Convocation



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Ergodic Theorists!



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Summer Home



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July 4th Cookout/Pool Party



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REU at SUNY Potsdam

Karol’s REU

In Potsdam, NY - 1 hour south of Canadian border, beautiful

sceneryLasted 8/9 weeks

13 people in 4 groups - Algebra, Knot Theory, Graph Theory,Algebraic Geometry

Topic: “Decompositions of Various Compact RiemannianSymmetric Spaces”

Weekly Colloquia, lunches with advisor, cookouts, Mathfest



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My Research Group



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Everyone



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Camping



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Montreal



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More Montreal



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Ottawa



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Hiking



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Mathfest



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Questions?



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