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| News and Events |
"Unofficial"
Undergraduate Tea and Cookies occurs every Friday at 3:30 PM
in the Fine Hall common room (3rd floor). Tea and
Cookies is a social tradition of the Princeton math
department. It provides an informal social setting to
encourage communication between math aficionados.
Although tea is open to everybody, it has been dominated by
graduate students and professors in the past. We hope to
change this habit by encouraging all Math Club members to
attend on Fridays. Try to come early or on time because
the cookies seem to disappear quickly!
Today's mathematical anniversaries, as recorded in the
History of Mathematics Archive at the University of St. Andrews.
News columns
by the Mathematical Association of
America.
What's New in Mathematics, articles by the
American Mathematical Society.
News in applied mathematics, by the
Society for Industrial
and Applied Mathematics.
Upcoming Events and Recent
News
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Wednesday
5/4/05 |
Special Guest Speaker: MAY 4th, 3:00pm, Location TBA.
"The idea of a moduli space" I'll try to get this idea across starting completely from scratch; the talk will be suitable for non-math majors but will (I
hope) contain some material of interest to the majors (in particular, I will try to say the word "functor" by the end.)
| Abstract: |
The study of moduli spaces is a staple of contemporary number theory and algebraic geometry. The precise definition is quite hard to state if you're not familiar with the language of category theory; however, the idea behind the definition is quite simple, and is in some sense a very natural generalization of the main idea of Cartesian geometry; that there's a one-to-one correspondence between pairs of real numbers and points on a plane.
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Saturday
11/13/04 |
Undergraduate Math Talk: 3:30pm in room 314, Fine Hall.
Prof. Jordan Ellenberg, "THE MATHEMATICS OF SET, or EVERYTHING I KNOW ABOUT COMBINATORIAL GEOMETRY I LEARNED PLAYING CARDS"
| Abstract: |
The game of Set is a simple but addictive card game played with a special 81-card deck. A standard "folklore question" among players of this game is: what is the largest number of cards that can be on the table which do not allow a legal play? I'll explain how this question, which seems to be about cards, is actually about geometry over a finite field, and I'll talk about what's known about this problem and related ones. If there's time, I'll try to convince you that this problem might have something to do with _algebraic geometry_, and if there's even more time, I'll try to convince you that, no, in fact, it really has to do with Fourier analysis.
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Sunday
10/3/04 |
Undergraduate Math Talk: 3:30 in room FINE314.
Nate Kaplan, "How I spent my Summer Vacation (Aside from Getting Arrested): Factorization Lengths in Numerical Monoids"
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Saturday
9/18/04 |
Undergraduate Math Talk: 3:30 in room 314, Fine Hall.
Matt Satriano '05, "Every positive integer is the sum of four squares." Followed by lots of Chinese food.
| Abstract: |
In 1772, Lagrange proved that every positive integer can be expressed as a sum of four integral squares. This theorem is proved in MAT 331 using Complex Analysis, but here we will see a much more elementary proof. The key ingredient will be Minkowski's generalization of the following intuitively obvious fact: if R is a region with finite area that is convex, symmetric with respect to the origin, and has area greater than 4, then R must contain some integral point other than the origin.
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Sunday
5/9/04 |
Undergraduate Math Talk: 5pm in room 314, fine hall.
Darsh Ranjan "lights out!"
| Abstract: |
on an original theory he has developed by studying the game "Lights out!". This will also take place in Fine 314. Food will follow the talk.
Also on Sunday after Darsh's talk, we will be discussing the future of the Math Club... so if you're interested in seeing the math club operate next year, you should come by.
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Friday
5/7/04 |
Undergraduate Math Talk: 4:30pm in room 314, fine hall.
John Mangual, "GeneratingFunctionology"
| Abstract: |
"In the words of Herbert S. Wilf of the University of Pennsylvania, "A generating function is a clothesline on which we hang a sequence of numbers to display." We shall construct the (extremely simple) generating functions of Fibonacci numbers, perfect squares and connect these ideas to Quantum Mechanics."
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Sunday
4/25/04 |
Undergraduate Math Talk: 6:00 pm, in room 314, Fine hall.
Sasha Bufetov, "Interval exchange transformations." Prerequisites: vague familiarity with measure theory
(or willingness to believe some intuitively clear statements).
| Abstract: |
Take a unit interval, cut it into several subintervals and permute
these subintervals. The resulting piecewise isometry of the unit interval
is called an interval exchange transformation.
The dynamics of interval exchanges is extremely complex
and little understood.
The talk would aim to give an introduction to this area.
I hope to formulate a number of open questions in the end.
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Friday
4/16/04 |
Undergraduate Math Talk: 5:00 pm Fine Hall, Room 314.
Professor Sinai: "Statistics of Convex Polygons". Followed by pizza.
| Abstract: |
I shall consider convex polygons whose vertices belong to the
lattice 1/nZ^2 and polygons which are inside the unit square.Uniform
distribution on the set of all such polygons lead to unexpected laws of
large numbers which show that there are preferable polygons with a
strictly defined shape. The analysis is based on elementary probabilty theory.
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Sunday
4/4/04 |
No Talk Just Food: 4:30 in 3rd floor common room, Fine Hall.
Lots of Pizza!
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Saturday
4/3/04 |
Undergraduate Math Talk: TBA.
Sadly, there was a conflict, and Professor Sinai's lecture has been postponed to Friday, April 16th.
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Sunday
3/14/04 |
Site Announcement-
The Putnam practice exams up to 2003 have been posted in the Resources section.
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Saturday
3/13/04 |
Site Announcement: MATH CLUB WEBSITE UPDATED.
math club website is under new adminstration, and shall be updated regularly. contact webmaster for any info or questions.
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Monday
4/22/02 |
Special Guest Speaker: 5:00P in room A10, Jadwin.
Alice Silverberg, "Elliptic Curves are Everywhere." This presentation will be accessible to people of all backgrounds.
| Abstract: |
Elliptic curves were used in the proof of Fermat's Last Theorem. They can also be used to factor integers, and to test whether integers are prime. There are elliptic curves in cell phones, wireless modems, handheld computers, internet microbrowsers, pagers, and smart cards. Some recent new applications of elliptic curves allow 3 parties to share a secret. What are elliptic curves, and why are they so powerful? Find out at this talk!
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Friday
12/7/01 |
Special Guest Speaker: 4:30P in (location to be announced).
Avi Wigderson, "The Digital Envelope - A Crash Course in Modern Cryptography." The talk is planned for a general audience, and no particular background is assumed.
| Abstract: |
With the advent of computer technology, the internet and electronic commerce, Cryptography has become an essential part of everyday life of us all. While Cryptography has existed for millenia,
much of the theory enabling this revolution has been developed within Theoretical Computer Science in a dazzling brief span of about 10 years starting in the late 70's.
In this talk I will try describe the fundamental assumptions of this theory, the exciting developement of ideas and notions (like one-way functions and zero-knowledge proofs), and how they enable basic tasks (like secure communication), as well as arbitrarily complex tasks (like
playing a game of Poker over the telephone).
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Saturday
12/1/01 |
The William Lowell Putnam Mathematical Competition: 10AM to 1PM and 3PM to 6PM (location to be announced).
The Putnam competition is *the* undergraduate math competition. There are substantial monetary prizes for the top scores.) If you would like to participate in the competition, you MUST sign up in Matthew Ferszt's office (3rd floor Fine) BY OCTOBER 5.
Last year, the math club organized practice sessions led by graduate students. We will organize similar sessions this year. If you are interested in participating, please e-mail us to let us know.
Finally, you can find links to information and previous exams from the Links section of the math club website.
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Sunday
11/4/01 |
Site Announcement-
Practice Putnam exams have been posted in the Resources section.
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Sunday
9/30/01 |
Rescheduled Undergraduate Math Talk: 1PM in room 214, Fine Hall.
See the news item at 9/12/01.
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Saturday
9/22/01 |
The Null Set CHESS Challenge-
Click here to download. Hand in your solutions by this Sunday/Monday,
in Erez Lieberman's mailbox in the Fine Hall lobby. A prize will be awarded
for the best solution found by a member of the Class of '05.
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Friday
9/14/01 |
Beginning of the Fall Term-
Welcome Back! The Math Club looks forward to a new year of Math Talks and Special Guest Speakers!
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Wednesday
9/12/01 |
Undergraduate Math Talk: 10:00 AM in room 214, Fine Hall.
Erez Lieberman, "A Few Large Numbers." This is the mathclub's orientation
week lecture, and no background is needed. To be followed by a luncheon,
"Large Quantities of Sushi and Chinese Food." Upperclass members of the
math department will also be on hand, to speak with interested freshmen.
NOTE: RESCHEDULED for Sunday, 9/30/01, see the news item above for details.
| Abstract: |
What happens when you count to infinity, add 17, divide by 2, and take
the square root? Finally: Answers to the really BIG questions.
Learn all about the mathematics of infinity amid an incessant torrent of jokes.
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Tuesday
9/11/01 |
Special Guest Speaker: 2:30 in Taplin Auditorium, Fine Hall.
John Conway, "Functions From Fruitful Fractions." To be followed by
a reception at 4:00 in the Eisenhart Tower Lounge.
NOTE: RESCHEDULED for Wednesday, 9/12/01, same time and place.
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Saturday
5/26/01 |
Summer Recess-
Have a great summer!
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Sunday
5/6/01 |
Special Guest Speaker: 2:00 PM in Taplin Auditorium, Fine Hall..
Professor Conway, "The Surreal Numbers."
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Sunday
4/29/01 |
Undergraduate Math Talk: 2:00 PM in Room 110, Fine Hall (see map on the Math Talks page).
Robert Lipshitz, "Counting Forever in Hebrew: Continuum and the Cardinal Numbers."
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Sunday
4/22/01 |
Undergraduate Math Talk: 2:00 PM in Room 110, Fine Hall (see map on the Math Talks page).
Erez Lieberman, "Cantor's Ordinal Infinities and A Really Good Way to Count on Your Fingers."
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Sunday
4/8/01 |
Special Guest Speaker: 2:00 PM in room 314, Fine Hall.
Mark Tygert. Familiarity with the Fourier and Fast Fourier Transforms recommended.
| Abstract: |
I would aim for an audience that is familiar with the Fourier transform and its basic properties, and perhaps also with the FFT. I would talk about Daubechies' and my senior year thesis work, which is now complete to my satisfaction. I would like the format to be more like a conversation than like a lecture. To entice people to come, I would note that our thesis work has generated many unresolved problems. I am not interested in solving these problems; some are too easy and many are too hard. Some of the problems are entirely abstract and pure; some of the problems have implications for a wide range of applications. There is also a class of problems that requires a broad knowledge of harmonic analysis to solve. I would solve these, but I have not yet studied the texts by Stein, Weiss, Coifman, and Meyer, nor do I understand the proof of the Carleson-Hunt Theorem. In any event, the audience should be able to tackle some of these open problems after the talk. I have posted a paper on the topic of the talk, the Dyadic Position-Oscillation-Scale Transform on the Real Line, at http://www.princeton.edu/~mwtygert/paper.ps (also available from my homepage). I know that some of the math club members attended my PACM Undergraduate Colloquium talk earlier this year. I would plan to cover that same material in the first five minutes of the talk, which seems reasonable for a more sophisticated audience.
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Friday
3/16/01 |
18th Annual Rose-Hulman Conference on Undergraduate Mathematics: 10 am 3/16 - 12 pm 3/17, Rose-Hulman Campus in Terre Haute, Indiana.
Our invited speakers are Suzanne Lenhart, University of Tennessee at Knoxville and Oak Ridge National Labs, who will speak on applications of optimal control to various population models, and Linda Petzold, University of California at Santa Barbara, who will speak on computational science and engineering. The main focus of the conference will be on undergraduate speakers, who are encouraged to submit abstracts of papers in any area of the mathematical sciences. We ask faculty to encourage their students to take advantage of this opportunity and submit an abstract by February 28th, 2001. In order to celebrate mathematics done by undergraduates, all of the talks (except the two invited talks) will be given by undergraduates.
For details, see the Conference's Website:
http://www.rose-hulman.edu/Class/ma/HTML/Conf/UndergradConf.html
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Thursday
3/1/01 |
Special Guest Speaker: 4:30 PM in room A01, Jadwin Hall.
Dr. Milnor, "Quantum cryptography and quantum computation".
A little bit about Dr. Milnor, for those who don't know about him. A brief bio (that I'm drawing on for the dates) can be found at: http://www-groups.dcs.st-andrews.ac.uk/history/Mathematicians/Milnor.html
A few highlights:
Milnor graduated from Princeton in 1951. He then went on to graduate school, also here at Princeton, and received his Ph.D. in 1954. (He was appointed to the faculty a year earlier, in 1953.) Milnor received the fields medal in 1962, the same year in which he became chair of the department. Milnor is now emeritus from Princeton and is on the faculty of SUNY Stoneybrook.
Milnor's work spans a wide range of fields in mathematics, from differential topology to algebraic geometry to dynamical systems. His writing is clear and elegant; I recommend his book Topology from the Differentiable Viewpoint to anyone who has taken 218 or above. Milnor also has a reputation for being an excellent speaker.
| Abstract: |
Physicists are interested in these potential applications of quantum theory because they help to hone our understanding of basic principles; and mathematicians because they involve some fascinating ideas. Finally, of course, both cryptography and computation are enormously important in the present world.
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Wednesday
2/28/01 |
Due Date for Abstract Submissions for the Rose-Hullman Conference-
See entry above (3/16/01) for details.
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Sunday
2/18/01 |
Undergraduate Math Talk: 2:00 PM in room 314, Fine Hall.
Leo Goldmakher, "The short, happy proof of Chebyshev's Theorem." Basic high school mathematics background necessary.
| Abstract: |
Howdy! Ever wondered why ANYONE would ever want to be a math major, or even worse, a mathematician? I certainly have. But if you are curious to see how math can be fun, I would love to see you at this talk. Basically, I'll prove Chebyshev's Theorem (for all natural numbers n, there is at least one prime number between n and 2n), along with some other neat things on the way. All you need to understand the talk is curiosity, and maybe a couple of basic facts about logarithms (though I would be happy to go over these if anyone wants me to). And just in case you're the pragmatic type: there will be LOTS of FREE food and drinks! Hope to see you all there!
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Friday
12/15/00 |
Winter Recess-
Winter Recess begins after your last class on Friday! Come to tea (3:30 in the Fine Hall common room on the 3rd floor) and have a great vacation!
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Saturday
12/2/00 |
The William Lowell Putnam Mathematical Competition: 10 am - 1 pm and 3 - 6 pm in room A10, Jadwin Hall.
Participants must have signed-up by October 6, 2000 (if you missed that deadline, remember to go to Fine 306 at the beginning of the next school year and sign up).
This is the big university-level mathematics competition. It consists of 12 questions, and lasts 6 hours (in two halves). The questions are mostly quite hard. For more information (rules, history, prizes, other questions) see Cheryl Singleton, the Undergraduate Coordinator, in Fine 306, or e-mail the math club and we'll try to help. Also, check the Links page for Putnam links.
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Thursday
11/30/00 |
Special Guest Speaker: 5:00 PM in room 214, Fine Hall.
Dr. Daubechies, "Wavelets: An overview, with recent applications."
The presentation will be followed by a reception in the Fine Hall common room on the third floor).
| Abstract: |
Wavelets have emerged in the last decade as a synthesis from many disciplines, ranging from pure mathematics (where forerunners were used to study singular integral operators) to electrical engineering (quadrature mirror filters), borrowing in passing from quantum physics, from geophysics and from computer aided design.
The first part of the talk will present an overview of the ideas in wavelet theory, and show how it fits into the different disciplines in which it is rooted. The second part of the talk will discuss applications
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Sunday
11/19/00 |
Undergraduate Math Talk: 3:00 PM in room 110, Fine Hall (see map on the Math Talks page).
Alex Kontorovich, "Nimpinski Gamagles." No background knowledge required.
| Abstract: |
Ever wonder about a possible connection between Nim Games and Sierpinski Triangles? Me neither. But there is one. Come find out how the two are related, and how, with the help of our ole friend, Pascal, we can derive a result that may be applied to Fraenkel's Conjecture on exact coverings of integers.
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Friday
11/10/00 |
Special Tea: 3:45 PM in the Common room on the third floor of Fine Hall.
This "special" tea and cookies, organized by Prof. Trotter, Cheryl Singleton, and Prof. Sarnak, is primarily aimed at undergraduates, so if you only come to one tea, come to this one! Some special "goodies" will be served. More details to be released.
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Wednesday
11/8/00 |
Presentation: 7:00 PM in room 314, Fine Hall.
Representatives from Watson Wyatt will give a presentation on the actuarial profession. (Probably more mathematics students are employed as actuaries than in any other nonacademic discipline, and most actuaries speak of very high job satisfaction. Watson Wyatt is one of the largest actuarial firms in the world.) Refreshments will be served.
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Sunday
10/29/00 |
Site Announcement-
Significant changes have been made to the Null Set site, including greater non-IE browser compatibility.
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Saturday
10/21/00 |
Site Announcement-
The new Null Set website has been launched!
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Sunday
10/8/00 |
Undergraduate Math Talk: 3:00 PM in room 110, Fine Hall (see map on the Math Talks page).
Rebecca Lehman, "Wallpaper, Billiards, and the Hyperbolic Plane." Some familiarity with algebra (group theory) is assumed.
| Abstract: |
This week's talk, "Wallpaper, Billiards, and the Hyperbolic Plane" will discuss the intrinsic connections between wallpaper patterns and pool shots, and why both are really hard unless you have a flat surface. But seriously, we'll discuss the hyperbolic plane and its tilings by triangles, and make use of the interplay between the algebra of the tiling group and the geometry of the billiard representation to examine the length spectrum of translations in the hyperbolic plane. We'll see a geometric test for when two group elements are conjugate, and a nearly trivial algebraic proof of a geometric fact about triangles.
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Sunday
9/17/00 |
Undergraduate Math Talk: 3:00 PM in room 110, Fine Hall (see map on the Math Talks page).
Erez Lieberman, "Utter Confusion: Undecideability, Entropy, Uncertainty, and Ethics." No background knowledge required.
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