Princeton Math Circle






Calendar
 
Saturday, May 15, 2010
1:00 - 4:00 pm


Rm. 314, Fine Hall at Princeton University,  Washington Road, Princeton, NJ 08540

 
Agenda / Speaker(s):

- "Voting and its Discontents", Vivek Shende, Dept. of Math., Princeton University.

- Problem Solving Session, Instructor: Alison Miller and Aaron Pixton, Dept. of Math, Princeton University.


 
Saturday, May 8, 2010
1:00 - 4:00 pm


Rm. 314, Fine Hall at Princeton University,  Washington Road, Princeton, NJ 08540
 
Agenda / Speaker(s):

- "Knots -- why we love them (a gentle introduction to the theory of knots)", Margaret Doig, Dept. of Math., Princeton University.

- Problem Solving Session, Instructor: Alison Miller, Dept. of Math, Princeton University.


 
Saturday, May 1, 2010
1:00 - 4:00 pm


Rm. 314, Fine Hall at Princeton University,  Washington Road, Princeton, NJ 08540
 
Agenda / Speaker(s):


- Problem Solving Session, Instructors: Ilya Vinogradov and Alison Miller, Dept. of Math, Princeton University.


 
Saturday, April 24, 2010
1:00 - 4:00 pm


Rm. 314, Fine Hall at Princeton University,  Washington Road, Princeton, NJ 08540
 
Agenda / Speaker(s):

- "Apollonian Circle Packings: Part II", Elena Fuchs, Dept. of Math., Princeton University.

- Problem Solving Session, Instructor: Alison Miller, Dept. of Math, Princeton University.

 
Saturday, April 17, 2010
1:00 - 4:00 pm


Rm. 314, Fine Hall at Princeton University,  Washington Road, Princeton, NJ 08540

 
Agenda / Speaker(s):


- "Algorithms for Sorting and Searching", Professor Avi Wigderson,  H. Maass Distinguished Professor at the School of Math, Institute for Advanced Study.

Abstract:

Assume you have n sealed envelopes on the table, each containing some secret number. In every step, you can perform a "comparison":  you point to two of the envelopes, and get as an answer which of the two contains a bigger number, or if the two are equal. Given the answer you can decide on another comparison, etc. Such a sequence of steps is a comparison algorithm.

How would you solve the following tasks, and how long would it take (in the worst case)? In other words, what is the most efficient comparison algorithm, and its performance as a function of n, for the following problems:

- Find the envelope containing the largest number
- Find the the envelopes containing two largest numbers
- Sort the envelopes so their numbers are in increasing order
- Find the median
- Find if two envelopes contain the same number


- Problem Solving Session, Instructor: Alison Miller, Dept. of Math, Princeton University.


 
Saturday, April 10, 2010
1:00 - 4:00 pm


Rm. 314, Fine Hall at Princeton University,  Washington Road, Princeton, NJ 08540

 
Agenda / Speaker(s):


- "Apollonian Circle Packings: what are they and why are they amazing", Elena Fuchs, Dept. of Math., Princeton University.

- Problem Solving Session, Instructor: Alison Miller, Dept. of Math, Princeton University.


 
Saturday, April 3, 2010
 
NO CLASS

(Closed for Spring Break)

 
Saturday, March 27, 2010

 
NO CLASS

(Closed for Spring Break)
 
 
Saturday, March 20, 2010
1:00 - 4:00 pm


Rm. 314, Fine Hall at Princeton University,  Washington Road, Princeton, NJ 08540
 
Agenda / Speaker(s):

- "Being Continuous Discretely," Slater Stitch, Princeton University.

- "Continuous and Discrete Mathematics", Hands-On Activities, Bianca Ray Avalani

- Problem Solving Session, Instructor: Adam Hesterberg, Dept. of Math, Princeton University.


 
Saturday, March 13, 2010
1:00 - 4:00 pm


Rm. 314, Fine Hall at Princeton University,  Washington Road, Princeton, NJ 08540
 
Agenda / Speaker(s):

- "Representing powers of numbers as subset sums of small sets", David Moulton, Center for Communications Research, Princeton University.

Abstract:

At the 1997 West Coast Number Theory Conference
 at Asilomar, Gerry Myerson asked the following
 question:  Is there a set $B$of $n$numbers,
 such that each power of $2$from $1$to $2^n$is
 the sum of the elements of some subset of $B$?
 We give the surprising answer to this question
 and discuss the general problem of how large a
 set must be for its subset sums to include some
 set of powers of a particular integer.

- Problem Solving Session, Instructor: Ashwath Rabindranath, Dept. of Math, Princeton University.



Saturday, March 6, 2010
1:00 - 4:00 pm


Rm. 314, Fine Hall at Princeton University,  Washington Road, Princeton, NJ 08540
 
 
Agenda / Speaker(s):

- "P-adics: Another Look at the Integers", Kevin Hughes, Graduate Student, Dept. of Math., Princeton University

- Problem Solving Session, Instructors:  Alison Miller and Aaron Pixton, IMO Gold Medalists, Athens, Greece, 2004,  Dept. of Math., Princeton University.


 
Saturday, Feb. 27, 2010
1:00 - 4:00 pm


Rm. 314, Fine Hall at Princeton University,  Washington Road, Princeton, NJ 08540
 
Agenda / Speaker(s):

- "Mathematical Magic of Black Holes,"  Prof. Sergiu Klainerman, Dept. of Math., Princeton University

- Problem Solving Session, Instructors: Ashwath Rabindranath and Aaron Pixton  (IMO Gold Medalist, Athens, Greece, 2004), Dept. of Math., Princeton University.

 
Saturday, Feb. 20, 2010
1:00 - 4:00 pm


Rm. 314, Fine Hall at Princeton University,  Washington Road, Princeton, NJ 08540

 
Agenda / Speaker(s):

- "Surreal Numbers," Prof. John H, Conway, John von Neumann Distinguished Professor of Mathematics, Dept. of Math., Princeton University

- Problem Solving Session, Instructor: Alison Miller  (IMO Gold Medalist, Athens, Greece, 2004), Dept. of Math., Princeton University.



Saturday, Feb. 13, 2010
1:00 - 4:00 pm


Rm. 314, Fine Hall at Princeton University,  Washington Road, Princeton, NJ 08540

 
Agenda / Speaker(s):

- "The Kakeya Needle Problem," Prof. Charles Fefferman, Dept. of Math., Princeton University

Abstract:

Call a region E in the plane "big enough" if a needle of length 1 meter can be turned through a full 360 degrees without ever leaving E. The original Kakeya Needle Problem is to find the least possible area of a "big enough" region E.

This talk explains the problem and its counterintuitive solution. If time permits, the talk will describe several related problems.

- Problem Solving Session, Instructors: Aaron Pixton (IMO Gold Medalist, Athens, Greece, 2004) and Ashwath Rabindranath, Dept. of Math., Princeton University.


 
Saturday, Feb. 6, 2010


 
NO CLASS

(Due to inclement weather)


 
Saturday, Jan. 30, 2010
1:00 - 4:00 pm


Rm. 314, Fine Hall at Princeton University,  Washington Road, Princeton, NJ 08540
 
Agenda / Speaker(s):

- "Graph Containment and Planar Graphs," Adam Hesterberg (Winner, 16th International Math Competition (IMC), Budapest, Hungary, 2008 / Winner, International Linguistics Olympiad, St. Petersburg, Russia, 2007 / Scored top marks at USMO, 2007 / US National Champion,  MATHCOUNTS, 2003), Dept. of Math., Princeton University

Abstract:

What should it mean for one graph to "contain" another? We
discuss several possible notions of "containment," and use one of them to prove a theorem that exactly characterizes graphs that can be drawn on paper with no edges crossing.

- "Graph Theory: 4 Color Theorem," Bianca Ray Avalani

- Problem Solving Session, Instructors: Ilya Vinogradov and Ashwath Rabindranath, Dept. of Math., Princeton University.

 
Saturday, Jan. 23, 2010
1:00 - 4:00 pm


Rm. 314, Fine Hall at Princeton University,  Washington Road, Princeton, NJ 08540

Agenda / Speaker(s):


- "Ramsey Theory: Order in Chaos," Prof. Avi Wigderson, H. Maass Distinguished Professor at the School of Math, Institute for Advanced Study, 2009 Godel Prize and 2008 Conant Prize Winner.

Abstract:

Consider the following statements:
- Among any three people, at least two have the same gender.
- Among any six people, there must be three who are mutual
acquaintances, or three mutual strangers.
- If a 101 people are standing in line, at least 11 of them are ordered by height  (either increasing or decreasing).
- In any way you color every integer either Red or Blue, there must be an arithmetic progression of length a million, which members are all colored Red or all colored Blue.

All statements above are theorems from "Ramsey Theory" (named after the British logician Frank Ramsey) showing roughly that in various "large enough" complex structures, there must always be a smaller part which is  very "organized".

We'll get a taste of this beautiful theory with examples, proofs, games and bounds on just how large is "large enough" (which in some cases is eeeenormous).

- "Fractals - Part II," Bianca Ray Avalani

- Problem Solving Session, Instructor: Alison Miller (IMO Gold Medalist, Athens, Greece, 2004), Dept. of Math., Princeton University.

 
Saturday, Jan. 16, 2010
1:00 - 4:00 pm


Rm. 314, Fine Hall at Princeton University,  Washington Road, Princeton, NJ 08540
 
Agenda / Speaker(s):

- "Tiling the Plane," Prof. Anna Wienhard, Dept. of Math, Princeton University

- "Fractals - Part I," Bianca Ray Avalani

- Problem Solving Session, Instructors: Alison Miller and Aaron Pixton (both IMO Gold Medalists, Athens, Greece, 2004), Dept. of Math., Princeton University.

 
Saturday, Dec. 19, 2009


 
NO CLASS

(Due to inclement weather)
 
Saturday, Dec. 12, 2009
1:00 - 4:00 pm


Rm. 314, Fine Hall at Princeton University,  Washington Road, Princeton, NJ 08540
 
Agenda / Speaker(s):

- "The Language of Modern Mathematics -- Group Theory - Part II," Sam Ruth, Dept. of Math., Princeton University

- Problem Solving Session, Instructor: Alison Miller, Dept. of Math., Princeton University.

 
Saturday, Dec. 5, 2009
1:00 - 4:00 pm


Rm. 314, Fine Hall at Princeton University,  Washington Road, Princeton, NJ 08540
 
Agenda / Speaker(s):

- "The Language of Modern Mathematics -- Group Theory - Part I," Sam Ruth, Dept. of Math., Princeton University.

- AMC-8 Review, Bianca Ray Avalani.

- Problem Solving Session, Instructors: Alison Miller, Dept. of Math., Princeton University, (Advanced Session).

 
Saturday, Nov. 28, 2009
 
 
NO CLASS

(Thanksgiving Holiday)

 
Saturday, Nov. 21, 2009
2:00 - 4:00 pm


Rm. 314, Fine Hall at Princeton University,  Washington Road, Princeton, NJ 08540

 
NO CLASS

(AMC-8 Exam)

 
Saturday, Nov. 14, 2009
1:00 - 4:00 pm


Rm. 314, Fine Hall at Princeton University,  Washington Road, Princeton, NJ 08540
 
Agenda / Speaker(s):

- "Graph Theory," Alexandra Ovetsky, Dept. of Math., Princeton University 

- Problem Solving Session, Instructors: Andrei Jorza and Aaron Pixton, Dept. of Math., Princeton University.


Saturday, Nov. 7, 2009
1:00 - 4:00 pm

Rm. 314, Fine Hall at Princeton University,  Washington Road, Princeton, NJ 08540

 
Agenda / Speaker(s):

- "Diophantine Equations," Maria Nastasescu, Dept. of Math., Princeton University 

- Problem Solving Session, Instructors: Maria Nastasescu and Alison Miller, Dept. of Math., Princeton University and Bianca Ray Avalani.


Saturday, Oct 31, 2009
1:00 - 4:00 pm

Rm. 314, Fine Hall at Princeton University,  Washington Road, Princeton, NJ 08540

 

 


Agenda / Speaker(s):


- "Sums of two squares," Stefan Patrikis, Dept. of Math., Princeton University 

- Problem Solving Session, Instructors: Adam Hesterberg and Ilya Vinogradov, Dept. of Math., Princeton University and Bianca Ray Avalani.


Saturday, Oct 24, 2009
1:00 - 4:00 pm

Rm. 314, Fine Hall at Princeton University,  Washington Road, Princeton, NJ 08540


Agenda / Speaker(s):

- "Generating Functions," Prof. Andrei Okounkov, Dept. of Math., Princeton University

- Problem Solving Session, Instructors: Alison Miller and Andrei Jorza, Grad. Students, Dept. of Math., Princeton University - Problem Set


Saturday, Oct 17, 2009
1:00 - 4:00 pm

Rm. 314, Fine Hall at Princeton University,  Washington Road, Princeton, NJ 08540

 

   

Agenda / Speaker(s):

- “Finite Fields:  one can't double the cube or trisect the angle with ruler and compass," Prof. Charles Fefferman, Dept. of Math., Princeton University

Abstract:

This talk explains why it's impossible to trisect an angle using only compass and straightedge.


- Problem Solving Session, Instructors: Ilya Vinogradov, Ph. D. Student, Adam Hesterberg, Undergraduate Student, Dept. of Math., Princeton University and Bianca Ray Avalani.   


Saturday, Oct 10, 2009
1:00 - 4:00 pm

Rm. 314, Fine Hall at Princeton University,    Washington Road, Princeton, NJ 08540


Agenda / Speaker(s):

- “Some infinities are bigger than the others," Slater Stich, Princeton University

- Problem Solving Session, Instructors:  Andrei Jorza and Boris Alexeev, Ph.D. Students, Dept. of Math., Princeton University.



Saturday, Oct 3, 2009
1:00 - 4:00 pm

Rm. 314, Fine Hall at Princeton University   Washington Road, Princeton, NJ 08540

 

 

 

 

  

Inauguration Day

Agenda / Speaker(s):

- Welcome Message - Bianca Ray Avalani

- "Numbers and Games," Prof. John H. Conway, John von Neumann Distinguished Professor of Mathematics, Dept. of Math., Princeton University

- Problem Solving Session, Instructors:  Ilya Vinogradov and Alison Miller, Ph.D. Students, Dept. of Math., Princeton University, and Bianca Ray Avalani 


Directions to Fine Hall:

From US 1 south, make a right on Washington Road.  Drive past the soccer field  on the right, followed by the Carnegie Lake. After the first light, the stadium will be on the right, followed by the Fine Hall building.

Parking for Fine Hall:

Cars can be parked at any metered parking on the campus.   

http://www.princeton.edu/~pumap/

(Select "Academic" and "Fine Hall" on the drop down menus to see the location of the building in the interactive campus map)

 

 

 

 

 

Practice Problem Sets:

Solutions: