Princeton Math Circle







Calendar
 
Saturday, Nov. 26, 2011
 
Thanksgiving Holiday
 
Saturday, Nov. 19, 2011
 
Thanksgiving Holiday
 
Saturday, Nov. 12, 2011

 
NO CLASS
 
Saturday, Nov. 5, 2011
2- 5 pm (middle school)
3- 6 pm (high school)


Rm. 110 and 314, Fine Hall at Princeton University,  Washington Road, Princeton, NJ 08540

(For directions to Fine Hall and parking, please scroll down to bottom of this page)
 
Agenda / Speaker(s):

- "The Elegant Approach to Modulo p", Minh-Tam Trinh, Dept. of Math., Princeton University

Abstract:

We prove elementary facts about the arithmetic of Fp, using elegant proofs of a combinatorial nature. Topics include why Fp is a field, Euler's Criterion, the multiplicativity of the Legendre symbol, and a theorem about the Gauss sum over the Legendre symbol.

- "Boolean Algebras and Applications - Part III",  Dr. R. Grabovskaya and Tatiana Ter-Saakov

 

 

- Problem Solving Session, Instructors: Ashwath Rabindranath, Tatiana Ter-Saakov and Bianca Ray Avalani

 
Saturday, Oct 29, 2011
2- 5 pm (middle school)
3- 6 pm (high school)


Rm. 110 and 314, Fine Hall at Princeton University,  Washington Road, Princeton, NJ 08540

(For directions to Fine Hall and parking, please scroll down to bottom of this page)

 
Agenda / Speaker(s):

- "The Secret Truth about Solving Polynomial Equations", Will Sawin, Dept. of Math., Princeton University

Abstract:

By day, the quadratic and cubic formulas appear to be just mild-mannered equations, but a mathematician sees them as manifestations of a deeper, awesome structure. The key ideas of this structure can be expressed without advanced mathematics, and that is what I will discuss in this talk.

- "Boolean Algebras and Applications - Part II",  Dr. R. Grabovskaya and Tatiana Ter-Saakov

 

 

- Problem Solving Session, Instructors: Sarah Trebat-Leder, Tatiana Ter-Saakov and Bianca Ray Avalani


 
Saturday, Oct 22, 2011
2- 5 pm (middle school)
3- 6 pm (high school)


Rm. 110 and 314, Fine Hall at Princeton University,  Washington Road, Princeton, NJ 08540

(For directions to Fine Hall and parking, please scroll down to bottom of this page)
 
Agenda / Speaker(s):

- "P-adics", Ila Varma, Dept. of Math., Princeton University

- "Boolean Algebras and Applications - Part I",  Dr. R. Grabovskaya and Tatiana Ter-Saakov

 

- Problem Solving Session, Instructors: Ashwath Rabindranath, Tatiana Ter-Saakov and Bianca Ray Avalani

 
Saturday, Oct 15, 2011


 
NO CLASS

(Closed due to building maintenance)



Saturday, Oct 8, 2011
2- 5 pm (middle school)
3- 6 pm (high school)


Rm. 110 and 314, Fine Hall at Princeton University,  Washington Road, Princeton, NJ 08540

(For directions to Fine Hall and parking, please scroll down to bottom of this page)

 
Agenda / Speaker(s):

- "Completion by Cauchy",  Kevin Wilson, Dept. of Math., Princeton University

- "Scientific Applications of Euclidean Geometry", Bianca Ray Avalani

 

- Problem Solving Session, Instructors: Alison Miller, Abhishek Lingineni and Bianca Ray Avalani

   
 

Saturday, May 14, 2011


 

Annual Luncheon

- Keynote Speaker: Bianca Ray Avalani


Saturday, May 7, 2011
2- 5 pm (middle school)
3- 6 pm (high school)


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

(For directions to Fine Hall and parking, please scroll down to bottom of this page)
 
Agenda / Speaker(s):

- "Mathematical Paradoxes", Arul Shankar, Dept. of Math., Princeton University

- "What's the difference? How to make functions from sequences",  Thomas Draper

 

- Problem Solving Session, Instructors: Thomas Draper, Wen Zhang and Bianca Ray Avalani

 
Saturday, April 30, 2011

2- 5 pm (middle school)
3- 6 pm (high school)


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

(For directions to Fine Hall and parking, please scroll down to bottom of this page)
 
Agenda / Speaker(s):

- "Every Polynomial Vanishes Somewhere", Michael McBreen, Dept. of Math., Princeton University

- "Nim & Tsyan-shizi", Prof. Vladimir Koronenko (Retd.), Voronezh University, Russia

 

Abstract:

Game Nim, different number systems and applications:  how binary system helps to investigate Nim and Fibonacci system game Tsyan-shizi.

- Talks on Math Topics by Middle School Students

 

- Problem Solving Session, Instructors: Doris Voina, Tatiana Ter-Saakov and Bianca Ray Avalani


Saturday, April 23, 2011
2- 5 pm (middle school)
3- 6 pm (high school)


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

(For directions to Fine Hall and parking, please scroll down to bottom of this page)
 
Agenda / Speaker(s):

- "Hensel's Lemma", Stefan Patrikis, Dept. of Math., Princeton University

 

- Talks on Math Topics by Middle School Students

 

- Problem Solving Session, Instructors: Ashwath Rabindranath and Bianca Ray Avalani

 
Saturday, April 16, 2011
2- 5 pm (middle school)
3- 6 pm (high school)


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

(For directions to Fine Hall and parking, please scroll down to bottom of this page)

 
Agenda / Speaker(s):

- "Probability and Fibonacci Series", Tim Kunisky, Dept. of Math., Princeton University

 

- "Linear Regression", Bianca Ray Avalani

 

- Problem Solving Session, Instructors:Alison Miller and Bianca Ray Avalani

 


 
Saturday, April 9, 2011
2- 5 pm (middle school)
3- 6 pm (high school)


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

(For directions to Fine Hall and parking, please scroll down to bottom of this page)
 
Agenda / Speaker(s):

- "How Can You Tell If It Is a Sphere?", Prof. Sun-Yang Alice Chang, Chairperson, Dept. of Math., Princeton University

 

Abstract:

One question which fascinates mathematicians is when can we  tell if a surface is a sphere?  It turns out this question can be answered by a "uniformization theorem" which classifies all (2-dimensional) surfaces. In this talk, I will discuss this theorem and some efforts by mathematicians to generalize this result to higher dimensional spaces.

- "What is Logic (and Fuzzy Logic)?", Bianca Ray Avalani

 

- Problem Solving Session:

 

  • Computational Complexity and Problems
  • Algebraic Logic

Instructors: Sarah Trebat-Leder and Bianca Ray Avalani

 

 
Saturday, April 2, 2011

2- 5 pm (middle school)
3- 6 pm (high school)


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

(For directions to Fine Hall and parking, please scroll down to bottom of this page)

 
Agenda / Speaker(s):

- "Projective Geometry", Ashwath Rabindranath, Dept. of Math., Princeton University

 

- "An Introduction to Logic", joint presentation by students

 

- Problem Solving Session, Instructors:  Wen Zhang, Doris Voina, Ken Anderson and Bianca Ray Avalani

 


 
Saturday, March 26, 2011

2- 5 pm (middle school)
3- 6 pm (high school)


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

(For directions to Fine Hall and parking, please scroll down to bottom of this page)
 
Agenda / Speaker(s):

- "An Introduction to Non-Euclidean Geometry: Sans Calculus", Jun Kitagawa, Dept. of Math., Princeton University

 

- "Euclidean Geometry", Bianca Ray Avalani

 

- Problem Solving Session, Instructors:  Cosmin Pohoata and Bianca Ray Avalani

 

 
Saturday, March 19, 2011

2- 5 pm (middle school)
3- 6 pm (high school)


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

(For directions to Fine Hall and parking, please scroll down to bottom of this page)

 
Agenda / Speaker(s):

- "An Introduction to Matroid Theory", Adam Hesterberg, Dept. of Math., Princeton University

 

- "Spherical Coordinates", Bianca Ray Avalani

 

- Problem Solving Session, Instructors:  Ashwath Rabindranath and Bianca Ray Avalani

 

 
Saturday, March 12, 2011
2- 5 pm (middle school)
3- 6 pm (high school)


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

(For directions to Fine Hall and parking, please scroll down to bottom of this page)
 
Agenda / Speaker(s):

- "An Introduction to Waring's Problem", Prof. Maria Nastasescu, Dept. of Math., Princeton University

 

Abstract:

Can any positive integer number be written as a sum of two squares? How about sum of three squares? Or four squares? How can we generalize the problem to sum of cubes or higher powers?

- "Nim and Some Variations of this Game", Prof. (Retd.) Vladimir Kononenko, Voronezh University, Russia

 

- Problem Solving Session, Instructors:  Prof. (Retd.) Vladimir Kononenko, Tatiana Ter-Saakov, Ashwath Rabindranath and Bianca Ray Avalani

 

 
Saturday, March 5, 2011

2- 5 pm (middle school)
3- 6 pm (high school)


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

(For directions to Fine Hall and parking, please scroll down to bottom of this page)
 
Agenda / Speaker(s):

- "Constructing the Real Line", Prof. Anna Wienhard, Dept. of Math., Princeton University

- "Magic Squares", Kij Saengtawesin

 

- Problem Solving Session, Instructors:  Alison Miller, Ila Varma, Kij Saengtawesin and Bianca Ray Avalani

 


Saturday, February 26, 2011
2- 5 pm (middle school)
3- 6 pm (high school)


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

(For directions to Fine Hall and parking, please scroll down to bottom of this page)

 
Agenda / Speaker(s):

- "Prime Numbers", Kevin Hughes, Dept. of Math., Princeton University

- "To Infinity....and Beyond!", Jeff VanderKam

 

- Problem Solving Session, Instructors:  Ashwath Rabindranath, Thomas Draper, Jeff VanderKam, Wen Zhang and Bianca Ray Avalani

 


Saturday, February 19, 2011

2- 5 pm (middle school)
3- 6 pm (high school)


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

(For directions to Fine Hall and parking, please scroll down to bottom of this page)

 
Agenda / Speaker(s):

- "Cryptography", Kevin Wilson, Dept. of Math., Princeton University

- "Statistical Modeling: Bayesian Models,  Deterministic vs. Stochastic", Bianca Ray Avalani

 

- Problem Solving Session, Instructors:  Horia Mania and Bianca Ray Avalani

 


Saturday, February 12, 2011
2- 5 pm (middle school)
3- 6 pm (high school)


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

(For directions to Fine Hall and parking, please scroll down to bottom of this page)
 
 
Agenda / Speaker(s):

- "Measure: How mathematicians think about volume", Ian Frankel, Dept. of Math., Princeton University

- "On Distinguishability and Selections", Bowei Liu, Princeton University

 

- Problem Solving Sessions:

 

    • Counting and Probability

    • Pigeon-Hole Principle

Instructors:  Sarah Trebat-Leder, Bowei Liu, Wen Zhang and Bianca Ray Avalani


Saturday, February 5, 2011
2- 5 pm (middle school)
3- 6 pm (high school)


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

(For directions to Fine Hall and parking, please scroll down to bottom of this page)
 
 
Agenda / Speaker(s):

- "Generating Functions", Alison Miller, Dept. of Math., Princeton University

- "Learning how to count", Matthew Superdock, Dept. of Math., Princeton University

 

- Problem Solving Session, Instructors:  Matt Superdock and Bianca Ray Avalani

 

 
Saturday, January 29, 2011

2- 5 pm (middle school)
3- 6 pm (high school)


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

(For directions to Fine Hall and parking, please scroll down to bottom of this page)
 
Agenda / Speaker(s):

- "Euler's Formula, Polyhedra and Surfaces", Andy Manion, Dept. of Math., Princeton University

 

Abstract:

How to make surfaces by gluing edges? What does it mean to orient a surface? Introduction to a method for classifying surfaces (topologically).  What are curvatures?

- "Introduction to Probability and Combinatorics", Bianca Ray Avalani

- "Introduction to Analytic Number Theory", Jeff VanderKam and Thomas Draper

 

- Problem Solving Session, Instructors:  Sarah Trebat-Leder, Thomas Draper, Jeff VanderKam and Bianca Ray Avalani

 

 
Saturday, January 22, 2011

2- 5 pm (middle school)
3- 6 pm (high school)


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

(For directions to Fine Hall and parking, please scroll down to bottom of this page)


Agenda / Speaker(s):

- "Turan Type Problems" (Graph Theory), Corina Panda, Dept. of Math., Princeton University

 

- Problem Solving Session, Instructors:  Alison Miller, Wen Zhang and Bianca Ray Avalani

 

 
Saturday, January 15, 2011
2- 5 pm (middle school)
3- 6 pm (high school)


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

(For directions to Fine Hall and parking, please scroll down to bottom of this page)
 
Agenda / Speaker(s):

- "Randomness with and without Probability", Francesco Cellarosi, Dept. of Math., Princeton University

 

Abstract:

Concepts like randomness and chaos are somewhat intuitive, but these are very hard mathematical concepts.  I will try to present the main mathematical ideas behind these concepts, partially using elementary Probability Theory. I will also discuss some real-life applications.  Be ready to flip a 3-sided coin!

- "Basic Rules of Modular Arithmetic", Ken Anderson

- Problem Solving Session, Instructors:  Alan Chang, Ken Anderson, Wen Zhang and Bianca Ray Avalani

 


Saturday, January 8, 2011

2- 5 pm (middle school)
3- 6 pm (high school)


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

(For directions to Fine Hall and parking, please scroll down to bottom of this page)

 
Agenda / Speaker(s):

- "The Close Binary Fraction: A Bayesian Analysis of SDSS M Dwarf Spectra", Ben Clark, National Winner of the 2010 Siemens Competition in Math, Science and Technology

 

- "Elliptic Curves", Ashwath Rabindranath, Dept. of Math., Princeton University

- "Number Theory", Bianca Ray Avalani

- Problem Solving Session, Instructors:  Thomas Draper, Jeff VanderKam and Bianca Ray Avalani

 


 
Saturday, December 11, 2010
2- 5 pm (middle school)
3- 6 pm (high school)


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

(For directions to Fine Hall and parking, please scroll down to bottom of this page)

Agenda / Speaker(s):

- "Wonders of Factorials", Kevin Wilson, Dept. of Math., Princeton University

 

- "Calculus and its Fundamental Theorem", Alan Chang, Dept. of Math., Princeton University

- Problem Solving Session, Instructors:  Ashwath Rabindranath, Bowei Liu, Wen Zhang and Bianca Ray Avalani

 

 
Saturday, December 4, 2010
2- 5 pm (middle school)
3- 6 pm (high school)


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

(For directions to Fine Hall and parking, please scroll down to bottom of this page)

 
Agenda / Speaker(s):

- "Continued Fractions", Djordjo Milovic, Dept. of Math., Princeton University

 

- "Graphs and Double Counting", Leonardo Stedile, Dept. of Math., Princeton University

- Problem Solving Session, Instructors:  Thomas Draper, Ken Anderson and Bianca Ray Avalani

 



 
Saturday, November 27, 2010

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

(For directions to Fine Hall and parking, please scroll down to bottom of this page)

 
Thanksgiving Holiday
 
Saturday, November 20, 2010

3- 6 pm (high school)

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

(For directions to Fine Hall and parking, please scroll down to bottom of this page)

 
Agenda / Speaker(s):

- "Topology, Surfaces and Knot Theory", Prof. David Gabai, Dept. of Math., Princeton University

 

Abstract:

We will introduce this beautiful subject that has many implications in and outside of mathematics.

- No Middle School Session: AMC-8 Exam

 
Saturday, November 13, 2010
2- 5 pm (middle school)
3- 6 pm (high school)


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

(For directions to Fine Hall and parking, please scroll down to bottom of this page)

 
Agenda / Speaker(s):

- "Pigeons Sometimes Have to Share Pigeonholes", Alexandra Fradkin, Dept. of Math., Princeton University

 

Abstract:

The pigeonhole principle states that if n objects are placed in k boxes, where k < n, then at least one of the boxes contains more than one object.

As obvious as this fact may sound, it has many non-trivial applications. In this talk I will survey some results that can be derived from the pigeonhole principle.

- "V-E+F = 2 and Platonic Solids", Sarah Trebat-Leder, Dept. of Math., Princeton University

- Problem Solving Session, Instructors:  Bowei Liu, Wen Zhang and Bianca Ray Avalani

 

 
Saturday, November 6, 2010
2 - 5 pm (middle school)
3 - 6 pm (high school)


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

(For directions to Fine Hall and parking, please scroll down to bottom of this page)

 
Agenda / Speaker(s):

- "Sums of Three Squares", Prof. Peter Sarnak, Eugene Higgins Professor of Mathematics, Dept. of Math., Princeton University

- "Local Optimization by the Greedy Algorithm", Bianca Ray Avalani

- Problem Solving Session, Instructors:  Sunny Xu, Ashwath Rabindranath and Bianca Ray Avalani

 


 
Saturday, October 30, 2010
2 - 5 pm (middle school)
3 - 6 pm (high school)


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

(For directions to Fine Hall and parking, please scroll down to bottom of this page)
 
Agenda / Speaker(s):

- "Why it's better to be a drunkard in two dimensions than in three", Elena Fuchs, Institute of Advanced Study

 

Abstract:

The theory of random walks, sometimes called drunkard's walks because they somehow simulate the steps a drunkard might take while stumbling home from the bar, is one of many applications of probability theory.  In this talk, we will recall some facts about probability theory, and see how it applies to many questions in real life (we'll even test some of these questions out on the audience). In particular, we'll try to get a handle on some rather surprising facts about random walks in different dimensions, and see what a famous Hungarian mathematician named George Polya had to say about them.  This talk will hopefully have something to offer for both more and less advanced students. metimc

- "Challenges of Infinity: from Limits to Rational Functions", Bianca Ray Avalani

- Problem Solving Session, Instructors:  Sarah Trebat-Leder, Kij Saengtawesin, Bowei Liu and Bianca Ray Avalani

 


 
Saturday, October 23, 2010
2 - 5 pm (middle school)
3 - 6 pm (high school)


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

(For directions to Fine Hall and parking, please scroll down to bottom of this page)

 
Agenda / Speaker(s):

- "Knot Theory", Erick Knight, Dept. of Math., Princeton University

- Problem Solving Session, Instructors:  Cosmin Pohoata, Sunny Xu, Wen Zhang and Bianca Ray Avalani

 

 
Saturday, October 16, 2010
2 - 5 pm (middle school)
3 - 6 pm (high school)


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

(For directions to Fine Hall and parking, please scroll down to bottom of this page)

 
Agenda / Speaker(s):

- "Combinatorial Identities and Pascal's Triangle", Alan Chang, Dept. of Math., Princeton University

- "An Abstract Algebraic Approach to Aboriginal Ancestry", Sarah Trebat-Leder, Dept. of Math., Princeton University

- Problem Solving Session, Instructors:  Ashwath Rabindranath, Amy Zhou and Bianca Ray Avalani

 


 
Saturday, October 9, 2010
2 - 5 pm (middle school)
3 - 6 pm (high school)


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

(For directions to Fine Hall and parking, please scroll down to bottom of this page)

 
Agenda / Speaker(s):

- "Hilbert's Hotel" (Hilbert's Paradox), Ila Varma, Dept. of Math., Princeton University

- "Groups and Symmetry", Hyunmoon Kim, Princeton University

- "Scalars and Vectors: From Navier-Stokes to Euler Equations", Bianca Ray Avalani

- Problem Solving Session, Instructors:  Alison Miller, Ken Anderson, Bowei Liu and Bianca Ray Avalani

 


 
Saturday, October 2, 2010
2 - 5 pm (middle school)
3 - 6 pm (high school)


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

(For directions to Fine Hall and parking, please scroll down to bottom of this page)
 
Agenda / Speaker(s):

- Welcome Message - Bianca Ray Avalani

- Keynote speech on "Dots, Boxes and Surreal Numbers" by Prof. John H. Conway, John von Neumann Distinguished Professor of Mathematics, Dept. of Math., Princeton University

- "Game Problems: How Never to Lose a Game Again", Matthew Superdock, Princeton University

- "Numbers in Nature and Beyond: Cardinality vs. Ordinality", Bianca Ray Avalani

- Problem Solving Session, Instructors:  Ashwath Rabindranath, Wen Zhang and Bianca Ray Avalani

 


   
 
Saturday, May 15, 2010
1- 4 pm


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

(For directions to Fine Hall and parking, please scroll down to bottom of this page)
 
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- 4 pm

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

(For directions to Fine Hall and parking, please scroll down to bottom of this page)
 
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- 4 pm

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

(For directions to Fine Hall and parking, please scroll down to bottom of this page)
 
Agenda / Speaker(s):


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


 
Saturday, April 24, 2010

1 - 4 pm

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

(For directions to Fine Hall and parking, please scroll down to bottom of this page)
 
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- 4 pm


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

(For directions to Fine Hall and parking, please scroll down to bottom of this page)

 
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 - 4 pm


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

(For directions to Fine Hall and parking, please scroll down to bottom of this page)

 
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 - 4 pm


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

(For directions to Fine Hall and parking, please scroll down to bottom of this page)
 
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 - 4 pm


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

(For directions to Fine Hall and parking, please scroll down to bottom of this page)
 
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 - 4 pm


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

(For directions to Fine Hall and parking, please scroll down to bottom of this page)
 
 
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 - 4 pm


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

(For directions to Fine Hall and parking, please scroll down to bottom of this page)
 
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 - 4 pm


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

(For directions to Fine Hall and parking, please scroll down to bottom of this page)

 
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 - 4 pm


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

(For directions to Fine Hall and parking, please scroll down to bottom of this page)

 
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 - 4 pm


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

(For directions to Fine Hall and parking, please scroll down to bottom of this page)
 
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 - 4 pm


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

(For directions to Fine Hall and parking, please scroll down to bottom of this page)

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 - 4 pm


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

(For directions to Fine Hall and parking, please scroll down to bottom of this page)
 
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 - 4 pm


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

(For directions to Fine Hall and parking, please scroll down to bottom of this page)
 
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 - 4 pm


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

(For directions to Fine Hall and parking, please scroll down to bottom of this page)
 
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 - 4 pm


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

(For directions to Fine Hall and parking, please scroll down to bottom of this page)

 
NO CLASS

(AMC-8 Exam)

 
Saturday, Nov. 14, 2009
1 - 4 pm


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

(For directions to Fine Hall and parking, please scroll down to bottom of this page)

 
Agenda / Speaker(s):

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

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


Saturday, Nov. 7, 2009
1 - 4 pm

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

(For directions to Fine Hall and parking, please scroll down to bottom of this page)

 
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 - 4 pm

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

(For directions to Fine Hall and parking, please scroll down to bottom of this page)

 

 

 


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 - 4 pm

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

(For directions to Fine Hall and parking, please scroll down to bottom of this page)


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 - 4 pm

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

(For directions to Fine Hall and parking, please scroll down to bottom of this page)

 

 

   


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 - 4 pm

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

(For directions to Fine Hall and parking, please scroll down to bottom of this page)


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 - 4 pm

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

(For directions to Fine Hall and parking, please scroll down to bottom of this page)

 

 

 

 

 

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, stay on Washington Road and go past the overhead breezeway - the stadium will be on the right, followed by the Fine Hall building also on the right.

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)

  

Parking:

Cars can be parked at the gravel parking lot right across from the Lewis Library (next to the Fine Hall) or at any metered parking on campus.

 

 

 

 

 

 


Practice Problem Sets:

Solutions: