Archives

1 Interactive recreational math presentation.

This presentation is open to people of all backgrounds.

The content is chosen so that it is new to most people.

2 Introductory problem solving workshop.

This is a relaxed problem solving workshop.

To see if this is right for you, check out these two problem sets:

If this one is too hard to start, then you are not ready yet.

If this one is too easy, then this is not for you.

3 Intermediate Problem Solving Workshop

Topic-based workshop covering algebra, geometry, combinatorics, and number theory. Our spring workshop will concentrate on AMC 10/12 level problems.

4 Advanced contest math.

This class is designed for those who are comfortable with the AMC 10/12 and wish to train for contests such as HMMT/PUMAC/ARML.

Summer 2025

AMC 8 and MATHCOUNTS Preparation Workshop

Presented by Warren Fu and Girish Prasad

The workshop is designed for 4th to 8th graders who are interested in solving AMC 8 / MATHCOUNTS problems.

Online Zoom: https://us06web.zoom.us/j/87914723806?pwd=dHBkNDNWOHBpdmdkT2xLbFBWTDZJUT09

Date: Wednesday and Saturday from July 10th to August 21st

Time: varies 4-4:45 pm or 7-7:45 pm depending on the date.

7/16/25 - The AMC 8 and Mathcounts (Warren & Girish @ 4pm)

7/19/25 - Primes & Modular Arithmetic (Warren @ 4pm)

7/23/25 - Relationships Between LCMs and GCDs (Girish @ 4pm)

7/26/25 - Bases (Warren @ 4 pm)

7/30/25 - Circles (Girish @ 4 pm)

8/2/25 - Polygons (Warren @ 4 pm)

8/6/25 - Similarity (Girish @ 4pm)

8/9/25 - Logic Puzzles (Warren @ 4 pm)

8/13/25 - Combinations and Permutations (Warren @ 4 pm)

8/16/25 - Constructive Counting (Girish @ 4 pm)

8/20/25 - Rates (Warren @ 4pm)

8/23/25 - Inequalities (Girish @ 4 pm)

8/27/25 - Lateral Thinking Puzzles (Warren @ 4 pm)

Spring 2025

Recreational Math Seminar

Our main event, open to all levels. Presenters and topics vary from week to week.

Location: Brownson Hall BR-218, Manhattanville University

Time: Tuesdays 6-7:30 pm

Feb 4

Title: Sums of quadratic polynomials

Speaker: Dr. Gautam Chinta,

Abstract: The solutions to a quadratic equation are intimately related to the discriminant of the polynomial. I will describe a remarkable

property of sums of a collection of quadratic polynomials with a fixed discriminant. The elementary questions that arise quickly lead to

unsolved problems in number theory. This talk should be accessible to anyone who knows the quadratic formula.

Bio: Dr. Chinta is a Professor of Mathematics at CUNY. He received his PhD in Mathematics from Columbia University and his undergraduate degree from Yale.

Feb 11

Title: Words, groups, and a dash of topology

Speaker: Dr. Matt Cushman

Abstract: A "word" over an alphabet of letters is simply what you get when you string a bunch of those letters together. For example, if the alphabet is {a,b}, then a, b, ab, and ba are all distinct words. This feels very discrete, combinatorial, and algebraic. What do substructues of this look like, for example, "the words of even length"? We will discuss this and related questions, which, surprisingly questions of continuity (topology) and infinity become important tools and considerations.

Bio: Matt is a regular contributor to the Westchester Area Mathematics Circle. He holds a PhD in Mathematics from the University of Chicago and undergraduate and masters degrees from Carnegie Mellon in Mathematics and Philosophy. He has applied mathematics to problems in technology and finance throughout his career, launching an electronic trading firm, Etale, and prior to that running quantitative teams at Citadel and Knight.

Feb 25

Title: The Cryptography Behind Crypto

Speaker: Dr Lisa Yin

Abstract: What is Bitcoin? How do you "mine" one? And how does it stay secure without a central authority? The answer lies in cryptography! This talk explores the mathematical tools that power Bitcoin—hash functions, digital signatures, and proof-of-work. Join us to uncover the magic behind Bitcoin and other digital gold!

Bio: Lisa Yin received her PhD in applied mathematics from MIT. Specialized in the field of cryptography and information security, Lisa has made major contributions in analyzing and breaking ciphers that are widely used in practice. Lisa is also passionate about sharing her love for mathematics with young mathletes. As a former parent coach for a middle school math team, she led the team to win the MATHCOUNTS state championship in Connecticut for three consecutive years.

Mar 4

Title: The Busy Beaver Problem

Speaker: Erik Brodsky

Abstract: In 1962, Hungarian mathematician Tibor Radó published a short paper introducing what he called the "Busy Beaver" sequence. Despite its cute name, this sequence is a ferocious mathematical beast: the exact value of the fifth busy beaver number was only proved last year!

In this seminar, we will discuss what the Busy Beaver sequence is, what makes it so complicated, and how it relates to the boundaries of achievable mathematics. And, along the way, we will get a really good answer to the following question: if given a pen, a piece of paper, and ten seconds to write anything, what is the largest finite number you can express?

Mar 11

Title: A Slice of Pi

Speaker: Dr. Henry Ricardo

Abstract: In anticipation of Pi Day 2025 (March 14), I offer a ‘slice’ of pi—a gallimaufry of information, a farrago of facts and fancy about this ubiquitous constant, an olio of awesome

revelations. Every attendee should find something new in this presentation.

Bio: Dr. Ricardo has been involved in the world of higher mathematics for almost 60 years, in both the academic field and in industry (IBM). He has graded AP Calculus exams for the College Board and has written two college textbooks. From 2008 to 2011 he served as Governor of the Metropolitan NY Section of the Mathematical Association of America. He retired from the City University of New York as Professor of Mathematics in 2009. He has been affiliated with the Westchester Area Math Circle since 2017, giving talks and conducting sessions on various topics for students participating in math competitions.

Mar 18

Title: Noisy Channels, Strings, and Graphs

Speaker: Dr. Rik Sengupta

Abstract: Imagine being given a 10,000-piece jigsaw puzzle of the cover of the Beatles’ White Album, which is famously almost entirely white. What’s worse, instead of solving it directly, you are only allowed to take a few pieces randomly out of the box, examine them, and then put them back into the box. How long would it take you to fully reconstruct the White Album cover, assembling your information piece by piece? In this presentation, I’ll set up the problem mathematically, give some insights into solving it, and connect it to important computational problems from today, such as mapping the internet, understanding the power of random coin flips, and identifying evolutionary patterns to discover common ancestors of seemingly unrelated species.

Bio: Rik Sengupta is a Research Scientist at IBM, based out of Cambridge. He has an undergraduate degree in mathematics from Princeton University, a master's degree in applied mathematics from MIT, and a PhD in theoretical computer science from UMass Amherst. When he is not working, he enjoys puzzles and board games.

Mar 25

Title: Coding theory and error detection

Speaker: Dr. Brooke Feigon

Abstract: On the back of most books is a 10-digit or 13-digit International Standard Book Number (ISBN) that uniquely identifies the book. Is 0-378-90040-3 a valid ISBN? What about 0-387-90040-3? Or 0-377-90040-3? In coding theory, we want to encode information in a way that can detect and ideally even correct errors in the message. We will explore this topic, starting with the example of the ISBN code.

Bio: Dr Feigon is a Professor of Mathematics at CUNY. She received her PhD in Mathematics from UCLA.

Apr 1

Title: On the Spacing Between Successive Prime Numbers and Writing Natural Numbers as the Sum of Squares

Speaker: Dr Jon Lenchner, IBM T.J. Watson Research Center

Abstract: In this talk I will discuss two famous topics in number theory: (i) the spacing between successive prime numbers and (ii) under what conditions you can write a natural number as the sum of two non-negative integers. I will show that there are arbitrarily large gaps between successive primes, yet also explain that there are intervals where you are sure to find a prime. We will then look closely at arithmetic mod a prime and use that to determine what primes can be written as the sum of two squares.

Bio: Dr. Jon Lenchner is a Senior Technical Staff Member at the IBM T.J. Watson Research Center in Yorktown Heights, NY. Previously he was the Chief Scientist of the IBM Research Africa labs in Kenya and South Africa. He has developed robots to help with data center energy efficiency and for greeting visitors at the IBM lab. He has also worked on highly instrumented, smart spaces and smart conference rooms, including a highly instrumented "war room" to help the professional basketball team, the Toronto Raptors, with trades and draft picks.

Apr 8

Title: Explorations in percolation

Speaker: Dr Ivan Corwin

Abstract: How does water find its way through sand, or stone? How do ideas or diseases spread? How does iron become magnetized? All of these questions are related to understanding probabilistic percolation models on graphs. We will explore some of these models and the remarkable scaling phenomena they display.

Bio: Ivan Corwin is a professor of mathematics at Columbia University, focusing on probability and mathematical physics. He did his Ph.D. at the Courant Institute, NYU.

Introductory Problem Solving Workshop

Presented by: Joyce Gong and Aaron Cushman

New to math competitions and problem solving? Join our free relaxed problem solving workshop based on AMC 8 and MATHCOUNTS material. Suitable for middle school students. Enjoy pizza after the end of the class.

Location: Brownson Hall BR-218, Manhattanville University

Time: Tuesdays, 5-5:50 pm

Feb 4 - 2025 AMC 8 Review

Feb 11 - Systems of equations

(winter break)

Feb 25 - Quadratics

Mar 4 - Similarity

Mar 11 - 3D geometry

Mar 18 -

Mar 25

Apr 1

Apr 8

Intermediate Problem Solving Workshop

Presented by Chinmayi Goyal and Chen Lei,

Interested in improving your AMC 10/12 score? Join us for a free topic-based workshop covering algebra, geometry, combinatorics, and number theory. Our spring workshop will concentrate on AMC 10/12 level problems.

Zoom: https://us06web.zoom.us/j/87914723806?pwd=dHBkNDNWOHBpdmdkT2xLbFBWTDZJUT09

Thursdays, 6-6:50 PM, Online

Feb 27: AIME 2025 Review

Mar 6: Quadratics, Polynomials, Vieta’s

Mar 13: Algebraic Manipulations and Factorizations I

Mar 20: No workshop

Mar 27: Probability & Combinatorics I

Apr 3: Probability & Combinatorics II

Apr 10: Number Theory: Factors, Divisors, and Bases

Apr 17: No workshop ( Spring break)

Apr 24: Number Theory: Diophantine Equations, Modular Arithmetic

Advanced Problem Solving Workshop

Presented by: Jai Paradkar, Ethan Shi, and Henry Xue

Comfortable with the majority of AMC 10/12 problems? Interested in team competitions? Come and train with us for more advanced team contests. We will use past GiM, CMIMC, Purple Comet, and ARML problems

Location: Brownson Hall BR-101, Manhattanville University

Time: Sundays, 3:00-4:30 pm

Feb 2 GiM

Feb 9 GiM

Feb 16 GiM

Feb 23 CMIMC

Mar 2 CMIMC

Mar 9 CMIMC

Mar 16 Purple Comet

Mar 23 Purple Comet

Mar 30 Purple Comet

Apr 6 (no workshop) - GAIM competition

Apr 13 Purple Comet

Apr 20 Purple Comet

Apr 27 (no workshop) - Purple Comet Competition

May 4 - ARML

May 11 - ARML

May 18 - ARML

May 25 - (no workshop) - Memorial Weekend

May 31 - ARML

Fall 2024

WAMC Info session

Presented by: Matt Cushman, Jay Tu, and Lucie Brodska

Information session for the parents. We will talk about WAMC workshops, seminars, and competitions that WAMC participates in. We will also answer questions which you may have about WAMC programs.

Sept 3, Tuesdays, 6-7 pm

Online Zoom: https://us06web.zoom.us/j/87914723806?pwd=dHBkNDNWOHBpdmdkT2xLbFBWTDZJUT09

Recreational Math Seminar

Our main event, open to all levels. Presenters and topics vary from week to week.

Location: Brownson Hall BR-218, Manhattanville College

Time: Tuesdays 6-7:30 pm

Sept 10

Title: The abc Conjecture

Speaker: Dr. Gautam Chinta,

The abc-conjecture has been called the “most important unsolved problem in Diophantine analysis.” The conjecture concerns the prime numbers dividing any one of a collection of three integers satisfying A+B+C=0. Dr. Chinta will discuss the history of this simple-sounding conjecture and the striking applications which would follow if it were proven.

Bio: Dr. Chinta is a Professor of Mathematics at CUNY. He received his PhD in Mathematics from Columbia University.

Sept 17

Title: Coin Flips: New Questions on an Old Topic

Speaker: Dr. Matt Cushman

Flipping a fair coin is just about the oldest and most simple objects of study in probability. A recent very active discussion on the social media platform formerly known as Twitter genetated a lively discussion and several preprints posted online by mathematicians. We’ll discuss the basics, conduct some polls, run a few simulations and look at the results of the recent discussions.

Sept 24

Title: The Secret Weapon of an Epic Rap Battle of Mathematics: Solving the Cubic

Speaker: Dr. Matt Cushman

Abstract: During the Renaissance, mathematicians often engaged in public competitions to solve challenging problems as a means to gain prestige and employment. In the 1530s, Niccolò Tartaglia triumphed over his rivals by secretly mastering the general solution to cubic equations. This formula, later published by Gerolamo Cardano and known today as the Cardano-Tartaglia formula, marked a pivotal moment in mathematical history. While the quadratic formula is a staple in high school algebra, the cubic formula is often unexplored. However, it's more than a historical curiosity: the nature of its solution (and the fact that it can be solved at all) points to much deeper structures in algebra. We will derive the cubic formula, delve into its rich history, and explore how it opened the door to the development of modern algebra.

Oct 1

Title: An Introduction to Graph Theory

Speaker: Dr. Brooke Feigon

Abstract: Is it possible to connect three houses to three separate utilities—gas, electric and water—without any of the utility lines crossing? What is the least number of colors you can use if you want to color a map of the United States without using the same color for states that share a border? Can you walk through NYC by crossing each bridge once and only once? Dr. Feigon will introduce graph theory and show how these problems and many more reduce to problems in graph theory.

Bio: Dr Feigon is a Professor of Mathematics at CUNY. She received her PhD in Mathematics from UCLA.

Oct 8

Title: Some Parenthetical Remarks About Counting

Speaker: Dr. Henry Ricardo

Abstract: My talk will introduce a remarkable sequence of numbers that “solve” many seemingly unrelated counting problems. Beginning with some observations about Pascal’s triangle and then moving into an analysis of a problem relating to non-associative operations, we will see the so-called Catalan numbers emerge. These ubiquitous integers have applications in combinatorics, algebra, analysis, number theory, probability theory, geometry, topology, and other areas.

Oct 15

Title: Unexpected Expectations

Speaker: Dr. Ivan Corwin

Abstract: We will explore the weird world of probability where intuition sometimes fails. Can you design three dice so that die A typically beats die B, die B typically beats die C, and die C typically beats die A? How many kids need to be in a room before it is likely that two kids have the same birthday? How many kids need to be in a school before it is likely that every day has at least one birthday? If in a class room everyone randomly chooses a desk, how many kids end up at their correct desk? We will explore these and other questions through hands-on activities and see what they tell us about probabilities and randomness. No prior knowledge of probability is expected.

Bio: Ivan Corwin is a professor of mathematics at Columbia University. His research focuses on probability theory and mathematical physics, in particular questions about how

small scale randomness leads to larger scale structure. Ivan lives in New Rochelle with his wife and four young children and looks forward to having the family participate in math activities around Westchester.

Oct 22

Title: Tiling Generalized Chess Boards with Polyominoes

Speaker: Dr. Jon Lencher

Abstract: We consider a chess board to be an 8x8 grid of squares in the plane. By a generalized planar chess board, we mean a chess board of dimensions n x m for some integer values of n and m. We also consider the further generalization of such boards to three and higher dimensions. We are interested in tiling these generalized chessboards with so-called polyominoes. A (planar) polyomino is a finite collection of edge-connected squares such that every square is connected to every other square via a path that only crosses at edge-edge junctions. We start by considering a beautiful result of Golomb’s about tiling with L-shaped trombones (polyominoes of just three squares, configured in an L shape), and go on from there.

worked on highly instrumented, smart spaces and smart conference rooms, including a highly instrumented "war room" to help the professional basketball team, the Toronto Raptors, with trades and draft picks.

Oct 29

Title: Palindromic pandemonium (part 2)

Speaker: Peder Olsen, Ph.D.

Abstract: We will continue where we left off last year and solve 3 problems if time permits. Problem 1: find all tuples of four distinct natural numbers such that the sum of their reciprocals are 1. Problem 2: Show that the reciprocal of 10 cannot be written as a sum of fewer than four reciprocal palindromes or the sum of 5 distinct reciprocal palindromes. Problem 3 will remain a secret. State-of-the-art GPT-4 was not able to solve a very simplified version of problem 2, yet last year's audience did in less than 5 minutes. Feel free to work on the problems before we meet up. This year will be interactive and there will be no lengthy presentation. Get ready to do lengthy calculations!

Previous Presentation:

Egyptian Palindromic Fractions

Palindromes

Introductory Problem Solving Workshop

Presented by: Joyce Gong and Aaron Cushman

Location: Brownson Hall BR-218, Manhattanville College

Time: Tuesdays, 5-5:50 pm

Sept 10 - Power of a Point

Sept 17 - Triangles, Median, Altitude, Angle Bisector Centroid, Incenter, Circumcenter, Special Triangles

Sept 24 - Quadratic Equations, Factoring, Quadratic Formula, Completing the Square

Oct 1 - Vieta's Formula

Oct 8 - Divisibility, Divisibility Rules, Definition of Mod

Oct 15 - More Modular Arithmetic

Oct 22 - Permutations and Combinations. Factorials, Choose Function

Oct 29 - Inclusion Exclusion, Venn Diagrams

Intermediate Problem Solving Workshop

Presented by Chinmayi Goyal and Chen Lei,

Zoom: https://us06web.zoom.us/j/87914723806?pwd=dHBkNDNWOHBpdmdkT2xLbFBWTDZJUT09

Thursdays, 6-6:50 PM, Online

Aug 22 Probability & Combinatorics I

Aug 29 Probability & Combinatorics II

Sept 5 Algebraic Manipulations I

Sept 12 Algebraic Manipulations II

Sept 19 Geometry I

Sept 26 Geometry II

Oct 3 Number Theory I

Oct 10 Number Theory II

Oct 17 AMC 10/12 Review I

Oct 24 AMC 10/12 Review II

Advanced Problem Solving Workshop

Presented by: Jai Paradkar, Ethan Shi, and Henry Xue

Location: Brownson Hall BR-101, Manhattanville College

Time: Sundays, 3:00-4:30 pm

Sept 8 - MMATHS

Sept 15 - HMMT

Sept 22 - MMATHS

Sept 29 - HMMT

Oct 6 - MMATHS

Oct 13 - HMMT

Oct 20 - MMATHS

Oct 27 - PUMaC

Nov 3 - HMMT

Nov 10 - PUMaC

Summer 2024

AMC 8 and MATHCOUNTS Preparation Workshop

Presented by Warren Fu and Emily Tian

The workshop is designed for 4th to 8th graders who are interested in solving AMC 8 / MATHCOUNTS problems.

Online Zoom: https://us06web.zoom.us/j/87914723806?pwd=dHBkNDNWOHBpdmdkT2xLbFBWTDZJUT09

Date: Wednesday and Saturday from July 10th to August 21st

Time: varies 4-4:45 pm or 7-7:45 pm depending on the date.

July 10th - The AMC 8 and MATHCOUNTS (4 pm)

July 13th - Primes & Modular Arithmetic (4 pm)

July 17th - Relationships Between LCMs and GCDs (7 pm)

July 20th - Bases (4 pm)

July 24th - Circles (7 pm)

July 27th - Polygons (4 pm)

August 31st - Similarity (4 pm)

August 3rd - Logic Puzzles (4 pm)

August 7th - Combinations and Permutations (4 pm)

August 10th - Constructive Counting (4 pm)

August 14th - Rates (4 pm)

August 17th - Inequalities (4 pm)

August 21st - Lateral Thinking Puzzles (4 pm)

If you are interested, please register at

https://forms.gle/CtC37PAr9UkAdcoS7

This is a registration for the entire summer workshop. You don't have to register separately for each session.

Spring 2024

Recreational Math Seminar

Our main event, open to all levels. Presenters and topics vary from week to week.

Location: Brownson Hall BR-18, Manhattanville College

Time: Tuesdays 6-7:30 pm

Jan 30

Title: Cryptography - Using Mathematics to Make and Break Secret Codes

Abstract:

Join us for an exciting journey into the world of cryptography! In this talk, we will delve into the fascinating history of encryption, from ancient secret codes to modern ciphers. We will explore some fundamental math concepts behind these secret codes and showcase applications of modern ciphers that impact our daily lives. Bring a pencil and a piece of paper. Get ready for an interactive experience, where you will create your own secret messages. By the end of the talk, you will be able to decipher this message -- fubswr lv frro :).

Speaker bio:

Lisa Yin received her PhD in applied mathematics from MIT. Specialized in the field of cryptography and information security, Lisa has made major contributions in analyzing and breaking ciphers that are widely used in practice. Lisa is also passionate about sharing her love for mathematics with young mathletes. As a former parent coach for a middle school math team, she led the team to win the MathCounts state championship in Connecticut for three consecutive years.

Feb 6

Title: Python and Primes: The Equation Expedition

Speaker: Dr. Matt Cushman

Step into a world where equations like ax + b = 0 and ax^2 + bx + c = 0 get a prime twist. You may be familiar with solving these equations over "normal" (real) numbers, but what if we wanted to solve them for integers only? Or, related, we might worry about when we can solve them up to divisibility by a prime. We will use computers and Python to explore these questions and look for patterns, from Fermat’s simple insights to the deeper waters of Euler and Gauss. This workshop isn't just solving equations; it's an adventure in uncovering hidden patterns and truths, all through the clear, concise lens of code. We might even prove a few of our conjectures along the way. Join us for a journey where math meets poetry in the rhythm of algorithms.

Feb 13 - Canceled due to weather

Feb 20 no seminar (public school winter break)

Feb 27

Title: Sperner’s Lemma

By Erik Brodsky

Lay a sheet of paper on a table, then crumple it up and put it back on top of its original position. Is there a point on the crumpled paper which is directly above its original location on the flat sheet of paper? The answer, perhaps surprisingly, is yes.

If a rectangle can be partitioned into smaller rectangles, each of which has at least one side of integer length, must this big rectangle also have at least one side of integer length? The answer, once again, is yes.

The two results above both have an elegant proof via a combinatorial result known as Sperner's Lemma. In this talk, we'll introduce and prove Sperner's Lemma, and then see how we can apply it to answer both of the questions above.

Mar 5

Title: The Nobel Prize Machine Quest

Speaker: Dr. Lior Horesh, IBM Research

Abstract:

Imagine we can build a machine that will make Nobel Prize worthy scientific discovery, wouldn't that be neat ? The scientific method has been transformative to humankind. However, there are signs that despite great investment in the area, scientific discovery is approaching a state of stagnation. For decades, scientists have pursued the discovery of mathematical models that describe the way our universe work. Most of their effort followed a first-principles approach, meaning, they (painstakingly) derived new laws of physics, by combining general principles (such as conservation of mass, momentum, energy, etc). With the advancement of computing power and algorithms, an alternative, data-driven approach for discovery has become popular. These approaches consumed a large amount of data, and made an attempt at finding consistent mathematical models that describe the data. While both approaches have their advantages, they also have (remarkably complementary) disadvantages. In this lecture, we will learn about the two breeds of discovery frameworks, explore recent attempts to bridge the divide between them, as to enable discovery of fundamental laws of nature at scale.

Bio: Dr. Lior Horesh is a Principal Research Scientist, Master Inventor, and Senior Manager of the Mathematics and Theoretical Computer Science department at IBM Research. His department's mission is to bring theoretical insights, craft innovative algorithms, and devise new analysis tools that fundamentally advance the fields of mathematics and AI. Dr. Horesh's own research ‎work focuses on algorithmic and theoretical aspects of tensor algebra, numerical analysis, non-linear optimization, inverse problems, active learning, quantum ‎computing and the interplay between symbolic and statistical AI in service of scientific discovery.

Mar 12

Title: THAT'S EASY TO SAY!

Speaker: Shiva Chaudhuri

Shiva Chaudhuri has a PhD in Computer Science from Rutgers University. He worked as a software developer in technology and finance for 25 years. Now retired, he pursues his interests in mathematics and music software, and volunteers various local organizations.

Abstract:

Mathematics is full of problems that are easy to state but hard to solve. Some of these are so easy to state that they require no knowledge of mathematics to understand. Many such problems are open, that is, no one has yet been able to solve them. So, despite being very easy to state and understand, they are difficult to solve. Solutions to these problems might be found by someone without advanced mathematical training, but with imagination, energy, and strong reasoning skills. Since these qualities are more likely found in younger people than older, we will discuss a couple of such problems in this talk. And hope that one of the audience will be the one to solve them!

Mar 19

Title: When Math Gets Difficult: Thoughts about a Mathematical Life

Speaker: Jon Lencher, Research Scientist at IBM TJ Watson Research Center

Abstract:

Many of us have been praised for the mathematical talent we have, and we often take this perceived talent as a source of personal pride. Doing well at math competitions reinforces this sense of pride. But at some point, math is going to be hard for you. You are going to have a hard time making sense of a concept, or you will not be able to solve a particular problem. Others will do better than you at a math competition. What are you going to do then? Is it the most important thing to be the smartest person in the room? Is that important at all? I will describe the difficult journey I took to answer these questions for myself and then open the floor for a general conversation on this topic.

Mar 26 no seminar (public school spring break)

Apr 2

Title: The Amazing Triangular Numbers

Speaker: Dr. Henry Ricardo

Dr. Ricardo has been involved in the world of higher mathematics for almost 60 years, in both the academic field and in industry (IBM). He has graded AP Calculus exams for the College Board and has written two college textbooks. From 2008 to 2011 he served as Governor of the Metropolitan NY Section of the Mathematical Association of America. He retired from the City University of New York as Professor of Mathematics in 2009. He has been affiliated with the Westchester Area Math Circle since 2017, giving talks and conducting sessions on various topics for students participating in math competitions.

Abstract:

Named and studied by Pythagoras and his followers, triangular numbers have inspired research by both amateur and professional mathematicians for centuries. In my talk, I will reveal some of the many properties of these amazing numbers and discuss their connections with other problems in pure and applied mathematics. The mathematics used will range from simple algebra to calculus.

Introductory Problem Solving Workshop

Presented by: Grace Lin and Chen Lei

New to math competitions and problem solving? Join our free relaxed problem solving workshop based on Lexington Math Tournament material. Suitable for middle school students. Enjoy pizza after the end of the class.

Location: Brownson Hall BR-18, Manhattanville College

Time: Tuesdays, 5-5:50 pm

Lexington Math Tournament Sample Problems

To see if this is right for you, check out these two problem sets:

Jan 30 (2024 AMC 8 review)

Feb 6

Feb 13

Feb 20 no workshop (public school winter break)

Feb 27

Mar 5

Mar 12

Mar 19

Mar 26 no workshop (public school spring break)

Apr 2

Intermediate Problem Solving Workshop

Presented by Chinmayi Goyal and Jai Paradkar,

Zoom: https://us06web.zoom.us/j/87914723806?pwd=dHBkNDNWOHBpdmdkT2xLbFBWTDZJUT09

Thursdays, 6-6:50 PM, Online

Jan 18 AIME Review

Jan 25 AIME Review

Feb 29 Quadratics, Polynomials, Vieta’s

Mar 7 Quadratics, Polynomials, Vieta’s

Mar 14 Algebraic Manipulations and Factorizations

Mar 21 Algebraic Manipulations and Factorizations

Mar 28 Combinatorics

Apr 11 Combinatorics

Apr 18 Probability, Expected Value, Geometric Prob, States

Apr 25 Probability, Expected Value, Geometric Prob, States

May 23 Number Theory: Factors, Divisors, and Bases

May 30 Number Theory: Diophantine Equations, Modular Arithmetic

Advanced Problem Solving Workshop

Presented by: Andrew Tu, Derek Xu, Vikram Sarkar

Location: Brownson Hall BR-101, Manhattanville College

Time: Sundays, 3:00-4:30 pm

Jan 28 - GiM material

Feb 4 - GiM material

Feb 11 - Purple Comet

Feb 18 - no workshop (President's Day weekend)

Feb 25 - CMIMC

Mar 3 - Purple Comet

Mar 10 - CMIMC

Mar 17 - Purple Comet

Mar 24 - CMIMC

April 7 - no workshop (Purple Comet competition)

April 14 - ARML

April 21 - ARML

April 28 - ARML

May 5 - ARML

May 12 - ARML

May 19 - ARML

Math Contests

AMC 8

January 21, 2024 at Manhattanville College

(make up date in case of bad weather January 23, 2024)

Last day to register: Jan 17, 2024

EMCC (middle school)

January 27, 2024 at Phillips Exeter Academy, NH

Two WAMC teams selected and registered

AIME I (by invitation only)

February 1, 2024

GiM (girls & non-binary only)

February 24, 2024 at Yale, CT

Two WAMC teams selected and registered

CMIMC (high school)

April 6, 2024 (date has been changed) at Carnegie Mellon, PA

Purple Comet (middle school)

April 7, 2024 at Manhattanville College

registration will open after AIME

Purple Comet (high school)

April 7, 2024 at Manhattanville College

registration will open after AIME

GAIM Elementary (grades 3-5, girls & non-binary only)

April 14, 2024 at Manhattanville College

registration will open after AMC 8

GAIM Middle School (grades 6-8, girls & non-binary only)

April 14, 2024 at Manhattanville College

registration will open after AMC 8

Lexington Math Tournament (middle school)

May 4, 2024 at Lexington, MA

ARML (high school, Westchester students only)

June 1, 2024 at Penn State. PA

Fall 2023

Recreational Math Seminar

Our main event, open to all levels. Presenters and topics vary from week to week.

Tuesdays 6-7:30 pm, In Person

Location: Brownson Hall BR-109, Manhattanville College

Date: Sept 12

Title: Loops and Roots: The Connection Between Two Mathematical Fundamentals

Presented by Matt Cushman, PhD

At the heart of mathematics lie "Fundamental" concepts and truths. One such truth is the Fundamental Theorem of Algebra, which asserts that every polynomial over the complex numbers has a root. This claim is foundational for our understanding of equations and their solutions. But how can we prove it? Enter the world of topology and the concept of the "Fundamental Group." Though seemingly distant from the world of polynomials and equations, this concept offers a unique and illuminating perspective on algebra. We will journey through these two mathematical territories, each labeled as "fundamental" in their respective fields. We will uncover the threads that link them as we explore and see how these connections hint at even deeper mathematical landscapes. Whether you're familiar with these ideas or hearing of them for the first time, join us for an exploration of these intertwined fundamentals.

Date: Sept 19

Title: Randomness as a tool

Presented by Yi Lin, Ph.D.

Randomness is associated with uncertainty. While we typically prefer reduced uncertainty, adding a dose of designed randomness can help solve many real

life problems. In this talk we give a few examples of such situations. The examples introduce interesting ideas, but are kept simple mathematically. While we touch upon some advanced concepts such as the randomized strategies in game theory, all the material requires only high school math.

Date: Sept 26

Title: Egyptian Palindromic Fractions

Presented by Peder Olsen, Ph.D.

Abstract: A fifth-grade problem challenging students to find distinct integers a,b,c,d,e such that 1 = 1/a+1/b+1/c+1/d+1/e made me realize how tricky fractions can be. These types of sums are called Egyptian factions. I will ask previously unexplored questions relating to Egyptian fractions and palindromes. Can every fraction be written as an Egyptian fraction with all palindromes, and what palindromic fraction representations are possible? Bring a pencil and paper to find out who is smarter than a fifth grader and have some fun with fractions. Here's a palindromic teaser: 1/98 = 1/99+1/9999+1/606606+1/707707.

Date: Oct 3

Title: Sylvester’s Problem, Point-Line Duality and the Projective Plane

Presented by Jon Lenchner, Ph.D.

In 1893, Sylvester asked the famous question: “Given n points in the plane not all of which lie on a single line, must there be some two points such that the line passing through the points does not pass through any additional point?” The problem was answered in the affirmative 50 years later by Tibor Gallai and the result is now known as the Sylvester-Gallai Theorem. I will describe my own proof of this theorem, and give a couple of others. I will also describe the concept of point-line duality and introduce you to the projective plane, which gives us a new way to think about point-line incidences.

Oct 10

Title: Certainty from Probability

Presented by Matt Cushman, PhD

Abstract: Probability is the mathematical study of uncertain events, such as the roll of a die. Surprisingly, arguments from probability can sometimes be used to prove "normal" mathematical statements, statements such as "there exists a mathematical structure with a certain property", or number theoretic/combinatorial identities, or even statements in geometry. We'll take a leisurely stroll through some examples of these, including solving some math competition problems (IMO and more!), and giving some proofs of problem that were open as recently as the late 20th century.

Oct 17

Title: Probability from Certainty II

Presented by Matt Cushman, PhD

We will continue our discussion of the uses of probability in proofs of non-random statements. This lecture will also be entirely self-contained, so please don’t fret if you missed the prior week. The “Probabilistic Method” is beautiful in its own right and very powerful for solving certain problems. Just like last week, we will hit some relatively recent research problems as well as some contest problems!

Oct 24

Title: Nested Radicals

Presented by Dr. Henry Ricardo

Introductory Problem Solving Workshop

Presented by: Grace Lin and Chen Lei

New to math competitions and problem solving? Join our free relaxed problem solving workshop based on Math Kangaroo and Moscow Math Circle material. Suitable for middle school students. Enjoy pizza after the end of the class.

To see if this is right for you, check out these two problem sets:

If this one is too hard to start, then you are not ready yet.

If this one is too easy, then this is not for you.

Tuesdays 5-5:50 PM, In Person

Location: Brownson Hall BR-109, Manhattanville College

Sept 12

Sept 19

Sept 26

Oct 3

Oct 10

Oct 17

Oct 24

Intermediate Problem Solving Workshop

Presented by Chinmayi Goyal and Jai Paradkar,

Getting ready for AIME? Interested in improving your AMC 10/12 score? Join us for a free topic-based workshop covering algebra, geometry, combinatorics, and number theory. Our winter workshop will concentrate on AIME level problems.

Zoom: https://us06web.zoom.us/j/87914723806?pwd=dHBkNDNWOHBpdmdkT2xLbFBWTDZJUT09

Thursdays, 6-6:50 PM, Online

Aug 24

Aug 31

Sept 7

Sept 14

Sept 21

Sept 28

Oct 5

Oct 12

Oct 19

Oct 26

Nov 2

Nov 9 - Review

Nov 16 - Geometry &Trigonometry

Nov 30 - Probability

Dec 7 - Algebra & Logarithms

Dec 14 - Complex Numbers

Dec 21 Number Theory

=====

Jan 4 - State Theory& Generating Functions

Jan 11 Miscellaneous

Jan 18 Review

Jan 25 Review

Advanced Problem Solving Workshop

Presented by: Andrew Tu, Derek Xu, Vikram Sarkar

Comfortable with the majority of AMC 10/12 problems? Interested in team competitions? Come and train with us for more advanced team contests. We will use past MMATH, PUMaC, ARML, and HMMT problems.

Sundays 3-4:30 PM, In Person

Location: Brownson Hall BR-109, Manhattanville College

Sept 10

Sept 17

Sept 24

Oct 1

Oct 8

Oct 15

Oct 22

Oct 29 - MMATH weekend

Nov 5

Nov 12 - HMMT weekend

EMCC Preparation session

Presented by: Andrew Zhang

4-week workshop that is designed for middle school and advanced elementary school student who would like to prepare for EMCC

Sunday 1:30-3:00 PM , in Person

Location: Brownson Hall BR-109, Manhattanville College

Nov 5,

Nov 12

Nov 19

Dec 3

Math Contests

MOAA

At Phillips Academy Andover on Oct 7, 2023

MMATH

At Yale on Oct 28, 2023

CMWMC

At CMU on Oct 28, 2023

AMC I0A/12A

At Manhattanville College on Wednesday, Nov 8, 2023

AMC I0B/12B

At Manhattanville College on Tuesday, Nov 14, 2023

HMMT

At Harvard on November 11, 2023

PUMaC

At Princeton on November 18, 2023

Summer 2023

AMC 8 and Mathcounts Preparation summer classes are back! Grace Lin and Warren Fu will be leading the session again.

This year's session will include a new set of topics and will go into more depth compared to previous years.

Classes will take place online at 4:00-4:45 PM every Tuesday and Thursday from July 11th to August 24th. They are designed for 4th to 8th graders who are interested in solving AMC 8 / Mathcounts problems.

Please register in advance for this meeting:

https://us06web.zoom.us/meeting/register/tZUudO-trDIrGtOCgbnv4l2HmI8SV-xIH555

After registering, you will receive a confirmation email containing information about joining the meeting.

July 11th - The AMC 8 and Mathcounts

July 13th - Polygons

July 18th - Similarity

July 20th - Primes

July 25th - Divisor Counting

July 27th - Relationships Between LCMs and GCDs

August 1st - Logic Puzzles

August 3rd - Modular Arithmetic

August 8th - Venn Diagrams & PIE

August 10th - Constructive Counting

August 15th - Radicals

August 22nd - Inequalities

August 24th - Lateral Thinking Puzzles

Spring 2023

Schedule

Introductory Problem Solving Workshop

Presented by: Grace Lin and Chen Lei

Tuesdays 5-5:50 PM, In Person

Location: Brownson Hall 14, Manhattanville College

Jan 24

It's a special introductory problem seminar this week: we will review the AMC 8 problems and solutions, so a great forum to review and learn from if you took it this past week.

Jan 31

(AIME break)

Feb 14

(winter break)

Feb 28

Mar 7

Mar 14

Mar 21

Mar 28

Recreational Math Seminar

Our main event, open to all levels. Presenters and topics vary from week to week.

Tuesdays 6-7:30 pm, In Person

Location: Brownson Hall 14, Manhattanville College

Jan 24

Title: Topology and The Game of Hex

Presented by Matt Cushman, PhD

Hex is a fun two-person strategy game played on a sheet of hexagonal graph paper. Discovered by Piet Hien and independently re-discovered and studied by John Nash, we'll play a game and study the theory behind it. The key fact about Hex is that no game ever ends in a draw: an intuitively obvious fact that is surprisingly subtle to prove... and will lead us to the equivalent result which says if you take a sheet of paper and crumple it in place, one point's location will remain unchanged.

Jan 31

Fun with Finite Fields I

Presented by Matt Cushman, PhD

You might have heard about "modulo" arithmetic or "clock" arithmetic -- it's simply just using remainders when dividing by a specified number n when doing addition and multiplication. It turns out that this is a surprisingly powerful idea in mathematics. We'll discuss the basics of how this works, and some of the amazing and fascinating structures that emerge when n is prime.

(AIME break)

Feb 14

Title: Turning Paper into Shapes, with Math

Presented by Luke Martin

Abstract: Origami is the art of folding paper into shapes. There is a lot of rich mathematics underlying the techniques. We'll discuss the basics of folding, mountain and valley folds, crease patterns, and flat-foldable-ness. Then we'll discuss crease intersections and study the mathematical restrictions on the number and type of creases and how they must meet at each intersection for a pattern to be flat-foldable.

(winter break)

Feb 28

Title: Randomness as a tool

Presented by Yi Lin, Ph.D.

February 28, 6-7:30 pm, Manhattanville College, Brownson Hall 14

Randomness is associated with uncertainty. While we typically prefer reduced uncertainty, adding a dose of designed randomness can help solve many real life problems. In this talk we give a few examples of such situations. The examples introduce interesting ideas, but are kept simple mathematically. While we touch upon some advanced concepts such as the randomized strategies in game theory, all the material should be understandable by high school students.

Mar 7

Title: Buffon’s Needle

Presented by Erik Brodsky

March 7, 6-7:30 pm, Manhattanville College, Brownson Hall 14

Your floor is made from long, parallel planks of wood, each of them 1 inch thick. If you drop a 1-inch long needle on your floor, what's the probability that it lands on a line between two of the planks? This is known as Buffon's Needle problem, and with some

clever tricks of probability theory, we can get a very elegant solution. Afterwards, we will look at how this innocuous question can be used to estimate pi

Mar 14

Title: Understanding expressivity in first order logic via simple combinatorial games

Speaker: Jonathan Lenchner, IBM T.J. Watson Research Center

Abstract: Ever since Frege in the late 1800s, mathematicians have sought to formalize mathematics in terms of the formal language of logic, leading to the famous Russel Paradox and Gödel’s Incompleteness Theorems, among many other important results. In this talk I will introduce the formal languages of first and second order logic. I will also describe the computational complexity classes P and NP, and describe the famous unsolved problem of whether P = NP. Then I will describe how computational complexity is connected to expressivity of problems in formal logical languages and how this problem can be studied by analyzing certain simple two player games.

Mar 21

Title: Proofs of the Infinitude or Primes

Presented by Gautam Chinta, Ph.D.

March 21, 6-7:30 pm, Manhattanville College, Brownson Hall 14

Euclid proved over 2000 years ago that there are infinitely many prime numbers. How many different proofs do you think Dr. Chinta can give in 1 hour? The audience member who gets closest to answering this question without going over will win a prize!

Mar 28

Title: Life, Death, and Water Jugs

Presented by Henry Ricardo (Professor of Mathematics at CUNY, retired)

In the movie Die Hard with a Vengeance, a terrorist challenges a police officer and a Harlem store owner with a life-and-death math problem involving a bomb and jugs of water. Starting with a film clip, I will solicit solutions to this problem, reveal the underlying mathematics, and discuss its generalizations.

May 7

Title: How to survive the ChatGPT invasion

Presented by Po-shen Loh

Speaker Info

Po-Shen Loh is a social entrepreneur and inventor working across mathematics, education, and healthcare. He is a math professor at Carnegie Mellon University and the national coach of the USA International Mathematical Olympiad team. He has pioneered innovations ranging from a scalable way for people to learn challenging math live online from brilliant people to a new way to control pandemics by leveraging self-interest.

He has earned distinctions ranging from an International Mathematical Olympiad silver medal to the USA Presidential Early Career Award for Scientists and Engineers. He was the coach of Carnegie Mellon University’s math team when it achieved its first-ever #1 rank among all North American universities, and the coach of the USA Math Olympiad team when it achieved its first-ever back-to-back #1-rank victories in 2015 and 2016, and then again in 2018 and 2019. He featured in or co-created videos totaling over 19 million YouTube views.

Event Description

The scale of global societal problems looks daunting. One person, or even a small team, is minuscule relative to the number of people who need help. For example, since ChatGPT has exploded onto the scene, our children's future employment prospects (and current educational experience, with ChatGPT-powered cheating) are in existential danger. There is an area close to mathematics, however, which devises solutions in which problems solve themselves even through self-serving human behavior: Game Theory.

The speaker is a pure math professor, researcher, and educator who transitioned to using Game Theory to develop new solutions for large-scale real-world problems. He will talk about his experience going from the ivory tower of academia into the practical mess of the real world.

He will also discuss educational strategies that build relevant skills to survive this new era of Generative AI (e.g. ChatGPT). He has been working extensively on this problem and draws from experience teaching across the entire spectrum, from underprivileged schools to the International Math Olympiad.

This event will be completely different from an ordinary math talk. It will be fun and thought-provoking.

Intermediate Problem Solving Workshop

Presented by Chinmayi Goyal and Jai Paradkar,

Zoom: https://us06web.zoom.us/j/89028596167?pwd=MWQ1UktDRERBSW9oY1dDVkNhMlg1Zz09

Thursdays, 6-6:50 PM, Online

Jan 5

Jan 12

Jan 19

Jan 26

Feb 2

Feb 9

possible additional sessions to go over AIME

Advanced Problem Solving Workshop

Presented by: Mathew Zhao, Jason Zhong, and Andrew Tu

Comfortable with the majority of AMC 10/12 problems? Interested in team competitions? Come and train with us for more advanced team contests. We will use past PUMaC, ARML, and HMMT problems.

Sundays 3-4:30 PM, In Person

Location: Brownson Hall 14, Manhattanville College

Jan 29

(AIME break)

Feb 12

(winter break)

Feb 26

Mar 5

Mar 12

Mar 19

Mar 26

(PUMaC)

AMC 8

Thursday, January 19, 2023, 5-6 PM

makeup day in case of bad weather - Sunday, January 22, 2023, 3-4 pm (I will just add an extra day to the Advanced Workshop when making the reservation)

AIME I

Tuesday, Feb 7, 2023. 3hours somewhere between 1:30 and 5:30 pm

Fall 2022

Schedule

Introductory Problem Solving Workshop

Presented by: Grace Lin, Chen Lei

This is a relaxed problem solving workshop based on Moscow Math Circle and AMC 8 materials. The course will be on a similar level like last year, but it will include new problems only.

Time: Tuesdays 5-5:50 pm (weekly)

Sept 20,27

Oct 4,11,18,25

Nov 1,22

Recreational Math Seminar

Time: Tuesdays 6-7:30 pm (weekly)

Sept 20, Matt Cushman - Platonic Solids

We all know what a triangle, square and hexagon are. You may have learned about polygons and regular polygons in geometry class. All of these objects dwell in two dimensions.. what would be their analogue for three dimensions? Join us as we explore this question, touching on a web of ideas running from the ancient Greeks (Plato), through Descartes and Euler through Gauss.

Sept 27, Yi Lin - Bayes Rules

Yi Lin will be leading a discussion of Bayes Rule:

Bayes Rule is the foundation for much of statistical and scientific reasoning. It's even been described as the most important equation for Machine Learning! Join our discussion of basic concepts in conditional probability with examples leading to Bayes formula and its applications.

Oct 4 Matt Cushman - "Fermat's L(ittle) Theorem"

Abstract: Fermat's Last Theorem famously was proved in the 1990s by Andrew Wiles after centuries of work by brilliant mathematicians. Fermat has another "L" theorem, which is actually much more important and which he actually proved. Known as "Fermat's Little Theorem", this forms the basis for a lot of number theory and algebra. We will discuss it, and a couple of different proofs as well as some applications.

Oct 11, Henry Ricardo (Professor of Mathematics at CUNY, retired)

Title: Digital Roots and the Hidden Design of the Universe

Abstract: Mystical qualities have been attributed to numbers by philosophers and mystics throughout the

ages. In particular, the digital root of a number has been endowed with cosmological

significance.

We will discuss (mathematically) the definition and basic properties of this number-theoretic

function, as well as more sophisticated results. For the purposes of our math circle, we note that

the digital root and related concepts have appeared in various mathematical and programming

competitions over the years. Audience participation will be encouraged. Exercises and

references will be provided.

Oct 18, Jon Lenchner (Research Scientist, IBM)

Title: On Some Card Games Related to the Card Game SET

Abstract: Dr. Lenchner will describe two mathematical card games that I have created that have some similarities to the popular card game SET. I will describe various mathematical properties of these games, allow the audience to play a few sample hands, and then I will describe the making of the physical and online versions of the games. I will also mention a handful of open problems connected to the games.

Oct 25, Yi Lin - Former professor of UW-Madison, Portfolio Manager at Verition

Title: Gambler's ruin and martingale

Abstract: Many games involve an element of chance. We will learn about how one can use math and probability theory to understand them (and sometimes win!). We will learn about Martingales which were one of the motivating examples of probability theory and continue to be an important concept in probability theory today.

Nov 1, Yicheng Zhong- Mortgage Specialist at Rokos Capital

Title: Predicting Mortgage Prepayment of U.S. Homeowners - Mathematical Modeling in Finance

Abstract: Majortiy of US homeowners fund their house purchases with mortgages, resulting in $8+ trln bonds derived from their pooled cashflow sold to global investors. Properly predicting homeowner behavior of prepaying their mortgages via sophisticated mathematical models becomes a heavily-invested field and one key success measure of such strategies. The presenter will lead you to discover the power of everyday, common-sense math in this field from a practitioner's point of view.

Nov 22, Yevgeniy Kostrov - Professor of Manhattanville College

Abstract: Professor Yevgeniy Kostrov will be introducing us to Difference Equations, with few financial applications.

Intermediate Problem Solving Workshop

Presented by Chinmayi Goyal, Jai Paradkar, and Jason Shi

Topic based seminars covering algebra, geometry, combinatorics, and number theory. The fall semester will concentrate on AMC 10/12 problems. The spring semester will introduce AIME level problems.

Time: Thursdays 6-6:50 pm (weekly)

Sept 15,22,29

Oct 6,13,20,27

Nov 3

Dec 1, 8

ARML Training

Presented by: Mathew Zhao, Jason Zhong, and Andrew Tu

This class is designed for those who are comfortable with the AMC 10/12 and wish to train for more advanced contests. We will be using past ARML problems.

Time: Sundays 3-4:30 pm (weekly)

Sept 25

Oct 2,9,16,23,30

Nov 6,20

Summer 2022

AMC 8 and Mathcounts Preparation summer classes are back! Grace Lin, who taught last year's session, will be leading the session again with help from Warren Fu.

This year's session will include a new set of topics and will go into more depth compared to last year.

Classes will take place online at 4:00-4:45 PM every Tuesday and Thursday from July 19th to August 25th. They are designed for 4th to 7th graders who are interested in solving AMC 8 / Mathcounts problems.

Please register in advance for this meeting:

https://us06web.zoom.us/meeting/register/tZAudemoqT4vGd2RL01eaaDwN1JWal6Nz7Gu

After registering, you will receive a confirmation email containing information about joining the meeting.

July 19th - Introduction to the AMC 8 and Mathcounts

July 21th - Arithmetic Series

July 26th - Geometric Series

July 28th - Circles

August 2nd - 3D Geometry

August 4th - Lateral Thinking Puzzles (Day 1)

August 9th - Casework

August 11th - Probability

August 16th - Logic Puzzles

August 18th - Linear Equations

August 23th - Factoring Polynomials

August 25th - Lateral Thinking Puzzles (Day 2)

Spring 2022

1. Recreational Math Seminar 5:30-6:50 NYC time on Wednesdays.

Presented by Paul Ellis.

March 16 - Magic Squares- David Nacin (William Paterson University)

March 23 - An intuitive look at the fundamental group - Matt Cushman (WAMC)

March 30 - The games of NIM and JIM - Paul Ellis (Manhattanville College)

April 6 - Infinite Logicians and Infinite Hats - Paul Ellis (Manhattanville College)

April 13 - Lobachevskian Geometry - Eric Brodsky (WAMC)

April 20 [4:30pm] - Padovan Patterns - David Nacin (William Paterson University)

April 27 [4:30pm] - Partitions and Puzzles - David Nacin (William Paterson University)

2. Introductory problem solving workshop. 6:00-6:50 NYC time on Thursdays.

Presented by Andrew Tu, Grace Lin, and Chinmayi Goyal

This is a relaxed problem solving workshop. To see if this is right for you, check out these two problem sets:

If this one is too hard to start, then you are not ready yet.

If this one is too easy, then this is not for you.

Jan 13,20,27

Feb 3,10,17

Mar 3,10,17,24,31

Apr 7,21,28

May 5,12,19,26

3. ARML Training. 3:00-4:30 NYC time on Saturdays.

Presented by Erik Brodsky, Matthew Zhao, and Jason Zhong

This class is designed for those who are comfortable with the AMC 10/12 and wish to train for more advanced contests. We will be using past ARML problems.

Jan 15,22,29

Feb 5,12,19

Mar 5,12,19,26

Apr 2,9,23,30

May 7,14,21,28

Fall 2021

1. Recreational Math Seminar 5:30-6:50 NYC time on Wednesdays.

Presented by Paul Ellis.

September 15 - Sona: Sand drawings from Angola (Paul Ellis, Manhattanville College)

September 22 - A Tricky Pair of Dice (Matt Cushman, Phd Math)

September 29 - Fermat's Last Theorem (Mervin Bierman, National Security Agency)

October 6 - Euler Characteristic (Matt Cushman, Phd Math)

October 13 - Hogan House Geometry (Maria Droujkova, Natural Math and Dawnlei Hunter Ben, Dzil Dit’loií School of Empowerment, Action, and Perseverance)

October 20 - Patterns That Do Not Last (Paul Ellis, Manhattanville College)

October 27 - Big Numbers (Matt Cushman, PhD Math)

November 3 - The Search for Perfect Numbers (Paul Ellis, Manhattanville College)

2. Introductory problem solving workshop. 6:00-6:50 NYC time on Thursdays.

Presented by Andrew Tu, Grace Lin, and Chinmayi Goyal

Sept 16,23,30

Oct 7,14,21,28

Nov 4,18 (off for AMC and Thanksgiving)

Dec 2,9,16

3. ARML Training. 3:00-4:30 NYC time on Saturdays.

Presented by Erik Brodsky, Matthew Zhao, and Jason Zhong

Sept 18,25

Oct 2,9,16,23,30

Nov 6,20 (off for HMMT and Thanksgiving)

Dec 4,11,18

Summer 2021: AMC8/Mathcounts preparation

Presented by Grace and Katherine Lin.

July 6th - Introduction to the AMC 8 and Mathcounts

July 8th - Divisibility Rules

July 13th - Arithmetic and Geometric Sequences

July 15th - Number Bases

July 20th - 3D Objects

July 22th - Proportions

July 27th - Percentages

July 29th - Exponent Rules

August 3th - System of Equations

August 5th - Factoring Polynomials

August 10th - Something a little different: Lateral Thinking Puzzles

Spring 2021 Meetings

Fall 2020 Meetings

Summer 2020 Meetings

All sessions presented by Katherine Lin.

Tuesday, July 28 - Angles, Stars, and Spirals

Thursday, July 30 - Chicken McNugget Theorem/Visual Approach to Solving Problems Like This

Tuesday, August 4 - One-Piece Chess

Thursday, August 6 - Get To Zero

Tuesday, August 11 - Nim with Two Piles

Thursday, August 13 - A Variation on Two-Pile Nim

Tuesday, August 18 - Prime Numbers

Thursday, August 20 - Tesselations

Tuesday, August 25 - Take and Split

Thursday, August 27 - Divisibility Rules

Spring 2020 Meetings

Fall 2019 Meetings

Spring 2019 Meetings

Interactive recreational math presentations. 5:30-6:50 on Wednesdays in Brownson 108

March 20 - Padovan Patterns - David Nacin (William Paterson University)

March 27 - Knot Theory - Paul Ellis (Manhattanville College)

April 3 - Jacobsthal Numbers - David Nacin (William Paterson University)

April 10 - SET and Super SET - Lauren Rose (Bard College)

April 17 - NO MEETING

April 24 - Fourier Transforms and Sound - Austin Purves (Manhattanville College)

May 1 - Pythagorean Triples - Yevgeniy Kostrov (Manhattanville College)

Advanced Contest Math Class presented by Derrick Xiong

Saturdays, 2:00-3:30 in Brownson 14

-March 9, March 16, March 23, March 30, April 6, May 4, May 11, May 18 (cancelled), May 25.

Fall 2018 Meetings

Spring 2018 Meetings

Fall 2017 Meetings

Spring 2017 Meetings

Feb 1 - An origami inspired adventure in Number Theory, with limits - Jeanine Meyer (Purchase College)

(Tuesday, Feb 7 - AMC 10A/12A)

Feb 8 - More fun with Number Theory - Marty Lewinter (Purchase College)

Feb 15 - AMC 10B/12B only (no presentation)

Feb 22 - NO MEETING (area schools' Winter Break)

Mar 1 - Dirichlet and His Pigeons - Henry Ricardo (CUNY)

Mar 8 at 5:00pm - Momathlon tryouts

Mar 8 - Dirichlet and His Pigeons, part 2 - Henry Ricardo (CUNY)

Mar 15 - NO MEETING (Manhattanville's Spring Break)

(Monday, Mar 20 - Westchester Momathlon)

Mar 22 - Computing the area of a parabola, from Archimedes to Calculus - Japheth Wood (Bard College)

Mar 29 - Topics in Computer Arithmetic - Mayan Moudgill (Optimum Semiconductors)

Apr 5 - Bayes Theorem - Austin Purves*

Apr 12 - NO MEETING (area schools' Spring Break)

Apr 19 - Volunteer Meeting

Apr 26 - ARML Tryouts and info session

May 3 - Solving the Cubic and the Quartic - Keith Hickey*

(*speaker is from Manhattanville College)

Fall 2016 Meetings

September 7 - Proofs Without Words, part 1 - Paul Ellis*

September 14 - Proofs Without Words, part 2 - Paul Ellis*

September 21 - HMMT and PUMAC Tryouts only (no presentation)

September 28 - Introduction to Game Theory - Mia Heissan*

October 5 - Some Parenthetical Remarks About Counting: Catalan Numbers - Henry Ricardo (CUNY)

October 12 - NO MEETING (Manhattanville Fall Break)

October 19 - Bulgarian Solitaire - Paul Ellis*

October 26 - Recounting the Rationals - Paul Ellis*

November 2 - EMCC tryouts only (no presentation)

November 9 - The Central Limit Theorem - Austin Purves*

(Saturday, Nov 12 HMMT)

(Tuesday, Nov 15 AMC 8)

November 16 - Magic Squares - Japheth Wood (Bard College)

(Tuesday, Nov 19 - PUMAC)

(*speaker is from Manhattanville College)

Spring 2016 Meetings

January 27 - The Game of Set and Steiner Triple Systems - Paul Ellis*

(Tuesday, Feb 2 AMC 10A/12A)

February 3 - How do we define the real numbers? - Mia Heissan*

February 10 - NO MEETING

February 17 - No Meeting - AMC 10B/12B

February 24 - Finite Fields, part 1 - Paul Ellis*

March 2 - Finite Fields, part 2 - Paul Ellis*

(Monday, March 7- Westchester MoMathalon)

March 9 - NO MEETING (Manhattanville's Spring Break)

March 16 - Patterns that do not last - Keith Conrad (University of Connecticut).

March 23 - Perfect Numbers - Japheth Wood (Bard College)

March 30 - ARML Tryouts

April 6 - The Poisson Distribution in Counting Experiments - Austin Purves*

April 13 - Senior Math Major Presentations

April 20 - P vs. NP - Jon Munson*

Fall 2015 Meetings

September 9 - How to Guard a Museum - Paul Ellis*

September 16 - Infinitely Many Primes - Paul Ellis*

September 23 - NO MEETING (Yom Kippur)

September 30 - Infinitely Many Primes, Part II - Paul Ellis*

October 7 - Arithmetic Sequences, Sets, and Infinitely many primes Part III - Paul Ellis*

October 14 - The use of Entropy in proving inequalities - Mayank Sharma (IBM Research)

October 21 - NO MEETING

October 28 - Some common inequalities and their applications. - Paul Ellis*

November 4 - Two faces of the universe: determinism vs. randomness - Tomasz Nowicki (IBM Research)

November 11 - Vectors Explain Gyroscopic Precession - Austin Purves*

November 18 - Complex Numbers and Geometry - Mia Heissan*

Spring 2015 Meetings

February 3 - AMC 10A/12A 6:30-8:00pm (This is a Tuesday!)

February 4 - Pick's Theorem - Paul Ellis

February 11 - Modular Origami - Paul Ellis (MoMathalon tryouts at 4:30)

February 18 - NO MEETING (Schools' Winter Break)

February 25 - AMC 10B/12B 4:30-6:00pm (No regular meeting)

March 4 - Spherical Geometry with the Lénárt Sphere - Paul Ellis

March 11 - NO MEETING (Manhattanville's Spring Break)

March 18 - Continued Fractions - Keith Conrad (University of Connecticut)

March 19 - Westchester MoMathalon snow date (This is a Thursday!)

March 25 - Catalan Numbers - Japheth Wood (Bard College, NYC Math Circle)

April 1 - NO MEETING

April 8 - NO MEETING (Schools' Spring Break)

April 15 - Circle Geometry I - The Power of a Point - Paul Ellis

April 22 - NO MEETING

April 29 - Circle Geometry II - Circle Inversion and the Poincare Disc Model of Hyperbolic Geometry - Paul Ellis

Fall 2014 Meetings

September 10 - Some thoughts about infinity - Paul Ellis*

September 17 - Some thoughts about infinity, part 2 - Paul Ellis*

September 24 - No meeting (Rosh Hashanah)

October 1 - Number Theory I, Mia Heissan*

October 8 - Number Theory II, Mia Heissan* [Schedule is changed today. Presentation at 5:30, and HMMT tryouts at 7:00]

October 15 - Fermat's Little Theorem, Paul Ellis*

October 22 - Chinese Remainder Theorem, Paul Ellis*

October 29 - No Meeting

November 5 - Bezout's Identity and The Chicken Nugget Theorem, Paul Ellis*

November 12 - Noncomputable Sets and Undecidable Problems, Russell Miller (Queens College)

November 19 - Wilson's Theorem, Paul Ellis*

*presenter from Manhattanville College

Spring 2014 Archives

February 4 - AMC 10A/12B - Note that this is a TUESDAY!!!

February 12 - Paul Ellis* - Modular Arithmetic

February 19 - AMC 10B/12B

February 26 - Mia Heissan* - Counting Methods

March 5 - Dennis Debay* - Three Dimensional Graphs

March 12 - NO MEETING (Manhattanville Spring Break)

March 19 - Keith Conrad (University of Connecticut) - The ABC Conjecture

March 26 - Dennis Debay* - Rational Tangles

April 2 - Dennis Debay* - The Perfect Shuffle

April 9 - Paul Ellis* - The 15 Puzzle and Group Theory

April 16 - NO MEETING (Area School Districts Spring Break)

April 23 - Dennis Debay* - Mathematical Origami

April 30 - Paul Ellis* - Knot Theory

*From Manhattanville College

Fall 2013 Archives

September 11 - Paul Ellis* - The mathematics of Sona (sand drawings from central Africa)

September 25 - Paul Ellis* - Mathematical Games (Handout 1, Handout 2)

September 18 - Paul Ellis* - The game of SET and finite geometries

October 2 - Dennis DeBay* and Mia Heissan* - PUMaC Tryouts and Free The Clones (source handout)

October 9 - Paul Ellis* - Bulgarian Solitaire.

October 16 - Marty Lewinter (Purchase College) - Fun with Number Theory

October 23 - Japheth Wood (Bard College & NYC Math Circle) - NIM and JIM (Japheth's NIM)

October 30 - Mia Heissan* - Graph Theory

November 6 - Ethan Akin (CCNY) - The 3x+1 Problem

November 13 - Dennis DeBay* - Sophisticated Child's Play: A look at Dots & Boxes

November 20 - Mia Heissan* - More Graph Theory

*From Manhattanville College

2012-2013 Archives

December 2, 2012 - First meeting! Colorings.

December 9, 2012 - Diophantine Equations.

December 16, 2012 - The Radical Axis.

January 6, 2013 - The Invertible Matrix Theorem.

January 13, 2013 - Cyclic Quadrilaterals.

January 20, 2013 - Sets.

January 27, 2013 - Series.

February 3, 2013 - Combinatorial Number Theory.March 3, 2013 - Inversion.

March 10, 2013 - Generating Functions.

March 17, 2013 - Polynomials.

March 24, 2013 - Burnside's Lemma.

March 31, 2013 - Easter, no meeting.

April 28, 2013 - Harmonic Divisions.

May 5, 2013 - Graph Theory.

May 12, 2013 - Mother's Day, no meeting.

May 19, 2013 - Graph Theory.

June 9, 2013 - Topic TBD.

The most important geometry article to ever read - Yufei Zhao (Canadian 2009 Winter IMO Training)

Projective Geometry - Alexander Remorov (2010 IMO Training)

Polynomials - Yufei Zhao (Canadian 2008 Summer IMO Training)

Harmonic Divisions - Cosmin Pohoata (Mathematical Reflections)

Graph Theory - Adrian Tang (IMO Training 2008)

Combinatorial Number Theory - Gabriel Carroll (Berkeley Math Circle)

1. Interactive recreational math presentation.

This presentation is open to people of all backgrounds.

The content is chosen so that it is new to most people.

2. Introductory problem solving workshop.

This is a relaxed problem solving workshop.

To see if this is right for you, check out these two problem sets:

If this one is too hard to start, then you are not ready yet.

If this one is too easy, then this is not for you.

3. Advanced contest math.

This class is designed for those who are comfortable with the AMC 10/12 and wish to train for contests such as HMMT/PUMAC/ARML.

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