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.
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)
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
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.
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.
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.
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.
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
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 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,
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
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
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 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
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.
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,
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
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
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 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
AMC 8
January 21, 2024 at Manhattanville College
(make up date in case of bad weather January 23, 2024)
Register at https://sites.google.com/site/westchestercountymathcircle/forms?authuser=0
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
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
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
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
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.
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,
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/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
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
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)
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
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
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
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.
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)
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)
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*
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*
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
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
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
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
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.