# Mathematics Club

## About Us

The Brooklyn College Mathematics Club is an undergraduate club for students interested in mathematics. We host a wide range of lectures, tutoring events, and parties.

## Faculty Advisers

Sandra Kingan, Associate Professor

Mark Gibson, Lecturer

## Connect With Us

If you would like to be involved in the Mathematics Club, e-mail Associate Professor Kingan or Lecturer Mark Gibson.

## More Information

### Mathematics Club Meetings

Mathematics Club meetings are primarily used to work on fun and interesting math problems, discuss mathematical-related theories/concepts, mention upcoming events/opportunities, and talk about any other math-related news.

E-mail Associate Professor Sandra Kingan or Lecturer Mark Gibson for more information.

### Past Events

#### 2022

##### An Invitation to Category Theory

Speaker: Noson Yanovsky, Department of Computer and Information Science

Tuesday, February 22, 2022, 12:30–1:30 p.m., 1146 Ingersoll Hall and via Zoom

Abstract: Category theory is a general study of structures. We will describe many many basic examples of categories and their related structures. This will help us see why category theory is a unifying language in mathematics, computer science, and physics. This talk is open to anyone.

#### 2019

##### What Is Moduli Space?

Speaker: Chaya Norton (University of Montreal)

March 5, 12:30–2 p.m., 1105 Ingersoll Hall

This was the Mathematics Club’s first colloquium of the spring semester. The abstract for this talk is below. Pizza and refreshments were served.

Abstract: Consider the collection of triangles in the Euclidean plane up to congruence. Three non-collinear points in the plane determines a unique triangle containing these points as its vertices. The classification problem is to understand which collection of points give rise to equivalent triangles. A moduli space is a geometric “space,” which describes the solution to a geometric classification problem. The property of solving a geometric classification problem implies that points in the moduli space correspond to unique objects considered up to the equivalence. More importantly mathematicians would like the moduli space to be equipped with a geometry which describes how the objects vary, namely nearby points correspond to objects which are small variations of each other. We will consider the simple moduli problem of equivalent triangles in order to demonstrate the notion of a moduli space and basic questions one may ask about the space constructed, as well as the complications that arise from automorphisms of the objects.

##### Pi Day Celebration

March 14, 12:30–2 p.m., 1146 Ingersoll Hall

The Mathematics Department and the Mathematics Club hosted a Pi Day celebration with free pizza and dessert pies. An integration bee took place (a tournament style competition where two people try and solve an integral in a timed race). The winner of this tournament received a $50 Amazon gift card and the runner-up got the book *17 Equations That Changed The World,* by Ian Stewart. After the competition, Assistant Professor Diana Hubbard gave a talk on how you can find Pi using just a spreadsheet and the Pythagorean Theorem. For those who attended, this was a fun day of math and pies.

##### Choosing a Career With a Math Degree

Speaker: Pearce Washabaugh, TrueFit

March 19, 12:30–2 p.m., 1146 Ingersoll Hall

The Mathematics Department and the Mathematics Club co-hosted this event. Speaker Pearce Washabaugh, who received his Ph.D. in math with Professor Stephen Preston, is now working as a senior data scientist at TrueFit. For more information about the talk, see the abstract below. Pizza and refreshments were served.

Abstract: It is not uncommon for mathematics students of all levels to have anxiety about finding a job. However, businesses desperately need people that can take in a large number of details to frame a problem, abstract away unnecessary details to get to the heart of a problem, and combine the tools and data at hand to arrive at a solution. You will note that these are precisely the skills that mathematics students are taught. In this talk, we will work on closing the gap between school and business. We will discuss my path from math student to data scientist, as well as the advice I got and lessons I have learned about getting a job in general.

##### The Geometric Approach to Fluid Mechanics

Speaker: Professor Stephen Preston, **Department of Mathematics**

April 11, 12:30–2 p.m., 1141 Ingersoll Hall

For more information, see the abstract below. Kosher pizza and drinks were served.

Abstract: On a curved surface, the shortest path between two points is not a line but rather a curve called a geodesic. The Gaussian curvature of a surface is a function on the surface that describes to what extent the surface looks like a sphere (positive curvature) or a hyperbolic saddle (negative curvature). Under positive curvature, geodesics may spread apart but eventually come together, while under negative curvature they diverge exponentially. The same ideas extend to higher dimensions and even infinitely many dimensions. In 1966 Vladimir Arnold showed how to write the Euler equations for a perfect fluid (no viscosity, incompressible, no external forces) as a geodesic equation in an infinite-dimensional manifold. He then computed some curvatures and showed that they tended to be negative, which can be viewed as an explanation of why weather prediction is hard. I will discuss the basics of differential geometry and how some of this works for fluids.

##### Patently Mathematical, or How I Lost a Billion Dollars in My Spare Time

Speaker: Professor Jeff Suzuki, **Department of Mathematics**

April 30, 12:30–2 p.m., 1105 Ingersoll Hall

The Mathematics Club hosted a talk given by Associate Professor Jeff Suzuki based on his new book, *Patently Mathematical, Or How I Lost a Billion Dollars in My Spare Time*. For more information on the talk, see the abstract below. Kosher pizza and refreshments were served.

Abstract: Build a better mousetrap, and the world will beat a path to your door. But the garage workshop, with the lone genius struggling to create a device that will change the world, is mostly a thing of the past. Today, building a better mousetrap requires the resources of an industrial giant and a laboratory with hundreds or even thousands of researchers. Inventions based on mathematics are the exception, for mathematical invention requires nothing more costly than a notebook and pencil. And while you cannot patent a mathematical formula, you can patent a device that uses a mathematical formula. In some cases, the mathematics is dauntingly complex, but in a surprising number of cases, the mathematics is so very elementary that any mathematics student could have secured the patent. We will take a look at the mathematics behind some recent patents, in fields ranging from web services, to online dating, to career advising. Along the way, we will confront an important problem: Patents are issued for devices, not for how the device is used. But the heart and soul of mathematics is its generalizability, so issuing a patent based on a mathematical formula risks giving the patent holder a stranglehold on every industry: Google could demand royalties from eHarmony, or IBM could try to obtain a cease and desist order against the NSA. We will close with some thoughts on how to improve the patent system’s approach to mathematical inventions.

##### Vertically Aligned Entries in Pascal’s Triangle and Connections to Number Theory

**Speaker: Professor Heidi Goodson, Department of Mathematics**

October 22, 12:30–1:30 p.m., 1141 Ingersoll Hall

Event Flier

The Mathematics Club sponsored this fun talk on Pascal’s Triangle and Number Theory given by Professor Heidi Goodson. She went over a theorem she found and proved about a linear dependence for the vertically aligned columns for Pascal’s triangle. She showed its application to number theory and ended with some of her research in hyperelliptic curves. For more information about the talk, see the abstract below. Kosher pizza and soda were served.

Abstract: The classic way to write down Pascal’s triangle leads to entries in alternating rows being vertically aligned. In this talk, I’ll explain and prove a linear dependence on vertically aligned entries in Pascal’s triangle. Furthermore, I’ll show how this result is related to a problem in number theory. Specifically, I’ll explain how a search for morphisms (functions) between hyperelliptic curves led to the discovery of this identity.

#### 2018

##### Spring 2018 Involvement Fair

January 30, 12:15–2:15 p.m., Student Center

This event was sponsored by the Student Activities, Involvement, and Leadership Center. They welcomed all students to attend this fair to find out more about clubs, departments, and other opportunities that students can become involved with. There was music, giveaways, and much more. Students stopped by our table to learn about what he have in mind for this semester. Students were also able to socialize with our members and provide us with ideas on the types of events they would like to see us hold during the semester.

##### Recursive Problem Solving

February 27, 12:30–2 p.m., 1141 Ingersoll Hall

We worked on problems involving deriving solutions to recursively defined expressions.

##### Fun With Math

Speaker: Marty Lewinter, Professor Emeritus, Purchase College and Dean, Learn America

March 6, 12:30–2 p.m., 1141 Ingersoll Hall

Abstract: We will highlight a few interesting gems taken from number theory and geometry. While studying and doing research in mathematics is a serious endeavor, we start to love math for its beauty and cleverness.

This talk was sponsored by the Mathematics Club.

##### Fermat’s Theorem on the Sum of Two Squares

Speaker: Professor Robert Sibner, Department of Mathematics

March 27, 12:30–1:45 p.m., 1141 Ingersoll Hall

Professor Robert Sibner gave a talk on “Fermat’s Theorem on the Sum of Two Squares.” He also went over the background knowledge needed to understand this proof.

Abstract: Questions about the possibility of the representation of an integer as a sum squares go back to Diophantus in the third century. Fermat stated in 1640 and, a century later, Euler gave the first proof, that a representation by the sum of two squares was possible for primes of the form 4n+1 and not for those of the form 4n-1. Since then, many proofs of this have appeared; usually the proofs use advanced mathematics or delicate arguments in number theory (see e.g. Wikipedia article). I will present a proof that is both simple and natural, using mathematics that is not so advanced and arguments that are not delicate. Since the proof is essentially a one-liner, in order that the talk lasts longer than two minutes, I’ll describe all the background mathematics in detail.

##### Graph Theory Day 75

April 14, starts at 9 a.m., 1141 Ingersoll Hall

Sponsored by the Metropolitan New York Section of the Mathematical Association of America and hosted by the Department of Mathematics and the School of Natural and Behavioral Sciences.

Graph Theory Day is a semi-annual conference in its 38th year. It is held at different locations in and around New York City. The goal is to provide a learning and sharing experience on recent developments.

There was a terrific roster of speakers who covered a range of topics in graph theory.

Invited speakers:

- David Aulicino, Brooklyn College
- Deepak Bal, Montclair State University
- Jonathan Cutler, Montclair State University
- Nathan Kahl, Seton Hall University
- Marty Lewinter, Purchase College
- Joe Malkevitch, York College (CUNY)
- Bhargav Narayanan, Rutgers University
- Louis Petingi, College of Staten Island (CUNY)
- John Saccoman, Seton Hall University
- Charlie Suffel, Stevens Institute of Technology
- Sanju Vaidya, Mercy College
- Christina Zamfirescu, Hunter College (CUNY) and CUNY Graduate Center

Two students also spoke at the event: Anthony Delgado (Columbia University) and Kevin Phillips (Horace Greeley High School).

During lunch, there was a poster session for anyone who wanted to present their recent research.

There was no registration fee. Breakfast, lunch, and coffee were provided thanks to a grant from the Mathematics Department and School of Natural and Behavioral Sciences.

Organizing Committee: Sandra Kingan (Brooklyn College), Armen Baderain (Nassau Community College), Ezra Halleck (City Tech, CUNY), Kerry Ojakian (Bronx Community College, CUNY), and Louis Quintas and Edgar Ducasse (Pace University).

Click here to find out more information about this event.

##### Confidence in the Census

Speaker: Professor Jeff Suzuki, Department of Mathematics

April 17, 12:30–2 p.m., 1141 Ingersoll Hall

Abstract: Every 10 years, the United States conducts a census to determine how many persons live in each of the states. Much depends on this information: most importantly, the number of Representatives in Congress for a state is determined by this “exact count.” The problem of allocating a discrete resource (in this case, the number of Representatives) among several recipients is known as the apportionment problem. We’ll take a look at various solutions to the apportionment problem, as well as examine some issues with the current method that will lead to malapportionment following the 2020 census.

##### Research Presentations

May 15, 12:30–2 p.m., 1141 Ingersoll Hall

Students who conducted mathematics research gave presentations on their work.

##### What Is Physical Mathematics?

Speaker: Professor Kishore Marathe, Department of Mathematics

October 25 and 30, 12:20–2 p.m., 1141 Ingersoll Hall

Abstract: Physical mathematics is a new and very active area of research at the interface of physics and mathematics. However, its roots go back to antiquity. We will discuss the ancient origins of this subject and highlight some important achievements in this area leading up to current developments. They have given us surprising new results and new perspectives on old results in mathematics starting with results from experimental and theoretical physics. A special session on “Physical Mathematics” was organized by Professor Kauffman and myself at the joint International meeting of the AMS and TIMC held at BHU, India, in December 2016. The theme of the 2017 Arbeitstagung honoring the work of Yuri Manin at MPIM, Bonn was “Physical Mathematics.”

Executive Board members:

- President: Eugene Dorokhin
- Vice President: Paul Magrini
- Treasurer: Sarah Coopersmith
- Secretary: Naomi Leader
- Club Connector: Alexander Hart

##### Elliptic Curves over Finite Fields

Speaker: Professor Heidi Goodson, Department of Mathematics

November 29, 12:30–2 p.m., 1146 Ingersoll Hall

Abstract: Elliptic curves are solution sets to cubic equations in two variables. Questions of how to find, count, and characterize points on elliptic curves have been studied since the days of Diophantus. Nearly 2,000 years later, the great mathematician Joe Silverman wrote, “the theory of elliptic curves is rich, varied, and amazingly vast.” In this talk, I will define what it means to be a point over a finite field and answer the question “How many?” We’ll discuss estimates, exact values, and surprising trends as the order of the field varies!

##### Vertex-to-Self Trajectories on the Dodecahedron

Speaker: Professor David Aulicino, **Department of Mathematics**

December 4, 12:30–2 p.m., 1141 Ingersoll Hall

Abstract: Starting at a vertex of a Platonic solid, is it possible to walk on the surface of it in a straight line so that we return to the vertex we started at without passing through another? Surprisingly, the answer depends on which Platonic solid we consider. We will review what the Platonic solids are and explain how to solve this problem for the tetrahedron. There will be lots of pictures, animations, and 3D models. Students are encouraged to bring scissors and tape!

#### 2017

##### PageRank

Speaker: Sandra Kingan, Department of Mathematics

February 21, 12:30–1:30 p.m., 1141 Ingersoll Hall

PageRank is Sergey Brin and Larry Page’s algorithm that launched Google, Inc. It is based on concepts from linear algebra and graph theory covered in undergraduate courses. This algorithm along with the background required to understand it were discussed at this event.

Executive Board members:

- President : Jonathan Hanon
- Vice President: Tova Baharlias
- Treasurer: Hindy Drillick
- Secretary: Chezky Steiner
- Club Connector: Eugene Dorokhin

##### Fun With Number Theory

Speaker: Marty Lewinter, Professor Emeritus of Mathematics, Purchase College and Dean of Mathematics, Learn America

February 28, 12:30–1:30 p.m., 1141 Ingersoll Hall

Lewinter examined classes of numbers including squares, triangular numbers, primes, Fibonacci numbers, and more. Various beautiful properties and identities were presented. The only prerequisite was high school algebra.

##### Pi Day

March 21, 12:15–2 p.m., 1141 Ingersoll Hall

We had a belated Pi Day event on March 21, as the snowstorm that occurred on March 14 resulted in the closure of the college on that day. In honor of Pi Day (March 14), we watched the movie *Pi*.

##### Random Fractals

Speaker: Christian Benes, Department of Mathematics

April 25, 12:30–1:45 p.m., 1141 Ingersoll Hall

One of the hottest topics of research in probability of the past few decades is a random fractal called the Schramm-Loewner Evolution (SLE). In recent years, two mathematicians were awarded Fields Medals for showing that SLE is related to well-known random processes such as loop-erased random walk and percolation. In this talk, Benes explained what fractals are and how random fractals appear naturally in a number of physical phenomena.

##### Establishing Your Career as an Actuary: M.S. in Actuarial Science at St. John’s University

Speaker: Paul Mucciarone, Assistant Director of Enrollment, St. John’s University

May 16, 12:30–2 p.m.

1141 Ingersoll Hall

The actuarial profession is consistently ranked as a top career path. Mucciarone’s talk explored why people with strong quantitative skills should consider pursing this lucrative and rewarding career. He defined the job functions of an actuary and the various skill sets needed to be successful in the field. He concluded the talk with details about the M.S. in actuarial science, including the curriculum, internship opportunities, career coaching, and scholarships.

##### Welcome Back!

September 5, 12:30–2 p.m., Occidental Lounge, Student Center

Attendees met the club’s new executive board, found out about upcoming events that the club had planned for the semester, and collaborated on solving a few interesting math problems.

##### The Octonions and the Laws of Nature

Speaker: Noson Yanofsky, Professor, Computer and Information Science Department

September 26, 12:30–2 p.m., 1141 Ingersoll Hall

Abstract: We will explore various philosophies about the laws of nature. What are they? How do they control the physical world? Do they control everything? We shall push a novel idea about the nature of the laws of nature. In order to prove our point we will make an analogy with various number systems like the complex numbers, the quaternions, the octonions and strange things like sedenions and 32-dimensional numbers.

##### Least Action Principles and the Equations of Classical

Mechanics

Speaker: Diogo Pinheiro, Associate Professor, Mathematics Department

October 24, 12:30–2 p.m., 1141 Ingersoll Hall

Abstract: Many of the laws of physics can be expressed in terms of least action principles. In this talk, we will discuss the deep connection between such least action principles and some famous equations from mathematical-physics and classical mechanics, namely the Euler-Lagrange equation and Hamilton’s equations.

##### End-of-Semester Party

December 12, 12:30–2 p.m., 1141 Ingersoll Hall

This was an end-of-semester party / problem-solving session. We celebrated the last day of class and worked on some problems.

#### 2016

##### Four Proofs of the Infinitude of Primes

Speaker: Alexander Gindes, Department of Mathematics

September 27, 12:30–1:30 p.m., 1146 Ingersoll Hall

Abstract: We will discuss one of the most beautiful theorems in all of mathematics—the infinitude of primes. We will give four proofs with variations: Euclid’s indirect proof, Euler’s analytic proof, Furstenberg’s topological proof, and Chaitin’s complexity proof. These proofs reflect the evolution of techniques in number theory and in mathematical proofs in general.

Executive Board members:

- President : Jonathan Hanon
- Vice President: Tova Baharlias
- Treasurer: Hindy Drillick
- Secretary: Chezky Steiner
- Club Connector: Eugene Dorokhin

##### Billiards in Polygons

Speaker: David Aulicino, Department of Mathematics

November 1, 12:30–1:30 p.m., 1127 Ingersoll Hall

Abstract: We will begin by considering a square billiard table and ask, “When is a billiard trajectory periodic?” We will give an answer to this question, and explain how this relates to a surface with a “flat geometry.” We will generalize this setting to other polygons and investigate some of their properties. We will conclude by stating an unsolved problem about triangles.

##### Linear Algebra—The Fourth Wave of Mathematics

Speaker: Professor Jeffrey Suzuki, Department of Mathematics

November 15, 12:30–2 p.m., 1146 Ingersoll Hall

Abstract: Big ideas in mathematics often lead to fundamental changes in human culture. Thus the invention of written numbers allowed the rise of cities and central government, while calculus played a key role in the scientific and industrial revolution. Some mathematicians believe that over the next 50 years, linear algebra will bring about profound changes in our society. We’ll take a look at how some very simple ideas from linear algebra are already beginning to change how we live, work, and play.

##### Category Theory by Example

Speaker: Noson Yanofsky, Department of Computer and Information Science

November 29, 12:30–2 p.m., 1127 Ingersoll Hall

Abstract: Category theory started as a branch of mathematics that studied various types of structures. Over the past few decades, category theory has arisen in almost every branch of mathematics, theoretical physics, and theoretical computer science. We give the basic definition of a category and discuss the relationships between categories. We then show the ubiquity of category theory by describing ten simple examples of categories from various fields of science. We conclude by showing how category theory is a unifying language of science by describing the relationships between these categories.

##### Actuarial Science

Speaker: Scott Goldstein, Guardian Life

December 8, 12:30–1:30 p.m., 1141 Ingersoll Hall

Scott Goldstein gave a brief overview of the actuarial profession, talked about the kind of work he does, gave an overview of how retirement products work, and then explained how variable annuities with living benefits work.

##### Math Club Holiday Party

December 13, 12:30–1:30 p.m., Math Library, Ingersoll Hall

#### 2015

##### The Dynamic Programming Principle for Ordinary Differential Equations

Speaker: Diogo Pinheiro, Department of Mathematics

February 24, 12:30–1:30 p.m., 1127 Ingersoll Hall

Abstract: We will introduced dynamic programming techniques to address optimal control problems associated with dynamical systems defined by ordinary differential equations. For such class of problems, we will obtain Bellman’s principle of optimality and the corresponding Hamilton-Jacobi-Bellman equation. It is worth remarking that such techniques were initially developed by Richard Bellman, a Brooklyn College alumnus.

##### A Theorem in Algebra, Geometry and Topology

Speaker: Kishore Marathe, Department of Mathematics

March 17 and 24, 12:30–1:30 p.m., 1127 Ingersoll Hall

Abstract: We will discuss a very special set of structures in algebra characterizing a finite set of integers and the surprising relation that they have with deep results in geometry and topology. Some knowledge of linear algebra and matrices will enhance your understanding of this fascinating theorem. The background in geometry and topology necessary to understand the theorem will be provided in the lectures.

##### Quantum Computing and Linear Algebra

Speaker: Noson Yanofsky, Department of Computer and Information Science

October 21, 12:30–1:30 p.m., 1127 Ingersoll Hall

Abstract: Quantum computing is a new and exciting field that tries to harness the strange and wonderful aspects of quantum mechanics to make computers better. Surprisingly, a large part of quantum computing can be simply understood with the knowledge of manipulating matrices with complex numbers. We will show the connection between complex linear algebra and quantum computing. We will start with small physical systems and explain what they have to do with computers. We will move on to give a small lesson in quantum mechanics. We will conclude with a simple algorithm for quantum computing.

#### 2014

##### Moonshine at 30—Part I

Speaker: Professor Kishore Marathe, Department of Mathematics

February 18, 12:30–1:30 p.m., 1127 Ingersoll Hall

Abstract: In my previous Math Club talks (Monster exists, 2012), I discussed the existence of the Monster, the largest sporadic group and the related Moonshine conjectures. In these talks I will discuss the tremendous developments that have taken place in the 30 years since then. They have led to even more surprising results extending to other groups and relating the corresponding Moonshine to conformal field theory and string theory in physics and Ramanujan’s mock theta functions and closely related mock modular and Jacobi forms.

##### Title: Moonshine at 30—Part II

Speaker: Professor Kishore Marathe, Department of Mathematics

February 25, 12:30–1:30 p.m., 1127 Ingersoll Hall

##### Optimal Life Insurance, Consumption and Investment Decisions

Speaker: Diogo Pinheiro, Department of Mathematics

March 18, 12:30–1:30 p.m., 1127 Ingersoll Hall

Abstract: We will discuss an extension to Merton’s famous continuous-time model of optimal consumption and investment, under which a wage earner with a random lifetime allocates some portion of her income to consumption and life insurance purchase, while investing her savings in a financial market. The wage earner’s problem is to find the optimal consumption, investment, and insurance purchase decisions in order to maximize the expected utility of her family consumption, of the size of her estate in the event of premature death, and of her total wealth at the time of retirement, provided she lives that long. We will see how to use optimal control techniques to obtain explicit solutions for such problem in the case of discounted constant relative risk aversion utility functions, providing also some economic interpretation. We will conclude with a discussion of possible extensions.

##### Math Clinic: The Math Club’s tutoring event for lower division math courses

April 8, 12:30–1:30 p.m., 1127 Ingersoll Hall

##### Random Fractals

Speaker: Associate Professor Christian Benes, Department of Mathematics

April 29, 12:30–1:30 p.m., 1127 Ingersoll Hall

Abstract: One of the “hottest” topics of research in probability of the past few decades is a random fractal called the Schramm-Loewner Evolution (SLE). In the last eight years, two mathematicians were awarded Fields Medals for showing that SLE is related to well-known random processes such as loop-erased random walk and percolation. In this talk, I’ll explain what fractals are and how random fractals appear naturally in a number of physical phenomena.

##### 2014–15 Elections for Mathematics Club Officers

May 13, 12:30–1:30 p.m., 1127 Ingersoll Hall

##### Quantum Computing and Linear Algebra

Speaker: Noson YanofsKY, Department of Computer and Information Science

October 21, 12:30–1:30 p.m., 1127 Ingersoll Hall

Abstract: Quantum computing is a new and exciting field that tries to harness the strange and wonderful aspects of quantum mechanics to make computers better. Surprisingly, a large part of quantum computing can be simply understood with the knowledge of manipulating matrices with complex numbers. We will show the connection between complex linear algebra and quantum computing. We will start with small physical systems and explain what they have to do with computers. We will move on to give a small lesson in quantum mechanics. We will conclude with a simple algorithm for quantum computing.

#### 2013

##### Elementary Problems about Polynomial Rings

Speaker: David Finston, Brooklyn College

February 5, 12:30–1:30 p.m., 1127 Ingersoll Hall

Abstract: The polynomial ring in finitely many variables over a field is an object of fundamental importance in algebra and algebraic geometry. For example, every commutative associative ring R containing the field k that can be generated over k by n elements is a homomorphic image of the polynomial ring k[x1,…,xn]. In geometry, k[x1,…,xn] is the ring of polynomial functions defined at all points of the n-dimensional space over k. Nevertheless, k[x1,…,xn] for n>1 remains mysterious in some respects. For example:

- It’s easy to see that x and y+x^5 are “variables” in the sense that the pair (x,y) can be recovered algebraically from them. But given arbitrary polynomials f,g how can one tell whether or not they are “variables”?
- If A is a finitely generated ring over k and t is a variable for which A[t] is isomorphic to k[x1,…,xn], is A isomorphic to a polynomial ring in n-1 variables?
- What is the structure of the group of automorphisms of k[x1,…,xn]?
- If f is a polynomial in n variables and k[x1,…,xn] /(f) is isomorphic to a polynomial ring in n-1 variables is f a variable?

These questions are versions of unsolved problems in affine algebraic geometry which will be discussed in the talk.

##### An Invitation to Category Theory

Speaker: Professor Noson Yanofsky, Department of Computer and Information Science

February 26, 12:30–1:30 p.m., 1141 Ingersoll Hall

Abstract: Category theory is a general study of structures. We will describe many many basic examples of categories and their related structures. This will help us see why category theory is a unifying language in mathematics, theoretical computer science, and theoretical physics. This talk is open to anyone.

##### Quickest Detection and Algorithmic Trading

Speaker: Professor Olympia Hadjiliadis, Brooklyn College

March 5, 12:15–1:05 p.m., 0105 Ingersoll Hall

Joint event with Stock Trading Club

Abstract: My presentation is on the topic of statistical surveillance and quickest detection. We begin by providing an example of statistical quality control in an industrial production process. We define the out-of-control and in-control states of the process and describe how we attempt to distinguish them by using statistics based on the observations of the process. We also discuss further applications of the problem of statistical surveillance and quickest detection in finance, detection of enemy activity, the internet surveillance problem and signal processing. We draw attention to a specific statistic called the CUSUM. We construct CUSUM-based trend following trading algorithms and assess their performance on high frequency data for US treasury bonds and notes sold at auction. It is seen that during regimes of instability drawdown based algorithms result in a profit while in periods of stability, they do not. We finally draw the connection of drawdown algorithms and cumulative sum (CUSUM) on line detection statistics. This talk is open to anyone.

##### Math Clinic: The Math Club’s Tutoring Event for Lower-Division Math Courses

May 14, 12:30–2:30 p.m., 1127 Ingersoll Hall

##### Perspectives on Graduate School

Speaker: Julio César Urenda Castañeda, New Mexico State University

March 19, 1–1:50 p.m., 0105 Ingersoll Hall

Abstract: I am a Mexican citizen residing in Juarez, Mexico, engaged in full time doctoral study at New Mexico State University. My thesis adviser is working in Brooklyn. I will discuss my educational background and the exigencies of doing doctoral research under these most unusual circumstances. If there is time and interest I will make some remarks about the nature of my thesis work on the embedding problem in affine algebraic geometry.

##### Speed of Reaction of the CUSUM

Speaker: Professor Olympia Hadjiliadis, Brooklyn College

April 9, 12:30–1:30 p.m., 0105 Ingersoll Hall

Abstract: In this event we will introduce a statistic known as the speed of reaction of the CUSUM. We will examine the information it conveys and how we may make use of this information in order to describe the trend of a time series. In the context of high-frequency data, we will also discuss its distributional properties and in particular its mean. We will then compare the speed of reaction statistic to a simple moving average statistic in making an inference about the mean of high-frequency observations.

##### Random Walk and Related Lattice Models

Speaker: associate Professor Christian Benes, Department of Mathematics

April 23, 12:30–1:30 p.m., 1127 Ingersoll Hall

Abstract: Many natural random phenomena are modeled on discrete lattice structures. One such model is random walk, which has been used for over a century as a model in biology, physics, and economics. In this talk, I will discuss gambling strategies for the game of roulette, explain why a drunken individual lost in Manhattan will always find a way home, and why butterflies have no such luck. If there is enough time, I will discuss other (surprisingly) related lattice models such as percolation and the Ising model.

##### Every Vote Counts, As Long As It’s In the Right Zip Code: The Theory and Practice of Gerrymandering

Speaker: Professor Jeff Suzuki, Department of Mathematics

May 2, 12:30–1:30 p.m., 1127 Ingersoll Hall

Abstract: In the United States and other democracies, voters in geographically defined districts choose a representative to serve in the legislature. But a sufficiently clever mapmaker could draw up a set of legislative districts to give one party a substantial advantage in the next election: this is a partisan gerrymander, and has been called the “pathology of democracy” by political scientists and social activists. The Supreme Court, claiming there is no “manageable standard” for measuring the extent of partisan gerrymandering, has given a green light to unlimited partisan gerrymandering. But to a mathematician, everything is measurable. We’ll take a look at some of the proposals for measuring the extent of partisan gerrymandering; analyze the claim that partisan gerrymandering is a “self-limiting enterprise”, and outline some areas of current research on the topic.

##### End of Semester Party and Math Club 2013–14 Academic Year Election

May 7, 12:30–1:30 p.m., 1127 Ingersoll Hall

##### Undergraduate Student Conference on Data Science

May 14, 12:30–2:30 p.m., 1127 Ingersoll Hall

##### An overview of volatility derivatives and recent developments

Speaker: Zhenyu Cui, Department of Mathematics

September 17, 12:30–1:30 p.m., 1127 Ingersoll Hall

Abstract: In this talk, I give an overview of the history and development of volatility derivatives, including variance/volatility swaps, options on variance/volatility, target volatility options, and timer options (or mileage options). I shall discuss the financial motivations behind these volatility derivatives products, review the literature, and also talk about some of my research in this area.

##### Approximation Methods in Derivatives Pricing

Speaker: Minqiang Li, Bloomberg LLC

September 24, 12:30–1:30 p.m., 1127 Ingersoll Hall

Abstract: In this talk, I will review various approximation methods that have been proposed to price financial derivatives, including moment matching, PDE perturbation, lower and upper bounds, distributional approximation, etc. The focus will then be shifted towards PDE perturbation methods with applications to pricing exotic derivatives such timer options.

##### NSF-CMACS Workshop at Lehman College

Speaker: Nancy Griffeth, Lehman College (CUNY)

October 1, 12:30–1:30 p.m., 1127 Ingersoll Hall

Abstract: Every January since 2010, we have held an undergraduate workshop on a quantitative biology topic at Lehman College. The 2014 topic is Cellular Signaling Pathways. Fifteen students are selected from the applicants to attend the workshop each year, and they receive a stipend of $1000. Several students from Brooklyn have attended and have been valued participants. In addition, many of them have gone on to internships or doctoral programs at prestigious institutions.

##### Math Clinic: The Math Club’s Tutoring Session for Lower-Division Math Courses

October 15 and 22, 12:30–2:30 p.m., 1127 Ingersoll Hall

##### Empirical Bayes and Stein’s Lemma, With Applications (Engineering and Financial)

Speaker: Professor Martin Raphan, Department of Computer and Information Science

October 29, 12:30–1:30 p.m., 1127 Ingersoll Hall

Abstract: A universal problem that arises across many disciplines is that of gathering information about an environment, subject to unavoidable imperfections in the measurement process. Of fundamental importance, then, is learning to estimate uncorrupted signals based on corrupted measurements. Classical solutions to this problem rely on prior information about the measured environment, either assumed, or learned during a training phase where uncorrupted data is available. In many situations, however, uncorrupted data is never available, so there can be no training and no basis for prior assumptions. In this talk, I will describe a general statistical framework for solving this estimation problem without prior information, relying only on knowledge of how the corruption process works. I will discuss the relationship between this framework, Stein’s Lemma and Empirical Bayes. I will also discuss applications of these methodologies to engineering and finance.

##### Halloween Party

October 31, 12:30–1:30 p.m., Math Library

##### Pressure and Temperature Dependence of the Deuteron Spin-Lattice Relaxation Times (T1) in Ionic Liquids

Speaker: Sophia Suarez, Department of Physics

November 5, 12:30–1:30 p.m., 1127 Ingersoll Hall

##### Math for America Information Session

Speaker: Juan Amayo, Math for America

November 19, 12:30–1:30 p.m., 1127 Ingersoll Hall

##### Measurement of the Spin Diffusion Rate in a Rigid Solid via NMR

Speaker: Professor Gregory Boutis, Department of Physics

December 3, 12:30–1:30 p.m., 1127 Ingersoll Hall

Abstract: An important question for many-body systems is how microscopic quantum mechanical parameters influence a corresponding dynamic at the macroscopic scale. Single crystal of calcium fluoride is an ideal test system for experimental investigation of such phenomenon-the spin degrees of freedom are well defined, relaxation times can be very long, and internal dynamics such as spin diffusion are kinematically simple. Experimentally, one can control the nuclear spin system by average Hamiltonian theory, developed by J.S. Waugh and coworkers, to study how a microscopic quantum property such as a spin state affects a macroscopic observable, such as a spin diffusion rate. A method of measuring diffusion in magnetic resonance is to encode a spatial modulation of magnetization in a sample and then measure it’s attenuation over time. The difficulty in measuring spin diffusion in solid crystals by these scattering methods is that the spin diffusion rate is very slow (of an order 1 x 10^-12 cm^2/s) and hence the displacement of spin coherence is very small (approximately 1 micron per hour). The experimental challenge for probing these dynamics is that a spatial modulation of the nuclear spin magnetization must be created with a wavelength on these length scales. In this talk I will describe the method by which spin diffusion can be measured, in addition to a scheme by which the homonuclear dipolar Hamiltonian can be effectively turned-off in NMR using average Hamiltonian methods. The talk will include a discussion of the measurement of the spin diffusion rate of a two-spin correlated state (dipolar order) in addition to a state that is linear in spin operators (Zeeman order) and comparison with theoretical predictions.

#### 2012

##### Who’s In Charge? An Introduction to Social Network Analysis

Speaker: Professor Jeff Suzuki, Department of Mathematics

March 6

Abstract: Social network analysis is an outgrowth of graph theory and is rapidly becoming one of the important tools in mathematical criminology. One of the key problems is the following: given some information about individuals in an illicit network, which figures are the most important to the operation of the network? We’ll take a look at some of the principal methods used to analyze networks, and show how after-event analysis suggests the potential of these methods for law enforcement and counter-terrorism.

##### CAS: A Tour of Enhanced Insight With Computer Algebra Systems

Speaker: John Velling, Brooklyn College

March 20

Abstract: We will explore two topics using the MAPLE computer algebra system. First, the approximation of complicated waves by superpositions of sine and cosine waves, i.e. Fourier series. The ability to do this is the fundamental insight underpinning the digitization of music (CDs), images (JPG and GIF), and movies (DVD). Second, the conjectured existence of infinitely many pairs of twin primes. We will obtain experimental evidence supporting this conjecture.

##### Random Fractals

Speaker: Associate Professor Christian Benes, Departmentof Mathematics

April 5

Abstract: One of the “hottest” topics of research in probability of the past few decades is a random fractal called the Schramm-Loewner Evolution (SLE). In the last 8 years, two mathematicians were awarded Fields Medals for showing that SLE is related to well-known random processes such as loop-erased random walk and percolation. In this talk, I’ll explain what fractals are and how random fractals appear naturally in a number of physical phenomena.

##### Some Results on the Infinite

Speaker: Lecturer Mark Gibson, Department of Mathematics

April 17

Abstract: We will look at some interesting results involving infinite sets. We will first construct some maps which put sets into one-to-one correspondences; sets that a priori seem to be of different sizes. We will eventually apply Cantor’s diagonalization argument on the real numbers to show the existence of different magnitudes of infinity. Time permitting, we will prove Cantor’s theorem in its most general form, from which it follows that there are an infinite number of distinct infinities. Finally, we will be prepared to state the continuum hypothesis: a proposal that (for decades) drove many great mathematicians crazy.

##### A Discussion of Infinite Sets

Speaker: Keith Harrow, Brooklyn College

April 24

Abstract: Can one infinite set be larger or smaller than another? Or do all infinite sets have the same size? In fact, what does it mean for two infinite sets to have the same size? Or to have two different sizes? After covering the essentials, some interesting implications of the properties of infinite sets will be discussed.

STEM majors recuriting event. This talk is for students in MATH 1011, 1021, 1026, 1201, 1206, 1401 and CORE 1311.

##### Statistical Quality Control

Speaker: Professor Olympia Hadijialidis, Brooklyn College

April 30, 5–6 p.m., 328 Ingersoll Hall Extension

Abstract: My presentation is on the topic of statistical surveillance and quickest detection. We begin by providing an example of statistical quality control in an industrial production process. We define the out-of-control and in-control states of the process and describe how we attempt to distinguish them by using statistics based on the observations of the process. We also discuss further applications of the problem of statistical surveillance and quickest detection in finance, detection of enemy activity, the internet surveillance problem and signal processing We draw attention to a specific statistic called the CUSUM and conclude by discussing some of its properties.

This talk fits the theme of Math Awareness Month “Mathematics statistics and the data deluge.”

##### A Day in the Life of a Quantitative Analyst

Speaker: Himanshu Almadi, Bank of America

April 30, 6:05–7 p.m., 328 Ingersoll Hall Extension

Abstract: Investors often experience the tension that exists between the desire to stick with a long-term financial strategy and the impulse to react to short-term market events. Of course, as the post-crisis paths of market amply demonstrate, financial data and investor psychology can often work at cross-purposes. We present probable solutions to both problems: building long-term financial strategy using goals-based processes, and managing short-term opportunities/constraints using a more dynamic asset allocation.

This talk fits the theme of Math Awareness Month “Mathematics statistics and the data deluge.”

##### The Legacy of Epimenides: The Contemporary Consequences of a 2,600-Year-Old Paradox

Speaker: Professor Noson Yanofsky, Department of Computer and Information Science

May 1

Abstract: We shall examine Epimenides paradox which essentially says that the statement “This sentence is false” is true if and only if it is false. We shall show that this ancient self-referential paradox has the exact same format as some of the most interesting developments in modern mathematics and computer science. We will examine the paradox in light of the famous barber paradox, Russell’s naïve set theory paradox, Cantor’s different levels of infinity, Gödel’s incompleteness theorem, and Turing’s Halting problem.

##### Market Making and Trading Puzzles

Speaker: Brett Bernstein, GETCO Securities

May 3, 1310 Ingersoll Hall

Abstract: An introduction to how market making works and a look at some puzzles that test your trading intuition. This talk fits the theme of Math Awareness Month “Mathematics statistics and the data deluge.”

##### Statistical Analyses Used to Understand Brain Dynamics

Speaker: Daniel Thengone, Weill Cornell Medical College

May 10, 12:30–1:30 p.m., 1127 Ingersoll Hall

Abstract: In neuroscience, the dynamical patterns of electrical activity of neurons provide a crucial bridge between cellular and behavioral levels of analysis. An electroencephalogram (EEG) is a test that measures such electrical activity via electrodes placed on the surface of the brain. During the last decade or so, a significant amount of research has gone into the development of signal processing tools to quantify these voltages measured from these electrodes. These statistical methods have been developed into signal processing algorithms and have been used extensively to model such stochastic processes. Power spectral analysis is a well-established method for the analysis of EEG signals. Spectral parameters can be efficiently used to quantify brain states during awake and sleep state via characteristic features that emerge in the frequency domain. This method coupled with numerous statistical tests has been applied to understand the dynamics in voltage oscillations measured from the brain surface. This talk will provide a brief survey of the quantitative measures used for analyzing continuous process signals like EEG, and how these methods are used to examine dynamics of neuronal response and their relationship to behavior.

This talk fits the theme of Math Awareness Month “Mathematics statistics and the data deluge.”

##### Got Techniques—Looking for Data

Speaker: Associate Professor Sandra Kingan, Department of Mathematics

May 15, 12:30–1:30 p.m., 1141 Ingersoll Hall

Abstract: The theme of Math Awareness month (April) this year was “Mathematics Statistics and the data deluge.” SIAM News has a front-page article titled Got Data: Now What that identifies the analysis of large data sets to provide understanding, and ultimately knowledge as one of the fundamental intellectual challenges of our time. While, Scientists have data and are looking for mathematical techniques to analyze their data, mathematicians, on the other hand, have techniques and are looking for data to try out their techniques. In this talk I will present the development and implementation of a course for math majors titled “Mathematical Methods for Analyzing Data.” Such a course has a built-in strong technology component as software is needed for handling data. But it also requires a strong civic engagement component because along with new applications come new ethical issues. Learning the mathematics in the context of difficult societal problems and thinking about how use it in an advocacy setting creates a much needed awareness of how mathematics applies to society. Moreover, students who take such a course are well-prepared to undertake an undergraduate student research project.

This talk fits the theme of Math Awareness Month “Mathematics statistics and the data deluge.”

##### Quickest Detection and Algorithmic Trading

Speaker: Professor Olympia Hadjiliadis, Brooklyn College

September 6, 12:30–1:30 p.m., 1127 Ingersoll Hall

Abstract: My presentation is on the topic of statistical surveillance and quickest detection. We begin by providing an example of statistical quality control in an industrial production process. We define the out-of-control and in-control states of the process and describe how we attempt to distinguish them by using statistics based on the observations of the process. We also discuss further applications of the problem of statistical surveillance and quickest detection in finance, detection of enemy activity, the internet surveillance problem and signal processing. We draw attention to a specific statistic called the CUSUM. We construct CUSUM-based trend following trading algorithms and assess their performance on high frequency data for US treasury bonds and notes sold at auction. It is seen that during regimes of instability drawdown based algorithms result in a profit while in periods of stability, they do not. We finally draw the connection of drawdown algorithms and cumulative sum (CUSUM) on line detection statistics.

##### The Monster Exists

Speaker: Kishore Marathe, Brooklyn College

September 13 and 20, 12:30–1:30 p.m., 1127 Ingersoll Hall

Abstract: The proof of the existence of the Monster, the largest finite simple group finished the proof of the classification theorem for finite simple groups. The proof of this theorem is arguably the greatest achievement of the 20th-century mathematics. Hundreds of mathematicians contributed to this proof which extends over 5,000 pages, makes essential use of results in algebra, arithmetic, geometry and theoretical physics (conformal field theory and string theory). We will give a survey of the history of this theorem and a brief sketch of the various ingredients that go into its proof. The main prerequisite is intellectual curiosity, although some knowledge of mathematics and physics would make it more interesting.

##### The Many Ways to Untie a Knot

Speaker: Mark Brittenham, University of Nebraska – Lincoln

October 4, 12:30-1:30 p.m., 1127 Ingersoll Hall

Abstract: Knot theory, the mathematical study of ‘knotted’ objects, had its beginnings in the 1880s with a now discredited theory of the structure of the atom. It has grown in both its power and usefulness, especially in recent years, and has made unexpected connections with a wide variety of disciplines. This talk will present a ‘picture history’ of some of these developments, mostly centered on the fundamental question: “how do you unknot a knot?”.

##### Finding Minimum Energy Paths of Droplets on Superhydrophobic Surfaces: A Phase Field Approach

Speaker: Kellen Petersen, Courant Institute of Mathematical Sciences

October 18, 12:30–1:30 p.m., 1127 Ingersoll Hall

Abstract: Interest in superhydrophobic surfaces has increased due to a number of interesting advances in science and engineering. A classical approach will be given as motivation for using a phase field model. After explaining our phase field model, I will discuss different methods for finding saddle points between minima with emphasis on the String Method. Resulting minimum energy paths will then be shown for different topographical and chemical surface characterizations.

##### A Quantitative Biology Workshop at Lehman College

Speaker: Nancy Griffeth, Lehman College (CUNY)

November 13, 12:30–1:30 p.m., 1127 Ingersoll Hall

Abstract: Every January since 2010, we have held an undergraduate workshop on a quantitative biology topic at Lehman College. Fifteen students are selected from the applicants to attend the workshop each year, and they receive a stipend of $1,000. Several students from Brooklyn have attended and have been valued participants. In addition, many of them have gone on to internships or doctoral programs at prestigious institutions. The next workshop will be on the subject of atrial fibrillation. Students will see wet lab demonstrations of the type of electrical activity that causes atrial fibrillation in the heart and will help collect data for the better understanding of atrial fibrillation.

##### Graphs and Matroids

Speaker: associate Professor Sandra Kingan, Department of Mathematics

November 20, 12:30–1:30 p.m., 1127 Ingersoll Hall

Abstract: Matroids are a modern type of synthetic geometry where the behavior of points, lines, planes, and higher dimensional surfaces are governed by combinatorial axioms. Hassler Whitney coined the term matroid in his 1935 paper “On the abstract properties of linear dependence.” In defining a matroid Whitney captured the fundamental properties of independence that are common to graphs and matrices. In this talk I will define and give examples of matroids and a flavor of some of the major structural results.

##### Introduction to GPU Computing

Speaker: Mark Ebersole, NVIDIA

November 27, 12:30–1:30 p.m., 1127 Ingersoll Hall

This talk is organized jointly with the CIS Club.

Abstract: Modern GPUs have grown past their graphics heritage and evolved into the world’s most successful parallel computing architecture. The introduction of this talk will briefly cover where the GPU came from and how it turned into this processing powerhouse. Next we will quickly cover the various methods used for programming for acceleration on GPUs. Finally, we will take a deeper dive into the model used to directly access this computational power using the CUDA C programming language.

#### 2011

##### Career Panel for Math and Math Education Majors

February 24, Math Library

##### Matroid Theory

Speaker: Associate Professor Sandra Kingan, Department of Mathematics

March 21, Time: 6–7 p.m., 1146 Ingersoll Hall

##### What Would It Feel Like Working for the World’s Largest Quantitative Investment Management Firm?

Speaker: Gunnar Klinkhammer, MAN/AHL Investments

April 6 3:40–4:30 p.m., 329 Ingersoll Hall Extension

##### Artificial Neural Networks: Modeling in Robots

Speaker: Professor Grasso, Department of Computer and Information Science

April 28

##### Game Theory

Speaker: Professor Thorne, Department of Computer and Information Science

May 5

##### Probability Theory

##### Speaker: Associate Professor Christian Benes, Departmentof Mathematics

May 10

##### Student Presentations

Speaker: Associate Professor Sandra Kingan, Department of Mathematics

May 17

#### 2010

##### Physical Mathematics: Old and New

Speaker: Professor Kishore Marathe, Department OF Mathematics

October 28

##### Voting Theory

Speaker: Professor Jeff Suzuki, Department OF Mathematics

November 4

##### Resources for Homework Help and Research Help

Speaker: Professor Cirasella, Library

November 9, 120 Library 120

##### Careers in Mathematics and Its Interrelated Fields

Speaker: Zavi Baynes, Career Counselor, Magner Career Center

November 16, 12:30–1:30 p.m., 1207 James Hall

##### Math and Music

Speaker: Professor James Kiernan, Department of Mathematics

November 23