# Spring 2017

Below is a list of seminars sponsored by the Mathematics and Computer Science department at Adelphi University. All talks are open to the public and most talks will be accessible to undergraduate students who have had linear algebra. If you have any questions feel free to contact Branden Stone.

Unless otherwise stated, all talks will be at the following location and time:

**Location: Science Building, Room 321;**

**Time: talks start at 1:30pm.**

Feel free to suscribe to the Google Calendar for the most recent information.

## Title: Assumptions, Approximations and Error

Abstract: We will warm up with a simple example of mathematical modelling, highlighting the need to make assumptions to convert a real-life problem into a mathematical one. We will then see a method on how to solve an inconsistent system of linear equations approximately, and if possible, find the error.## Title: Fiber Arts and Math: Modeling Hyperbolic Spaces

Abstract: For centuries, mathematicians thought that Euclid’s geometric postulates always worked. But sometimes they don’t… Using crocheted models, we will explore the properties of the hyperbolic plane. Come learn about the spaces that stumped mathematicians for decades, and about which Farkas Bolyai once said, “You must not attempt this approach to parallels. I know this way to its very end. I have traversed this bottomless night, which extinguished all light and joy of my life. I entreat you, leave the science of parallels alone….”# Fall 2016

Below is a list of seminars sponsored by the Mathematics and Computer Science department at Adelphi University. All talks are open to the public and most talks will be accessible to undergraduate students who have had linear algebra. If you have any questions feel free to contact Branden Stone.

Unless otherwise stated, all talks will be at the following location and time:

**Location: Science Building, Room 321;**

**Time: talks start at 1:30pm.**

Feel free to suscribe to the Google Calendar for the most recent information.

## Title: Statistics to Algebra and Back Again

Abstract: In this talk, we’ll consider a routine problem from statistics, maximum likelihood estimation in a small coin flipping example, and find a solution using algebra. The goal of the talk is not really how to solve this problem, but to demonstrate how new courses of study in algebra arise by considering such problems from statistics. [PDF Poster]## Title: Into the Unknown

Abstract: This talk will be a wild ride of new and interesting mathematics. Come find out what glorious things await in this talk of unknown content. Who knows, maybe all of your wildest dreams will come true. This talk is open to students at all levels. [PDF Poster]## Title: Irrationality: Like Blackness in the Night Sky

Abstract: Recall that every real number falls into exactly one of two categories: either it’s rational (that is, it can be expressed as a ratio, or fraction, of two whole numbers), or it’s not. Though you probably learned this seemingly fundamental fact in middle school or high school, it’s important to remember that the concept of irrationality was not always so widely accepted. In fact, the discovery of irrational numbers (by the Pythagorean philosopher Hippasus in the 5th century BC) is rumored to have greatly angered the gods. Despite the fact that mankind’s relationship with irrational numbers has come a very long way in the past two-and-a-half millennia, we still seem to favor rational numbers. It’s famously been said that rational numbers are like the stars in the night sky. In this talk, however, we will focus on the often-overlooked blackness in the night sky: the irrational numbers. And we will do this by considering “rational approximations” of them. Through this process, we will uncover a number which is more irrational than all of the others. And, what’s even more surprising: this particular number is ubiquitous in nature precisely because of its irrationality! [PDF Poster]## Title: Monomial orders uniquely determined by their induced orders

Abstract: When were are asked to write the polynomial $p(x)=3x^2+x^4+7-x$ in standard form we know our answer is $x^4+3x^2-x+7$, because the only way to order powers of $x$ is the natural one: degree wise! Complexity is introduced when we are asked to write $q(x)=2x^3yz^2-6x^4z+x^2y^3z$ in standard form and we have to define what standard form means in this setting. In this talk, we will present the three classical monomial orders (\textit{lexicographic}, \textit{degree lexicographic} and \textit{reverse lexicographic}), explore a curious property they possess (hint hint: It is the title) and discuss whether other monomial orders possess this property. [PDF Poster]# Spring 2016

Below is a list of seminars sponsored by the Mathematics and Computer Science department at Adelphi University. All talks are open to the public and most talks will be accessible to undergraduate students who have had linear algebra. If you have any questions feel free to contact Branden Stone.

Unless otherwise stated, all talks will be at the following location and time:

**Location: Science Building, Room 321;**

**Time: talks start at 1:30pm.**

Feel free to suscribe to the Google Calendar for the most recent information.

## Title: Flows on Graphs

Abstract: This is an expository talk on the theory of flows on a graph. We will define the flow on a directed graph and discuss several solved problems and current open problems. No prior knowledge of graph theory is necessary. [PDF Poster]## Title: A truly random talk

Abstract: Most people can intuitively classify binary sequences as “random” or “not random.” However, as mathematicians, we want a precise mathematical definition. In this talk, I will define randomness with concepts from computability theory using three different intuitive approaches as starting points: unpredictability, incompressibility, and a lack of distinguishing properties. At the end, I’ll present an example of a random sequence and talk about current directions in the field. [PDF Poster]## Title: How elliptic curves can keep secrets and prove theorems

Abstract: Elliptic curves (and their higher dimensional analogues) have proven to be interesting, powerful, and enigmatic objects of study; on one hand elliptic curves are often a topic in undergraduate courses on group or number theory, yet there are deep open problems that arise from simple questions about their structure. In this talk we will think about how to do arithmetic on small sets, define elliptic curves in two different ways, explore their geometric and algebraic structure, and explain some of their uses within and outside of mathematics. Only the definition of a prime number will be assumed. [PDF Poster]## Title: A Combinatorial Variation of Fermat's Last Theorem

Abstract: The equation is a degree-, falling-factorial version of the Fermat equation, where . In this talk, I will give combinatorial interpretations of and in terms of a probabilistic game and make some observations on their combinatorial properties using these interpretations. [PDF Poster]## Title: Math/Computer Science Careers at NSA

Abstract: The talk will include an overview on NSA, its history, mission areas, and career fields. There will be information on student programs and full-time employment to include hiring requirements and benefits. The talk also includes pros and cons of working at NSA, then some specifics on how math is used throughout the agency. If there is time, we can discuss career paths, advancements, and some unique opportunities that the agency provides to employees. [PDF Poster]# Fall 2015

Below is a list of seminars sponsored by the Mathematics and Computer Science department at Adelphi University. All talks are open to the public and most talks will be accessible to undergraduate students who have had linear algebra. If you have any questions feel free to contact Branden Stone.

Unless otherwise stated, all talks will be at the following location and time:

**Location: Post Hall, Room 207;**

**Time: talks start at 1:30pm.**

## Title: Primeor(d)ial Soup: The Hunt for Large Primes

Abstract: Why do mathematicians look for primes? Are all primes created equal or are some primes more special than others somehow? The answer to the second question is a qualiﬁed yes. One type of special prime, called a Mersenne prime, consists of primes of the form: One reason that Mersenne primes are special is due to nicer-than-average ways of testing their primality. As a result, the largest known prime numbers have almost always been Mersenne primes (with the few known counterexamples coming from very closely related numbers!) This talk will cover a whirlwind history of the prime numbers, the search for large primes and adventures in primality testing. Finally, how can YOU get involved in the search for large (titanic!) primes and how can you win up to $50,000 doing it? Come to ﬁnd out! [PDF Poster]## Title: Factorization in Integral Domains

Abstract: From one point of view, factorization (the multiplicative decomposition of elements in an integral domain) is very basic and elementary. Indeed, it is basic and central to any mathematical structure where multiplication plays a role. But there are hazards to the assumption of “elementary”. Indeed, a well-known “proof” of Fermat’s Last Theorem from the mid 19th century collapsed when it was realized that not all rings of algebraic integers enjoyed the unique factorization property (and it should be noted that the final proof took another 150 years).In the last 20 years or so, there has been a renaissance in the study of factorization in the realm of integral domains. In this general (mathematical) audience talk, we will look at some of the recent developments in the world of factorization. Many examples to illustrate the concepts will be presented, and some new directions/developments/questions will be explored. [PDF Poster]

## Title: Pennies, nickels, dimes, quarters and….Hilbert functions!

Abstract: In this talk we will see a brief overview of Hilbert functions, a very powerful and well established tool in Algebra, Combinatorics, and in many other fields of Mathematics, even in more applied ones. We will go through some computations, with particular emphasis on the relations with singularities of curves: for example, the cuspidal curve $y^2 = x^3$ has a singular point (a cusp) at the origin, while the parabola $y = x^2$ is a nice and smooth curve. We will see how the Hilbert function detects the difference between these two objects. We will also briefly discuss how to use Hilbert functions as a tool for counting vertices, edges and faces of a simplicial complex (essentially, a generalized version of a triangle). As a more practical application, we will see how to determine all possible ways of giving change for a dollar. [PDF Poster]# Spring 2015

Below is a list of seminars sponsored by the Mathematics and Computer Science department at Adelphi University. All talks are open to the public and most talks will be accessible to undergraduate students who have had linear algebra. If you have any questions feel free to contact Branden Stone.

Unless otherwise stated, all talks will be at the following location and time:

**Location: Post Hall, Room 207;**

**Time: talks start at 1:30pm.**

## Title: How Singular Can a Curve Be?

Abstract: We all have an intuitive idea for what singular means. If you draw the plots of $y^2 - x$, $y^2 - x^3$, and $y^2 - x^2(x+1)$, one quickly notices that points on the first one all look similar where as the origin in the second two plots seems a bit more interesting/strange than the other points. We call these points singular points for the curve. In this talk, we will discuss some natural ways to study how singular a curve can be and how this changes if we think about not only curves over real (or complex) numbers, also with coefficients modulo a prime. [PDF Poster]## Title: Solvability by Radicals

Abstract: Given a quadratic equation, the quadratic formula tells us what the roots are in terms of the coefficients in the equation. The question we will explore in this talk is whether we have similar formulae for polynomials of higher degree. We will describe some of the attempts made by mathematicians over centuries to answer this question, and see a remarkable result of Abel, which states that such a formula is not possible for an arbtrary polynomial of degree 5. You will also learn what cats and commas have in common. [PDF Poster]## Title: Blank Space

Abstract: Sudoku’s a game, wanna play? It turns out that algebra is more than just x’s and torturing high school students. Algebra has been used to solve problems from biology, physics, and economics. In this talk, I’ll walk through an example of using algebra to solve a slightly less ambitious problem: a 4 by 4 sudoku puzzle. We’ll develop all the tools used to solve the ``big’’ problems, too. [PDF Poster]## Title: Game of Crowns

Abstract: The generalized crown, $\mathbb{S}^k_n$, is a well-known family of bipartite graphs whose order dimension is given in terms of the parameters $n$ and $k$. To each generalized crown one can associate a graph of critical pairs whose chromatic number is bounded above by the order dimension of the poset. In this talk we characterize the adjacency matrix of these graphs and through Mathematica can quickly produce an image of these graphs. [PDF Poster]# Fall 2014

Below is a list of seminars sponsored by the Mathematics and Computer Science department at Adelphi University. All talks are open to the public and most talks will be accessible to undergraduate students who have had linear algebra. If you have any questions feel free to contact Branden Stone.

Unless otherwise stated, all talks will be at the following location and time:

**Location: Post Hall, Room 207;**

**Time: talks start at 1:30pm.**