Student Talks:
Jane Akhuetie and Lorena Dema
College of Mount Saint Vincent jakhuetie.student@mountsaintvincent.edu,
ldema.student@mountsaintvincent.edu
Sponsor Dr. Alison Setyadi alison.setyadi@mountsaintvincent.edu
An Introduction to Cryptography
We will discuss one aspect of cryptography.
level: 1
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Daniel Baller
United States Military Academy daniel.baller@usma.edu
Sponsor MAJ Anthony Johnson aa1646@usma.edu
Specific Communication Network Measure Distribution Estimation
A new method is proposed to estimate the probability distribution of specific communication network measures. Real world communication networks are dynamic, thus reliably estimating network measures is challenging. Communications between two individuals that are socially connected, may vary, yet their basic relationship remains unchanged.
A real world communication network is modeled from empirical data using the network probability matrix (NPM). The NPM estimates the edge probabilities between two individuals in a network. This framework is then used to model and simulate the communication network. A statistical distribution is fit to the density measure, that can be used in change detection.
level: 2
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Jenae Beauchamp
Eastern Connecticut State University beauchampj@stu.easternct.edu
Sponsor Professor Bonsu Osei oseib@easternct.edu
Data Processing Using Wavelets
Wavelets have lately been used in processing large amounts of data. This psentation shows step by step how this mathematical process can be broken down into a more elemental method using matrix algebra to produce the final wavelet transform. A real world application demonstrating how this technique works will be psented as an example case.
level: 1
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Rachel Brudnicki
Norwich University smithr@norwich.edu
Sponsor Susan Diesel sdiesel@norwich.edu
Title: Now I Know My ABCs
Now I know my ABCs...Sometimes the alphabetic way is not always the best way. What if the ABCs were the CBAs? Why does X always come before Y? Orders are an essential part of everyday life as well as in mathematics. But are the standard orders always the best? This talk will discuss various ways of ordering monomials and polynomials, ordering vectors, and using Groebner Basis.
Will require a knowledge of linear algebra and algebraic geometry.
level: 2
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Laura E. Boyle
Manhattan College LBoyle.student@manhattan.edu
Sponsor Dr. Richard Goldstone Richard.Goldstone@manhattan.edu
Can Wrong be Right?
Can you get the rules of differentiation wrong and still ace the test? Maybe, if the functions involved just happen to allow it. Here, we will investigate how to mess up the quotient rule and live to tell the tale!
level: 1
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Matt Buchta
Western Connecticut State University buchta005@wcsu.edu
Sponsor Dr. Barry Mittag mittagb@wcsu.edu
A Problem of Ramanujan on Infinite Nested Radicals
An extension of a problem on infinite nested radicals posed and solved by Ramanujan in 1911. We somewhat generalize Ramanujans result psented on Question 289 in the Journal of the Indian Mathematical Society.
level: 2
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Leslie Cheteyan
Montclair State University, TBOheadump@aol.com
Sponsor Michael A. Jones, jonesm@mail.montclair.edu
Chutes and Ladders for those with a Short Attention Span or The Effect of Spinner Size on the Length of Chutes and Ladders
I will review the rules and game board for Chutes and Ladders, define a Markov chain to model the game with any spinner size, and describe how properties of Markov chains are used to determine that the optimal spinner size of 15 minimizes the expected number of turns for a player to complete the game. Because the Markov chain consists of 101 states, we demonstrate the analysis with a 10-state variation with a single chute and a single ladder. The resulting 10 x 10 transition matrix is easier to display and the manipulations are comparable.
level: 2
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Peter Czere
WCSU csere001/wcsu_student@WCSU_STUDENT
Sponsor Lydia S. Novozhilova novozhiloval@wcsu.edu
Maplets in elementary statistics: STATS CALCULATOR
A set of Maple procedures will be psented. The procedures are used for creating Maplets aimed at replacing obsolete tables still used in elementary statistics courses. Using the Maplets will raise appciation of both mathematics, underlying the traditional tables or "black box" type programs like Minitab, and easy-to-use Maple functionalities.
level: 1
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Christina Desmarais
Marist College tina101085@gmail.com
Sponsor Tracey McGrail Tracey.Mcgrail@marist.edu
Packing Tips
Can you fill a 720x200x100 box with 15x12x10 bricks? I will attempt to answer this question and many others about tiling and packing, using results such as the Two Bricks Theorem, the Two Tiles Theorem, Klarner's Theorem, Kelly's Theorem, and the Two Squares Theorem. I will use real-world examples to illustrate the relevance of this topic.
level: 1
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Andrew Dunn and Yates Monteith
Manhattan College adunn.student@manhattan.edu and lrddpy@gmail.com
Sponsor Marvin Bishop marvin.bishop@manhattan.edu
Computer Modeling of Linear and Star Polymers in Three dimensions
A set of C++ programs have been developed to simulate linear and star polymers in three dimensions. Random numbers are used to select pivot points as well as random angles of rotation. Two different kinds of models are studied: random walks in which there is no interaction between the units and self-avoiding walks for which units are not allowed to overlap. The mean-square radius of gyration, the g ratio and the asphericity are calculated by averaging over the resulting configurations. These quantities are compared to theoretical and other simulation works.
level: 1
Tamara Frakes, Michelle Westby
Manhattan College tfrakes.student@manhattan.edu,
Sponsor Dr. Rosemary Farley rosemary.farley@manhattan.edu
The orbit of a complex number
Suppose that z is a complex number. The set O(z) ={z^n | n is a natural number} is called the orbit of z. Under what conditions will O(z) be a finite set?
level: 1
Reid Ginoza
Bennington College rginoza@bennington.edu
Sponsor Andrew McIntyre amcintyre@bennington.edu
Mathematics for the Faithful
Finding the qibla, the direction of the Mecca on the horizon, is a part of daily spiritual life for a Muslim. Finding this direction is relatively simple today, but what about in the 9th Century, before the use of three-dimensional drawings? This psentation focuses on a geometric method, an analemma, created by Habash al-HÄsib that allows one to determine the angle to the Mecca using only one drawn circle.
level: 1
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Peter Golbus(Bob McGrail)
Bard College pgolbus@gmail.com
Sponsor Robert W. McGrail mcgrail@bard.edi
Constraint Satisfaction Problems over Knot Quandles
The knot quandle is a classifying invariant of knots. Moreover, finite algebras, such as finite quandles, give rise to constraint satisfaction problems. This talks introduces a notion of constraint satisfaction problem over a knot and emphasizes the role of quandles in this construction.
level: 2
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Harold L. Gomes
Queens College, CUNY hlpgomes@gmail.com
Sponsors Dr. Joshua Brumberg joshua.brumberg@qc.cuny.edu Queens College and Dr. Nicholas T. Carnevale Yale School of Medicine
Applied Mathematical Modeling: Effect of Neuronal Morphology on Action Potentials
The cerebral cortex of the brain performs many higher cognitive computations such as perception of the sensory environment and motor planning. Neurons are the basic building blocks of the cerebral cortex, and action potentials (voltage impulses) are in the core of the information encoding-decoding process. Neurons can be classified based upon their physiological and geometrical features which have been shown to vary in biological experiments. These differences are thought to influence their computational abilities. Six morphological groups were identified in a different study in our lab (Golgi neurons from layer 6 of mouse somatosensory cortex). Here we have investigated the role of cell geometry on repetitive firing of action potentials. Using NEURON simulation environment software we have imported and simulated 146 actual neurons with Hodgkin-Huxley Na+, K+ channel-properties under six different models, to compare and contrast the electrophysiology amo!
ng the morphological groups. We have injected current to find the corresponding voltage-frequency response of neurons. Geometric variables were the only parameters that varied in each cell (i.e., actual cell morphology). All other experimental variables were constants in any specific model. Our results indicate that there are indeed differences and similarities in electrophysiology to compare across the different neuronal groups. Since all six different computational models that we have implemented indicate similar results, the degree of validity of our modeling technique is high. Thus, we believe that neuronal geometry can strongly influence action potential properties.
level: 2
Bryan Harris
Marist College bryharris17@gmail.com
Sponsor Tracey McGrail Tracey.McGrail@marist.edu
Are You Ready For a Coin Flip?
Does the coin flip hold too much influence over the outcome of overtime in a NFL game? I will show how Markov Chains can be used to find the probability of a team winning in overtime and how the probability changes under a possible new rule.
level: 2
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Melissa Harrigan
Southern Connecticut State University harriganm1@southernct.edu
Sponsor Dr. Ray Mugno mugnor1@southernct.edu
Maximization of Profit: An Application of the Bootstrap and Regression Analysis
The concepts of the bootstrap and regression analysis have been around for centuries; however, it hasn’t been until recently that the uses and applications of the bootstrap have appeared in statistical research. One of the main reasons for this is that the bootstrap and regression analysis are both applications that require the use of computers and computer programming. Since technology has improved recently, it has become easier to make the complicated calculations that are associated with creating models using the bootstrap and regression analysis. This study will demonstrate that the uses of the bootstrap and regression analysis are efficient and accurate ways to maximize the profit of an at-home EBay business. Regression analysis was used in this study to create a model that would estimate the profit of the business, and from this model it was possible to find a way to maximize profit. Bootstrapping was then used to determine the accuracy of the results from the regression model. The results of this thesis show how to maximize profit for each type of rock sold and through bootstrapping; the model that was used was found to be extremely accurate.
level: 1
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Milton A Herrera
LaGuardia Community College herrera.milton@yahoo.com
Sponsor Dr Frank Wang fwang@lagcc.cuny.edu
MONTECARLO METHOD FOR A EUROPEAN OPTION
The Monte Carlo Method is a common tool used to price financial options. Nowadays, technology gives good possibilities to simulate,calculate and repsent analytical estimations of financial trends. This project psents simulations of call option pricing, and demonstrate the implementation with MATLAB. A difference equation model for change in stock price over a period is used to generate an ensemble of stock prices. Different sample trajectories are generated to observe variability in their behavior. The Monte Carlo procedure is applied to find the estimate for different initial stock prices. The accuracy of the estimate is verified with the Black-Scholes formula.
level: 1
Jeremy Holden
Norwich University jholden@student.norwich.edu
Sponsor Daniel McQuillan dmcquill@norwich.edu
Vertex-magic total labelings of 2-regular graphs
Graph labeling is the field in which elements are assigned to graph components. Specifically, we assign an integer to each component. If the labeled graph satisfies certain properties, it could be called graceful, harmonious, magic, or any number of things. There are dozens of different types of labelings. In this talk, we will introduce the concept of vertex-magic total labelings, and discuss some of the main results in the field and open questions.
level: 1
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Chase Hunter
United States Military Academy chase.hunter@usma.edu
Sponsor Dr. Frederick Rickey Frederick.Rickey@usma.edu
Math History: African Americans, Hispanics/Latinos, and Native Americans in the Department of Mathematical Sciences at USMA
Historically, each year fewer than three percent of the new PhDs in Mathematics are African American, Hispanic, or Native American. Women have also been underrepsented in the Mathematical Sciences. The history of minority faculty members in the Department of Mathematical Sciences at USMA is a recent one. This capstone is intended to study the trends regarding the underrepsentation of minorities not only in the United States, but more specifically in the Mathematical Sciences department at USMA. For our capstone we will research and gather information from various sources in an attempt to compile statistical trends regarding minority professors and faculty members here at USMA.
level: 1
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Leigh Johnson, Theresa Sampson, Heather O'Conner
St. Joseph's College LTJohnson@Optonline.net
Sponsor Dr. Donna Marie Pirich DPirich@sjcny.edu
Phi in Nature and Beyond
While conducting research for Senior Seminar in Mathematics, three students find particular interest in, “The Distance of the Planets from the Sun and Their Atmospheric Composition” by Charles William Johnson. In this paper, Johnson postulates the existence of a Phi pattern in the distances of the planets from the Sun, if Ceres is included as a dwarf planet repsentative of the asteroid belt between Mars and Jupiter. The student authors validate Johnson’s work with data retrieved from NASA databases. However, the question remains. What happens if Ceres is not included? The student authors answer this question using linear regression, tables, and graphs. The reduced data set shows Jupiter as an outlier, and a Phi pattern does not exist. To address the situation, the student authors postulate the existence of a missing planet via regression analysis techniques. The location of the missing planet is statistically within the domain of Ceres, and the Phi pattern is evident. The student authors apply similar techniques in searching for the existence of Phi patterns elsewhere in our solar system. In particular, they conduct research on Neptune, Uranus, and Saturn, with respect to the location of their moons. The student authors illustrate the existence of Phi patterns within the planetary systems of Neptune, Uranus, and Saturn. Additional research can be expected using this material. The student authors suggest further exploration of the impact of Kepler’s Law, the possibility of the existence of other planets in out solar system, and finally, applications to other galaxies and solar systems.
level: 1
Wai-Ting Lam
St. Francis College lwai-ting@stfranciscollege.edu
Sponsor Ioannis Farmakis ifarmakis@stfranciscollege.edu
Application of Linear Algebra on Banach Number
We would like to psent a method calculating the n Fibonacci numbers for n goes to infinity using tools from Linear Algebra. Other than that, we prove by considering the group GL(2,R) to prove that limit as n->infinity Xn is approximately equal to (1/(5^(1/2))[(1+(5^(1/2))/2]^(n+1), where Xn is the n-th banach number.
level: 2
Joseph Landry
Norwich University landryj@student.norwich.edu
Sponsor Darlene Olsen dolsen1@norwich.edu
Good Vibrations and Partial Differential Equations
Partial Differential Equations unlike ordinary differential equations have several unknown variables. The derivatives of such functions of several variables are partial derivatives. Because Partial Differential equations have no unifying theme like first order differential equations, they are not nearly as understood as ordinary differential equations. My talk will focus on analytical methods for solving such familiar partial differential equations like the vibrating string and drum using inner product spaces and Fourier analysis. I will show how such partial differential equation systems respond to damping and forcing functions, and that even the most difficult partial differential equations can be solved.
level: 2
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Bono Lee
St. Francis College hlee@stfranciscollege.edu
Sponsor Erez Shochat eshochat@stfranciscollege.edu
Tower of x
Let t(x) = X^(x^(x^(x^(...)))), a tower of x. We first investigate the problem is there an x such that t(x) = 2. After answering this question positively, we ask: For what value c, is there an x such that t(x) = c.
level: 1
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Kimberly Lockrow
Bennington College klockrow@bennington.edu
Sponsor Jason Zimba jzimba@bennington.edu
The Leverrier-Fadeev Method
The Leverrier- Fadeev Method provides a method for solving systems of homogeneous and non-homogenous differential equations. I will introduce the algorithm, which requires basic knowledge of linear algebra, and derive the main equation. If time permits I will run through a specific non-homogenous 2x2 case and discuss why this algorithm is so powerful and elegant comparing it to other methods of solving the same system.
level: 1
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Rachel Masciotti and Katherine Oggeri
Marist College Rachel.Masciotti1@marist.edu, Katherine.Oggeri1@marist.edu
Sponsor Tracey McGrail tracey.mcgrail@marist.edu
An Investigation into Tennis Serves
Tennis is not just about talent; it is also about racket length and how this can affect service accuracy. Basing our psentation on Tom Roper's "Anyone for Tennis?" we will discuss how trigonometry, proportions, and similar triangles are needed to grasp a further understanding of perfecting a serve. Serving does not only involve skill, but also directly depends upon the height of the player and racket length. Surprisingly, the racket's length increases the player's percentage of accuracy, but this percentage will decrease as the player's height increases.
level: 1
Mona Merling
Bard College mm386@bard.edu
Sponsor Robert McGrail mcgrail@bard.edu
Toward Quandle Dichotomy
Feder and Vardi(1993)discovered a strong correspondence between finite algebras and computational complexity through the constraint satisfaction problem (CSP). It allows a classification of algebras according to their complexity within NP. We focus on quandles, algebras that arise via knot theory. In particular, we demonstrate that all finite quandles that are not locally connected are NP-complete. Furthermore, we psent recent progress on the classification of locally connected quandles.
level: 2
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Mona Merling
Bard College mm386@bard.edu
Sponsor Robert W. McGrail mcgrail@bard.edu
Toward Quandle Dichotomy
This talk introduces a method for computational classification of finite quandles, algebras that arise in many areas of mathematics, through the constraint satisfaction problem. It will be shown that non totally connected quandles are NP-complete and that quasigroup quandles are tractable. Moreover, several open problems related to further computational classification of the remaining finite quandles will be introduced.
level: 2
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Stela Mihneva
St. Francis College stelamihneva@yahoo.com
Sponsor Fotios Paliogiannis, PhD. fpaliogiannis@stfranciscollege.edu
Solving ODE by the Differential Operator
We psent a technique that enables us to solve ODE using the notion of differential operator. These operational methods are mainly used to find particular solutions for non-homogeneous differential equations. Here, we extend it further to find general solutions of ODE. The technique is illustrated by working out several examples.
level: 1
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Dusan Milanovic
St. Francis college dusan666m@yahoo.com
Sponsor Fotios Paliogiannis fpaliogiannis@stfranciscollege.edu
Geometry of equations
Geometry of equations is a relatively new area in mathematics and it brought some interesting new ideas. Using projective geometry and dual planes we will see how we can solve equations using geometrical ideas as the notion of "envelopes". Starting with the quadratic and cubic equation as example, we will psent the general equation of the "envelope".
level: 1
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Steven Morse
United States Military Academy steven.morse@usma.edu
Sponsor Dr. Elisha Peterson Elisha.Peterson@usma.edu
A Diagrammatic Approach to Linear Algebra: Some Results and Trivial Proofs
This talk explores the application of diagrammatic techniques to various problems in mathematics. Specifically, in this talk we will use special diagrams, often known as “spin networks” or “birdtracks”, to explore topics in linear algebra and the study of trace algebras, with special attention to diagrams of dimension 3. The talk focuses on a diagrammatic proof of Dodgson's Condensation Method for calculating the determinant, a clever result of a classical theorem by Jacobi. We will hint at the doodles' use in the Fricke-Vogt theorem for trace relations in $\SL(3,\C)$ and the structure of the diagrams, particularly in $\C3$.
level: 2
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Stephanie Ostapchuk and Matt Lamoureux
Quinnipiac University matthew.lamoureux@quinnipiac.edu
Sponsor Jill Shahverdian jill.shahverdian@quinnipiac.edu
A Look at Quaternions
Abstract: The set of quaterions is a four-dimensional extension of the two-dimensional complex numbers. We will discuss a short history of quaterions, explore their properties as a division algebra, and examine reasons why a three-dimensional extension fails.
level: 1
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Anthony Penoro, Karsten Bischoff
Manhattan College apenoro.student@manhattan.edu
Sponsor Dr. Richard Goldstone richard.goldstone@manhattan.edu
Proof of the Euler Line using Linear Algebra Methods
We will establish the existence of the Euler line by incorporating Linear Algebra methods and Geometric transformations to show that the centroid, circumcenter and orthocenter of a triangle all lie on a single line. The same methods are then used for further developments, including the Nine Point Circle of a Triangle.
level: 1
Alexandra Phelan
Manhattan College aphelan.student@manhattan.edu
Sponsor Dr. Goldstone richard.goldstone@manhattan.edu
Fermat's Theorem for Matrices
Fermat's Theorem in Number Theory states that for any integer n that is not a multiple of a prime p, that n^(p-1) ~ 1 (mod p). In this talk, we consider an integer matrix version of Fermat's Theorem. For matrices over the integers modulo p, we investigate the connection between Fermat's Theorem for matrices and diagonalizability.
level: 2
Alicia Psillos and Maeve FitzSimmons
Manhattan College alicia.psillos@yahoo.com
Sponsor Dr. Farley rosemary.farley@manhattan.edu
Orbits of Linear Transformations
Let T be a linear transformation from R^n to R^n and let A be the n x n matrix associated with the transformation. Let x0 be an arbitrary point in R^n. Let x1 = A * x0, x2 = A*x1, … xn = A * xn-1. The sequence {xi} is called the orbit of the transformation. We will discuss the orbits of linear transformations from R2 to R2 and from R3 to R3 with emphasis on transformations whose corresponding matrices have complex eigenvalues.
level: 1
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Emma Schlatter
Smith College eschlatt@email.smith.edu
Sponsor J. Henle jhenle@email.smith.edu
Chicken: a new take-away game
Chicken is similar to a class of combinatorial games known as take-away games. In take-away games, two players take turns removing given numbers of counters from one or more piles, and the first player unable to move loses the game. But chicken has a twist: the number of counters a player can remove depends on the number her opponent removed on the pvious turn. The result is a complicated and mysterious game. I'll share some of the things we've discovered about Chicken and questions still open.
level: 1
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Pradeep Subedi
St. John's University pradeep.subedi04@stjohns.edu
Sponsor David Rosenthal rosenthd@stjohns.edu
Coloring as a Knot Invariant
The psentation introduces coloring of knot diagrams as a way to distinguish different knots. In particular, we consider tricolorings and its generalization to p-coloring using linear algebra, and it connection to Alexander Polynomial.
level: 2
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Yubin Wang
Western Connecticut State University yubin.wang@lmh.oxon.org
Sponsor Xiaodi Wang xiaodiwang1@yahoo.com
Trinomial Method for option pricing in Finance
The trinomial method can be summarized in the following steps
1.Create the trinomial tree structure.
2.Initialize the call option values in the tree.
3.Compute the vector pay off.
4.Compute the call values at pvious steps.
In this paper, I will give an introduction to the trinomial method & discuss it & its relationships with the finite difference method for corresponding Stochastic Differential Equations, show the relevance and importance of the finite difference method. I will also show how to apply this method to pricing options.
level: 2
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Thomas Zugibe
Marist College Thomas.Zugibe@gmail.com
Sponsor Scott Frank Scott.Frank@marist.edu
Isolation of Near-Receiver noise from Teleseismic Events
Since seismic waves are composed of radial, tangential and depth component variations, a receiver function is a deconvolution of the radial component with one of the other two. Receiver functions are utilized as a means of establishing the depth of the Earth's crust at one point. Ammon investigated these methods in order increase the accuracy of the receiver function technique. These procedures aim to isolate certain propagation effects found near the receiver. In addition, Ammon also introduced the benefits of developing absolute amplitudes for receiver functions in order to measure the signal strength of the converted phases relative to the source-receiver distance.
level: 2
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Faculty Talks:
Vito Faraci Jr.
VFJ Engineering vfaraci@optonline.net
One Mathematician's Accomplishments in Engineering
Math students will hear, in the proposed psentation, an overview of what one pure mathematician accomplished in an occupation other than teaching; in this case, electrical and mechanical engineering. This subject involves calculating probability of failure of electrical and mechanical equipment as a function of time. This topic, now known as Reliability, has become a science by itself.
After reading NASA’s research on Markov Analyses, limitations in the engineering community’s methods for solving non-combinatorial type probability problems were discovered. By giving seminars and lectures across the country, the community’s level of awareness of these problems was raised, and various solutions were psented.
level: 2
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Ross B. Gingrich
Southern Connecticut State University gingrichr1@southernct.edu
Cardano's Solution of the Cubic Equation
While the quadratic formula is well known, many students have not seen Girolamo Cardano’s method for solving the general cubic equation x3+b*x2+cx+d=0. Cardano published his solution in his Ars Magna or The Rules of Algebra in 1545 CE. We will look at the history of his solution, the method that he used, and its modern formulation. We shall see that his solution was a process (or an algorithm), not an algebraic formula, and that instead of solving the general cubic, he solved thirteen separate cases of the cubic.
level: 1
Walton Gutierrez
Touro College waltong@touro.edu
THE OPTIMAL FORM OF DISTRIBUTION NETWORKS
A model is proposed to minimize the total volume of the main distribution networks of fluids in relation to the organ form. The minimization analysis shows that the overall exterior form of distribution networks is a modified ellipsoid, a geometric form that is a good approximation to the external anatomy of the kidney and lung.
level: 2
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Harvey J. Hindin
Emerging Technologies Group hhindin@etg.com
Lewis Carroll, Arctan Series Summations, Difference Equations, and Fibonacci Numbers
Sums from one to infinity, as well as finite sums, of arctangent functions of various arguments have been studied for years. A variety of techniques, both old and new, are available for their evaluation in closed form. The Rev. C. L. Dodgson (Lewis Carroll of Alice in Wonderland fame) developed a particularly useful relationship that I use for evaluating such sums. His technique, among others, is applied to arctangent arguments which are functions of Fibonacci and other numbers that are solutions to difference equations. Many results, some which may be new, are psented using Carroll's work, and the work of more contemporary mathematicians.
level: 2
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Mary C. Krembs
Bard College krembs@bard.edu
Classification and Approximation of Voronoi Nets
Determining the Voronoi diagram for a set of points in the plane is a well studied computational geometry topic. This talk focuses on the inverse problem and related questions.
The definition of 'net' is formalized and topological, graph theoretic and geometric properties of a net are discussed. A new definition of a Voronoi diagram is provided that admits multiple sets of sites. A complete theoretical solution is psented to the inverse problem of "Given an arbitrary net, determine whether or not it is a Voronoi net. If it is, find all sets of sites that generate the net."
level: 2
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Darlene Olsen
Norwich University dolsen1@norwich.edu
Mathematical Ties to Tying Neckties
Did you ever ask the question of how many possible ways there are to tie a necktie? Furthermore, what factors determine an aesthetic tie knot? This problem can be answered using mathematics. The mathematical ways for describing how to tie necktie knots will be examined and tie knots will be classified according to their size and shape. You will be provided with a list of all 10 "aesthetic" knots as determined by Thomas Fink and Yong Mao
level: 1
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Ellen Tufano
St. John's University tufanoe@stjohns.edu
The Role of Mathematics in Internet Security
E-commerce is the fastest growing segment of the global economy. Mathematics plays a central role in protecting personal information entered into online e-commerce forms. Data encryption algorithms are used to protect confidential data prior to transmission across the Internet.
level: 1
Frank Wang
LaGuardia Community College fwang@lagcc.cuny.edu
The Laplace-Runge-Lenz Vector
The Kepler problem is a common example in Calculus III to illustrate the utility of vectors. However, most textbooks offer a derivation of Kepler’s First Law (a planet moves around the sun in an ellipse) using the Laplace-Runge-Lenz vector. As most books fail to state explicitly that the Laplace-Runge-Lenz vector is peculiar to the exact inverse square force law only, students are often puzzled by the steps in constructing such a vector. In this psentation, we guide students to employ computer software to examine dynamical equations through their numerical solution, and visualize the Laplace-Runge-Lenz vector to gain a deeper understanding.
level:1
