Inside this content area:
Relevant unomaha.edu links:
Web Archive
The department keeps a web archive of containing past newsletters, details of past colloquia, and other useful information.
The archive is currently in the process of being reorganized. Once complete, the newly organized archive will appear here. However, in the interim it can still be accessed in its original form here.
Congratulations to the May 2012 Graduates
Posted: May 30, 2012
Mathematics Teacher Assistant of the Year Awards
The first Mathematics Teacher Assistant of the Year awards were presented during a ceremony on May 1st at the UNO Alumni Center. The two recipients were Hayley Verboon and Roger McKnelly II. Hayley is a Civil Engineering and Math major, while Roger is studying Architectural Engineering. For details on the Mathematics Teacher Assistant Program.
Posted: May 30, 2012
Daniel Miller, Math Department Honoree
Daniel Miller is the 2011-2012 Math Department Honoree. Each April, an outstanding undergraduate Math major is honored with an award at the Student Honors Convocation. Congratulations Daniel!
Posted: May 11, 2012
Winning projects from the Kerrigan Research Minigrants Program announced
The three winning projects from the Kerrigan Research Minigrants Program are:
1st place: Rodney Tembo
2nd place: Andrew Tew
3rd place: Stephen Dodds
For more details on the KRMP program or to see this year's projects, visit the program page here.
Posted: May 9 2012
Dr. Todd, Kerrigan Award for Excellence in the Teaching of Mathematics Recipient
Dr. Todd has been selected as the recipient of the 2012 Kerrigan Award for Excellence in the Teaching of Mathematics. The award is offered every year to one member of the Mathematics Department at UNO to recognize their contribution to the teaching of mathematics at the University of Nebraska at Omaha. The benefactor is Mr. Patrick Kerrigan.
Posted: May 9 2012
Dr. Swift, UNO Alumni Outstanding Teaching Award & College of Arts and Sciences Excellence in Teaching Award recipient
Dr. Swift has been selected as a recipient of the 2012 UNO Alumni Outstanding Teaching Award and the 2012 College of Arts and Sciences Excellence in Teaching Award. The Alumni award was presented to Dr. Swift at the Faculty Honors Convocation on April 12 2012. The College of Arts & Sciences award was presented to Dr. Swift at a college reception on April 20 2012.
Posted: May 9 2012
Brianna Kallman, 2012 CCSW Student Scholarship Award Recipient
Math major Brianna Kallman was honored by the Chancellor's Commission on the Status of Women. Brianna is also pursuing a teaching certificate in secondary education. She has been named to the Dean's List and the Chancellor's List all five semesters that she has been at UNO. Brianna is a member of the UNO chapter of Pi Mu Epsilon National Mathematics Honorary Society, the Math Club, and the National Council for Teachers of Mathematics. Brianna is also the Treasurer of Delta Epsilon Iota Academic Honor Society, the Secretary and Treasurer of Omicron Delta Kappa National Leadership Honor Society and she's a Section Leader in the UNO Symphonic Wind Ensemble. Congratulations Brianna!
Posted: May 9 2012
Taking Math Outside
During the recent warm weather, Dr. Love chose to hold her MATH 2050 Linear Algebra class outside, allowing the students to create some beautiful and interesting sidewalk art. Click the images to enlarge.
Posted: March 19 2012
Jessica Jolkowski, Teachers of Mathematics Scholarship Recipient
Jessica Jolkowski of Burke High School is the latest recipient of the Teachers of Mathematics Scholarship.
Posted: February 9 2012
Dr. Paul A. Haeder
Dr. Paul A. Haeder, Former Math Department Chair 1968-1973, passed away December 3rd at the age of 96. Omaha World Herald Obituary
Posted: December 7 2011
Tamara Pendergrass, Wu-King Scholarship Recipient
Through a donation from Horace Wu and Kate King, a $1500 scholarship is awarded annually, designed to support outstanding students who are pursuing Graduate degrees in Mathematics and Science. The individual must be a K-12 teacher, pursuing a Graduate degree, and should have at least a 3.25 GPA.
Posted: November 23 2011
UNO Fall Job Fair
The UNO Fall Job Fair will take place on Wednesday, September 21 from 10 am until 2 pm in the MBSC Ballroom.As of right now, over 75 employers are registered for the event and ready to recruit our students for full-time, part-time, and internship positions! This event will allow students to network with employers from various industries! Students may view the list of employers that will be attending on Maverick HireWire. The UNO Career Center also offers a variety of Career Preparation Workshops and On-Campus Interviews throughout the semester. To access these schedules please visit http://unoceo.unomaha.edu
Posted: September 16 2011
Tuesday September 18 2012, 2:30pm - 3:30pm, Location 116 DSC (Cool Math Talk)
Dr. James Tanton
Some Fibonacci Surprises
The Fibonacci numbers 1,1,2,3,5,8,13,... have been studied and probed and generalized and analyzed in most every possible way for centuries (well, for 810 years to be precise; well, ... longer actually if you read Sanskrit) and one might think there is little more to say about them. Let me surprise you then with a whole host of new appearances of the Fibonacci numbers. (And this talk comes with an invitation for you to find more of your own!)
Believing that mathematics really is accessible to all, James Tanton (PhD, Mathematics, Princeton 1994) is committed to sharing the delight and the beauty of the subject. In 2004 James founded the St. Mark's Institute of Mathematics, an outreach program promoting joyful and effective mathematics education. He worked as a full-time high school teacher at St. Mark's School in Southborough MA,(2004-2012) and he conducted, and continues to conduct, mathematics graduate courses for teachers though Northeastern University and American University. He also gives professional development workshops across the nation and Canada.
James recently relocated to Washington D.C. and is working with the Math For America program in D.C. and with the Mathematical Association of America.
James is the author of SOLVE THIS: MATH ACTIVITIES FOR STUDENTS AND CLUBS (MAA, 2001), THE ENCYCLOPEDIA OF MATHEMATICS (Facts on File, 2005), MATHEMATICS GALORE! (MAA, 2012) and twelve self-published texts. He is the 2005 recipient of the Beckenbach Book Prize, the 2006 recipient of the Kidder Faculty Prize at St. Mark's School, and a 2010 recipient of a Raytheon Math Hero Award for excellence in school teaching.
He also publishes research and expository articles, and through his extracurricular research classes for students has helped high school students purse research projects and also publish in mathematical journals.
More about James can be garnered from his website www.jamestanton.com
Friday September 28 2012, 2:30pm - 3:30pm, Location 116 DSC (Cool Math Talk)
Kyle Duckert, Instructor, Mathematics Department, University of Nebraska at Omaha
The physics of a sandbox: An introduction to granular hydrodynamics
We study interactions between shocks and standing wave patterns in continuum simulations of vertically oscillated granular layers. Layers of grains atop a plate with sinusoidal oscillations in the vertical direction leave the plate at some time during the cycle if the accelerational amplitude of oscillation is greater than the acceleration of gravity. Above a critical acceleration, standing waves form stripe patterns. In these same shaken layers, shocks are produced when layers collide with the plate after leaving the plate earlier in the cycle. We simulate vertically shaken layers using numerical solutions of continuum equations to Navier-Stokes order to find number density, average velocity, and granular temperature as functions of time and location within the cell. We compare shocks and standing waves coexisting in this system; pressure gradients produced by shocks play a significant role in the formation of standing wave patterns.
Tuesday October 9 2012, 2:30pm - 3:30pm, Location 116 DSC (Cool Math Talk)
Dr. Elliott Ostler, Professor, Teacher Education, University of Nebraska at Omaha
Mathematics, Measurement, and Machines
The National Council of Teachers of Mathematics has called measurement the forgotten standard. You might ask, how could something so important be so easily forgotten? Simple, like so many other things, we take for granted what we assume is easily understood, but did you know you can measure time, roots, rational exponents, and other complex mathematical quantities with a standard ruler? It's true! This informative session will take you through a series of measurement techniques and even show you how to build machines for measuring and calculating using measurement.
Elliott Ostler is a former Junior High and High School mathematics and science teacher in Nebraska, Iowa, and Washington. He has been a professor of STEM Education at UNO for 18 years and specializes in creating manipulative geometric applications and representations for common numeric and algebraic concepts. He is also active in brining mobile technology into classrooms to help students better understand STEM concepts. He has worked directly with some of the nation’s leading education service and support institutions such as the College Board, Texas Instruments, NASA, Jet Propulsion Laboratories, and the NCTM. His current research in STEM learning is related to helping students understand how machines are engineered through careful measurements and geometric concepts we see so often but regularly take for granted.
Friday November 9 2012, 1:00pm - 2:00pm, Location 254 DSC (Cool Math Talk)
Kathryn Haymaker, Mathematics Department, University of Nebraska Lincoln
Combinatorics and the game SET
SET is a multi-person card game in which the goal is to collect particular sets of three cards from a group of 12 (or more). The person with the most SETs by the end of the game wins. It turns out that a SET corresponds to a line in a 4-dimensional version of Tic-Tac-Toe! I'll explain how that game works, and we will use the correspondence along with some counting techniques to answer interesting questions about the game, including: what is the size of the largest group of cards that does not contain a SET?, and, what is the most likely type of SET?
Kathryn Haymaker, of Hellertown, PA, is a Ph.D. student in mathematics at UNL. She studies coding theory, which originated with the need to send information reliably and efficiently over a communication or storage channel. Her dissertation research includes the use of mathematical structures to design codes for flash memories and write-once memories. In fall 2011, she spent two months at a thematic program on coding theory at a technical institute in Lausanne, Switzerland. She received the G.C. Young and W.H. Young Award for scholarship in the UNL math department, and the 2012-2013 Presidential Graduate Fellowship. She graduated with honors in mathematics from Bryn Mawr College in 2007.
Monday November 12 2012, 2:30pm - 3:30pm, Location 116 DSC (Cool Math Talk)
Howard Alcosser, Diamond Bar High School, California
How to Succeed in Teaching Calculus to Students - MOTIVATE
High school students take Calculus for many different reasons - most of them have nothing to do with the love of math! I'll talk about some of these reasons and how I motivate students to be successful both in my class and at the universitydespite their wide range of mathematical abilities.
Howard Alcosser has taught AP Calculus AB and BC and IB Higher Level Math in Diamond Bar, California for 30 years where he has been the architect of the AP Calculus program that was designated "Best in the World" in 2005 and "Best in the Nation" in 2007 by the College Board in their Report to the Nation and California's Best by the Siemens Foundation in 2008. The College Board named Howard in 2006 as one of 20 Exemplary AP Teachers in the Western Region.
Howard has been an AP Calculus Reader for the past 11 years and has led workshops across the country.
Howard is also referred to as "Mister Calculus", as he has a website for teachers and students to access much information regarding Calculus via "Ask Mister Calculus": http://home.roadrunner.com/~askmrcalculus/index.html
Thursday November 15 2012, 2:30pm - 3:30pm, Location 256 DSC (Cool Math Talk)
Ivars Peterson, Director of Publications at the Mathematical Association of America
The Jungles of Randomness
From slot machines and amusement park rides to dice games and shuffled cards, chance and chaos pervade everyday life. Sorting through the various meanings of randomness and distinguishing between what we can and cannot know with certainty proves to be no simple matter. Inside information on how slot machines work, the perils of believing random number generators, and the questionable fairness of dice, tossed coins, and shuffled cards illustrate how tricky randomness can be.
Ivars Peterson is an award-winning mathematics writer. He is currently Director of Publications for Journals and Communications at the Mathematical Association of America. He worked for 25 years as a columnist and online editor at Science News and continues as a longstanding columnist for the children's magazine Muse. He wrote the weekly online column Ivars Peterson’s MathTrek. He is the author of a number of popular mathematics and related books. Ivars Peterson received the Joint Policy Board for Mathematics Communications Award in 1991 for "exceptional skill in communicating mathematics to the general public over the last decade". For the spring 2008 semester, he accepted the Wayne G. Basler Chair of Excellence for the Integration of the Arts, Rhetoric and Science at East Tennessee State University. He gave a series of lectures on how math is integral in our society and our universe. He also taught a course entitled "Communicating Mathematics".
Monday November 26 2012, 2:30pm - 4:00pm, Location 115 DSC
Ginger McKee, Wolfram Research, Inc
Mathematica in Education and Research
This talk illustrates capabilities in Mathematica that are directly applicable for use in teaching on campus. Topics of this technical talk include: Free form input, 2D and 3D visualization, Dynamic interactivity, On-demand scientific data, Example-driven course materials, Symbolic interface construction, Practical and theoretical applications.
Friday November 30 2012, 2:30pm - 3:30pm, Location 116 DSC (Cool Math Talk)
Dr. Doug Downey, Assistant Professor, EECS, Northwestern University
Web Information Extraction: Theory and Applications
Search engines are extremely useful tools for answering simple questions.
However, for more complex questions -- e.g., "which nanotechnology companies are hiring on the West Coast?" -- existing search engines are less effective, because the answers are not contained on just a single page. Answering these questions requires extracting and synthesizing information across multiple documents. Currently, this is a tedious and error-prone manual process.
In this talk, I will describe my research toward automating the extraction of information from the Web. I will present a theoretical model of the redundancy inherent in the Web, and show how the model enables the autonomous extraction of facts from Web text. I will then highlight our ongoing work toward more powerful information extraction capabilities and applications.
Doug Downey is an assistant professor in the EECS Department of Northwestern University. He obtained his PhD from the University of Washington, where he was advised by Oren Etzioni. His research interests are in the areas of natural language processing, machine learning, and artificial intelligence, with a particular interest in utilizing the Web to autonomously extract large knowledge bases.
Tuesday January 24 2012, 2:30pm - 3:30pm, MBSC Dodge Rooms
Dr. Michael Matthews, Assistant Professor, Mathematics Department, University of Nebraska at Omaha
Mathemagic: Magic in the Mathematics Classroom
We will be presenting several different magic tricks that are based on mathematical principals or "Mathemagic". Magic can be a powerful tool for mathematics teachers if used properly. Of course, since it is entertainment, it can be used to dazzle the students. Thus it makes a great hook into a particular lesson. Or of course, it could be used as another "5 minute fillers". However, used properly mathemagic can be used to teach concepts as a core part of a lesson. Such magic tricks can also be a basis for good questions for homework or projects. Magical Tricks will be presented that are appropriate for grades 3-12.
Tuesday February 28 2012, 2:30pm - 3:30pm, MBSC Dodge Rooms
Dr. Dana C. Ernst, Assistant Professor, Mathematics Department, Plymouth State University
The Futurama Theorem
In the episode "The Prisoner of Benda" of the television show Futurama, Professor Farnsworth and Amy create a mind switching machine, only to afterwards realize that when two people have switched minds, they can never switch back with each other. Throughout the episode, the Professor, with the help of the Globetrotters, try to find a way to solve the problem using two or more additional bodies. The solution to this problem is now called the Futurama Theorem, and is a real-life mathematical theorem, invented by Futurama writer Ken Keeler, who holds a PhD in applied mathematics. In this talk, we will introduce the mathematics behind the Futurama Theorem and present its proof.
Friday March 9 2012, 12:00pm - 1:00pm, 261 PKI (Joint colloquium with PKI)
Dr. Mahboub Baccouch, Assistant Professor, Mathematics Department, University of Nebraska at Omaha
Superconvergence and a posteriori error estimation for the local discontinuous Galerkin method applied to the second-order wave equation
Discontinuous Galerkin (DG) methods have gained in popularity during the last fifteen years because of their ability to address problems having discontinuities, such as those that arise in hyperbolic problems. DG methods allow discontinuous bases, which simplify both h- refinement (mesh refinement and coarsening) and p-refinement (method order variation). However, for DG methods to be used in an adaptive framework one needs a posteriori error estimates to guide adaptivity and stop the refinement process. The solution space consists of piecewise continuous polynomial functions relative to a structured or unstructured mesh. As such, it can sharply capture solution discontinuities relative to the computational mesh. It maintains local conservation on an elemental basis. The success of the DG method is due to the following properties: (i) does not require continuity across element boundaries, (ii) is locally conservative, (iii) is well suited to solve problems on locally refined meshes with hanging nodes, (iv) exhibits strong superconvergence that can be used to estimate the discretization error, (v) has a simple communication pattern between elements with a common face that makes it useful for parallel computation and (vi) it can handle problems with complex geometries to high order.
The local discontinuous Galerkin (LDG) finite element method is an extension of the DG method aimed at solving ordinary and partial differential equations containing higher than first-order spatial derivatives. In this talk, we present new superconvergence results for the LDG method applied to the second-order scalar wave equation in one space dimension. We show that the leading terms of the spatial discretization errors for the p-degree LDG solution and its spatial derivative are proportional to the (p + 1)-degree right Radau and (p + 1)-degree left Radau polynomials, respectively. More precisely, we prove that the global discretization error for the LDG solution is O(hp+3/2) superconvergent at the roots of the right Radau polynomial of degree p + 1 and the solution’s derivative converges as O(hp+3/2) at the roots of the (p + 1)-degree left Radau polynomial while a local error analysis and computational results and show higher O(hp+2) convergence rates at the roots of Radau polynomials of degree p + 1 on each element for both the solution and its derivative. These results are used to construct asymptotically correct a posteriori error estimates. We further show that the LDG discretization error estimates converge to the true spatial errors under mesh refinement. Finally, we prove that the global effectivity indices, for both the solution and its derivative, in the L2-norm converge to unity at O(h1/2) rates. Several numerical simulations are performed to validate the theory.
Thursday April 12 2012, 2:30pm - 3:30pm, 115 DSC, Math Awareness Month Keynote Speaker
David W. Tyner, U.S. Strategic Command
Mathematics and Operations Research at USSTRATCOM
Located at Offutt Air Force Base near Omaha, Neb., U.S. Strategic Command (USSTRATCOM) is one of nine unified commands in the Department of Defense. USSTRATCOM integrates and coordinates the necessary command and control capability to provide accurate and timely information for the President, the Secretary of Defense, other National Leadership and regional combatant commanders. Its responsibilities include space operations; Defense Department information operations; global missile defense; and combating weapons of mass destruction. This presentation will include information on operations research and general mathematical applications at USSTRATCOM. Specific focus will be on reliability testing and the use of Mann Grubbs in confidence interval determinations. Also presented will be information on mathematical programs and careers at USSTRATCOM and the US Department of Defense.
Wednesday October 5 2011, 2:30pm - 3:30pm, 115 DSC
Dr. Jing Chu, CAS Research Center on Fictitious Economy & Data Science, Beijing, China
Identification of Lambda-Measures Based on Partial Information
In information science, we cannot get rid of incomplete information or information with errors. When the information appears as a set function, one eligible method to deal with such kind of information is to identify it with a lambda-measure, which is a typical non-additive measure placing a historical important role in information science. In this paper, by using a genetic algorithm, a general identification of lambda-measure based on partial and/or imprecise information is discussed. The method and strategy developed in this paper are also available for the identification of other types of non-additive measures, such as k-interactive measures and belief measures.
Wednesday October 12 2011, 2:30pm - 3:30pm, 115 DSC (Cool Math Talk)
Dr. Andrew W. Swift, Assistant Professor, Mathematics Department, University of Nebraska at Omaha
Statistics in Action: ESPN and the Mystery of the US Open Draw
On August 15 2011, the ESPN program “Outside the Lines” ran a segment about the annual US Open tennis tournament. Their claim was that the tournament draw was favoring the top seeds even beyond the advantage gained by the seeding process. They backed their claim with statistical analysis of the tournament drawings from the past 10 years.
In this talk, a deeper look at ESPN’s analysis will be presented, as well as a discussion of statistical decision making in general. No prior understanding of statistical analysis is required.
A link to the ESPN story can be found here: http://tinyurl.com/3e6ra4d
Wednesday October 26 2011, 2:30pm - 3:30pm, 115 DSC
Dr. Stephen R. Dunbar, University of Nebraska, Lincoln and MAA American Mathematics Competitions
The Common Core State Standards and Math on the AMC Contests
I will discuss the setting and content of the new Common Core State Standards in Mathematics along with their short history. I will then take problems from the middle-school and high-school level competitions from the MAA and map them back to the Common Core Standards. The goal is to find the match between math that mathematicians find interesting and challenging for students and the Standards. In the process I will show that the Common Core Standards fail to contain some fundamental topics and often underestimate the grade level difficulty of topics that are covered.
Friday November 4 2011, 3:30pm - 4:30pm, Old Gym 306, Creighton University (Joint colloquium with CU)
Dr. Ellen Gethner, Associate Professor, University of Colorado
To the Moon and Beyond
If Earth colonizes its Moon, and cartographers elect to color the corresponding map, they are faced with two planar maps (the map of Earth and the map of its Moon) with an extra coloring constraint: a country and its colony are to be assigned the same color; such a map is called an "Earth-Moon Map."
More generally, the thickness of a graph G, denoted Theta(G), is the smallest integer t such that G can be represented as the edge-disjoint union of t planar graphs. We say that G has thickness t or that G is a thickness-t graph and write Theta(G)=t. Thus if G is planar, then Theta(G)=1. And the graph corresponding to an Earth-Moon map has thickness at most two. In 1959 Gerhard Ringel asked: what is the largest chromatic number of any thickness-two graph? An exact answer continues to be elusive, and the folklore amongst graph colorers is that finding that answer is at least as hard as the proof of the Four Color Theorem, if not harder.
But there are other related problems that are reasonable and interesting to investigate. For example, the r-inflation of a graph G, denoted by G[r], is the graph obtained by replacing each vertex of G with a K_r and then taking the join of neighboring (K_r )s. If chi(G)=k, then chi(G[r]) <= rk and the bound is sharp. What can be said about the thickness of G[r] when, for example, G is planar? This problem and others will be discussed, with open problems given along the way.
Friday November 11 2011, 2:30pm - 4:00pm, 115 DSC
Christopher Goodrich, GTA, University of Nebraska, Lincoln
Partial Hölder Continuity for Minimizers of Functionals with Continuous Coefficients
In this talk we shall discuss some recent regularity results for minimizers of the functional
|
Thursday December 8, 2:30pm - 4:00pm, 402 RH
Judith Covington , Louisiana State University in Shreveport
The game of SET and Geometry
What exactly does the game of SET have to do with geometry? The game of Set deals with matching or not matching four different characteristics. Geometry deals with points, lines and planes. This talk will briefly describe the game of set and discuss how to use the SET cards to describe a finite geometry model.
Student: Rodney Tembo. Advisor: Dora Matache
Boolean network modeling of social networks as distributed prediction markets.
Random Boolean Networks are networks of nodes that can be in one of two possible states ON or OFF, and whose evolution from one time point to another is governed by given Boolean rules. Each node's evolution is influenced by the state of other nodes called its parents. We consider a social network of traders and marketers. The marketers aggregate trader information and share it with other marketers and traders. The traders use this information, as well as outside information from media and their own beliefs to model their dynamics from one time step to another. At the same time the traders can be considered part of a social network of traders in which they make predictions of the other traders' behavior and use them to make their own decisions or to influence the marketers and consequently the entire market.
Student: Andrew Tew. Advisor: Robert Todd
4-move reducibility of cables of (2p+1,2) torus knots.
Nakanishi conjectured in 1979 that the 4-move operation on a knot diagram is an un-knotting move. Though the conjecture is consider to be false, no counter-example has been found and it has been show that there is no counter-example with 12 crossings or fewer. For some time it was thought that the 2-cable of the trefoil knot was a counter-example, however Askitas presented a sequence of 4-moves that reduced it to the unknot. In that paper he mentions that he believes that there is an inductive proof to show that all cable of (2p+1,2) torus knots are 4-move reducible. Our goal is to explore this avenue. To do this project a student should be in the later part of their degree having taken 2230 and at least one other proof class, and the student should like drawing pictures.
Student: Stephen Dodds. Advisor: Mahboub Baccouch
Robotic manipulators: Modeling, Numerical methods, and control.
Robotic manipulators are a major component in the manufacturing industry. They are used for many reasons including speed, accuracy, and repeatability. Increasingly, robotic manipulators are finding their way into our everyday life. In fact in almost every product we encounter a robotic manipulator has played a part in its production. The goal of this project is to allow the student to apply the techniques of numerical methods to an engineering design problem. Matlab is selected as the programming tool.
In this project, we consider the two-link robotic manipulator which is a classic example studied in introductory robotics courses. The equations of motion for the two arms are described by nonlinear differential equations. Because closed-form solutions are not available, the equations of motion are numerically studied using the numerical methods. We propose to apply robust numerical methods to solve these differential equations. Special interest is devoted to determine the motion of the two arms to yield a desired xy-position of the robot hand.
Student: Benjamin Knutson. Advisor: Mahboub Baccouch
Relation of Shape Equations (ROSE) Analysis: Comparison of Shapes in Weapon Detection Systems.
A metal detector is a device which responds to concealed metal. Most current metal detectors can infer the approximate size, density, and material composition of detected objects, but cannot discriminate against harmless objects such as metallic watches and jewelry, which must first be removed. It is our goal in this analysis to statistically compare the shapes of detected objects so that metal detectors can quickly and accurately infer the presence of concealed metal weaponry, thereby making them a more practical means of security. Though potentially useful in many areas, this shape analysis will be developed for further implementation of weapon detection systems in public buildings, specifically in schools.
Two shape equations are built from creating a helical mesh which wraps around the surface of each object. One shape equation denotes the coordinates of the surface points as distances from a central axis; the other as distances from the origin. A relation of shape equations (ROSE) compares the detected object's equations with those of other objects in a library to determine the relative amount of work it would take to transform the detected object into each member of the library. An Analysis of Variance test statistically compares the work values. The probability that the detected object is of the same class of objects as those in the library is given by the F-test.
The shape analysis will be performed on a test prism with respect to a library of prisms. The performance will measure the strength and efficiency of the analysis.
Student: Mickey Loos. Advisor: Andrew W. Swift
A Statistical Investigation into the Existence of the "Home Run Derby Effect" in Baseball.
Each July, approximately halfway through the baseball season, Major League Baseball holds an All-Star game. The day before the All-Star game 8 players (4 from each league) take part in a Home Run Derby. The Home Run Derby usually features players that have hit a high number of home runs in the first half of the season. Once the second half of the season resume, if any of the home run derby participants suffer a performance slump it will be usually be followed by media articles stating that performing the derby was the cause. In this project the student will collect and analyize data to investigate whether the is an significant (negative) effect from competing in the home run derby. The student will be expected to collect data from available sources and to analyize it using statistical software. A knowledge of STAT 3800 or MATH 4740/4750 is highly recommended, but all interested students should feel free to contact the project advisor.
Student: Andrew Montgomery. Advisor: Robert Todd
The hyperbolic Law of Cosines.
In this project we will read from several sources to understand the hyperbolic upper-half plane. Then we will develop the tools we need to do some hyperbolic trigonometry with the goal of understanding the hyperbolic Law of Cosines. This project is best suited to an upper level undergraduate who has taken Modern Geometry.
Student: Li Westman. Advisor: Zhenyuan Wang
A Discussion on the St. Petersburg Two-Envelope Paradox.
The St. Petersburg Two-Envelope Paradox is a widely spread probability problem. It evokes a heated discussion for many years by mathematicians, including some Fields Medal receivers. Is it a real paradox?
Student: Jason Wohlgemuth. Advisor: Dora Matache
Boolean network modeling of layered social networks.
Random Boolean Networks are networks of nodes that can be in one of two possible states ON or OFF, and whose evolution from one time point to another is governed by given Boolean rules. Each node's evolution is influenced by the state of other nodes called its parents. This project aims at constructing a Boolean model for a social network in which nodes represent people interacting in a business venture with possibly multiple types of nodes, layers, and interactions (e.g. writers co-working with other writers and people that produce drawings for their books). The precise type of social network under consideration is chosen by the student.
Student: Vladimir Ufimtsev. Advisor: Vyacheslav Rykov
A Scalable Group Testing Based Algorithm for Finding d-highest Betweenness Centrality Vertices in Large Scale Networks.
We will study a group testing approach to identify the first d vertices with the highest betweenness centrality. Betweenness centrality (BC) of a vertex is the ratio of shortest paths that pass through it and is an important metric in complex networks. The Brandes algorithm computes the BC cumulatively over all vertices. Approximate BC of a single vertex can be computed by selective vertex sampling. We will discover the method where we will sample a set of vertices and compute their combined BC. For small values of d, the number of tests required to find the d-highest BC vertices is logarithmic in the total number of vertices. This algorithm can be highly scalable since the samples are independently selected and therefore each test can be performed in parallel.