# News

## Janet Anderson Defense

A Study of arc strong connectivity of digraphs

Abstract: This dissertation studies the extremal, structural and minimax properties related to digraph arc strong connectivity. Motivated by the former researches by Mader and Matula, we defined the digraph arc strength of a digraph $D$ to be the maximum arc strong connectivity of subdigraphs of $D$, and investigate extremal conditions for a strict digraph that is saturated with respect to the condition that it digraph arc strength is bounded by a positive integer $k$. Extremal size of such digraphs are obtained and structural characterization of the extremal digraphs are also obtained. In addition, a minimax duality theorem to determine the digraph arc strength of a digraph is found. Similar minimax results on related desity functions of digraphs are also obtained.

Date: 4/7/2017
Time: 3:30PM-5:00PM
Place: 315 Armstrong Hall

All are welcome.

Date, Location:
2017-04-07

## Celebrating Einstein

When Black Holes Collide! Gravitational Waves and Other Tales from the Horizon

As part of the month-long Celebrating Einstein event here at WVU, Dr.  Zach Etienne  from Department of Mathematics will be giving a public lecture this Friday on black holes and gravitational waves.   A planetarium show on the top  floor of White Hall will follow immediately after  his lecture.   His talk is accessible to general audience and even kids may enjoy the talk and the show.

Abstract:What happens if you fall into a black hole? Einstein's theory of gravity provides us a means to answer questions that, like this one, fuzz the boundary between science fiction and science fact. But the equations behind this theory are extremely complex, and solving them to advance our scientific understanding--particularly now that gravitational waves have been discovered--usually requires the use of supercomputers. In a nutshell, this is my field of expertise. I will review my career path and present results from some of my latest supercomputer simulations, which have given us both deeper insights into the gravitational waves we have already observed, as well as important predictions for those we are likely to observe in the near future.

Immediately after the lecture, at 8:30PM, there will be a planetarium show on the top floor of White Hall.

Press Release

Official Poster

Television Commercial

Official Webstie

Date: 4/07/2017
Time: 7:30PM
Place: White Hall Room G09

All are welcome.

Date, Location:
2017-04-07

## 4th Annual Integration Bee

This will be an integration contest open to all WVU students.
All integrals can be solved by techniques of Math 156.

Website
Flyer

Charis Tsikkou: tsikkou@math.wvu.edu
Casian Pantea: cpantea@math.wvu.edu

Date, Location:
2017-03-01

## Mr. Xiangming Wu Dissertation Prospectus

A Comparative Study of Three Versions of Calculus I

Date: 1/20/2017
Time: 11:00AM-1:00PM
Place: 320 Armstrong Hall

All are welcome.

Date, Location:
2017-01-20

## Mr. Salah Hamad Dissertation Prospectus

Compactification and Asymptotics for Banach and Hilbert Spaces and applications.

Date: 12/14/2016
Time: 3:30PM-5:30PM
Place: 315 Armstrong Hall

All are welcome.

Date, Location:
2016-12-14

## Capstone Talks

Several of the December Math Graduating seniors will give their Capstone Talks. The titles of the talks and times are included below.
Please consider joining us to hear our senior math majors talk about their capstone projects.

Join the Department in congratulating our seniors for their accomplishment and hard work!

Date: 12/7/2016
Time: 1:30PM-3:30PM
Place: 422 Armstrong Hall

Alex Abrahamian: 1:30 - 2:00
Title of Talk "Regularization and the Bias-Variance Tradeoff in Prediction"
Bachelor of Science Candidate
From Martinsburg, West Virginia

Toriane Graal: 2:00 - 2:30
Title of talk "An Analysis of Active and Passive Learning in the Classroom."
Senior Mathematics Major
Bachelor of Arts Candidate
From Massillon, Ohio

Robert Orzewicz: 2:30 - 3:00
Title of Talk TBA
Bachelor of Industrial Mathematics and Statistics Candidate
From Havre de Grace, Maryland

Georgette Goodwin: 3:00 - 3:30
Title of Talk "Extreme Value Theory: An Application Related to Insurance Losses"
Bachelor of Arts Candidate
From Morgantown, WV

Date, Location:
2016-12-07

## Brittany Vincent Defense

First Semester Calculus Students’ Concept Definitions and Concept Images of the Tangent Line and How These Relate to Students’ Understandings of the Derivative

The purpose of this dissertation is to examine how students define and think about the tangent line in first semester calculus and investigate the influence of these ways of thinking on their understandings of the derivative. Students’ conceptions of the tangent line were explored through four primary tasks: defining and constructing tangent lines, sketching the derivative, and graphically interpreting the formal symbolic definition of the derivative. The first two tasks were designed to access students’ knowledge of tangent lines, and the second two tasks drew upon their ability to apply this knowledge and connect the tangent line to the derivative. In this dissertation, I describe students’ responses in terms of overlap or lack of overlap with how the tangent line and derivative are formally defined. The Tangent Line Framework of this dissertation and the Derivative Framework developed by Zandieh (2000) were used to structure this knowledge. The frameworks present a diagrammatic way to illustrate the understandings evidenced by the students and graphically contrast these for the concepts of tangent line and derivative. The results of this analysis revealed ways in which students’ concept images of the tangent line and derivative relate.

Date: 11/17/2016
Time: 10:30AM-11:30AM
Place: 313 Armstrong Hall

All are welcome.

Date, Location:
2016-11-17

## Fairouz Elmagbri Defense

Moment-type Nonparametric Estimation in Some Direct and Indirect Models

Date: 11/11/2016
Time: 10:30AM-12:30PM
Place: 139 Stansbury Hall

All are welcome.

Date, Location:
2016-11-11

## Darrah and Graduate Student Featured

Professor Marjorie Darrah of the Mathematics Department, and her research assistant, Marcela Mera Trujillo, a graduate student in the Mathematics Ph.D. program, were recently featured in the cover article of the most recent issue of the DSIAC Journal, a quarterly publication of the Defense Systems Information Analysis Center (DSIAC). Their work, discussed in the article "Real-Time Tasking and Retasking of Multiple Coordinated UAVs" involves the development of intelligent algorithms and computer systems to coordinate and optimize, under the control of an operator in real-time, the paths of multiple unmanned aerial vehicles (UAVs) tasked to accomplish a range of evolving surveillance missions, both military and civilian. The mathematical foundation for their work is the field of genetic algorithms, in which solutions are optimized using computational methods motivated by evolutionary processes such as mutation and natural selection. Ms. Mera Trujillo was also part of a team at the local technology company 4D Tech Solutions that filed a patent application for a UAV flight control system utilizing related technology.

Date, Location:
2016-11-03

## Janet Anderson Prospectus

A Study of Arc-Strong Connectivity of Digraphs

We study the extremal and structural properties of graphs and digraphs closely related to subgraph and subdigraphs connectivity. We obtained a best possible bound for the size of strict digraphs that do not have a subdigraph with high arc strong-connectivity, but adding any additional arc to it will result in a subdigraph with high arc strong-connectivity. We also obtain several minimax theorems concerning subdigraph strength measures. We propose to continue investigating the strength of digraph networks of other typesin this direction.

Date: 11/02/2016
Time: 3:30PM-5:00PM
Place: 315 Armstrong Hall

All are welcome.

Date, Location:
2016-11-02