In addition to teaching, he has authored a second volume textbook, “Numerical Methods and Applications,” which was recently published by the American Institute of Mathematical Sciences.

The textbook will serve as an educational resource for undergraduate students with an interest in numerical methods. Specifically, those in the academic fields of mathematics, computer science and engineering.

The textbook is intended for use in a two-semester course, particularly Missouri State’s Numerical Analysis I and II.

“The book provides an introduction to a fundamental part of applied mathematics: solving mathematical problems by developing or applying algorithms that are accurate, eﬃcient and robust,” Rebaza-Vasquez said.

Rebaza-Vasquez also authored the textbook “A First Course in Applied Mathematics” published in 2012 by Wiley.

]]>One of the reasons fractions are perceived to be difficult is what members of the math community call gap reasoning.

Gap reasoning can limit students’ understanding of the problem. The method leads students to assess distances as equal by appearance over measurements.

In their paper “Escaping the gap,” Dr. Patrick Sullivan and Professor Joann Barnett use an original classroom activity to establish gap reasoning as an ineffective comparison strategy.

Sullivan and Barnett investigated elementary students’ use of gap reasoning.

From early education, students often struggle to make fraction comparisons using valid reasoning. Students may reach correct answers using gap reasoning, but for the wrong reasons.

For example, when comparing 1/3 and 1/4, a student who uses gap reasoning would claim that 1/3 is greater than 1/4 because 1/3 is two away from the whole while 1/4 is three away from the whole.

While students would reach the correct answer following that logic, the same result would not apply to a comparison of 5/6 and 7/8. Students using gap reasoning would incorrectly identify the fractions as equal.

Addressing errors in reasoning at the early stages of education can prevent problems with fractions from continuing into adulthood. Failure to understand fractions can often bring frustration to adults.

“People see it as the F word of elementary mathematics,” said Sullivan.

Sullivan and Barnett avoided focusing on students’ ability to reach right answers. Instead, they directed their attention to understanding students’ reasoning for each answer.

The results of their study allowed Sullivan and Barnett to bring awareness to the importance of asking students to share their reasoning from the early stages of the education process.

“It is critical that we, as educators and parents, ask our students the why to explore how students’ understanding of fraction concepts is developing,” said Sullivan.

Barnett’s work related to her master’s degree thesis, which served as the genesis of their research.

]]>The event will take place from 3-4:30 p.m. Jan. 28 at the Level 1 Game Center inside of Plaster Student Union.

Pizza, bowling and other games will be included.

]]>Bray collaborated with Dr. Boris Rubin, from Louisiana State University, for two of the papers.

Bray has known Rubin for more than 20 years, having first collaborated in 1997.

Both papers study transformations in real hyperbolic space. They studied inversion formulas in that space as well.

Both papers involve construction inversion formulas for Radon type transforms in real hyperbolic space.

The two publications are:

- “Radon transforms over lower dimensional horospheres in real hyperbolic space”, Transactions of the American Mathematical Society, volume 372 (2019).
- “Inversion formulas of integral geometry in real hyperbolic space”, Contemporary Math, volume 733 (2019).

Ellen Hunt, 2016 M.S. mathematics alumnae, used some of her thesis topic to work on this paper with Bray.

“We obtained energy equipartition principles for problems,” Bray said. “This tells us how energy splits into two forms, kinetic and potential.”

Hunt and Bray wrote “Wave equations and energy”, AIMS Math 4 (2019).

Congratulations, Dr. Bray! Keep on publishing.

]]>This required a proposal about what each professor would teach and why it was important to students in China. About 100 professors from 25 different countries were chosen to teach this summer.

The professors who taught in China this summer were:

- Babur Mirza, assistant professor of biology
- Patrick Sullivan, assistant professor of mathematics
- Sanjay Tewari, assistant teaching professor of engineering
- Stephanie Thomas, instructor of engineering

Tewari taught water and wastewater engineering over the summer to master’s and PhD students, as well as some Chinese faculty.

“Meeting with local faculty, getting to know about their research and visiting research labs were some of the things that I really enjoyed academically,” Tewari said.

Sullivan also enjoyed teaching students in his introductory probability and statistics course.

“The students were wonderful. I have never received an ovation at the end of a lesson,” Sullivan said.

This was Tewari and Sullivan’s first trip to China. Each were surprised and impressed by the school and their experiences.

“Interacting with local students and faculty in and outside of the classes was a good experience,” Tewari said. “They introduced me to the local culture and various fun activities that locals do on a daily basis.”

Tewari was also grateful for the accommodations his hosts made for his vegetarian diet.

One thing Sullivan and Tewari noted was the language barrier.

“I have much greater empathy for students coming to the United States with English as their second language,” Sullivan said. “I am much more sensitive to the barriers they face.”

]]>From June 3-July 26, Haller worked with professors, other mathematics educators and high school students at a Research Experiences for Undergraduates (REU).

There were five teams at the REU that worked with different mathematics problems for about seven weeks.

Haller and her team worked on a graph they called “H.” They solved the spectrum problem for a three-uniform, two-regular hypergraph. The graph Haller worked on had three vertices on each edge.

Haller hopes to present the research later this year.

Haller also helped plan and execute a week-long math camp for high school students across Chicago.

Haller got to teach mini sessions, run the camp and work with students as a table monitor. Each high school student worked on his/her own research and presented it at the end of the week.

“It was fascinating to see how students who were unsure about their math skills at the beginning of the camp were the most enthusiastic about their findings by the end,” Haller said. “Many, if not all, of the students didn’t want to leave at the end of the week. Most were thrilled that they had found this new love of mathematics.”

Haller worked with three professors at Illinois State:

- Dr Saad El-Zanati, distinguished professor of mathematics
- Ryan Bunge, instructional assistant professor of mathematics
- David Barker, associate professor of mathematics

Dr. Patrick Sullivan, assistant professor in mathematics, is her Missouri State adviser.

The National Science Foundation (NSF) funds universities to work with undergraduate research in mathematics.

REUs let faculty mentors bring in 12 students from around the United States to mentor and work on research for eight weeks during the summer. These students are among the best math majors in the country.

]]>Abstract:

Many fundamental operators arising in analysis are governed by sets of directions that they are naturally associated with. What are some of these operators? Why are they important? How do direction sets affect their behavior? This talk will survey a few representative results in this area, and report on some new developments.

]]>This conference focused on how much women could do in a male-dominated field.

Klement learned from both students and professors that presented.

It also gave Klement new ideas on research.

“Seeing examples of possible research topics and how they were structured was beneficial,” Klement said. “I was introduced to a lot of higher-level math concepts that I am excited to continue to explore.”

Klement is mistaken for being a mathematics education student instead of an applied mathematics major with minors in computer science and Spanish.

Though it’s annoying, Klement thinks it’s worth it to stay in mathematics.

“It’s important for women to be in STEM fields because diverse perspectives are crucial to effective problem solving,” Klement said.

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Abstract:

We will discuss the Dirichlet problem for the Laplace-Beltrami operator acting on scalar functions in regular Semmes-Kenig-Toro subdomains of a Riemannian manifold M. When all objects and structures involved are smooth the standard elliptic theory based on pseudodifferential operator methods applies. In our work we consider rough subdomains of M, a setting which renders the latter approach ill-suited. As an alternative, we resort to the theory of singular integral operators with variable coefficient kernels on uniformly rectifiable sets which we further refine and adapt to the present framework.

]]>With advancement comes new snags and problems to address and fix.

Dr. Xingping Sun, professor of mathematics, studies the combination of his first love, mathematics and his second, computer science.

Hand in hand, Sun explores the effects they have on each other.

Learn more about Sun’s research

The Colorado School of Mines in Golden, Colorado, invited Sun to a colloquium Feb. 1.

Dr. Greg Fasshauer, head of the applied mathematics and statistics department at Colorado School of Mines, asked Sun to speak.

Sun and Fasshauer are currently collaborating on a paper.

Sun’s presentation, “Kernel based Monte Carlo approximation methods,” looks at an important problem in machine learning.

The Monte Carlo method is using randomness to predict something. A kernel-based Monte Carlo is an algorithm that adapts a realistic model.

“For example, scientists in weather forecasting use limited data obtained at scattered sites to establish different models needed for predicting weather phenomena,” Sun said.

Sun’s presentation was in two parts.

In phase one, he used approximation methods. In the second phase, he used the Monte Carlo method.

Combined, they open up discussion on machine learning and how to better it.

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