# The Demarcus D. Smith III Mathematics Scholarship

## About the Demarcus D. Smith Scholarship

Mr. Demarcus D. and Mrs. Fran Smith have established a Mathematics Scholarship Fund to support full-time undergraduate students in the Department of Mathematics at LSU. The scholarship supports the careers of outstanding students whose efforts embrace both mathematics research and mathematics education.

Guided by mathematics faculty, scholarship recipients engage in inquiries and investigations that make creative contributions to mathematics and/or the teaching of mathematics. They identify and describe an original, math-intensive disciplinary or interdisciplinary research question and articulate research findings through papers, posters, and oral presentations. With the Demarcus D. Smith III Scholarships, these students gain multi-semester extracurricular experience in

Teaching ‣ Investigating ‣ Guiding ‣ Exploring ‣ Researching ‣ Serving.

These experiences will help them to master the strands of mathematical proficiency specified in the National Research Council’s report Adding It Up: adaptive reasoning, strategic competence, conceptual understanding, procedural fluency, and productive disposition—habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy. These experiences will help when applying for employment, admission to graduate school, awards, or fellowships.

## Fall 2018 Demarcus D. Smith Scholars

### Aaron Cao

#### Brief biography

I grew up in Lafayette, Louisiana and first became interested in mathematics through competitions such as the AMC. I'm a senior majoring in Mathematics (Actuarial Concentration) and one of the instructors of the LSU Math Circle. My main research area is financial mathematics, which I hope to pursue further in graduate school. My other hobbies include watching anime and playing Magic: The Gathering. I hope to help develop mathematical outreach programs in Louisiana and later work in financial data science.

#### Mathematical and Educational Activities

For the majority of my undergraduate career, I've been concerned with developing an intuitive and comprehensive mathematics enrichment curriculum for gifted high school students. My current avenue for deploying my curriculum is competition mathematics. In many ways, I believe that competition mathematics gives unique opportunities for Louisiana high schoolers to shine. By contributing content to programs such as the LSU Math Circle, we can begin to enhance the mathematics background of students in the Baton Rouge area and hopefully expand to the entire state.

My background in mathematics education began when I was a middle and high school student partaking in the MAA series of competitions beginning with the American Mathematics Competition. Through summer programs such as AwesomeMath and the Ross Mathematics Program, I became exposed to the high school competition mathematics community. It was easy to realize that the majority of students in Louisiana, even mathematics enthusiasts, did not have access to the resources that a competition community can provide, so upon graduating high school I spent several summers working as a teaching assistant at AwesomeMath.

During my early undergraduate years at LSU, I was also introduced to the LSU Math Circle. Though I would not extensively participate with Math Circle until my later undergraduate years, I immediately saw an opportunity to share my knowledge and experience with the growing Baton Rouge math competition community. In high school, I was able to qualify for the USA Mathematics Olympiad, and I have a reasonable grasp of the topics the students would need to know. During Steven Olsen's tenure as Math Circle coordinator, I began gradually transitioning the previous, more laidback, Math Circle curriculum to a more rigorous form.

Through hours upon hours of work in collaboration with the current coordinator Brooke Mendoza, I was able to write expansive mathematics curricula in the four main competition topics: Algebra, Combinatorics, Number Theory, and Geometry. I believe that the Math Circle program under our leadership is has become competitive with some of the best math prep programs in the nation. I believe that establishing this sort of intellectual base for high schoolers will lay the groundwork for Louisiana students to truly shine in the years to come.

My work with the LSU Math Circle is perhaps the proudest achievement of my time as an undergraduate, but I am also looking forward to my career prospects after graduation. As an actuarial student, I have undertaken a bibliometrics research project under Dr. Lawrence Smolinsky. I have also passed the preliminary Probability Exam in the actuarial track and plan on taking the second Financial Mathematics exam in the winter. I am most interested in careers utilizing statistics and data science, and I'm currently in the interview process with several companies for potential data analytics positions after graduation.

### Rohin Gilman

#### Brief biography

I am a freshman mathematics and physics major from Baton Rouge, LA. For the past year, I have worked as a teaching assistant at the Louisiana Math Circle Summer Program and the Louisiana Math Circle Competition Team. This year, I have done research with Dr. Neubrander, and I have been a member of the LSU Math Club and the LSU Society of Physics Students.

After my undergraduate education, I intend to go to graduate school for mathematics.

### Lucica Mai

Lucica Mai is a mathematics major at LSU.

### Matthew McCoy

#### Brief biography

I am a freshman at LSU. I am currently double majoring in Math and Physics. I am a member of the LSU Math club and I am a TA for LSU Math Circle, a Math club for high school students interested in math. My interests and hobbies include playing computer games and watching videos about math on YouTube.

#### Mathematical and Educational Activities

I plan on attending graduate school and getting a PhD in mathematics or applied mathematics. Then I plan on working in the realm of applied mathematics or I could possibly go into academia and math education. I am currently undecided.

### Dylan Spedale

I am a freshman majoring in mathematics, and I am hoping to include a secondary major under physics or computer science. I have a strong interest in mathematics, but I have not delved long and deep enough into its numerous areas to choose a particular field. But based on my experience with competition mathematics, my interests lie in discrete mathematics, particularly combinatorics. I am pursuing a mathematics concentration with aspirations to pursue research. Pure mathematics has a special place in my heart, and I hold it — as well as its practitioners — in very high respect due to its existence and development being for its own sake. I aspire to one day develop my own original mathematical ideas as I see this as the utmost expression of creativity and passion. My second greatest interest behind mathematics is weightlifting. I currently do this causally, but I hope to join the LSU powerlifting team in the future and compete in events.

#### Brief biography

As of now, my mathematical endeavors involve developing the foundations in various areas of mathematics that I will need for future learning, including number theory, real analysis, and abstract algebra. I strive to improve my mathematical knowledge through self-studying and hope to develop strong bases of knowledge from which I may approach more advanced topics in the future. I have interests in mathematical research, and I hope to pursue it further and in more detail in my coming years. Most of all, my greatest desire is to reach a point of sophistication wherein I may converse with professors and other professionals about mathematical topics, including research topics. Belonging to the community is a great desire of mine.

#### Mathematical and Educational Activities

While I have never sought any official teaching positions, I have greatly enjoyed the times that I had to try to teach someone something new. I particularly enjoy teaching someone a topic that I previously struggled with, as it invokes in me a feeling of compassion and service to the student. It is especially exciting if the insight that explained the topic “at a glance” for myself resonates in the same way with the student. Furthermore, teaching topics have been an invaluable tool for helping me check my understanding of a topic and identifying any implicit assumptions I may have in my knowledge. I do not plan to pursue a teaching career as of now, but I do plan to tutor students in my coming years at university.

## Spring 2018 Demarcus D. Smith Scholars

### Jonathan Cangelosi

#### Brief biography

I am a junior double majoring in mathematics and computer science with a minor in physics. I have special interests in number theory, topology, and algorithm development. In high school, I was a competitive member of Mu Alpha Theta. After graduating, I worked as a TA at LSU Math Circle, a summer program in which I had participated the past three years. My hobbies include learning, teaching, competing in Super Smash Bros. Melee tournaments, playing video games in general, thinking philosophically, and watching political/social commentary videos. After getting my Bachelor’s, I hope to get my Ph.D. and eventually become a professor of mathematics.

#### Mathematical Activities

Throughout high school, I taught competitive math as a member of my school's Mu Alpha Theta E-Board. Last summer, I worked as a TA at LSU Math Circle, a program that introduces high school students to college-level math. During my freshman year, I did research in computational mechanics under Dr. Bourdin. We used differential equations that govern heat transfer to model crack propagation in slabs with different material properties and geometries. In the future, I intend to participate in at least one REU and continue to do research during the school year.

#### Educational Activities

Throughout my freshman year at LSU, I tutored high school students in calculus and physics, and I helped my classmates in Calculus III and linear algebra/differential equations. I enjoy teaching because I like to explain things in layman's terms to make my insights more accessible to other students. I find that too many students who are good at math are intimidated by it or simply do not like it, perhaps because of the way it is presented to them. As I continue to expand my knowledge of mathematics, I hope to use my passion for teaching to stir the same passion for math in other students.

### Blake Tillman

#### Brief biography

I’m a junior from Alexandria, Louisiana dual-majoring in Computer Science and Mathematics. Upon entering college, I was planning to major in Computer Science and minor in Mathematics. When a new Mathematics concentration was introduced in the 2016–2017 calendar year, I decided to switch the minor to a second major. Last summer, I interned at Google in Mountain View, California as a Software Engineer. This upcoming summer, I’m going to be interning at Apple in Cupertino, California.

#### Mathematical and Educational Activities

I’ve had a strong passion for math since elementary school and have spent countless hours preparing for math competitions. In middle school, I qualified for and competed in the national level of MATHCOUNTS. In high school, I took the AMC and AIME exams, and competed in dozens of Mu Alpha Theta math competitions across Louisiana. I also stayed after school to tutor freshmen and sophomores in math. In college, I’ve taken the Putnam exam every year and was the top scoring individual at LSU on the 2017 exam. I’m interested in assisting with regional math competitions after I graduate from college.

## Fall 2017 Demarcus D. Smith Scholars

### Logan Hart

I am a senior in Pure Mathematics at Louisiana State University. Recently, I have been taking graduate courses and doing research with Prof. Frank Neubrander. Prior to my college career at LSU, I attended Catholic High School in Baton Rouge. There, I was a member of the Track & Field Team, as well as a member of Mu Alpha Theta. In my free time I enjoy to run, read, and to spend time with friends and family. On a forward-looking note, after I obtain my Bachelor’s degree I plan on applying to a graduate program to obtain my Ph.D.

#### Brief biography

I recently became a sophomore majoring in Pure Mathematics at Louisiana State University. Last semester I was studying Mechanical Engineering and felt that this field was not my destiny. I have always enjoyed math and decided that I should just follow what I love regardless of financial security. My main goal in life is find meaning and understanding in the world. I think pursuing a career into Math is the best course of action to obtain said goal. I have lived in Baton Rouge, Louisiana for nineteen years, which just so happens to be my entire life. Prior to my college career at LSU, I attended Catholic High School in Baton Rouge. There, I was a member of the Track & Field Team, as well as a member of Mu Alpha Theta. In my free time I enjoy to run, read, and to spend time with friends and family. On a forward-looking note, after I obtain my Bachelor's degree I plan on applying to a graduate program to obtain my PhD.

#### Mathematical Activities

Currently, I am working on research projects with Dr. Yaniv Almog with a focus on functional minimization with the use of Fourier Series. I predominantly use Matlab to minimize certain functions in a functional and comment on the spacing of the minimized points. Recently we have taken a more analytical approach to the minimization problem. I plan on continuing my research with Dr. Almog for as long as possible.

#### Educational Activities

In the fall semester of 2016, Ms. Soula O'Bannon assisted me with becoming a math tutor. Within a couple of weeks fellow LSU classmates were seeking my help to tutor them in both Calculus II and Calculus III. At first I was apprehensive about tutoring but after that first session my whole view on the subject completely changed. I am grateful for the opportunity Ms. Soula O'Bannon provided me, and I hope to tutor more students this coming Spring Semester in Differential Equations and Linear Algebra. Depending on my academic schedule, I might explore opportunities relating to being a member of the Geaux Teach program and student organization.

### Brooke Mendoza

I am a freshman majoring in mathematics and computer science. I am Editor of LSU Math Club and enjoy spending my free time helping to TA LSU Math Circle. My interests include machine learning and natural language processing, which I hope to eventually pursue further in graduate school. My other hobbies include watching anime, listening to vocaloid, and immersing myself in other cultures through language and art.

### Daniel Rockwell

I am a sophomore at LSU seeking a dual degree in Computer Science and Mathematics, with a minor is Business Administration. I am working on a research project with Professor Stephen Shipman involving spectral theory of quantum graphs. I also tutor mathematics at LSU.

#### Brief biography

I am a sophomore seeking a dual degree in Computer Science and Mathematics, with a minor is Business Administration. I am a huge outdoorsman and thoroughly enjoy rock climbing, bouldering and top-roping. Here at LSU, I was a member of ASME prior to engaging in pure Mathematics and its relation with Computer Science. The switch from mechanical engineering to this dual degree was chosen specifically to satisfy a thirst for WHY things are and WHERE they are going. I feel that Mathematics is the why and Computer Science is the where. The future is a combination of what we learn from the past and present. Prior to my college career at LSU, I attended Mandeville High School and was a 4-year varsity member of the Tennis Team, 3-year All-State Honor Band Participant for the Clarinet, and a member of Mu Alpha Theta.

#### Mathematical Activities

I am working on a research project with Professor Stephen Shipman involving spectral theory of quantum graphs. It beautifully incorporates complex variables, differential equations, linear algebra, algebraic geometry, and graph theory. This research opportunity for me is still in the infant stages, and I feel that I will gain an immeasurable amount of knowledge in fields I have not studied yet and a more solid feeling of knowledge in fields I have already studied.

#### Educational Activities

After being immersed with mathematics in my full Spring 2017 semester, I was driven to be able to share my knowledge and engage in educational activities here at LSU. Therefore, I worked as a tutor at the LSU Math Lab in Middleton Library. There, I helped tutor College Algebra and College Trigonometry to my peers. The experience has been undoubtedly beneficial in my mathematical growth. Knowing a subject is invaluable, but being able to explain more or less difficult material in a way that relates to your fellow peers truly makes you aware of previously learned material. This opportunity has provided me with remarkable teaching experience, IT incorporation with education, and a way to deepen my knowledge as I progress into mathematics.

## Spring 2017 Demarcus D. Smith Scholars

### Jonathan Cangelosi

#### Brief biography

I am a freshman double majoring in mathematics and computer science with a minor in physics. I have special interests in number theory, topology, and algorithm development. In high school, I was a competitive member of Mu Alpha Theta. After graduating, I worked as a TA at LSU Math Circle, a summer program in which I had participated the past three years. My hobbies include learning, teaching, competing in Super Smash Bros. Melee tournaments, playing video games in general, thinking philosophically, and watching political/social commentary videos. After getting my Bachelor’s, I hope to get my Ph.D. and eventually become a tenured college professor of mathematics.

#### Mathematical Activities

Throughout high school, I taught competitive math as a member of my school's Mu Alpha Theta E-Board. Last summer, I worked as a TA at LSU Math Circle, a program that introduces high school students to college-level math. During my freshman year, I did research in computational mechanics under Dr. Bourdin. We used differential equations that govern heat transfer to model crack propagation in slabs with different material properties and geometries. In the future, I intend to participate in at least one REU and continue to do research during the school year.

#### Educational Activities

Throughout my freshman year at LSU, I tutored high school students in calculus and physics, and I helped my classmates in Calculus III and linear algebra/differential equations. I enjoy teaching because I like to explain things in layman's terms to make my insights more accessible to other students. I find that too many students who are good at math are intimidated by it or simply do not like it, perhaps because of the way it is presented to them. As I continue to expand my knowledge of mathematics, I hope to use my passion for teaching to stir the same passion for math in other students.

### Christopher Mai

#### Brief biography

I am a sophomore seeking a dual degree in Mathematics and Mechanical Engineering, and am a member of the Honors College. I am an officer of the LSU Club Tennis Team, and I also enjoy playing piano and drawing with charcoal. I tutor students in all applied Mathematics related fields such as Calculus I–III, Physics, and Differential Equations. Originally, I had planned on studying medicine, but my interest in mathematics has led me to where I am today. I love anatomy, so upon graduation at LSU, I plan on attending graduate school in Biomechanics, with heavy emphasis on the mathematics side of robotics.

#### Educational Activities

I really enjoy teaching Math and Physics to students, especially Calculus courses, since a solid framework in Math can bring a student down any path (such as myself). I am always looking for opportunities to continuously develop my Mathematics skills, and will be seeking this opportunity both through extensive research with Dr. Murphy, as well as through the plethora of advanced Mathematics courses and faculty at LSU.

## Fall 2016 Demarcus D. Smith Scholars

I am a junior majoring in mathematics with a concentration in secondary education and a minor in French. I am currently the president of the GeauxTeach Student Organization and a student in the Ogden Honors College. My hobbies include making study guides and playing with my pet pig, Ned. Read more about Amy from Fall 2015…

### Heewon Hah

#### Brief biography

I am a sophomore majoring in Mathematics with a concentration in pure mathematics at Louisiana State University. I am also a member of the Honors College. In my free time, I enjoy listening to music, watching Korean TV shows, and spending time with friends and family. After I get my Bachelor’s degree, I plan on applying to a graduate program in applied mathematics. Read more about Heewon from Spring 2016…

### Calla Harper

#### Brief biography

I am a junior majoring in Mathematics with a concentration on Secondary Education at Louisiana State University. I am a member of the Geaux Teach Program and an officer of the Geaux Teach Student Organization. When I am able, I tutor local high school students struggling with math. In the summer of 2016, I worked as a Residential Assistant for the camp Math Circle at LSU. Currently, I am working on a research project with Dr. Stephen Shipman that focuses on improving teaching methods for Vector Calculus. In the future, I hope to become an educator capable of truly inspiring students, in the same way that my past teachers have inspired me.

#### Mathematical and Educational Activities

Currently, I am involved in a research project with Dr. Stephen Shipman that involves improving teaching methods for Vector Calculus. I plan on presenting my work with Dr. Shipman at the Discover Day at LSU in the spring of 2017. In addition, I will continue to tutor local high school math students. I also plan to be an active member of the Geaux Teach program and student organization. In the summer, I will apply to be a teaching assistant in the summer enrichment program called Math Circle at LSU. Over the next few semesters I have left at LSU, I will continue to develop my teaching abilities, as well as expand and refine my knowledge in mathematics.

### Logan Hart

#### Brief biography

I recently became a sophomore majoring in Pure Mathematics at Louisiana State University. Last semester I was studying Mechanical Engineering and felt that this field was not my destiny. I have always enjoyed math and decided that I should just follow what I love regardless of financial security. My main goal in life is find meaning and understanding in the world. I think pursuing a career into Math is the best course of action to obtain said goal. I have lived in Baton Rouge, Louisiana for nineteen years, which just so happens to be my entire life. Prior to my college career at LSU, I attended Catholic High School in Baton Rouge. There, I was a member of the Track & Field Team, as well as a member of Mu Alpha Theta. In my free time I enjoy to run, read, and to spend time with friends and family. On a forward-looking note, after I obtain my Bachelor's degree I plan on applying to a graduate program to obtain my PhD.

#### Mathematical Activities

Currently, I am working on research projects with Dr. Yaniv Almog with a focus on functional minimization with the use of Fourier Series. I predominantly use Matlab to minimize certain functions in a functional and comment on the spacing of the minimized points. Recently we have taken a more analytical approach to the minimization problem. I plan on continuing my research with Dr. Almog for as long as possible.

#### Educational Activities

In the fall semester of 2016, Ms. Soula O'Bannon assisted me with becoming a math tutor. Within a couple of weeks fellow LSU classmates were seeking my help to tutor them in both Calculus II and Calculus III. At first I was apprehensive about tutoring but after that first session my whole view on the subject completely changed. I am grateful for the opportunity Ms. Soula O'Bannon provided me, and I hope to tutor more students this coming Spring Semester in Differential Equations and Linear Algebra. Depending on my academic schedule, I might explore opportunities relating to being a member of the Geaux Teach program and student organization.

### Connor Martin

#### Brief biography

I am a freshman at Louisiana State University and I am triple majoring in Mathematics with a concentration in Mathematics, Physics with a concentration in Physics, and Computer Science with a concentration in Software Engineering; I am also minoring in German. I am a member of the Honors College, Society for Physics Students, Collegiate 4H, Baptist Collegiate Ministry, and the LSU Rugby Club.

#### Mathematical Activities

This past semester I completed, a group poster on the weak interactions between standard model neutrinos and primordial plasma, and how they affect the resonant production of sterile neutrino dark matter. This semester I am working on a poster with Dr. Frank Neubrander that is on fractals. I plan on doing a Research Experience for Undergraduates this summer, but have not chosen a specific program at this point in time.

#### Educational Activities

I am the programming mentor in C++, Java, and LabVIEW for two high school First Robotics Competition Teams: 4209 here in Baton rouge and 4336 in Lafayette. I also tutor math and physics to a range of students, from 4th graders to University freshmen.

### Chandler McArthur

I am a senior majoring in Mathematics and Classics at LSU. As President of our Math Club, I help organize our meetings so that fellow math majors can get to know each other. I help prepare LSU's MathCircle sessions as a TA. In my spare time, I enjoy reading, blogging, studying classical languages, and traveling.

#### Brief biography

I am a senior majoring in Mathematics and Classics at LSU. As President of our Math Club, I help organize our meetings so that fellow math majors can get to know each other and share mathematics. I enjoy reading, blogging, studying classical languages, and traveling.

#### Mathematical Activities

I'm currently studying fractals with Dr. Neubrander, working to develop a poster to be presented; specifically, I am investigating the effects of the Collage Theorem and the ways iterated function systems can be used for image compression.

#### Educational Activities

I work as a teaching assistant for LSU's high school MathCircle, where I help to prepare the daily sessions.

### Brooke Mendoza

#### Brief biography

I am a freshman majoring in mathematics and computer science. I am Editor of LSU Math Club and enjoy spending my free time helping to TA LSU Math Circle. My interests include machine learning and natural language processing, which I hope to eventually pursue further in graduate school. My other hobbies include watching anime, listening to vocaloid, and immersing myself in other cultures through language and art.

### Megan Stelly

#### Brief biography

I am an undergraduate junior majoring in Mathematics with a concentration in Secondary Education through the Geaux Teach program. I tutor students after school in math to help them better understand the concepts they learn in class. In turn, it also helps me with my math skills. Aside from learning, I enjoy cooking, swinging, photography, and serving at my church.

I am currently enrolled in the Geaux Teach program at LSU for secondary math education. After graduating from LSU, I plan on becoming a high school math teacher. Ever since I was a little girl, my dream has always been to become a teacher. Teachers have the ability to make a difference in the lives of young children. I want to be a teacher because of the love and passion I have for education. All of my teachers have made a difference in my life, and one day I hope to make a difference in the life of one of my students.

### Austin Swanlaw

#### Brief biography

I am a freshman at LSU from Alabama, majoring in Mathematics and minoring in Latin and Physics. I am currently a student of the Honors Ogden College. In my spare time out of the classroom, I enjoy reading and writing.

#### Mathematical Activities

This semester I am doing research with Dr. Neubrander and will make a poster along with several other students about a topic of our choice. I am also performing research with Dr. Rubin on Integral Geometry through the Presidential Future Leaders in Research program.

#### Educational Activities

I have tutored in math before, and this past semester I, with a few others, tutored groups of students in Calculus I on a daily basis at LSU. I am also involved in GeauxTeach and recently taught a class of 5th graders a lesson on decimals as part of my final grade.

## Spring 2016 Demarcus D. Smith Scholars

### Heewon Hah

#### Brief biography

My name is Heewon Hah, and I am a freshman majoring in Mathematics at Louisiana State University. I am also a member of the Honors College. I have lived in Baton Rouge for eleven years and attended McKinley High School. In my free time, I enjoy reading, watching Korean variety shows, and spending time with friends and family. After I get my Bachelor's degree, I plan on applying to a graduate program in applied mathematics.

#### Mathematical Activities

I am working on research projects with Dr. Oliver Dasbach on applied discrete mathematics. I mainly studied the Leibniz formula for the determinant and used it to prove different properties of determinants. Currently, I am compiling C++ programs for the topics we have covered. I plan on continuing to do research with Dr. Dasbach, and this summer, I will work on a group research project for the Pennington Biomedical Research Center.

#### Educational Activities

In the fall semester of 2015, I participated in the GeauxTeach program and had the opportunity to student teach fourth graders at Bernard Terrace Elementary School. To continue the teaching experience, I hope to tutor math or help high school math clubs such as Mu Alpha Theta.

### Margarite LaBorde

My name is Margarite LaBorde, and I am an undergraduate sophomore at LSU double majoring in mathematics and physics, both with concentrations in pure mathematics. I am a member of both the Honors College and the Society of Physics Students, and I am a McNair’s Scholar. Currently, I work in undergraduate research with Dr. Johnathan Dowling in the Quantum Information and Technology research group, where I enjoy applying my math and physics skill simultaneously. I also return to my previous high school to assist in tutoring algebra and geometry. During my down time, I enjoy reading, practicing archery, and going on long runs.

#### Brief biography

My name is Margarite LaBorde, and I am an undergraduate sophomore at LSU double majoring in mathematics and physics, both with concentrations in pure mathematics. I am a member of both the Honors College and the Society of Physics Students, and I am a McNair's Scholar. During my down time, I enjoy reading, practicing archery, and going on long runs.

#### Mathematical Activities

I work in undergraduate research with Dr. Jonathan Dowling in the Quantum Information and Technology research group, where I enjoy applying my math and physics skill simultaneously. I am participating in research in theoretical physics such as optimizing applications of boson sampling for better metrology and computation time. During the summer I am working in the Math Consultation Clinic with Dr. Wolenski and a group of graduate and undergraduate students on developing a mathematical interface for the modeling of the feeding behavior of infants.

#### Educational Activities

In my previous high school, I assist in tutoring algebra and geometry. I am also continuing to advocate STEM disciplines to middle schools and high schools in the Baton Rouge area, particularly through mathematics tutoring and physics outreach.

### Megan Stelly

#### Brief biography

My name is Megan Stelly, and I am an undergraduate sophomore majoring in Mathematics with a concentration in Secondary Education through the Geaux Teach program. I tutor students after school in math to help them better understand the concepts they learn in school. In turn, it also helps me with my math skills. Aside from learning, I enjoy cooking, swinging, photography, and serving at my church.

I am currently enrolled in the Geaux Teach program at LSU for secondary math education. After graduating from LSU, I plan on becoming a high school math teacher. Ever since I was a little girl, my dream has always been to become a teacher. Teachers have the ability to make a difference in the lives of young children. I want to be a teacher because of the love and passion I have for education. All of my teachers have made a difference in my life, and one day I hope to make a difference in the life of one of my students.

## Fall 2015 Demarcus D. Smith Scholars

I am a sophomore majoring in Mathematics with a concentration in Secondary Education and a minor in French. I am a member of the Geaux Teach program and the Honors College at LSU. I have been engaged in a research project on the asymptotic properties of second-order linear difference and differential equations. I have also helped out with the LSU Math Circle, a summer enrichment program for high school students interested in math, and with the Mu Alpha Theta team at McKinley High School here in Baton Rouge.

#### Brief biography

My name is Amy Adair, and I am a sophomore majoring in Mathematics with a concentration in Secondary Education and a minor in French. I am a member of the Geaux Teach program and the Honors College at LSU.

#### Mathematical Activities

In the summer of 2015, I participated in the Robert Noyce Summer Research Internship, through which I worked on a research project with Dr. Frank Neubrander. My research project investigated the asymptotic properties of second-order linear difference and differential equations. While my summer project focused on solving the equations using transform methods and creating a graphical representation of the asymptotic properties, I plan on continuing to work with Dr. Neubrander in pursuing other aspects of the topic, including the inversion of the Laplace transform and the existence of almost periodic functions. I look forward to exploring deeper into these topics in mathematics and presenting my research again at conferences in the future.

#### Educational Activities

During the summer, I also helped out with the Math Circle, a summer enrichment program for high school students interested in math. Since then, I began tutoring math and assisting the Mu Alpha Theta team at McKinley High School here in Baton Rouge. The club meets once a week and consists of a number of incredibly bright and enthusiastic students who share an infectious sense of excitement for learning math. I plan on continuing working with both the tutoring lab and the Mu Alpha Theta team during the spring semester.

### Sierra Martin

#### Brief biography

My name is Sierra Martin and I am currently a junior at LSU majoring in Mathematics with a concentration in Secondary Education.

#### Mathematical and Educational Activities

My goal has always been to teach and I can't wait to graduate and begin sharing my enthusiasm for math with various high school students. I am excited to be giving back to the education field and getting to know my students. Ultimately I would love to teach at the Louisiana School of Deaf. After graduating, I plan on becoming fluent in both Spanish and Sign Language in order to reach a greater range of students from all different backgrounds.

### Amanda Mayhall

#### Brief biography

Amanda Mayhall is a senior at Louisiana State University pursuing a degree in Applied Mathematics and a minor in Entrepreneurship. Originally from Fort Worth, Texas, Amanda came to LSU to experience the unique Louisiana culture, participate in the Honors College, and find opportunities to get involved with research. She is an Honors College Advocate, a member of AIAA, an S-STEM Scholar, and an Event Coordinator for CHAARG.

#### Mathematical and Educational Activities

In 2015, Amanda was awarded the Supervised Undergraduate Research Experience (SURE) grant to work under the direction of Dr. Oliver Dasbach. Amanda participated in an REU at NC State during the summer of 2015. Her project was titled "First-Order Methods for Linear Programming" and she presented her work at the Joint Mathematics Meeting in Seattle in January. Amanda has been working on her Honors Thesis with Dr. Dasbach exploring Mahler measure and its application in various problems in Topology and Number Theory, as well as perfect matchings. She will graduate with College Honors in May 2016. In her free time, she enjoys practicing AcroYoga, running and watching Gilmore Girls.

### Emily Ribando-Gros

#### Brief biography

My name is Emily Ribando-Gros, and I am an undergraduate sophomore studying Mathematics and Computer Science at Louisiana State University. Read more about Emily from Spring 2015…

### Sarah Schott

#### Brief biography

My name is Sarah Schott; I am in the Geaux Teach program at LSU, and I will be graduating with a mathematics degree in the Spring of 2016. I've completed math-related research projects at LSU as well as engineering education projects at Utah State University.

#### Mathematical Activities

The research projects that I've contributed to include: low-dimensional topology research regarding distinguishing knots under Dr. Shea Vela Vick, properties of simultaneously conjugate permutations under Dr. Robert Perlis, and perceptual, conceptual, and emotional blocks in first year engineering students under Dr. Idalis Villanueva.

#### Educational Activities

Currently, I am a part-time math educator at Mount Carmel Academy in New Orleans, Louisiana. I plan on teaching high school temporarily in New Orleans and then returning to graduate school to obtain a master's degree in Mathematics.

## Spring 2015 Demarcus D. Smith Scholars

### Emily Ribando-Gros

#### Brief biography

My name is Emily Ribando-Gros, and I am an undergraduate sophomore studying Mathematics and Computer Science at Louisiana State University. This year, I started undergraduate research in integral geometry under Dr. Boris Rubin. Currently, I volunteer at BRYC tutoring high school math, which continues to improve my fundamental math skills. In my free time, I like doing logic puzzles and playing strategic board games. Being from New Orleans, I enjoy driving back home to enjoy the good food and live music.

#### Mathematical and Educational Activities

My research is in integral geometry, under Dr. Boris Rubin. Currently, I am studying Radon-like transforms and my goal is to obtain an explicit representation and inversion formula for the hyperbolic slice transform. Aside from my research, I enjoy volunteering at the Baton Rouge Youth Coalition to tutor high school math. At LSU, I continue to explore many diverse areas of math through the math club where I am able to share this passion with other undergraduate students.

### Derek Walker

#### Brief biography

My name is Derek Walker, and I am currently a freshman double majoring in math and physics. My hometown is Luling, Louisiana and while there I attended Hahnville High School. I am a member of the Honors College and the Society of Physics Students. Studying mathematics is a passion of mine, and I am currently working Dr. Stephen Shipman in his Quantum Graph research group. I also pursue some research in the fields of physics and biology. Outside of academics, I love to golf and study the design of golf courses. I am also an avid reader, with my favorite story being One Piece.

#### Mathematical and Educational Activities

In the mathematics department, I am currently working with Dr. Stephen Shipman on the topic of Quantum Graphs. As for my other research areas, I am working Dr. Rosby, from the biology department on looking at the affects of repressed ribosome synthesis in yeast cells. In the physics department, I'm working with Professor Tzanov and am currently working on things related to the CAPTAIN Neutrino project. After my time here as an undergraduate, I want to pursue a Ph.D. in a field with strong mathematical ties. I would love to be a professor not only to do research, but also to help teach up-and-coming mathematicians and scientists. My goal is create an engaging class that interests even the non-mathematics major in the beauty of the subject.

## Fall 2014 Demarcus D. Smith Scholars

### Victoria D'Antonio

#### Brief biography

My name is Victoria D'Antonio and I am a senior at Louisiana State University pursuing my Bachelor's degree in Mathematics. Along with my math degree, I am concentrating in Secondary Education and minoring in mathematics. I absolutely love math and solving puzzles and could not think of better way to spend the rest of my life than sharing this passion with others. This is why the GeauxTeach program has been a great fit for me. I am currently student teaching at West Feliciana Middle School in a 6th grade classroom. Outside my education, I enjoy crocheting, reading, and hanging out with friends and family. As of this semester, my roommates and I have adopted a bunny named Lilly Belle whom we absolutely adore!

#### Mathematical Activities

Upon graduation I will pursue a Masterâ€™s degree in Natural Science here at LSU, where I hope to continue the research I am working on as my Master Thesis.

#### Educational Activities

With the help of Dr. Neubrander, I am currently researching the math problems involved in middle school math competition teams. While the problems presented to these students only require math skills learned in 6th, 7th, and 8th grade, the problem solving strategies the students must use to work through these problems are elaborate. I will be focusing on a couple of these problems and exploring the complex nature that lies beyond. To begin this research I have started a math competition team at West Feliciana Middle School. The students' enthusiasm while persevering through these problems is inspiring.

### Morgan Landry

#### Brief biography

My name is Morgan Landry, and I am currently a 22-year old senior in Mathematics concentrating in Secondary Education here at LSU. My free time is usually spent hanging out with my friends and family; usually walking, hiking, biking, or camping in the outdoors. I have always had a love for teaching. Even as a kid, I’d help my two younger brothers with their math homework. Maybe this is because my mom is a teacher, so I was brought up being encouraged to help others and always trying to make something a learning experience. I am currently student teaching Algebra II at West Feliciana High School to tenth and eleventh, and so far, it has been a phenomenal experience. I am constantly amazed by the students, which makes me feel confident in the career path that I have chosen.

#### Mathematical and Educational Activities

Currently, I am working under Dr. Stephen Shipman with a group of other undergraduates in mathematics. This group meets every Thursday to talk about projects and learn about new topics related to quantum graphs. We are all working with quantum graphs, but each has an individualized project. My partner, Melanie Dutel, and I presented a poster entitled "Waves in a String with Decaying Defect Density" in the summer of 2014 and in October 2014, where I also gave an oral presentation. Melanie and I are working to expand our research to include a wider range of data so we can hopefully expand upon fractal patterns we observed.

In the future, I plan to attend graduate school in mathematics to earn a Masters degree. After that, I want to work at a university so I am able to teach a few college level math courses, while also working with math education. I would like to be able to use my teaching and math experience to help aspiring teachers like my current self.

### Alexa Martin

My name is Alexa Martin, and I am currently a junior at LSU. I am pursuing a degree in Mathematics with a concentration in Secondary Education. I still live in my hometown of Gonzales, Louisiana and drive back and forth to LSU to continue my education. I love the environment at LSU and all the opportunities that have been given to me while being a student here at LSU. I plan to teach and give back to kids in high school and hopefully teach and guide them to love math just as much as I do. I am currently working with Dr. Stephen Shipman exploring Quantum Graphs in Mathematics.

#### Brief biography

My name is Alexa Martin, and I am currently a junior at LSU. I am pursuing a degree in Mathematics with a concentration in Secondary Education. I still live in my hometown of Gonzales, Louisiana and drive back and forth to LSU to continue my education.

#### Mathematical and Educational Activities

I love the environment at LSU and all the opportunities that have been given to me while being a student here at LSU. I plan to teach and give back to kids in high school and hopefully teach and guide them to love math just as much as I do. I am currently working with Dr. Stephen Shipman exploring Quantum Graphs in Mathematics.

### Amanda Mayhall

#### Brief biography

Amanda Mayhall is a junior at Louisiana State University pursuing a degree in Applied/Discrete Mathematics and a minor in Entrepreneurship. Originally from Fort Worth, Texas, Amanda came to LSU to experience the unique Louisiana culture, participate in the Honors College, and find opportunities to get involved with research. She is an Honors College Advocate, a member of CHAARG and AIAA, and an S-STEM Scholar. She was recently accepted in the Supervised Undergraduate Research Experience (SURE Program) under the direction of Dr. Oliver Dasbach. In the coming semesters, Amanda will explore Mahler measure and its application in various problems in Topology and Number Theory. Amanda plans to graduate with College Honors, so she will begin work on her Honors Thesis this spring. In her free time, she enjoys practicing AcroYoga, running and watching Gilmore Girls.

#### Mathematical and Educational Activities

Last semester, I worked with Dr. Dasbach on Mahler measure using SAGE. Now that I am accepted into the SURE Program, Dr. Dasbach and I plan to continue our research and expand into how Mahler measure is used in Topology and Number Theory problems. I hope to present a poster in the future. Next week, I will begin tutoring College Algebra; I believe that a strong math foundation is one of the most important things one can learn in college. Last year, I put on “AP Monday,” a day where high school students could tour LSU and take a mock AP Calculus AB exam. The day went so well that I was asked to hold the event again, so I plan to get in touch with my contacts to see about setting up the next AP Monday.

### John Everett Moser

#### Biography

I am currently a sophomore at Louisiana State University working on a double major in Mathematics and Computer Science. Aside from school work, I spend my free time working on programming projects for myself and others. Initially, I was strictly a Computer Science major. However, when I was given the opportunity to do research in Mathematics, I realized I should also pursue Mathematics as well. From there, I have worked on a research project under Dr. Neubrander and began helping students as a calculus tutor.

#### Mathematical and Education Activities

Currently, I am working on a research project under Dr. Neubrander, where we investigate distributional solutions to second order linear ordinary differential equations. I presented my first poster at the LSU Undergraduate Research Conference with preliminary conclusions drawn about the topic. From there, I will continue to work on another poster with the same topic, and I plan to present a new poster at LSU Discover Day. As I am currently working as a Calculus tutor for MATH 1550 for Evangeline Residential Hall, I intend to work as a pre-calculus TA at Louisiana School for Math, Science, and the Arts this summer to further extend my educational experiences.

### Steven Olsen

#### Brief biography

My name is Steven Olsen and I am a junior mathematics major at LSU. My passion for math led me to pursue a degree in mathematics. While studying at LSU, I have engaged in undergraduate research and challenging upper-level coursework, which have helped me to develop problem-solving techniques and critical-thinking skills. Ultimately, I plan to apply the mathematical knowledge I have gained at LSU to pursue an MD, specializing in neuroscience.

#### Mathematical and Educational Activities

My research this year has been in control theory with Dr. Michael Malisoff at LSU. Specifically, in the area of curve-tracking, I studied Dr. Malisoff's theory of "robustly forwardly invariant hexagons" (hexagonal regions in which trajectories of a system will stay after a given time) and their use in a fixed-point curve-tracking scenario. I then attempted to generalize this model to a scenario in which the point being tracked is itself moving. I presented my findings as a poster at the 2014 LSU Undergraduate Research Conference in October.

While research is important to me, I focus my efforts primarily on mathematics outreach. In 2012, I organized the first team ever to compete in the Harvard-MIT Mathematics Tournament, one of the top math competitions in the country for high school students. Since then, our HMMT team has competed annually with impressive results; most recently, we competed in the 2014 HMMT November Tournament, where our students placed 36th out of 135 teams. As organizer and sponsor, I plan weekly training sessions for our members and coordinate the logistics of tournament transportation, housing, and registration. We continue to hold practices every Sunday in preparation for our next tournament, the American Regional Mathematics League (ARML) Competition.

In addition to heading the HMMT team, I am also the coordinator of the 2015 LSU Math Circle, a summer program for local high schoolers designed to introduce them to advanced concepts in mathematics not normally taught in a high school setting. As coordinator, I am in charge of all planning, logistics, and execution for the program, including: creating a website, designing a lesson plan, advertising to students, hiring and training teachers, planning field trips, and ensuring the success of the program. The LSU Math Circle will be held for three weeks in June 2015.

### Colleen Robichaux

#### Brief biography

Growing up in Houma, Louisiana, Colleen observed her mother preparing for lessons and seeing her love for education, which inspired Colleen's own interest in education. During her freshman year at LSU, she began participating in an undergraduate group researching generalized functions with Dr. Neubrander. Colleen participated in REUs at Missouri State University with Dr. Les Reid in the summer of 2013, and at the University of Minnesota Twin Cities in the summer of 2014 with Dr. Pavlo Pylyavskyy. She has presented her work at several research venues.

#### Mathematical and Educational Activities

Currently, I am working with my research group from this summer at the University of Minnesota Twin Cities in revising our paper for submission to the Electronic Journal of Combinatorics. In this project we researched K-Knuth equivalence for increasing tableaux under the guidance of Professor Pavlo Pylyavskyy. Later this month, I will be presenting a poster of this research at the Joint Mathematics Meetings and at the Nebraska Conference for Women in Mathematics. This semester I am working as an undergraduate learning assistant for a Calculus II class, helping students develop a deeper understanding of the course material. I also continue to tutor students privately and remain in the Geaux Teach program, in which I am looking forward to student teaching. After graduating, I will pursue a graduate degree in Mathematics so that I may teach at a higher level.

### Sarah Schott

#### Brief biography

My name is Sarah Schott and I am in my fourth year of undergraduate studies as a Mathematics major at Louisiana State University. During the summer of 2013, I was chosen as a Noyce Scholar and participated in low-dimensional topology research under Dr. Shea Vela-Vick.

#### Mathematical and Educational Activities

The following summer, I took an opportunity to teach gifted high school students at Georgia Tech about topology and fractals. Both of these experiences solidified my plans of becoming a mathematics teacher after I graduate. Some of my favorite things (besides math) are: reading, writing, corny jokes, and my dogs. Currently, I am working on a number theory research project under Dr. Robert Perlis that involves pairs of conjugate permutations.

### Avery St. Dizier

#### Brief biography

Avery St. Dizier is an undergraduate mathematics student at LSU. His interests lie in pure mathematics, particularly in Probability Theory and Combinatorics. Avery has worked at the University of Nebraska - Lincoln studying discrete calculus under Dr. Allan Peterson and at Cornell University studying Jacobian groups of regular matroids under Dr. Farbod Shokrieh. At LSU, he has done work on the matrix exponential and the Laplace transform under Dr. Frank Neubrander. He currently works as a tutor for Dr. Neubrander’s calculus classes, and also as a private tutor. He has taken multiple graduate level mathematics courses as an undergraduate and has presented at several research conferences at LSU and elsewhere.

#### Mathematical and Educational Activities

My long-term goal is to become a research mathematician and to spend my life creating new mathematics and inspiring the next generation of students to embrace mathematics. In the course of discovering my own research interests, I transitioned from computational work, implementing mathematical algorithms, to more pure work, including matroid theory and combinatorics. My diverse research experiences have broadened my mathematical toolkit while focusing my interests.

In my first semester at Louisiana State University (LSU), I dove into research with Dr. Frank Neubrander. When I started college, I only knew basic calculus. However, Dr. Neubrander relentlessly pushed my peers and me each week, opening our minds to the vibrant world of higher math. After a couple of months of weekly, late-night lectures, he introduced us to our research topic. Motivated by sharp error estimates for approximating strongly continuous operator semigroups using higher order Pade Approximations, he tasked us with implementing and testing new algorithms for approximating the matrix exponential using Mathematica and Matlab. We then carried the computation of the matrix exponential into the numerical inversion of the Laplace Transform. Despite what was suggested by the sharp error bounds, we discovered that the scaling and squaring used by the mainstream algorithms remained more computationally efficient than higher order approximations. I was then tasked with summarizing the algorithms and results in a technical report. We continued on to produce a poster which we presented at the Louisiana State University Undergraduate Research Conference. Dr. Neubrander showed me how research is actually done, not by following a predetermined path from the problem to the solution, but by slowly breaking down a seemingly impenetrable question into manageable pieces that can yield insight into the bigger mathematical picture.

After a year of working with Dr. Neubrander, I attended the Summer Research Program in applied mathematics at the University of Nebraska-Lincoln (UNL). I was mentored by Dr. Allan Peterson in the area of discrete calculus. Working with a larger group of students, I applied the knowledge of the Laplace Transform and the research philosophy that I had gained working with Dr. Neubrander to develop an analogue of the Laplace Transform in a radically different setting. We considered a set called the scaled number line, consisting of the orbit of a fixed based point under an affine map and its inverse. On this set, we first examined the expected analogues of the elementary functions and verified that they possessed properties similar to those of their continuous counterparts. Then, we focused on the discrete integral and the basic theory of difference equations. Guided by our intuitions from calculus, we formulated a definition for the discrete Laplace Transform, derived its properties, proved convergence and injectivity results, and demonstrated its effectiveness in solving discrete difference equations on the scaled number line. We collected our results into a paper that we submitted to the Pan-American Mathematical Journal. I also presented a poster on the research at the LSU Discover Research Conference and again at the 2014 Joint Mathematics Meeting. My research at UNL was my first experience contributing to mathematical theory. I greatly enjoyed the project, and it drew me to studying more abstract subjects when I returned to LSU. As I worked throughout the next semester to complete and submit the paper, I also began delving into my newfound interests by taking the first-year graduate courses in algebra, complex analysis, and topology.

Once I had completed a year of graduate-level coursework, I was able to pursue the new interests in pure mathematics that I had been exploring since the previous summer by attending Cornell University's REU program. I worked with another undergraduate, Esco He (Cornell University), and was mentored by Professor Farbod Shokrieh in the area of chip-firing games on graphs. Given a finite, connected graph with no loops, a chip-firing game is played by first assigning integer values, called “chips,” to each vertex. The objective of the game is to get each vertex out of “debt,” that is to make each vertex have a nonnegative value through a sequence of moves, where a move consists of allowing a vertex to fire by sending one chip to each adjacent vertex. The analysis of this game motivates the study of the Jacobian group, a quotient of the group of initial chip configurations under addition.

One interesting property of the Jacobian group is that the order of the group is exactly the number of spanning trees of the graph. There are many different, known explicit bijections between the set of spanning trees and the Jacobian group. However, all known bijections depend heavily on the graph-theoretic notion of vertices. Our goal was to construct a combinatorial bijection that could be extended to regular matroids, structures that capture the dependence relations between the columns of real matrices in which all subdeterminants are 0, 1, or -1. We began by studying an equivalent definition of the Jacobian compatible with regular matroids. Then, we analyzed a geometric construction that encoded the set of spanning trees as a tiling of space by higher-dimensional parallelepipeds and encoded Jacobian elements as corners of the parallelepipeds modulo an equivalence relation derived from the cycles in the matroid. After repeatedly varying the parameters and working out dozens of low-dimensional examples, I established a method for recreating the geometric bijection using only the combinatorics of the underlying matroid with no reference to the geometry. I then proved the equivalence of the geometric and combinatorial methods, establishing that the combinatorial method was indeed a bijection. However, unlike the geometric bijection, which has a natural inverse, the combinatorial bijection is difficult to invert. The project is ongoing, and we are in the process of drafting a paper with our results.

Since last summer, I have been focusing on probability theory. During the Cornell REU, I attended several fascinating seminars, including talks on mixing times of stochastic processes and connectivity of randomly growing networks. I have taken graduate courses in probability theory and real analysis in previous semesters, and I am currently taking stochastic analysis to prepare to undertake graduate studies in probability theory. I have applied to a number of graduate schools with strong programs and active research in probability theory, and I am eagerly awaiting replies.

### Jessica Wojtkiewicz

#### Brief biography

Jessica Wojtkiewicz is an undergraduate student pursuing a degree in Computational Mathematics at Louisiana State University. After taking Discrete Dynamical Systems with Dr. Peter Wolenski, Jessica was given the opportunity to work with the Math Consultation Clinic and an engineering firm in order to develop a Graphical User Interface in MATLAB to track a microwave transceiver on a hand-held device using eight optical-flow sensors. After this opportunity, Jessica learned that her mathematical interests could be found in real-life applications. Along with working on mathematical problems, Jessica is also a Resident Assistant for the Global Connections Residential College on LSU's campus. Jessica spends a lot of her time mentoring first-year students and is known to tutor a few of them in mathematics. In the future, Jessica plans to attend a graduate school to obtain a doctorate degree in Computational/Applied Mathematics.

#### Mathematical and Educational Activities

Mathematics has been a passion of mine since I was a young girl, but I never truly realized how much I loved mathematics until I had a couple of wonderful mathematics teachers throughout middle and high school. These teachers were able to show me how fascinating numbers were while teaching me how to apply this fascination with numbers to a multitude of real-life applications. It was this passion that these teachers instilled in me that led me to set a goal to pursue mathematics in college.

Currently, I am working towards acquiring a Bachelor of Science degree in Mathematics with a concentration in Computational Mathematics. My goal beyond graduation is to pursue a PhD in Computational/Applied Mathematics to create mathematical models and algorithms for industries or government labs. To help prepare myself for the rigor of graduate level research and to open up future possibilities in mathematics, I have participated in the Math Consultation Clinic at Louisiana State University with Dr. Peter Wolenski, Dr. Stephen Shipman, and Dr. Ameziane Harhad, as well as three graduate students and three undergraduate students pursuing degrees in mathematics. With this opportunity, I was able to create a Graphical User Interface in MATLAB that incorporated an algorithm that we developed in order to track a microwave transceiver on a hand-held device using eight optical-flow sensors. Exposure to this type of research will be advantageous when it is time for me to make my goals more clear, specific, and measurable by applying to certain graduate schools that specialize in Computational/Applied Mathematics.

Not only have these professors taught me about mathematics, but they have also continuously fueled my love and passion for mathematics simply by giving me opportunities to challenge myself with the mysteries of mathematics. Without the help and passion given to me by these very special teachers and mentors in my life, I do not believe that I would be pursuing a degree in mathematics and ultimately be the student that I am today.

## Spring 2014 Demarcus D. Smith Scholars

#### Brief biography

My name is Michelle Laskowski and I am a transferred junior, coming from school and home in Chicago. I came for the culture-filled adventure of LSU but stayed for the Geaux Teach program, which I found to be extraordinary. Also, as I ventured further into conceptual math, my passion and interest mathematics has exponentially increased, leaving me continually on the edge to learn more. I am currently working on a research team being guided by Dr. Neubrander and am honored to continue research on this summer as a Robert Noyce Intern.

#### Mathematical and Educational Activities

My current research is on Discrete Dynamical Systems and the Generation of Fractals. This is my first taste of research and after only a short period of time I've realized I would like to continue exploring mathematics through the involvement of research. As a member of the Geaux Teach program, I plan to open the eyes and minds of high school students while continuing my own education and in time pursuing a Master's degree, in mathematics.

### Amanda Mayhall

#### Brief biography

Amanda Mayhall is a sophomore at Louisiana State University pursuing a degree in Applied/Discrete Mathematics and a minor in Entrepreneurship. Originally from Fort Worth, Texas, Amanda came to LSU to experience the unique Louisiana culture, participate in the Honors College, and find opportunities to get involved with research. She is an Honors College Advocate, a member of the I3 Student Governing Council, and an S-STEM Scholar. She is currently working with Dr. Neubrander exploring Discrete Dynamical Systems and the Generation of Fractals. Amanda also works with the Academic Center for Student Athletes tutoring algebra and calculus. In her free time, she enjoys attending LSU football games, going to concerts, and visiting the Friends of the Animals Dog Adoption House.

#### Mathematical and Educational Activities

I am currently researching Discrete Dynamical Systems and the Generation of Fractals with Dr. Neubrander. We are using Mathematica to generate images of “exploding” noncontractive functions similar to the Sierpinski triangle and Barnsley's fern. I hope to present a poster in the future. I am also working with ACSA tutoring algebra and calculus to student athletes. In the I3 Governing Council, we are working to put on a mock AP test day on LSU's campus for high school students.

### Paige Thibodeaux

#### Brief biography

Paige Thibodeaux is a sophomore undergraduate at Louisiana State University majoring in Computational Mathematics with a minor in Philosophy while also concurrently fulfilling premedical requirements. She is currently involved in a research group exploring the topic of Discrete Dynamical Systems and the Generation of Fractals with Dr. Frank Neubrander, and she is part of a group planning an AP Calculus Day at LSU, which is intended to assist area high school AP Calculus students in the preparation for their AP test. She also works as a caregiver for an autistic woman and spends much of her free time searching for area trails to run.

#### Mathematical and Educational Activities

My research endeavors are currently limited to my involved in research with Dr. Neubrander on the topic of Discrete Dynamical Systems and the Generation of Fractals. While I am an undergraduate, I hope to continue to expand my knowledge of the subject of mathematics through involvement in research, especially in topics with potential to broaden my understanding of mathematical biology. My teaching endeavors are similarly limited to my current involvement in a group that is planning an AP Calculus Day for area high school AP Calculus students. I also hope to be involved in tutoring for local public schools in the future as an undergraduate student.

### Jeremy Tillay

#### Brief biography

I am a 20-year old sophomore at LSU pursuing a degree in Pure Math. I am a LA-STEM Research Scholar, Honors College Student, and have been doing undergraduate research since my first semester of freshman year. I have always known that I wanted to major in math, but it was not until I started taking higher-level maths that I was certain I wanted to pursue my PhD. I have competed in two math tournaments while at LSU and won first place in both of them! Outside of school, I am a member of the Honors College Advocates, and I love literature. I enjoy reading both fiction and nonfiction. Also, I enjoy writing fiction as a hobby when I want to explore artistic interests.

#### Mathematical and Educational Activities

I tutor classmates and students in classes I have taken before regularly. So far, I have not asked for pay, as it's always been a fun activity for me that keeps my knowledge of material fresh.

As far as research, I have studied the resonance in one and two dimensional lattices under the advisement of Dr. Shipman. Studying these systems has given me insight that is now allowing me to research quantum graphs that model graphene tubes. It is my hope that I can find a way to add defects to the system that will allow for a resonant interaction in the model. This research has really helped me see higher-level math for what it is, and it has been an interesting experience to need to employ a large variety of mathematical tools to solve a problem. Computer programming, theoretical math, paper-and-pencil calculations, research into graph theory, among other efforts are what have solved these problems in the past. It's very different from completing a homework assignment that can be done in a few hours. I have to work on these problems for days and sometimes reach numerous dead ends, but I wouldn't trade it for the world. I hope that early in my senior year, I can have a paper published on carbon nanotubes.

## Fall 2013 Demarcus D. Smith Scholars

### Bruno Beltran

#### Brief biography

Bruno Beltran is an undergraduate mathematics and computational science student at LSU. His interests lie in applied mathematics, especially applications in computational and quantitative biology. He is a Goldwater, LA-STEM, and HHMI-EXROP scholar. Bruno has worked at Arizona State University under Dr. Castillo-Chavez in population dynamics and modeling aneurysm formation, and at Yale modeling the chemical processes that allow chromosome segregation in C. crescentus under Dr. Jacobs-Wagner. At LSU, he has done work on approximating the matrix exponential and the Laplace transform under Dr. Neubrander. He currently serves as Linux sysadmin for the Nandakumar lab, as a private tutor, and is working on the en0vation grant under Dr. Robert Kooima to design state of the art 3D interfaces, all while taking a heavy graduate math course load. He has presented his work with posters at LSU's 2012 Undergraduate Research Conference, SACNAS 2012, and the SIAM Mid-Atlantic Student Conference. He has given talks at the 2013 JMM, LSU's 2012 and 2013 Undergraduate Research Conferences, the 2013 SIAM Mid-Atlantic Student Conference (at which he was invited to chair a session), and Brown's 2013 SUMS Research Conference. He was invited to give a talk on his research with Dr. Neubrander for a 2013 spring colloquium series at Humboldt State University.

#### Summary of current and future projects

The research I was involved in last summer at Yale is close to being ready for submission to an academic journal. I have taken some time off of my work with Dr. Nandakumar to focus on this and my work with Dr. Robert Kooima on experimental interface design. I will be building a video game to exposit my work with Dr. Kooima before leaving for Imperial College London for the summer, where I will work on problems in the unification of microfluidics at various scales.

#### Mathematical and educational activities

My mentors can be said to have formed an exact sequence, iteratively evincing my dream of eventually leading an interdisciplinary research group where I can apply my training in mathematics and computation to tackle problems in quantitative biology. Beginning my first semester at LSU, each of my mentors' disparate strengths and advice pushed me squarely into the kernel of the next, allowing me to systematically hone my interests while acquiring experience in diverse areas from approximating operator semigroups to modeling chemical signals that facilitate chromosome segregation. My background working with mathematicians, engineers, and physicists has left me ideally poised to approach my interests in biology with an interdisciplinary perspective; it has shown me how diverse problems can all be successfully approached from the unified framework of mathematical modeling. [The reader may jump to last paragraph without loss of cohesion.]

Having garnered an introduction into formal mathematics from MIT's OpenCourseWare offerings in high school, I dove into research weeks after arriving at LSU under the tutelage of Dr. Frank Neubrander. My first research project involved investigating whether new error estimates for approximating operator semigroups could be applied to more efficiently to calculate the matrix exponential, an object ubiquitous in scientific computation. Dr. Neubrander's patient exposition allowed me to fall in love with the challenges inherent in decomposing a research problem into manageable components. Specifically, I was tasked with implementing the new algorithms using Matlab, Mathematica, and pure C, and testing them for efficiency and accuracy. Although the existing methods were marginally more efficient on modern architectures, the experience of challenging the cutting edge in scientific computation primed my interest in computational science, concluding in a poster presentation at LSU's 2012 Undergraduate Research Conference.

Having focused my sights on mathematical research, I participated in the Mathematical and Theoretical Biology Institute's REU under Dr. Carlos Castillo-Chavez at Arizona State University the summer after my freshman year. Because of Dr. Castillo-Chavez's inspirational leadership and example as both a mathematician and a spokesperson, the summer experience became far more than the first experience with interdisciplinary research it was designed to be. My team (composed of three undergraduate mathematicians and a biology major) independently developed a research question pertaining to aneurysm formation and used the C++-based open source fluidics toolkit OpenFOAM to investigate whether turbulence caused by aneurysms in the Circle of Willis might influence downstream secondary aneurysm formation. A technical report on our findings was printed in the REU's internal journal. Beyond the research itself, however, I learned the importance of championing my work, giving talks at the 2013 JMM and Brown's 2013 SUMS Conference, chairing talks and presenting at the Mid-Atlantic SIAM meeting, and presenting a poster on my work at SACNAS.

Returning to LSU my sophomore year, I enrolled in graduate math classes while continuing research with Dr. Neubrander exploring applications of his work in semigroups to the computation of the Laplace transform. I again implemented and tested the new algorithms in Matlab, Mathematica, and pure C. Although they were once again were marginally less efficient than existing methods, it was for my talk on this work that I won a presentation award at LSU's 2013 Undergraduate Research Conference. I was also personally invited to give my hour-long presentation on this work for a colloquium series at Humboldt State University (a California State University).

The following summer, I was accepted into the Howard Hughes Medical Institute's EXROP program to work at Yale University under Dr. Christine Jacobs-Wagner. It was at Yale, through creating, testing, and applying mathematical models for post-replication chromosome segregation in C. crescentus, that I realized that my future was in quantitative biology. I worked alongside chemists, physicists, and biologists, and I reveled in the challenge of communicating my mathematical perspective to everyone in my lab. With the help of Dr. Jacobs-Wagner and my friend Dr. Ivan Surovtsev, I learned what it takes to succeed in biological research; I learned what it takes to convince people from various backgrounds of the utility of a mathematical perspective, a perspective of which they are often inordinately skeptical. I learned what it takes to build models that agree both quantitatively with the data you are studying and qualitatively with the established ideas of the field. We are now working on getting a paper written including the models I built over the summer.

Now that I have returned to LSU once again, it may seem that I have put aside my interests in biological research to further pursue studies in mathematics, given my heavy graduate-level course load. In actuality, I am working my way through Wade's Organic Chemistry, Watson's Molecular Biology of the Gene, and books on the cell and neuroscience in my spare time, a preparation reminiscent of my high school days learning on ocw.mit.edu that so successfully prepared me for my studies of mathematics. Further, I will be travelling to Imperial College London over the summer in preparation for my future in biological research by partaking in research in microfluidics, a phenomenon integral to almost all cellular mechanisms.

Dr. Neubrander narrowed my interests to mathematics. Dr. Castillo-Chavez taught me to be a spokesperson. Dr. Jacobs-Wagner's lab showed me the joy of applying mathematics to cutting-edge problems in quantitative biology. Individually the morphisms on my character that these influences induced have images in areas foreign to each other. However, in combination, they have provided a holistic sampling of important perspectives, all preparing me for a successful career as a researcher in computational and quantitative biology.

#### Brief biography

My name is Christopher Kennady; I am a sophomore here at LSU now in my second semester of Mathematics. I am the oldest of two children, I have a younger sister who is fifteen and a sophomore in high school. My passions are found in sports and the outdoors. My time is spent hunting, fishing, or just anything to keep my outside. My family and I live for LSU sports so I have bled purple and gold since the day I was born. It has always been my dream to be a Tiger and attend LSU. As a freshman I enrolled as an Industrial Engineer major but quickly I found that this is not the path I wanted to follow and felt Mathematics was my true calling. My dream job is to become a high school math teacher and to coach football along with track and field. Being able to influence young students to find their love for Mathematics along with helping young athletes everyday will be a great blessing in my life. With this goal in my sights I have begun a research project along with the guidance of Dr. Neubrander.

#### Mathematical and Educational Activities

My current research topic is The Schröder Functional Equation and Koopman Operators for Dynamical Systems. Being awarded this scholarship will really allow me to dedicate a serious time and effort into mathematics research. This will allow me to use the time I may be using to have to work, to help me offset costs and to have spending money of my own, to serious research and time I could help other students. I am very excited about beginning my path into different types of research in mathematics. Having this scholarship will definitely help me dedicate plenty of time towards my research and helping my dream life come true. I am blessed and grateful for this opportunity given to me by those apart of the Demarcus D. Smith Scholarship.

### Morgan Landry

#### Brief biography

My name is Morgan Landry, and I am currently a 21-year-old junior at Louisiana State University from Lafayette, Louisiana. I went to Comeaux High School, where I was on the swim team, and was a member of the robotics club. After graduating, I moved to Baton Rouge, where I started studying mathematics and became a member of the Geaux Teach program. Although my parents and two younger brothers still live in Lafayette, I am extremely happy here at LSU, where I am pursuing a degree in Math/Secondary Education with a minor in Philosophy.

#### Mathematical and Educational Activities

Dr. Frank Neubrander and I are currently working to expand upon the research that I did during the summer of 2013 through the Noyce program. Last summer, my research was on the field of sequences and the z-Transform, but now I am working to expand the topic by including asymptotic cases. Each week, Dr. Neubrander and I meet to discuss my progress and talk about any questions I have regarding content I am studying. I am working toward writing a paper and re-writing my current poster to include the new material I have been researching.

After graduating from LSU, I intend to go to grad school to continue my studies and hopefully get a Ph. D in Math Education. In order to prepare myself for this, I am going to continue doing mathematical research with Dr. Frank Neubrander, and present another poster on my updated research in March. Also I plan to apply for a research position at Utah State University to conduct research on education over the summer of 2014. I believe that these experiences will give me the upper hand when applying to graduate schools and help me further understand what is to come in my future.

### Emelie Mativi

#### Brief biography

I am a junior at LSU pursuing a math major with a concentration in secondary education. I am a three year member of the Geaux Teach program as well as the Honors College. My passion for education led me to become a Noyce Scholar and commit two years to teaching in a high needs school district. I have been participating in research at LSU for over two years, and am now working on a thesis project. I received Sophomore Honors distinction and the Tiger Excellence Award. I am a member of the Distinguished Communicators program and the National Society of Collegiate Scholars. When I am not focused on school I really enjoy volunteering. I have volunteered for three years at an equestrian center for special needs children. I am also a member of the LSU quiz bowl team and love competing in tournaments. I will be student teaching in the fall of 2014, and then I will continue in pursuit of a Master's in education.

#### Mathematical and Educational Activities

I began work on my thesis last semester, but the research began over two years ago. I worked with Dr. Shipman to develop an understanding of resonance in lattice systems, and I gained understanding of advanced mathematical concepts along the way. Learning these concepts in the form of a project instead of in a traditional classroom setting gave me a deeper understanding of the material. I realized how helpful this form of teaching could be, and I wanted to attempt to develop a curriculum using it. For my thesis project I am combining my passion for math and education to produce a series of lesson plans that incorporate upper level math concepts into a high school level curriculum. I am using the same material that has been the foundation of my research throughout my college career, but I am presenting it in a geometric sense. So far, I have completed a high school unit plan that incorporates concepts such as complex variables, calculus, and trigonometry. I have also completed detailed scripts of multiple lessons, so that others can see exactly how I imagine these concepts being taught. I am going to finish my thesis this semester by completing a poster that presents the material covered in the lessons as well as how the upper level concepts were incorporated. I hope to convince other instructors that it is possible to integrate difficult concepts into the current curriculum, and I want to show how beneficial this style of teaching would be to students. I also hope that spending a year on a project like this will help me when I begin my career as a teacher.

### Mandonesia Maurice

#### Brief biography

Mandonesia Maurice is a sophomore Mathematics student at Louisiana State University. was born and raised in Kenner, LA. She attended Bonnabel High School in Kenner and graduated in the top 10 of her class. She has always dreamed of attending Louisiana State University. As a Louisiana native, Mandonesia enjoys dance, great food, music and culture. She is a member of Sigma Lambda Gamma National Sorority Incorporated, LSU's first and only multicultural sorority. Currently she is pursuing a degree in Mathematics-Secondary Education. Maurice is also a student of Geaux Teach, an organization that provides LSU students with pedagogy as well as field experience. In the near future, she plans to further her education, travel the world a bit, and teach less fortunate children. “Math is beautiful. Unlike the variation that other subjects may have in other countries, 2+2 will always equal 4.”

#### Mathematical and Educational Activities

Mandonesia applied for the Robert Noyce Undergraduate Research Experience in the spring semester of her freshman year, without any experience in research and only Calculus I knowledge. She worked with Dr. Robert Perlis, chair of the Math Department at LSU, which allowed her to secure strong ties and a head start on other Math courses at LSU. Her research utilized the Harmonic Series and Mathematical Induction, among other skills, to solve a problem. As a Geaux Teach student, Mandonesia has gained experience in teaching as well. She has taken courses directly related to pedagogy and courses exercising field experience. Maurice has taught third graders, 6th graders and is currently assigned to an Algebra II classroom. In addition to teaching the lessons, Geaux Teach students are required to plan and write their own lesson plans, so Mandonesia has experience there as well.

### Steven Olsen

#### Brief biography

I'm Steven Olsen and I'm a sophomore Mathematics major at LSU. Though born and raised in Baton Rouge, I'm studying abroad in France for the 2013–2014 school year. I've loved math for as long as I can remember, and consequently I'm always trying to teach my friends cool new math tricks or helping someone with their calc homework. My other interests include tennis and linguistics. Although I'm in France, I'm currently researching the Schröder functional equation with Dr. Frank Neubrander.

#### Mathematical and Educational Activities

My current research is on Schröder's equation, which I plan to present in the form of a poster along with a paper. When I return from France in May 2014, I will continue my involvement in the Louisiana Harvard-MIT Mathematics Team and once again assume an active role in its leadership in preparation for the 2015 tournament. During my senior year, I will most likely complete my Senior Honors Thesis in mathematics with Dr. Neubrander as my advisor. While my future after college is, at this point, fairly uncertain, I do plan to go to graduate school in either Mathematics or Aerospace Engineering.

Schröder's equation is an eigenvalue equation for the composition operator $C$ acting on $C[0,1]$, which sends a function $f(x)$ to $f(h(x))$. It is used to analyze the orbits $h^n (x)$ of discrete dynamical systems and their embeddings into continuous dynamical systems. I'm currently working on formulating a rough draft in LaTeX, which will then pave the way for the final paper and a poster.

### Colleen Robichaux

#### Brief biography

Growing up in Houma, Louisiana, Colleen Robichaux often observed her mother preparing for lessons and seeing her mother's love for education, which inspired Colleen's own interest in education. During her freshman year at Louisiana State University where she majored in Mathematics with a concentration in Secondary Education, she began participating in an undergraduate group researching generalized functions. Finding this research quite interesting, Colleen continued the same project in an REU at Louisiana State University with Dr. Neubrander during the summer of 2012 for which Colleen produced and presented a poster twice at two LSU research conferences. Enjoying the previous REU so thoroughly, she participated in an REU at Missouri State University with Dr. Les Reid in the summer of 2013 and returned in the fall to present her research at a conference. Colleen is continuing research and tutoring and is looking forward to student teaching in the Geaux Teach program. After graduating, rather than immediately teaching in a high school, she now plans to pursue a graduate degree in Mathematics so that she may teach at a higher level.

#### Mathematical and Educational Activities

Currently, Colleen is continuing the project which she began last summer at a Research Experience for Undergraduates at Missouri State University. In this project she is researching properties of non-commuting graphs under the guidance of Professor Les Reid at Missouri State University. Colleen plans on completing this project to produce a paper and a poster, which she will present at the LSU Discover Research Day. This semester Colleen is working as an undergraduate learning assistant for a Linear Algebra and Differential Equations class, helping students develop a deeper understanding of the course material. She also continues to tutor students privately and remains in the Geaux Teach program, in which she is looking forward to student teaching.

### Avery St. Dizier

#### Brief biography

I was born right here in Baton Rouge, and I have lived here my whole life. I went to St. Aloysius for elementary school, where I joined the Boy Scouts and later became an Eagle Scout. I continued on to Redemptorist High School, where I joined Mu Alpha Theta and discovered that math was actually fun and was the thing for me. I am now a junior mathematics major here at LSU, and I am enjoying every day here. I live on campus with three other math majors, and I love the dynamic that we have when we work together and help each other out. I enjoy regular trips to the UREC with my friends for rock climbing and racquetball.

#### Mathematical and Educational Activities

In an effort to better understand the intricacies and difficulties of communicating mathematics, I regularly tutor in various subjects. I enjoy the challenge of working to convey what I know in a cohesive form to someone else. Communicating the ideas I have been taught exposes the gaps in my own understanding and helps me to consolidate my knowledge, keeping me up to date on information from classes that I might otherwise forget from disuse. Tutoring also allows me to give back to the mathematical community at LSU, which often supports me, particularly in providing opportunities for undergraduate mathematical research.

This semester I am enrolled in an independent reading course under Professor Achar. I intend to complete the groundwork for an undergraduate honors thesis project this semester and to write the thesis next semester or over the summer, time permitting. We will be studying reflection groups.

Reflections are mappings from a Euclidean space to itself that are isometries whose set of fixed points is a hyperplane. Concretely, in two dimensions, a reflection would be like folding a piece of paper. Points located along the fold line are fixed, they do not move. Points not along the fold line are sent to their mirror image across the fold. It is also easy to visualize a reflection in three dimensions: the only difference is that we reflect across a plane instead of a line. Reflections can be defined mathematically in any finite number of dimensions.

When we take a set of reflections and combine them in all possible ways, what we get is called a reflection group. It is a collection of transformations of space, each of which can be described as a series of reflections. Reflection groups have remarkable geometric and group theoretic properties. We will be exploring various topics in reflection groups and their more general counterparts, Coxeter groups.