In this section I describe several ways that I have contributed to the academic environment. These activities range from working with colleagues to creating a new major, to working closely with students as they explore new topics outside of the classroom. It has been rewarding working with colleagues and students to promote more meaningful experiences for our students. Most of the topics listed in this section are also described in more detail in other sections of this website.
I begin by describing several new courses that I have developed.
Developing and Teaching New Courses
In 2021, I developed several new course ideas that are outside the Florida Southern math curriculum and that are tailored to the student audience. The description of these courses, each of which I have also taught as an experimental course, are provided below.
In spring 2022, I offered a special topics course called "Cryptology and its History", which included historical development and key figures. This course was meant to introduce concepts in number theory that are not prevalent in the Florida Southern curriculum. I also co-taught a class with James Farrell, a Finance faculty at Florida Southern, called "Math Behind Finance" that was meant for applied math majors with a business-related concentration. In the future I will create a two-course sequence that could be used “in-house” as the finance component of an applied math major. I have also taught a course called "Geometry and its History" that is meant for secondary education math majors—a growing audience. It is my hope that these courses will become popular and ultimately supplement and become part of the usual curriculum.
COURSE DESCRIPTION OF CRYPTOGRAPHY
Two hours. Students will explore many encryption schemes starting from the Roman Empire to the Present. The course will introduce the material chronologically while also describing the historical figures who either created a cryptography scheme or developed a technique to break a certain type of cipher. These schemes include the Mono-alphabetic substitution cipher, Vigenère cipher, frequency analysis, cipher machines, Enigma and the attacks on it, key distribution problem, Diffie-Hellman key exchange, discrete log problem, ElGamal key exchange, RSA, digital signatures, and quantum cryptography.
COURSE DESCRIPTION OF MATH BEHIND FINANCE
Four hours. Prerequisites: MAT 2050 or MAT 2311 and MAT 2022 or MAT 2032 or BUS 3320. This course covers finance topics from a mathematical perspective. Key topics include interest rates and the time value of money, stocks and equity, dividends, bonds, and stock options. The course concludes with the Black-Scholes option pricing model, as well as other asset valuation models as time permits.
The purpose of this course is to expand one's knowledge of the mathematical models underpinning finance topics:
1. Understand and apply concepts of time value of money;
2. Understand the techniques for fundamental and technical valuation models;
3. Understand and apply the Black-Scholes option pricing model to equity options;
4. Evaluate the impact of risk preference on investment choices and risk premiums.
COURSE DESCRIPTION OF GEOMETRY
Four hours. Prerequisites: MAT 2311.
My idea for this course is to be especially for secondary-ed math majors, those wanting to teach math in high school. Since we do not offer a course in geometry, I thought it would be good to do one. I would also call the course "geometry and its history". In addition to the geometry, I will present geometry alongside its historical development. It turns out the history and discovery and different types of geometries is quite vibrant. We also visit those who found/discovered the concepts.
Much of the plane geometry done in high school was mostly chiseled in Ancient Greece by a man named Euclid around 300 BC. We'll explore what his axioms of geometry were that allowed him to prove his geometry propositions. We will also explore geometric constructions, using straight edge and compass to construct geometric figures, like an equilateral triangle. There are also mathematical proofs alongside these constructions. Lines and circles created from constructions fascinated mathematicians for over 2000 years, and we will discover some of the reasons why.
The course will also introduce Modern Geometry, which are different models of geometry you likely have not seen before. This includes finite geometries, geometry on the sphere, and even geometries where parallel lines meet at the "point at infinity"! Toward the end of the course, I plan to cover basic logic and simple proof techniques needed to do geometry proofs that are done in high school. I usually include an essay where students research and write about a topic or person of their choosing.
Developing an Applied Math Major and Supplementing the Mathematics Curriculum
During my first few years at FSC, the mathematics faculty worked together to develop a new applied math major. We decided to include possible concentrations within the major, and I worked to put together a science and engineering concentration. I also helped to update the existing generic syllabi to correlate with the new changes. I will describe my contributions to these efforts in the "Committee Work" section of this website.
Serving on Faculty Searches
I have served on three search committees for new hires within the Florida Southern math department. As part of those committees, I reviewed applications and participated in all interviews. In fall 2022, I served on a search committee for a physics faculty. Unfortunately, the first round of candidates we invited to capmus did not work out. So we have to redo the interview process the following semester in January. Fortunately, there was at least one new candidate that had applied after the deadline, and the position became filled. I was invited to be a part of the search committeee via email. Being the only faculty with a physics background in the Florida Southern math department, I felt I should be part of that search committee and was happy to accept the invitation. I also describe these hiring committees in the "Committee Work" section of this portfolio.
Hosting a "Professional Development Initiative"
At Florida Southern College, the professional development initiative (PDI) is a paid workshop for faculty to gain knowledge or learn something new. In spring 2020, I co-hosted a PDI on alternative grading with Christian Robertson (the computer science chair). This PDI was meant to introduce faculty to the paradigm of specifications grading and assist them as they try to restructure one of their courses to be more mastery-based. Through this PDI, I met several faculty on campus that I did not know had already been implementing a form of mastery grading. Among these faculty was the biology chair, Nancy Morvillo. She and some of her faculty were considering restructuring their BIO 1500 general education course to be more mastery based. I talked with them throughout the workshop, trying my best to understand their needs and how biology problems and assessments were structured. I continued working with Nancy even after the workshop had ended, and the biology department at Florida Southern has since been using mastery grading with their BIO 1500 quizzes.
Creating Spaces Outside the Classroom for our Students to get Involved
There are three main ways I have created spaces outside the classroom for students to get involved. I became the founding faculty advisor of the Florida Southern Math Club in 2021. This has been an outlet for students to get involved and host fun events. I will discuss my involvement with the Math Club in the "Faculty Advisor to Student Group" section of this website. The second way is how I have mentored many students through an independent or dependent study, which introduces students to material outside of our usual curriculum. The last way is how I have mentored several honors theses, each of which have been up to two years in length. One was about the math behind finance (measure theory and the valuation of stock options) and another was independent research by the student (which I describe more in the "Collaborative Work with Students" section of this website).