Mathematical History:
Independent Educational Video Development (2022-present)
- I am currently focusing on developing lecture videos for Youtube. This process involves literature research, independent mathematical research, learning video editing techniques, and creating visualizations. Highlights include:
- Introducing Model Theory with Ehrenfeucht-Fraïssé Games on Linear Orderings: Submission to the Summer of Math Exposition #2
- Regular Languages and Model Theory: A long lecture series with the goal of guiding a mathematically mature audience through the necessary automata and model theory to make sense of my PhD thesis.
- A Teaching Book Report: "Why Don't Students Like School?" A summary of what I learned reading through a book by Daniel Willingham about the cognitive science of learning.
- Hyperdo Zometool Model Build: Understanding the 120-cell (from 2021): A build video of a model of a 4D platonic solid along with an explanation of the model.
Assistant Professor, Landmark College (2019-2022)
- Taught:
- College Algebra
- Calc 1
- Introduction to Calculus
- Calc 3
- Computer Graphics
Independent Educational Software Development (2018-2019)
- I spent a year focusing on developing educational interactives to supplement various mathematics courses and communicate mathematical ideas that are important to me. All my interactives are accessible from https://trkern.github.io/. Highlights include:
- Velocity Meant to guide students towards stumbling across the limit definition of a derivative on their own.
- Electronic Polynomial Educational Experience A demo of a long term project to produce a computation assistant, allowing students to focus on which rules to apply when without worrying about applying them correctly.
- Transforming Functions Allows students to visualize how changing a function transforms its graph.
- Linear Transformations Visualize the effects and properties of 2x2 matrixes.
- Ehrenfeucht-Fraïssé Game Explore the first order logic of graphs through this common model-theoretic tool.
Visiting Assistant Professor, SUNY Oswego (2017-2018)
- Taught:
- College Algebra
- Introductory Statistics A
- Matrix Algebra
Visiting Assistant Professor, Cornell University (2016-2017)
- Taught:
- Calculus I
- Multivariable Calculus
Ph.D. in Math, M.S. in Computer Science, Cornell University (2009-2016)
- My dissertation was on Nonstandard Models of the Weak Second Order Theory of One Successor, under Anil Nerode
- Automata Theory
- Model Theory
- Assisted Maria Terrell in the development of Calculus with Applications
- Taught:
- Calculus I
- Led Recitations:
- Linear Algebra
- Multivariable Calculus for Engineers
- Theoretical Linear Algebra and Calculus
- Honors Calculus II
- Multivariable Calculus
- Calculus for Engineers
- Served as organizer for the Cornell Math Department Teaching Seminar
- Also Studied:
B.A. in Math, Dartmouth College (2005-2009)
- Mathematical Research:
- Models of Failures of the Axiom of Choice
- Model Theory of Linear Orderings
- Symmetric Chromatic Polynomials on Graphs
- Introducing Model Theory with Ehrenfeucht-Fraïssé Games on Linear Orderings: Submission to the Summer of Math Exposition #2
- Regular Languages and Model Theory: A long lecture series with the goal of guiding a mathematically mature audience through the necessary automata and model theory to make sense of my PhD thesis.
- A Teaching Book Report: "Why Don't Students Like School?" A summary of what I learned reading through a book by Daniel Willingham about the cognitive science of learning.
- Hyperdo Zometool Model Build: Understanding the 120-cell (from 2021): A build video of a model of a 4D platonic solid along with an explanation of the model.
- College Algebra
- Calc 1
- Introduction to Calculus
- Calc 3
- Computer Graphics
- Velocity Meant to guide students towards stumbling across the limit definition of a derivative on their own.
- Electronic Polynomial Educational Experience A demo of a long term project to produce a computation assistant, allowing students to focus on which rules to apply when without worrying about applying them correctly.
- Transforming Functions Allows students to visualize how changing a function transforms its graph.
- Linear Transformations Visualize the effects and properties of 2x2 matrixes.
- Ehrenfeucht-Fraïssé Game Explore the first order logic of graphs through this common model-theoretic tool.
- College Algebra
- Introductory Statistics A
- Matrix Algebra
- Calculus I
- Multivariable Calculus
- Automata Theory
- Model Theory
- Calculus I
- Linear Algebra
- Multivariable Calculus for Engineers
- Theoretical Linear Algebra and Calculus
- Honors Calculus II
- Multivariable Calculus
- Calculus for Engineers
- Models of Failures of the Axiom of Choice
- Model Theory of Linear Orderings
- Symmetric Chromatic Polynomials on Graphs