Introduction:
I grew up in Berkeley, California and attended the University of California, Los Angeles for my undergraduate studies. After graduating in 2017, I pursued a Ph.D. in Mathematics at the University of California, San Diego. At UC San Diego, I was very fortunate to be advised by Jacques Verstraete and wrote my dissertation on "The combinatorics of intersecting set systems", which I successfully defended in 2022. I am now very honored to be an Assistant Professor here in the Mathematics Department at Cal State LA! My Erdös number is 2.
Outside of Math, I like to watch basketball, go for runs, and juggle. My current best is four balls, but I am working towards being able to juggle five balls.
Teaching:
In the Fall 2024 semester, I will be teaching PreCalculus (Math 1040). My office hours and corresponding course material will be posted on Canvas. Please also feel free to email me if you are interested in Combinatorics research and/or would like to explore a directed reading course.
For letters of recommendation, please give me at least two weeks prior notice when asking for a letter.
Past Teaching:
I maintain course lecture notes for these courses and these complete set of course notes can be made available via email request. At Cal State LA, I have taught the following courses:
In the Spring 2024 semester, I taught Calculus 3 (Math 2130), Advanced Topics in Combinatorics and Graph Theory (Math 5540), and served as a Belonging Coordinator for the PreCalculus sequence.
In the Fall 2023 semester, I taught Calculus 1 (Math 2110) and served as a Belonging Coordinator for the PreCalculus sequence.
In the Spring 2023 semester, I taught Calculus 1 (Math 2110).
In the Fall 2022 semester, I taught Calculus 3 (Math 2130) and Theory of Probability (Math 4740).
Student Mentoring:
Students at Cal State LA who may be interested in Math Research and/or pursuing higher degrees in Mathematics are strongly encouraged to reach out regarding a potential Undergraduate Directed Study (Math 4990) course. I am honored to be mentoring the following students:
Gary Ruiz-Navarro is a fourth-year Cal State LA undergraduate interested in Probability and Combinatorics. We are currently reading Noga Alon and Joel Spencer's The Probabilistic Method and are focusing on Chapter 1-4. In addition to this directed reading, we are exploring some Ramsey type problems.
Israel Wilbur is a graduate student here at Cal State LA since Spring 2024 having joined through the LSAMP ”Bridge to Doctorate” program. His current research interest is in Combinatorics, but more specifically, Ramsey theory. Outside of math, he enjoys reading, going to the theatre, and playing basketball
Jonathan Davidson is a graduate student here at Cal State LA since Spring 2024. He is passionate about educational outreach and has represented CSULA Math department with the AVID Outreach Program and PCC Pi Day Conference. In his free time, he enjoys hiking and making math animations.
AMC Faculty Coordinator:
Together with Tuyetdong Phan-Yamada, I help organize the American Mathematics Competitions (AMC) at Cal State LA. We offer the AMC 8, AMC 10 and AMC 12, where the numerical value corresponds to the latest grade a student can be in while taking the corresponding exam. If you know someone interested in taking the exam, please feel free to email me (joneill2@calstatela.edu) or Tuyetdong Phan-Yamada (tuyetdong.phan-yamada3@calstatela.edu).
We also offer a DMAS contest for students in Grades 3 through 8 in the Spring. DMAS, which stands for Division, Multiplication, Addition and Subtract entails using these binary operations on integers in a three by three grid to come up with a "Magic" number. This game was invented by Tuyetdong Phan-Yamada and interested students may practice this game the following link.
More information on the exam and other mathematics extracurricular activities may be found at the Cal State LA Math Circle website.
Research Interests:
My research interests lie in extremal combinatorics. Broadly speaking, extremal combinatorics entails maximizing the size of a collection of objects given constraints on the collection of objects.
Papers and preprints:
- A note on intersection saturation (with Jacques Verstraete) - In preparation
- A few new oddtown and eventown problems (with Griffin Johnston) - Submitted, Preprint
- A short note on supersaturation for oddtown and eventown - Discrete Applied Mathematics, 334, 2023, Journal PDF
- Saturation problems in convex geometric hypergraphs (with Sam Spiro) - European Journal of Combinatorics, 110, 2023, Journal PDF
- Odd covers of graphs (with C. Buchanan, A. Clifton, E. Culver, J. Nie, P. Rombach, M. Yin) - Journal of Graph Theory, 2023, Journal PDF
- A note on k-wise oddtown problems (with Jacques Verstraete) - Graphs and Combinatorics, 38 (101), 2022, Journal PDF
- Extremal problems for pairs of triangles (with Zoltán Füredi, Dhruv Mubayi, Jacques Verstraete) - Journal of Combinatorial Theory Series B, 155, 2022, Journal PDF
- A generalization of Bollobás set pair inequality (with Jacques Verstraete) - The Electronic Journal of Combinatorics, 28(3), 2021, Journal PDF
- Nontrivial d-wise intersecting families (with Jacques Verstraete) - Journal of Combinatorial Theory Series A, 178, 2021, Journal PDF
- On the poset and asymptotics of Tesler matrices - The Electronic Journal of Combinatorics, 25(2), 2018, Journal PDF
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Exploration of Tesler Matrices -- Unpublished undergraduate research with Alejandro Morales, 2015, PDF