Interests


My current areas of work include analytic number theory, integer partitions, and q-series. I plan to defend my PhD thesis in April 2024.

Prior to an abrupt change of research area in Fall 2021 due to personal reasons, I had lengthy study in hyperbolic (Laplacian-) spectral geometry. In addition, I have previously been interested in mathematical physics, topology, and cryptography.

Publications


T. Daniels, Legendre-signed partition numbers, to be submitted for publication; Feb. 2024 preprint: arXiv; 40 pp.

T. Daniels, Vanishing coefficients in two q-series related to Legendre-signed partitions, to be submitted for publication; Jan. 2024 preprint: arXiv; 10 pp.
[A Mathematica notebook documenting and implementing the computations in this paper is publicly avaiable here.]

T. Daniels, Biasymptotics of the Möbius- and Liouville-signed partition numbers, submitted for publication; Oct. 2023 preprint: arXiv; 38 pp.

T. Daniels, Bounds on the Möbius-signed partition numbers, submitted for review; Oct. 2023 preprint: arXiv; 35 pp.

T. Daniels, D. Smith-Tone, Differential Properties of the HFE Cryptosystem,, Post-Quantum Cryptography – 6th Intl. Workshop, PQCrypto 2014, Univ. of Waterloo, Waterloo ON, Canada; Sept. 2014

Teaching


I've been teaching and grading math for about 10 years now, and in Summer 2015 I was an instructor in a Mandarin Chinese language-learning program for middle school students. For my work as a grader/TA in Fall 2020, I was awarded one of the Math Dept.'s Excellence in Teaching Award.

In particular, I have instructed courses in Applied Calculus I and II, recitatitions in Calculus I--III, real analysis, and complex analysis, and I have graded for a number of courses, including: real analysis, complex analysis, Galois theory, measure theory, PDEs, and linear algebra.