Welcome to my homepage. I am a Professor (and Department Chair) in the Department of Mathematics and Statistics at California State University, Chico. My research is in Number Theory. In slightly more detail: My research is in algebraic, analytic, and computational number theory. Specific interests include Euclidean number fields, arithmetic statistics, character sums, and primitive roots. |
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Address Department of Mathematics and Statistics California State University, Chico Holt 181 400 West First Street Chico, California, 95929 |
Office Holt 341 kmcgown at csuchico dot edu |
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Documents: Click here to see a complete list of courses taught. Fall 2019 Math 235 (Linear Algebra) Math 330 (Methods of Proof) Math 465 (Complex Analysis) Spring 2020 Math 120 (Calculus I) Math 317 (Cryptography) Math 421 (Advanced Calculus II) |
Fall 2020
Math 260 (Differential Equations) Math 465 (Complex Analysis) Spring 2021 Math 120 (Calculus I) Math 420 (Advanced Calculus) Fall 2021 Math 217 (Discrete Math) Math 337 (Number Theory) Spring 2022 Math 317 (Cryptography) |
| If you are an undergraduate student interesting in working on research in number theory, please feel free to contact me. I am available to advise honor's theses or other research projects. If you have an interest in this, I would recommend taking Math 337, 420, and 449 as soon as possible. Working on a Master's degree in Computational Mathematics under my supervision (through the Interdisciplinary Studies program) is also possible. In order to be eligible for this, you will want to complete a B.S. in the General Math option and at least a minor in Computer Science. |
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And some papers in in preparation...
(with Amanda Tucker) An Improved error term for counting D4-quartic fields. (arxiv) (with Meher Lippmann) The Counting function for Elkies primes. (arxiv) (with Jon Sorenson) Computation of the least primitive root. (arxiv) (with Kyle Hammer and Skip Moses) Euclidean rings of S-integers in complex quadratic fields. American Mathematical Monthly. Accepted. (arxiv) (with Amanda Tucker and Frank Thorne) Counting quintic fields with genus number one. Mathematical Research Letters, Vol. 30, No. 2 (2023), pp. 577--588. (arxiv, article) (with Daniel Vallieres) On abelian l-towers of multigraphs III. Annales mathematiques du Quebec. Accepted. (arxiv) (with Amanda Tucker) Statistics of genus numbers of cubic fields. Ann. Inst. Fourier (Grenoble) Vol. 73 (2023), no.4, 1365--1383. (article, arxiv) (with Daniel Vallieres) On abelian l-towers of multigraphs II. Annales mathematiques du Quebec. Accepted. (arxiv) (with Enrique Treviño) The least quadratic non-residue. Mexican mathematicians in the world -- trends and recent contributions, 205--231, Contemp. Math., 775, Amer. Math. Soc., 2021. (preprint) (With Jongwoo Choi) Counting Eisenstein polynomials satisfying a condition from genus theory. Integers 20 (2020), Paper No. A58, 6 pp. (article) (with Bryce Kerr and Tim Trudgian) The least primitive root modulo p^2. J. Number Theory 215 (2020), 20--27. (article) (with Tim Truegian) Explicit upper bounds on the least primitive root. Proc. Amer. Math. Soc. 148 (2020), no. 3, 1049--1061. (arxiv) (With Ma, Shilin; McGown, Kevin; Rhodes, Devon; Wanner, Mathias) Explicit bounds for small prime nonresidues. J. Number Theory 204 (2019), 599--607. (arxiv) (with Jonathan Sands and Daniel Vallieres) Numerical evidence for higher order Stark-type conjectures. Math. Comp. 88 (2019), no. 315, 389--420. (arxiv) (with Shilin Ma, Devon Rhodes, and Mathias Wanner) On the number of primes for which a polynomial is Eisenstein. Integers 18B (2018), Paper No. A101. (with Pierre Lezowski) The Euclidean algorithm in quintic and septic cyclic fields. Math. Comp. 86 (2017), no. 307, 2535--2549. (arxiv) (with Enrique Treviño and Tim Trudgian) Resolving Grosswald's conjecture on GRH. Funct. Approx. Comment. Math. 55 (2016), no. 2, 215--225. (arxiv, code) On the S-Euclidean minimum of an ideal class. Acta Arith. 171 (2015), no. 2, 125--144. (preprint) On the second smallest prime non-residue. J. Number Theory 133 (2013), 1289--1299. (preprint) Norm-Euclidean Galois fields and the Generalized Riemann Hypothesis. J. Theor. Nombres Bordeaux 24 (2012), no. 2, 425--445. (preprint) Norm-Euclidean cyclic fields of prime degree. Int. J. Number Theory 8 (2012), no. 1, 227--254. (preprint) On the constant in Burgess' bound for the number of consecutive residues or non-residues. Funct. Approx. Comment. Math. 46 (2012), no. 2, 273--284. (preprint) (with J. William Helton and M. L. Walker) Conditions for stabilization of the tokamak plasma vertical instability using only a massless plasma analysis. Automatica, 46 (2010), no. 11, 1762--1772. (article) (with Harold R. Parks) An elementary proof of a generalization of Bernoulli's formula. Elem. Math. 65 (2010), no. 2, 68--77. (preprint, article) (with J. William Helton and M. L. Walker) Conditions for a massless plasma analysis to predict stabilization of the tokamak plasma vertical instability. IEEE 47th Annual Conference on Decision and Control (2008), 3761--3768. (with Harold R. Parks) The generalization of Faulhaber's formula to sums of non-integral powers. J. Math. Anal. Appl. 330 (2007), no. 1, 571--575. (with Paul Cull and Ananda Leininger) Knight's tour on boards with holes is NP-complete. Bull. Inst. Combin. Appl. 45 (2005), 33--40. |