# Enrique Treviño

### Associate Professor of Mathematics

#### Areas of Specialization

Analytic Number Theory

Computational Number Theory

#### Education

PhD Dartmouth College 2011

Thesis: Numerically Explicit Estimates for Character Sums

Advisor: Carl Pomerance

MA Dartmouth College

BA University of Texas at El Paso

#### Selected Honors

Travel grant from the American Mathematical Society to attend the 1st Congress of the Americas held in Guanajuato in August 2013.

Swarthmore College Research Award (2011-2013)

GAANN Fellowship (2006-2007)

Top 200 in the 66th Putnam exam, Dec. 2005

#### Selected Courses Taught

MATH 499: Great Theorems in Mathematics (Senior Seminar)

MATH 491: Tutorial (Topology)

MATH 411: Real Analysis II

MATH 375: Combinatorics

MATH 340: Geometry

MATH 331: Modern Algebra II

MATH 330: Modern Algebra I

MATH 329: Number Theory

MATH 311: Real Analysis I

MATH 230: Abstract and Discrete Mathematics

MATH 214: Differential Equations

MATH 210: Multivariable Calculus

MATH 160: Math Methods and Applications

MATH 150: Introduction to Probability and Statistics

MATH 110: Calculus I

MATH 109: Calculus 1b

MATH 108: Calculus 1a

CS 112: Introduction to Programming

FIYS 169: Recreational Mathematics

MATH 53 (Swarthmore College): Analytic Number Theory

MATH 77 (Swarthmore College): Algebraic Number Theory

MATH 27 (Swarthmore College): Linear Algebra

MATH 25 (Swarthmore College): Calculus II

MATH 20 (Dartmouth College): Discrete Probability

#### Publications

#####
**Books**

**Cuban Mathematical Olympiads.** Written by Robert Bosch. Translated by Enrique Treviño. Published by XYZ Press (**2017**). ISBN: 978-0-9968745-4-0

#####
**Articles**

**16.** **A birthday in St. Petersburg**.

The College Mathematics Journal vol. 50, no. 1, pp. 36-40.

**15. An Inclusion-Exclusion Proof of Wilson’s Theorem**.

The College Mathematics Journal vol. 49 (**2018**), no. 5, pp. 367-368.

**14. Walking on rational numbers and a self-referential formula**

with M. Fortman*, K. Kupiec*, and M. Rawlings*. Elemente der Mathematik 73 (**2018**), no.4, 161-169.

**13. A short proof of a sum of powers formula**

American Mathematical Monthly 125 (**2018**), no. 7, 659-659.

**12. Finding the four squares in Lagrange’s Theorem** (with Paul Pollack). Integers 18A (**2018**), article A15, 16 pages (electronic).**
11. Counting Perfect Polynomials** (with U.C. Cengiz and P. Pollack). Finite Fields and Their Applications 47C (

**2017**) pp. 242-255 DOI information: 10.1016/j.ffa.2017.05.006.

**(with K. McGown and T. Trudgian) Functiones et Approximatio, Commentarii Mathematici 55.2 (**

**10. Resolving Grosswald’s conjecture on GRH****2016**), pp. 215-225.

**International Journal of Number Theory Vol. 11, No. 5 (**

**9. The Burgess inequality and the least k-th power non-residue****2015**), pp. 1-26.

**8.**The smoothed Pólya-Vinogradov inequality (with K. Adamczewski), Integers 15 (

**2015**), 11 pages (electronic).

**7.**The least k-th power non residue Journal of Number Theory 149 (

**2015**), pp. 201-224. DOI information: 10.1016/j.jnt.2014.10.019

**6.**

**(with P. Pollack), American Mathematical Monthly 121 (**

**The primes that Euclid forgot****2014**), no. 5, 433-437.

**5.**

**Sets of monotonicity for Euler’s totient function**(with P. Pollack and C. Pomerance), The Ramanujan Journal 30 (

**2013**), no. 3, 379-398.

**4.**

**On the maximum number of consecutive integers on which a character is constant**Moscow Journal of Combinatorics and Number Theory (

**2012)**, vol.2, iss. 1, pp. 56-72.

**Corrigendum**appeared in Moscow Journal of Combinatorics and Number Theory (

**2017**), vol.7, iss. 3.

**3. The least inert prime in a real quadratic field**, Mathematics of Computation, vol. 81, no. 279, July

**2012**, pp. 1777-1797.

**2. Multi-dimensional Frobenius problem**(with J. Amos, I. Pascu, V. Ponomarenko and Y. Zhang), Involve, a Journal of Mathematics 4-2 (

**2011**), 187—197.

**1. On the counting function for the generalized Niven numbers**(with R. Daileda, J. Jou, R. Lemke-Oliver and E. Rossolimo), J. Théor. Nombres Bordeaux 21 (

**2009**), no. 3, 503—515.

#### Articles Accepted for Publication

**1.** Probabilistic Proof that 1+2+…+n = n(n+1)/2.

To Appear in American Mathematical Monthly.

**2.** Expected number of dice rolls for the sum to reach n.

To Appear in American Mathematical Monthly.

#### Undergraduate Thesis Directed

The Fundamental Theorem of Algebra by William Braubach, Fall 2016.

Transcendental Numbers by Jacob Juillerat, Spring 2016.

#### Richter Projects Supervised

What’s so rational about the alphabet? by Kevin Kupiec and Marina Rawlings, Summer 2014 (3-week project).

Finding perfect polynomials mod 2 by Ugur Caner Cengiz, Summer 2014 (10-week project).

On Tupper’s Self-Referential Formula by Margaret Fortman, Summer 2015 (4-week project).

First-world solutions to First-year problems by Robert Mecham, Summer 2015 (10-week project).

Beatty Sequences and the Prime Race by Noel Orwothwun, Summer 2016 (4-week project).

#### Mathematical Olympiad

2000-2001, participated as a student. Won a gold medal at the Mexican Mathematical Olympiad in Nov. 2001.

2003-present, member of the Chihuahua Math Olympiad Committee. I have trained many students from the state of Chihuahua.

2015-present, member of the Mexican Math Olympiad Committee.

Deputy Leader of the Mexican team participating in the sixth European Girls Mathematical Olympiad in Zurich, Switzerland from April 6, to April 12 2017.

Leader of the Mexican team participating in the seventh European Girls Mathematical Olympiad in Florence, Italy from April 9 to 15 2018.

#### Contact

**Phone:** 847-735-6187

**Email:** trevino@lakeforest.edu

**Personal Website:** http://campus.lakeforest.edu/trevino