# Enrique Treviño

### Assistant 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 340: Geometry

MATH 330: Modern Algebra 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

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

#####
**Articles**

** Resolving Grosswald’s conjecture on GRH** (with K. McGown and T. Trudgian) Functiones et Approximatio, Commentarii Mathematici 55.2 (2016), pp. 215-225.

**International Journal of Number Theory Vol. 11, No. 5 (2015), pp. 1-26.**

The Burgess inequality and the least k-th power non-residueThe Burgess inequality and the least k-th power non-residue

**(with K. Adamczewski), Integers 15 (2015), 11 pages (electronic).**

**The smoothed Pólya-Vinogradov inequality****Journal of Number Theory 149 (2015), pp. 201-224. DOI information: 10.1016/j.jnt.2014.10.019**

**The least k-th power non residue****(with P. Pollack), American Mathematical Monthly 121 (2014), no. 5, 433-437.**

**The primes that Euclid forgot****Sets of monotonicity for Euler’s totient function**(with P. Pollack and C. Pomerance), The Ramanujan Journal 30 (2013), no. 3, 379-398.

**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.

**The least inert prime in a real quadratic field**, Mathematics of Computation, vol. 81, no. 279, July 2012, pp. 1777-1797.

**Multi-dimensional Frobenius problem**(with J. Amos, I. Pascu, V. Ponomarenko and Y. Zhang), Involve, a Journal of Mathematics 4-2 (2011), 187—197.

**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.

#### 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.

#### Contact

**Phone:** 847-735-6187

**Email:** trevino@lakeforest.edu

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