Mathematics and Computer Science

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/CS 323: Cryptography
MATH 311: Real Analysis I
Math 231: Linear Algebra
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

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

Books

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

Articles

31. Introducción a la Teoría de Números Probabílistica. Published in Tzaloa (2023) no. 3, pp. 1-15.
30. Many proofs that 1+2+... = n(n+1)/2 with Tom Edgar. Published in Ganit Bikash (translates to Mathematics Development) an Assamese journal, Vol. 75 (2022), pp. 38-61. The version in English is here. 
29. Generalizing Parking Functions with Randomness with M. Tian*. Electronic Journal of Combinatorics Vol. 29 (2022), no. 3, P3. 13, 13 pages (electronic).
28. On the sum of k-th powers in terms of earlier sums with S. J. Miller. The College Mathematics Journal, Vol. 53 (2022), no. 3, pp. 220-225.
27. The least quadratic non-residue with K. McGown. Mexican Mathematicians in the World: Trends and recent contributions published by Contemporary Mathematics of the AMS (2021), pp. 205-232. 
26. On a sequence related to the factoradic representation of an integer with M. Sánchez Garza*. Journal of Integer Sequences, Vol. 24 (2021), Article 21.8.5, 13 pages (electronic).
25. On sets whose subsets have integer mean. Integers 21 (2021), article A79, 11 pages (electronic).
24. On Egyptian fractions of length 3 with C. Banderier, C. A. Gómez Ruiz, F. Luca, and F. Pappalardi. Revista de la Unión Matemática Argentina, Vol. 62 (2021), no. 1, pp. 257-274.
23. An unusual recursive formula to answer a question regarding fixed points in permutations with M. Tian*. The College Mathematics Journal vol. 52 (2021), no. 3, pp. 219-220.
22. A writing-intensive FYS course on Recreational Mathematics. Published as Chapter 30 in book "Mathematical themes in a first-year seminar" published by MAA Press (2021), pp. 301-306.
21.  Sums of proper powers with Paul Pollack. The American Mathematical Monthly vol. 128 (2021), no.1, p. 40.
20.  On sums of consecutive triangular numbers (with P. Pollack and D. Subramaniam*). Integers 20A ( 2020), article A15, 10 pages (electronic).
19. Expected number of dice rolls for the sum to reach n.
American Mathematical Monthly vol. 127 ( 2020), no. 3, p. 257.
18. On generalizing happy numbers to fractional base number systems (with M. Zhylinski*).
Involve vol. 12 ( 2019), no. 7, pp. 1143-1151.
17. Probabilistic Proof that 1+2+…+n = n(n+1)/2.
American Mathematical Monthly vol. 126 ( 2019), no. 9, p. 840.
16. A birthday in St. Petersburg.
The College Mathematics Journal vol. 50 ( 2019), 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.
10. Resolving Grosswald’s conjecture on GRH (with K. McGown and T. Trudgian) Functiones et Approximatio, Commentarii Mathematici 55.2 ( 2016), pp. 215-225.
9. The Burgess inequality and the least k-th power non-residue International Journal of Number Theory Vol. 11, No. 5 ( 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. The primes that Euclid forgot (with P. Pollack), American Mathematical Monthly 121 ( 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.

The probabilistic method by Melanie Tian, Lake Forest College, Fall 2021.
The Fundamental Theorem of Algebra by William Braubach, Lake Forest College, Fall 2016.
Transcendental Numbers by Jacob Juillerat, Lake Forest College, Spring 2016.
Saltos pequeños entre primos by Juan Ramón Camacho Cordero, Universidad de Guanajuato, 2012.

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).

Playing with Triangular Numbers by Dipika Subramaniam, Summer 2018 (4-week project).

Solving Stable Matching Problems With the Gale-Shapley Algorithm by Christian Reyes, Summer 2019 (4-week project).

The Mathematics of Consociational Democracy by Arthur J. Brown, Summer 2019 (4-week project).

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 teams participating in the sixth European Girls Mathematical Olympiad in Zurich, Switzerland from April 6, to April 12 2017, and in the eight European Girls Mathematical Olympiad in Kiev, Ukraine from April 7 to April 13, 2019.

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

Leader of the Mexican team participating in the Ibero American Mathematical Olympiad hosted in Guanajuato, Mexico from September 11 to September 19 2019.

Leader of the Mexican team participating in the Cyberspace Mathematical Competition from July 12 to July 21 2020.

Leader of the Mexican team at the International Mathematical Olympiad in Norway, July 2022.

Leader of the Mexican team at the Ibero Math Olympiad in Brazil, September, 2023.

Co-editor in chief of the United States Mathematical Olympiad, 2022-Present.

http://campus.lakeforest.edu/trevino/