(You may want to see also my Students page.)

Masters students:

- Daniel Donado.
*Metric spaces on under determinacy*– co-advised with Ramiro de la Vega. In Spanish. June 2010. - Tommy Chartier.
*Coloring problems*. December 2011. - Summer Kisner.
*Schur’s theorem and related topics in Ramsey theory*. May 2013. - Shehzad Ahmed.
*-determinacy and sharps*. May 2014*.* - Monica Agana.
*The classical theory of rearrangements*. December 2015.

Although my input was minimal, I supervised some undergraduate research in Spring 2015 by Ian Cavey. This resulted in a short note on *Volumes of sphere-bounded regions in high dimensions*. Ian gave a talk on these results at the MAA centenary meeting. His slides are here.

I directed an internship in Fall 2012-Spring 2013 for Luke Velloti.

I served as mentor in the McNair Scholars Program in 2009 for Shawn E. Davis, resulting on the paper *Representing Propositional Logic Connec**tives with Modular Polynomials*, published in the *Boise State McNair Scholars Research Journal*, Vol. 6 (2010), 1-12.

While at Caltech, I mentored Will Sladek in 2007 on the *Mathematical Writing* course, resulting in the nice paper *The termite and the tower*.

I have taught the following courses:

**Boise State University**, 2008-2015

(Material from these courses can be accessed through the list of categories on the right.)

- 311-Foundations of geometry. Spring 2015.
- 403-Advanced linear algebra. Spring 2015.
- 287-Communication in the mathematical sciences. Fall 2014.
- 414/514-Analysis I. Fall 2014.
- 314-Foundations of analysis. Spring 2014.
- 403-Advanced linear algebra. Spring 2014.
- 170-Calculus I. Honors. Fall 2013. (Syllabus)
- 414/514-Analysis I. Fall 2013.
- 170-Calculus I. Honors. Spring 2013.
- 403-Advanced linear algebra. Spring 2013.
- 580-Topics in set theory. Fall 2012.
- 197-Introduction to mathematical thought. Honors. Fall 2012.
- 515-Analysis II. Spring 2012.
- 305-Abstract algebra I. Spring 2012.
- 414/514-Advanced calculus (Analysis I). Fall 2011.
- 187-Discrete and foundational mathematics I. Fall 2011. (Syllabus)
- 403/503-Advanced linear algebra. Spring 2011.
- 175-Calculus II. Spring 2011. (Syllabus)
- 507-Advanced number theory. Fall 2010. (Errata for the book)
- 170-Calculus I. Fall 2010. (Syllabus)
- 187-Discrete and foundational mathematics I. Spring 2010. (Syllabus)
- 403/503-Advanced linear algebra. Spring 2010.
- 175-Calculus II. Fall 2009. (Syllabus)
- 502-Logic and Set Theory. Fall 2009.
- 598-Graduate student seminar. Fall 2009.
- 305-Abstract Algebra. Spring 2009.
- 580-Topics in Set Theory. Spring 2009.
- 175-Calculus II. Fall 2008.
- 275-Calculus III. Fall 2008.

I have also directed some (undergraduate and graduate) independent studies:

- Forcing axioms. Spring 2009. (Nathan Bailey)
- Topics in Ramsey theory (regressive functions). Fall 2009. (Thomas Chartier)
- Colorings of the plane. Fall 2010, Spring 2011. (Thomas Chartier)
- Pell’s equation. Fall 2011. (Summer Kisner)
- Schur’s theorem in Ramsey theory. Spring 2012. (Summer Kisner)
- Complex analysis. Fall 2012. (Shehzad Ahmed)
- Automorphism groups of complex domains in the plane. Fall 2012. (Erron Kearns)
- Determinacy. Spring 2013. (Shehzad Ahmed)
- Descriptive set theory. Fall 2013. (Shehzad Ahmed)
- Algebraic graph theory. Spring 2014. (Kyle Beserra)
- Functional analysis. Spring 2014. (Shehzad Ahmed)
- Rearrangements of series and descriptive set theory. Fall 2014. (Monica Agana)
- The density topology on the real line, and variants. Fall 2014. (Stuart Nygard)
- A topological variant of the partition calculus on ordinals. Fall 2014. (Rustyn J. Yazdanpour)

**California Institute of Technology**, 2005-2008

- Mathematical Logic (4 terms). The pages for the courses on
*the incompleteness theorems*and*introduction to set theory*can be found by looking at the entries under the categories**116b**and**116c**, respectively. - Introduction to Discrete Mathematics.
- Topics in Set Theory.
- Computability Theory (2 terms): Undecidability (look at the entries under the category
**117b**) and Decidability. - Topics in Ramsey Theory.

**University of California, Berkeley, Mathematics Department,** 1997-2003

*Instructor:*

- Calculus and Analytic Geometry (life and social sciences sequence).
- Integral Calculus (natural science sequence).
- Linear Algebra and Differential Equations.
- Complex Analysis.
- Numerical Analysis.

*Teaching Assistant:*

- Integral, differential, and Multivariable Calculus (natural science sequence).
- Calculus and Analytic Geometry (life and social sciences sequence).
- Linear Algebra and Differential Equations.

*Grader:*

- Set Theory (undergraduate).
- Differential equations (graduate).

**Universidad de los Andes, Departamento de Matemáticas**, 1993-1997

*Instructor:*

- Analytic Geometry.
- Integral Calculus.
- Logic.

*Teaching assistant:*

- Pre-calculus.
- Differential Calculus.
- Differential Equations.

I also served as* trainer* of the **Colombian Mathematical Olympiads** Team, 1993-1994.