(For additional information on projects by former students, see my Students page.)

I have taught the following courses in the past:

**Boise State University**, 2008-present

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

- 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 Hansen)

And I served as mentor in the McNair Scholars Program in 2009 for Shawn E. Davis.

Masters students:

- Daniel Donado.
*Metric spaces on under determinacy*-In Spanish. June 2010. - Tommy Chartier.
*Coloring problems*. December 2011. - Summer Hansen.
*Schur’s theorem*. Expected: June 2013.

**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.

I also mentored Will Sladek in 2007 on the *Mathematical Writing* course.

**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.