Previous courses

(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 \omega_1 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


  • 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.


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

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


  • 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.

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