Past teaching

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

Masters students:

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 Connectives 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


  • 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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