In the past 20 years I have taught a variety of graduate and undergraduate courses at New Mexico State University. The syllabi of the courses I have taught are available below.
- Point-Free Topology, Fall 2011
- General Topology, Spring 2017, Spring 2007.
- Lattice Theory, Spring 2011, Spring 2007, Spring 2006.
- Mathematical Structures in Logic, Spring 2020, Spring 2018.
- Universal Algebra, Fall 2016, Fall 2012, Fall 2003.
- Modern Algebra II, Spring 2003.
- Modern Algebra I, Fall 2002.
- Topics in Algebra, Spring 2012.
- Foundations of Geometry, Spring 2002.
- Axiomatic Set Theory, Spring 2016, Spring 2001.
- Mathematical Logic, Fall 2015, Fall 2013, Fall 2010, Fall 2008, Fall 2006, Fall 2004.
- Gödel’s Incompleteness Theorems, Fall 2009.
- Vector Spaces and Matrix Algebra, Spring 2010 (Distance Education Course), Spring 2009 (Distance Education Course), Spring 2005, Spring 2004.
- Introduction to Linear Algebra, Spring 2013, Fall 2005.
- Introduction to Modern Algebra, Spring 2014, Fall 2000.
- Introduction to Higher Mathematics, Fall 2018, Spring 2014, Fall 2011, Spring 2011, Fall 2006, Spring 2005, Spring 2001, Fall 2000.
- Discrete Mathematics for Computer Science, Fall 2009.
- Discrete Mathematics, Fall 2001.
- Ordinary Differential Equations, Spring 2013, Spring 2010 (Distance Education Course), Spring 2006.
- Calculus and Analytic Geometry III, Fall 2003.
- Calculus and Analytic Geometry II Honors, Spring 2020, Spring 2018, Spring 2017, Spring 2016.
- Calculus and Analytic Geometry II, Spring 2019 Section 1, Spring 2019 Section 2, Fall 2018, Fall 2016, Fall 2013, Fall 2012, Fall 2010, Spring 2003, Fall 2002.
- Calculus and Analytic Geometry I, Fall 2019 Section 2, Fall 2019 Section 5, Fall 2015, Spring 2012, Fall 2005.
- Mathematics Appreciation, Spring 2004, Spring 2002, Fall 2001.
In 1999 I also taught the following graduate courses at Tbilisi State University, Tbilisi, Georgia.
- Logic and Set Theory: Fall 1999.
- Lattice Theory and Categorical Logic: Spring 1999.
I have taught at BLAST, ESSLLI, TACL, and the Tbilisi-Vienna summer schools.
- A Non-Pointfree Approach to Pointfree Topology, BLAST 2019, May 20-24, 2019, Boulder, Colorado. Lecture 1, Lecture 2, Lecture 3.
- A Semantic Hierarchy for Intuitionistic Logic, Thirteenth International Tbilisi Summer School in Logic and Language, September 25-29, 2017, Tbilisi, Georgia. Lecture 1, Lecture 2.
- Frames, Topologies, and Duality Theory, TACL 2015, June 15-19, 2015, Salerno, Italy. Lecture 1, Lecture 2, Lecture 3, Lecture 4.
- Lattices and Topologies, ESSLLI 2008, 11–15 August 2008, Hamburg, Germany (jointly with Mamuka Jibladze).
- Lattices and Topology, Third International Tbilisi Summer School in Logic and Language, 27–28 September 2007, Tbilisi State University (jointly with Mamuka Jibladze).
I have developed several teaching modules in logic and discrete mathematics based on original historical sources:
- Are All Infinities Created Equal?
- An Introduction to Elementary Set Theory (with Eachan Landreth)
- An Introduction to Symbolic Logic (with Wes Fussner)
- Henkin’s Method and the Completeness Theorem
- Peano Arithmetic
- Goedel’s Incompleteness Theorems
- Church’s Thesis
- Undecidability of First-Order Logic (with Larry Moss)
More information about teaching discrete mathematics and computer science via original historical sources can be found at Learning Discrete Mathematics and Computer Science via Primary Historical Sources and Teaching Discrete Mathematics via Primary Historical Sources.