Teaching

 

I have been in charge of several graduate and undergraduate courses in the Department of Mathematical Sciences of New Mexico State University. The syllabi of the courses I have taught are available below.

 

Graduate Courses

1.       Point-Free Topology, Fall 2011

2.       General Topology, Spring 2007.

3.       Lattice Theory, Spring 2011, Spring 2007, Spring 2006.

4.       Universal Algebra, Fall 2003.

5.       Modern Algebra II, Spring 2003.

6.       Modern Algebra I, Fall 2002.

7.       Foundations of Geometry, Spring 2002.

8.       Axiomatic Set Theory, Spring 2001.

9.       Mathematical Logic, Fall 2010, Fall 2008, Fall 2006, Fall 2004.

10.   Gödel’s Incompleteness Theorems, Fall 2009.

 

Undergraduate Courses

1.       Vector Spaces and Matrix Algebra, Spring 2010 (Distance Education Course), Spring 2009 (Distance Education Course), Spring 2005, Spring 2004.

2.       Introduction to Linear Algebra, Fall 2005.

3.       Introduction to Modern Algebra, Fall 2000.

4.       Introduction to Finite Mathematics, Fall 2011, Spring 2011, Fall 2006, Spring 2005, Spring 2001, Fall 2000.

5.       Discrete Mathematics for Computer Science, Fall 2009.

6.       Discrete Mathematics, Fall 2001.

7.       Ordinary Differential Equations, Spring 2010 (Distance Education Course), Spring 2006.

8.       Calculus and Analytic Geometry III, Fall 2003.

9.       Calculus and Analytic Geometry II, Fall 2010, Spring 2003, Fall 2002.

10.   Calculus and Analytic Geometry I, Fall 2005.

11.   Mathematics Appreciation, Spring 2004, Spring 2002, Fall 2001.

 

Summer Schools

I have also been involved in teaching at summer schools. The courses that I taught are available below.

1.       Lattices and Topologies, European Summer School in Logic, Language, and Information 2008 (ESSLLI 2008), 1115 August 2008, Hamburg, Germany (jointly with Mamuka Jibladze).

2.       Lattices and Topology, Third Vienna-Tbilisi Summer School in Logic and Language, 2728 September 2007, Tbilisi State University (jointly with Mamuka Jibladze).

 

Teaching with Original Historical Sources

With fellow faculty Jerry Lodder and David Pengelley of the Department of Mathematical Sciences of New Mexico State University, Hing Leung and Inna Pivkina of the Department of Computer Science of New Mexico State University, Janet Barnett of Colorado State University - Pueblo, and Desh Ranjan of Old Dominion University, I have been involved in developing curricular material for teaching discrete mathematics and computer science via original historical sources. Below are the historical projects that I have developed:

 

1.       Are All Infinities Created Equal?

2.       An Introduction to Elementary Set Theory

3.       An Introduction to Symbolic Logic

4.       Henkin's Method and the Completeness Theorem

5.       Peano Arithmetic

6.       Goedel’s Incompleteness Theorems

7.       Church's Thesis

8.       Undecidability of First-Order Logic

 

For more information consult our webpages Learning Discrete Mathematics and Computer Science via Primary Historical Sources and Teaching Discrete Mathematics via Primary Historical Sources.