What I've taught

Spring, 2007

• 3450:307 Fundamentals of Advanced Mathematics. We studied logic, sets, relations, functions, limits, etc., all with an eye for learning how to do proofs... and seeing why proofs matter.

Fall, 2006

• 3450:411/511 Abstract Algebra I. We studied what's been going on behind the scenes.
• 3450:611 Topics in Algebra. We studied group actions, modules, and canonical forms.

Summer, 2006

• Research Experiences for Undergraduates, a program sponsored by the National Science Foundation.

Spring, 2006

• Linear Algebra (MAT223S) at the University of Toronto.
• Master's thesis research: An elementary classification of the groups of order 81. We later generalized this to handle the groups of order p⁴ for p an odd prime.

Summer, 2005

• Research Experiences for Undergraduates, a program sponsored by the National Science Foundation.

Spring, 2005

• 3450:412/512 Abstract Algebra II. We continued with the study of groups, rings, and fields. Our aim was to solve some of the great mathematical problems of antiquity. You can read the course rules and course plan (which lists most of the homework assignments).

Fall, 2004

• 3450:135 Excursions in Mathematics. (This course was previously called Mathematics for Liberal Arts.) Need to take a math course? This one is different from any that you have ever taken before. Check out the course materials to see if it is right for you. (The textbook also has a web page of its own.)
• 3450:411/511 Abstract Algebra I. We will study what's been going on behind the scenes.

Spring, 2004

• 3450:135 Mathematics for Liberal Arts. This course has since been renamed: Excursions in Mathematics.
• 3450:412/512 Abstract Algebra II. We continued with the study of groups, rings, and fields. Our aim was to solve some of the great mathematical problems of antiquity. You can read the course rules, and a draft of the course plan (which lists most of the homework assignments).
• Graduate Seminar. This was team-taught with Dr. Riedl. He introduced his recent work on ascending central series of p-groups, and then made you do some computations of your own. Then I covered the basic theory of modules, which simultaneously generalizes several theories that you have already seen. You then applied the theory to one of the following: representation theory, linear algebra, the classification of finitely-generated abelian groups, or "abstract nonsense" (a technical term that I did not make up).

Fall, 2003

• 3450:411/511 Abstract Algebra I

Spring, 2003

• 3450:135-002 Mathematics for Liberal Arts (MWF 1:10-2:00). (The textbook has a web page.)
• 3450:489/589-003 Algebraic Number Theory (MW 2:15-3:30).
• 3450:692 Seminar in Mathematics: Small Finite Groups
• 3450:692 Seminar in Mathematics: Abstract Algebra
• 3450:697 Individual Reading

Fall, 2002

• 3450:135-002 Mathematics for Liberal Arts (MWF 1:10-2:00).
• 3450:149-007 Precalculus (MTWF 2:15-3:05).

Spring, 2002

• 3450:135-002 Mathematics for Liberal Arts (MWF 12:05-12:55).
• 3450:221 Analytic Geometry-Calculus I (MTWF 8:50-9:45).
• 3450:692 Seminar in Mathematics: p-adic numbers
• 3450:697 Individual Reading

Fall, 2001

• 3450:135-002 Mathematics for Liberal Arts (MWF 9:55-10:45).
• 3450:611-001 Topics in Algebra (MWF 11:00-11:50).

Spring, 2001

• 3450:135-002 Mathematics for Liberal Arts (MWF 12:05-12:55).
• 3450:208-080 Introduction to Discrete Mathematics (MW 6:05-7:45).
• 3450:498 Senior Honors Project: Applications of Algebraic Topology

Fall, 2000

• 3450:135-001 Math for Liberal Arts (MWF 12:05-12:55).
• 3460:418/518-080 Discrete Structures (MW 6:40-7:55).
• 3450:489-002 Topics in Mathematics: Algebraic Topology

Spring, 2000

• 3450:135-002 Math for Liberal Arts (MWF 12:05-12:55).
• 3450:210-002 Calculus with Business Applications (MWF 11:00-11:50).

Fall, 1999

• 3450:135-080 Math for Liberal Arts (MW 5:10-6:25pm).
• 3450:513-080 Theory of Numbers (MW 6:40-7:55pm)

Spring, 1999

• 3450:489/589 Seminar on Chaos and Fractals
• 3450:149 Precalculus
• 3450:208 Discrete Mathematics

Fall, 1998

• 3450:149 Precalculus
• 3450:208 Discrete Mathematics

Spring, 1998

• MAT447S: Galois Theory (at the University of Toronto)
• MAT335S: Chaos, Fractals, and Dynamics (at the University of Toronto)

Spring, 1997

• MAT335S: Chaos, Fractals, and Dynamics (at the University of Toronto)

Winter, 1994

• Math 111: Studies in Mathematics 2 (at the University of Chicago)

Spring, 1994

• Math 110: Studies in Mathematics (at the University of Chicago)

Fall, 1993

• Math 110: Studies in Mathematics (at the University of Chicago)

Spring, 1992

• Math 110: Studies in Mathematics (at the University of Chicago)

Fall, 1991

• Math 111: Studies in Mathematics 2 (at the University of Chicago)

Spring, 1991

• Math 110: Studies in Mathematics (at the University of Chicago)

Fall, 1990

• Math 111: Studies in Mathematics 2 (at the University of Chicago)