What I've taught
Summer, 2009
- Symmetry groups,
an undergraduate research project by Brian Waligorski.
Spring, 2009
- MATH 222-001 Calculus II Honors,
MTh 11:20am-12:35pm, W 11:20am-12:20pm,
room TBA.
We will use
WeBWorK
for some of our homework.
- MATH 513-001 Rings 'n' Fields, TTh 6:45-8:00pm,
room TBA, but it's probably Gray 104.
We continue with our study of what's going on behind the scenes of everything,
concluding with the solutions to some problems that stood open for centuries.
- MATH 590-002 P-adic Analysis, time TBA.
This is an independent-study course for Erik Borke.
Fall, 2008
- MATH 221-002 Calculus I Honors,
TF 11:20am-12:35pm, W 11:20am-12:20pm,
Ward 205.
We used
WeBWorK
for some of our homework.
- MATH 512-001 Modern Algebra, TTh 6:45-8:00pm,
Gray 104.
This is the study of what's going on behind the scenes of everything,
almost.
Summer, 2008
- Factorization methods,
an undergraduate research project by Hamman Samuel.
We work remotely, as he is at the
American University of Nigeria.
- Limits of groups, and infinite Galois theory,
an undergraduate research project by Erik Borke.
Spring, 2008
- Calculus II. MTh 12:45-2:00pm, W 12:45-1:45pm.
We tried out
WeBWorK.
- Linear Algebra. MTh 2:10-3:25pm.
Fall, 2007
- Calculus I. MTh 9:55-11:10am, W 9:55-10:55am.
- Linear Algebra. MTh 2:10-3:25pm.
Except when otherwise specified, I taught the courses listed
below this line at the University of Akron.
Summer, 2007
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.
-
Master's thesis research with Niklos Holik:
Nonstandard hulls of groups.
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
Spring, 2006
-
Linear
Algebra (MAT223S)
at the University of Toronto.
-
Master's thesis research with Mike Garlow, co-advised by Ethel Wheland:
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.
Together with Dr. Price, I supervised a project on
Generalized Fibonacci-Lucas pairs.
Together with Dr. Levin (in the history department), I supervised
a project on
Reading encrypted diplomatic correspondence.
The results of this latter project have now been published.
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
Spring, 2002
Fall, 2001
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
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)
Except when otherwise specified, I taught the courses listed
below this line at the University of Chicago.
Winter, 1994
- Math 111: Studies in Mathematics 2.
Spring, 1994
- Math 110: Studies in Mathematics.
Fall, 1993
- Math 110: Studies in Mathematics.
Spring, 1992
- Math 110: Studies in Mathematics.
Fall, 1991
- Math 111: Studies in Mathematics 2.
Spring, 1991
- Math 110: Studies in Mathematics.
Fall, 1990
- Math 111: Studies in Mathematics 2.
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