Teaching
Current
- Topology – Topology: Geometry without distance. Points, neighborhoods, and continuity.
- Homology – Selected Topics in Topology (Homology): Distinguishing spaces with linear algebra.
Previous semesters
Fall 2023
- ANA-I EN – Foundations of Analysis: Numbers, limits, and continuity.
- ANA-III EN – Functions of Many Variables: Multivariate analysis and metric topology
Spring 2023
- Topology – Topology: Geometry without distance. Points, neighborhoods, and continuity.
- Homology – Selected Topics in Topology (Homology): Distinguishing spaces with linear algebra.
Fall 2022
- ANA-I EN – Foundations of Analysis: Numbers, limits, and continuity.
- ANA-III EN – Functions of Many Variables: Multivariate analysis and metric topology
Spring 2022
- Topology – Topology: Geometry without distance. Points, neighborhoods, and continuity.
- Minicourse on Combinatorial Alexander Duality
Fall 2021
- ANA-I EN – Foundations of Analysis: Numbers, limits, and continuity.
- ANA-III EN – Functions of Many Variables: Multivariate analysis and metric topology
Spring 2021
- Topology – Topology: Geometry without distance. Points, neighborhoods, and continuity.
- Homology – Selected Topics in Topology (Homology): Distinguishing spaces with linear algebra.
Fall 2020
- ANA-I EN – Foundations of Analysis: Numbers, limits, and continuity.
- ANA-III EN – Functions of Many Variables: Multivariate analysis and metric topology
Spring 2020
- PhD course on Topological Combinatorics
Fall 2019
- ANA-I EN – Foundations of Analysis: Numbers, limits, and continuity.
- ANA-III EN – Functions of Many Variables: Multivariate analysis and metric topology
- DM-I EN – Set Theory: Logic, sets, and proofs.
Spring 2019
- MVAJ – Mathematical Topics in English I/II: Generating functions.
- Topology – Topology: Geometry without distance. Points, neighborhoods, and continuity.
- Homology – Selected Topics in Topology (Homology): Distinguishing spaces with linear algebra.
Fall 2018
- ANA-I EN – Foundations of Analysis: Numbers, limits, and continuity.
- DM-I EN – Set Theory: Logic, sets, and proofs.
Spring 2018
- MVAJ – Mathematical Topics in English I/II: Proofs from the book.
- Topology – Topology: Geometry without distance. Points, neighborhoods, and continuity.
Fall 2017
- ANA-I EN – Foundations of Analysis: Numbers, limits, and continuity.
- DM-I EN – Set Theory: Logic, sets, and proofs.
Old notes
Several handouts from courses I taught in my time at Washington University in St. Louis have gotten a lot of interest, and I've moved to hosting them here. I'm providing these as-is, and there may be typos or errors.
- Polynomial rings and unique factorization domains, including a brief introduction to the face ring of a simplicial complex (from Modern Algebra, Spring 2009)
- Zorn's Lemma and maximal ideals (from Modern Algebra, Spring 2009)
- Some notes on the symmetric group (from Modern Algebra, Spring 2009)
- Proof of the continuous Chebyshev inequality (from Probability, Fall 2010)
- The Central Limit Theorem for medians (from Mathematical Statistics, Spring 2011)
- Differentiating under the integral (with help from Kabe Moen, from Mathematical Statistics, Spring 2011)
- Two (similar) handouts on finding upper bounds using the triangle inequality, for lower-level courses. Applied to:
Historical
- Teaching pages from my time at Mississippi State University (Fall 2012 – Spring 2017).
(Dead link — archived on the Wayback Machine.) - Teaching pages from my time at Washington University at St. Louis (Fall 2008 – Spring 2012).
Awards
I won the Guido Weiss Teaching and Service Award while at Washington University in St. Louis, given by the math department each year for “excellence in the teaching of mathematics and in service to the department and students”. Here's a picture of Guido Weiss giving me the award. It's interesting to note that Guido was born in Trieste, about 15 minutes from where I now work in Koper.