professor . san francisco state university
profesor adjunto . universidad de los andes . colombia
. research . teaching . society . outreach . cv . interviews . other .
MATH 850: Representation theory of algebras.
MATH 350: Geometry.
In 2007-2013 I taught classes jointly at SFSU and Los Andes, and posted the lecture videos, lecture notes, homework, and other resources for anyone to use freely. For more information, please visit the SFSU-Colombia Combinatorics Initiative.
Matroids: website . youtube . index
Polytopes: website . youtube . index
Coxeter groups: website . youtube . index
Hopf algebras and combinatorics: website . youtube . index (courtesy of Sara Billey)
Combinatorial commutative algebra: website . youtube . index
Enumerative combinatorics: website . youtube . no index yet
I am certainly not a proponent of online teaching as a substitute for in-person teaching. These courses filled a need at the time, when there was no one offering courses on these topics in Colombia. Other groups and people have told me they have found them useful, so I have been happy to keep these resources online.
I designed these courses with a low floor, high ceiling approach. I tried to make them as accessible and deep as I could, to serve a variety of students meaningfully. For most of them, the prerequisites were familiarity with proofs and linear algebra. (The courses on Coxeter Groups, Hopf Algebras, and Combinatorial Commutative Algebra assumed knowledge of groups, rings, and fields.)
A few previous topics courses:
Combinatorics. (sfsu, spring 2017)
Representation theory of groups. (sfsu, spring 2016)
Algebraic combinatorics. (sfsu, fall 2014)
Combinatoria algebraica. (los andes, spring 2003)