Tuan Pham
Graduate Student
Contact Information
- Department of Mathematics, Statistics, and Computer Science
- University of Illinois at Chicago
- Office: 632 SEO
- Phone: (312) 996-8745
- Email: anhtuan AT math DOT uic DOT edu
FALL 2009 Teaching Schedule
- MATH 180 09:00am - 09:50am TR 321 TH
- MATH 180 10:00am - 10:50am TR 312 TH
All information for these classes can be found at MATH 180 Info
Research
Resume
I do not have a specific research area yet. In general, I am interested in
- Algebra (algebraic geometry, commutative algebra, group theory)
- Algebraic Topology (its connection with algebra)
- Theoretical Computer Science (graph theory, coding theory and cryptography).
I did my undergraduate thesis on the structure of idempotents
in a finite dimensional algebra over an arbitrary field. In a finite dimensional commutative algebra,
the set of idempotents is finite and forms a distributive lattice. In this lattice, the set of minimal
idempotents are linearly independent and all idempotents can be obtained by summing up a subset of the set
of minimal idempotents. This gives an interesting one-to-one correspondence between the minimal idempotents
in the sub-algebra generated by an element and the irreducible factors of its minimum polynomial. This gives
a construction of minimum polynomial from minimal idempotents and a method to compute minimal idempotents given
the minimum polynomial. This also leads to the proof of the cyclicality of commutative finite dimensional
algebra with no nilpotents over algebraically closed fields.
Personal
- Other interests: badminton, skiing, rock climbing, swimming, weight lifting, and the game of Go.
- More about me, see my blog
- A glimpse of Viet Nam, the beautiful country where I'm from, Bonjour Vietnam
A Few of My Favorite Things (on YouTube)
- Monty Python
- Some Funny Science Songs
Miscellaneous Stuff