Master's and senior theses advised by Tim Hsu

I'm interested in advising master's theses of SJSU mathematics graduate students in the areas of algebra, combinatorics, or more generally, in most any area of discrete mathematics. I'm also happy to advise master's theses in other areas; my other interests include geometry and topology, various quantum topics, and mathematics related to computation (e.g., see Amy Vu's thesis from 2001-2002). I even occasionally think about functional analysis, if absolutely necessary (e.g., see the theses of Sejal Dharia and Mitra Bandari).

For more about my research, check out this list of publications. Again, students working with me are certainly not limited to topics I've worked on; in fact, I've had some past success advising theses where I initially knew almost nothing about the topic and learned it along with my advisee.

If you'd like to talk to me about your master's thesis, please e-mail me at, and we can set up an appointment. (Or just drop by my office hours; check my weekly schedule for times.)

Below is a list of all of the master's theses and senior theses I've advised. Most of the theses below have been expository (i.e., descriptions of someone else's work), with a few cases of original work as noted.

Master's theses at San Jose State


Student: Peter Hansen
Title: Construction and simplicity of the large Mathieu groups


Student: Sejal Dharia
Title: Modules over non-commutative rings

Student: Nina Vazquez
Title: Elliptic curve cryptography


Student: Mitra Bandari
Title: The Hilbert-Schmidt Theorem
Brief description: This thesis gives an exposition of the proof of the Hilbert-Schmidt theorem, which states: If A:H -> H is a compact self-adjoint operator on a Hilbert space H, then there exists an orthonormal basis for H consisting of eigenvectors of A whose eigenvalues approach 0. (In particular, any nonzero eignvalue has finite multiplicity.)

Student: Parvaneh Darafshi
Title: Fermat's factoring algorithm and the Lanczos algorithm
Brief description: The Quadratic Sieve algorithm is an algorithm for factoring large numbers, based on an idea of Fermat. As part of Quadratic Sieve, it is necessary to solve very large sparse systems of linear equations over finite fields. This thesis describes the Generalized Lanczos Algorithm, due to Coppersmith, Odlyzko, and Schroeppel, which is an iterative method that can solve such systems efficiently. In particular, a full proof of the effectiveness of the algorithm is given; such a proof does not seem to be easily found in the existing literature. The thesis also describes the Quadratic Sieve algorithm and explains how these large linear systems are needed to make the algorithm work.
Currently: Instructor, Cañada College

Student: Katherine Shelley
Title: Matchwebs
Brief description: A matchweb is a minimal connected normalized matching bipartite graph. This thesis defines matchwebs and begins the reduction of the problem of classifying matchwebs to the enumeration and classification of their underlying structures: core graphs and bases. After classifying matchwebs with |X| = 1 and 2, the thesis continues by systematically enumerating all bases up to order 8, and classifying all matchwebs with the n-pod, n-spider, and n-fence cores. The main theoretical results of the thesis are: (1) There is at most one matchweb Lambda(X,Y) with n = |X|, k = |Y|, and a given core; and (2) Matchweb solutions are unique mod n. (All of these results are original work.)
Honors received: 2008 University Outstanding Thesis Award (two awarded at San Jose State each year)
Currently: Aviation analyst, ATAC


Student: James Kittock
Title: The isoperimetric problem in finitely presented groups
Brief description: This thesis concerns the isoperimetric function of a group, which gives a quantitative measure of how useful finite presentations are for computation within that group. After a thorough exposition of some key ideas in combinatorial and geometric group theory (including material that is either not done or not done well in the standard reference literature), the thesis introduces an algorithm for estimating the Dehn function of a finitely presented group and shows results of computer experiments with this algorithm.
Honors received: 2004 University Outstanding Thesis Award (two awarded at San Jose State each year)
Currently: Senior Product Manager, My Yahoo! (Previously: Instructor, Mission College, Fall 2004-Spring 2006)


Student: Amy Vu
Title: Quantum factoring
Brief description: This thesis describes Shor's algorithm for factoring large integers quickly using a (hypothetical) quantum computer. The material is developed from linear algebra and fundamentals of quantum mechanics to the quantum Fourier transform and the algorithm itself.
Currently: Instructor, West Valley College

Senior theses at Pomona College


Student: Michael Dickerson
Title: A family of Fourier transformations
Brief description: This thesis describes the standard Fourier series transformation, the discrete Fourier transform (i.e., the finite version of the Fourier series transform), and the fast Fourier transform (a fast method for computing the DFT).
Currently: Manger, Google

Student: Jed Singer
Title: The taping number
Brief description: Think of a given polyhedron as pieces of cardboard (say, cardboard triangles or squares) held together by tape. The taping number of a polyhedron is the minimum number of pieces of tape required to hold that polyhedron rigid. In this (original) thesis, the taping number is defined rigorously, and the taping numbers of all of the regular polyhedra are determined, using a combination of combinatorics, geometry, and calculus on manifolds.
Honors received: Pomona College departmental honors
Currently: Neuroscientist, Children's Hospital Boston

Student: Eric Zupunski
Title: Real division algebras
Brief description: A real algebra is a real vector space A with a bilinear multiplication that gives A the structure of a ring, except possibly without associativity. A real division algebra is a real algebra that is also a division ring (again, possibly without associativity). This thesis describes real division algebras, and gives an exposition of why the theorem that the only real division algebras are in dimensions 1, 2, 4, and 8 is equivalent to a certain theorem in algebraic topology (the Hopf invariant one theorem of J. F. Adams).


Student: Anna Draganova
Title: Classification of rational quadratic forms
Brief description: This thesis describes a proof of the Hasse-Minkowski theorem, which gives a complete set of invariants classifying rational quadratic forms. The material is developed from basic definitions to the p-adic ideas underlying the theorem to a proof of the theorem itself.
Honors received: Pomona College departmental honors
Currently: Associate consultant, McKinsey & Company

Student: Rod Huston
Title: Networks, the inverse Dirichlet problem, and the Axl theorem
Brief description: The Dirichlet problem on a network of resistors is: Given a network of known resistors and batteries, determine the voltages at all nodes (or equivalently, the currents on all resistors). The inverse Dirichlet problem is: Given a resistor network of known topology but unknown resistance, figure out the resistances by attaching appropriate batteries and measuring the resulting currents. This thesis, based on (original) summer research done at the University of Washington, gives a method for solving the inverse Dirichlet problem on certain very symmetrical resistor networks.

Student: Carol Meyers
Title: Constructions of "good" codes and lattices
Brief description: This thesis works out an alternate method for obtaining the construction of, and the standard results on, certain exceptional binary linear error-correcting codes and Euclidean lattices in 8 and 24 dimensions that are closely related to several of the sporadic finite simple groups. The basic approach is implicit in remarks of J. H. Conway and others, but much of the substance of the proof is original work.
Honors received: Pomona College departmental honors
Currently: Systems and Decision Sciences section, Lawrence Livermore National Lab


Student: Ryan Derby-Talbot
Title: Lengths of geodesics on Klein's quartic curve
Brief description: Klein's quartic curve is a surface of genus 3 that can be described both geometrically, in terms of a certain hyperbolic structure, and algebraically, in terms of certain matrices. This thesis, based on (original) summer research done at the Rose-Hulman Institute, uses a combination of algebraic and geometric techniques to solve the geometric problem of finding the shortest closed geodesics ("straight lines") on Klein's quartic curve.
Honors received: Pomona College departmental honors
Currently: Assistant professor, Quest University, BC (Canada)

Senior theses at the University of Michigan


Student: Stephanie Salomone (nee Molnar)
Title: Through the looking-glass and what Escher found there
Brief description: This thesis is essentially a "coffee table book" giving a mathematical exposition of Escher's so-called regular division drawings. A wide variety of mathematical material is explained for a general audience, including group theory and Euclidean geometry, and Escher's drawings are analyzed using these mathematical tools. Perhaps most notably, the exposition is done in some unusual ways, ranging from elaborate color pictures to interactive "pop-up" displays.
Honors received: Virginia Voss Award for writing by a senior woman
Currently: Assistant professor (tenure-track), University of Portland

Return to: Home page of Tim Hsu

(This page last updated June 12, 2002)