Mathematics Department

Honors

There are many possible areas in which qualified mathematics majors can do Honors projects. Also, there are undergraduate research opportunities supported by research grants of the College or individual faculty members. In particular, students with double majors are welcome to do interdisciplinary research for their Honors or other research projects. Students are welcome to discuss these possibilities with the Honors projects coordinator, Professor Leemis and Spitkovsky, or any mathematics professor.

Some Previous Honors Projects
  • Student: H.Chiang (Highest honors), 2003
    Thesis: Doubly stochastic matrices and linear preservers.
    Advisor: Chi-Kwong Li
    Publications: H. Chiang and C.K. Li, Linear maps leaving the alternating group invariant, Linear Algebra Appl. 340 (2002), 69-80.
    H. Chiang and C.K. Li, Linear Maps Leaving Invariant Subsets of Nonnegative Symmetric Matrices, Bulletin of Australian Math. Soc., 68 (2003), 221-231.
    H. Chiang and C.K. Li, Generalized Doubly Stochastic Matrices and Linear Preservers, Linear and Multilinear Algebra, to appear.

     

  • Student: F.Curtis (Highest honors), 2003
    Thesis: Special Classes of Zero-One Matrices.
    Advisors: Chi-Kwong Li and Rex Kincaid.
    Publication: F. Curtis, J. Drew, C.K. Li, and D. Pragel, Central Groupoids, Central Digraphs, and Zero-One Matrices $A$ Satisfying $A^2 = J$, J. Combinatorial Theory, Series A, 105 (2004), 35-50.

     

  • Student: Cynthia Bowers (highest honors), 1999
    Thesis: Linear Orderings: a Sampler
    Advisor: David Lutzer

     

  • Student: Brad Arkin (highest honors), 1998
    Thesis: Algebraic structures in Feistel Ciphers and an analysis of GOST
    Advisors: Bill Bynum (CS dept.) and Chi-Kwong Li, joint supervision.

     

  • Student: Ingrid Nelson (highest honors), 1997
    Thesis: Error-Correting Codes on the Towers of Hanoi Graph
    Advisor: Chi-Kwong Li
    Publication: C.K.Li and I. Nelson, Perfect Codes on the Towers of Hanoi Graph, Bulletin of the Australian Math. Soc. 57 (1998), no. 3, 367-376.

     

  • Student: Carrie Pohanka (honors), 1997
    Thesis: Estimating the extreme singular values of matrices
    Advisor: Chi-Kwong Li
    Publication: C.K.Li and C. Pohanka, Estimating the Extreme Singular Values of Matrices, Mathematical Inequalities and Applications 1 (1998), 153-169.

     

  • Student: Laura Vignati (high honors), 1996
    Thesis: Analysis of the flat tax system
    Advisor: Larry Leemis
    Publication: L. Vignati and L. Leemis, "Solving for APR in a Dynamic Fund", submitted for publication.

     

  • Student: Yuki Horiguchi (high honors), 1996
    Thesis: Matrix Inequalities as Hermitian Completion Problems
    Advisor: Hugo Woerdeman

     

  • Student: Laura Jackson (high honors), 1995
    Thesis: Discrete Billing for a Continuous Service Deriving an Optimal Billing Schedule
    Advisor: Charles Johnson

     

  • Student: David Finberg (high honors), 1994
    Thesis: The Spectra of Triangle-Free Graphs
    Advisor: Charles Johnson

     

  • Student: Anne-Louise Klaus (high honors), 1994
    Thesis: A study of the vector (p,q) norms and the induced (p,q) norms
    Advisor: Chi-Kwong Li
    Publication: A.-L. S. Klaus and C.K.Li, Isometries for the vector $(p,q)$ norm and the induced $(p,q)$ norm, Linear and Multilinear Algebra 38 (1995), 315-332.

     

  • Student: John Karro (high honors), 1994
    Thesis: An examination of the extreme points of the set of positive semidefinite doubly stochastic matrices
    Advisor: Chi-Kwong Li
    Publication: J. Karro and C.K.Li, A unified elementary approach to matrix canonical form theorem (with J. Karro), SIAM Review 39 (1997), 305-309.

     

  • Student: Andrew Martin (high honors), 1994
    Thesis: Essays on the Stochastic Dominance of First Improving Decision Mechanisms in Local Search Heuristics
    Advisor: Rex Kincaid

     

  • Student: Rosemary Berger (high honors), 1992
    Thesis: Placement of Structural Dampers in Large Truss Structures
    Advisor: Rex Kincaid

     

  • Student: Lynne Yellin (high honors), 1991
    Thesis: Noxious Facility Locations: the P-dispersion-sum Problem
    Advisor: Rex Kincaid

     

  • Student: Christos Xenophonotos (high honors), 1991
    Thesis: Irreduciblity and Primitivity of Perron Complements: Application of the Compressed Directed Graph and Other Related Issues
    Advisor: Charles Johnson

     

  • Student: Jonathan Rubin (high honors), 1991
    Thesis: Deterministic Communicable Disease Models
    Advisor: Leiba Rodman

 

  • Student: Laura Jarrait (high honors), 1990
    Thesis: A Heuristic Approach to Examiniation Scheduling
    Advisor: Margaret Schaefer

 

  • Student: Philip Ellis (high honors), 1990
    Thesis: Approximating the Shortest Path Length Distribution in Directed Stochastic Networks
    Advisor: Douglas Shier

 

  • Student: William Atkinson (high honors), 1990
    Thesis: Fourth Down Decisions in Professional Football
    Advisor: Margaret Schaefer

 

Other Research Projects
  • Student: Sita Nataraj (Wilson Interdisciplinary Study), 1996
    Thesis: Game theory
    Advisor: Chi-Kwong Li
    Publication: C.K.Li and S. Natanaj, Some matrix techniques in game theory (with S. Nataraj), Mathematical Inequalities and Applications, 9 pages.