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Mathematics Department

Mathematics Department

Fall 2007

1. Math 490 Seminar: Investigating Linear Algebra

Instructor: Charles Johnson (crjohnso@math.wm.edu)

With the assistance of the instructor, each student will choose either a research topic (appropriate for the student's background) in elementary linear algebra to be explored, or a well-developed topic in advanced linear algebra to be learned.  The instructor will suggest a number of research topics fitting into broader questions, and will offer a list of advanced topics (e.g. linear matrix equations. Lyapunov's theorem, special classes of matrices, etc.) for students in the course.  In each case, participants will be guided by the instructor, will write about their progress, and will give two talks to the group as a whole about their work.  Enrollment in the course will be limited and students need to consult with the instructor before registering for the course.

2. Math 490-01 Senior seminar.
    (targeted for but not limited to prospective teachers) 

Instructor: Chi-Kwong Li  (ckli@math.wm.edu)

In this seminar, we will study various approaches in teaching and learning mathematics in different countries, and different time of history. We will also consider different methods in generating interest in studying mathematics. One  focus will be on finding interesting problems in recreative, applied or theoretical settings that may stimulate interest in studying mathematics. Students are required to do one or two projects on the above themes.
 

Spring 2007

1. Senior Seminar, Instructor: Leiba Rodman (lxrodm@math.wm.edu)

Description: Students will study a narrow topic of mathematics, make oral presentations for discussion in class, and write a report. The topic need not be the same for all students. The choice of topic(s) is flexible and may reflect particular interests of each student.

 

2.       Computational Topology and Dynamics, Instructor: Sarah Day (sday@math.wm.edu)

Textbook: Computational Homology, by T. Kaczynski, K. Mischaikow, and M. Mrozek, Applied Mathematical Sciences 157, Springer 2004.

homology is used to study a pattern generated from a nonlinear partial differential equation. Another application of computational topology is in numerical studies of dynamical systems. Numerical techniques based on topological tools are now being used to prove the existence of chaos in dynamical systems models in fields from ecology to mechanics. In this course we will study the mathematical theory behind homology, discuss efficient means of computation, and study applications. Related topics include techniques for image processing and the efficient implementation of algorithms on large data sets. This will be a discussion based class and students are encouraged to pursue and present individual topics of interest related to the course material.

course flyer (in pdf)