Department

Math 380: (Spring 2006) Special Topic in Mathematics
Instructor: George Rublein
The subject will be the mathematics of chemical thermodynamics. Topics will include: An elementary treatment of differential forms, Heat reservoirs, Heat capacities and the equation of state, Quasi-static processes: Reversible, adiabatic, isothermal. Ideal gases and the first and second laws. Enthalpy as a measure of heat exchange, Entropy as a measure of irreversibility. Free energy functions and equilibrium phase changes: Clausius-Clapeyron and the Poynting correction. More as time permits.

Math 410: (Spring 2006) Ecology and evolution of metapopulation (colisted as Biol 404)
Instructors: Sebastian Schreiber (Mathematics) and John Swaddle (Biology)
Pre-requisites: Biol 204, and either Math 302 or Math 345 (or Math 410 -Introduction to Mathematical Biology), or permission of instructor
A metapopulation is a collection of semi-isolated populations that interact via dispersal and gene flow. In a time where anthropogenic forces are altering and fragmenting species' habitats, understanding the ecological and evolutionary dynamics of metapopulations is becoming increasingly important. With readings from the primary literature, computer labs, and field trips, this course will cover core metapopulation concepts including metapopulation viability, source-sink dynamics, deterministic and stochastic patch occupancy models, fugitive species, and natural selection and speciation in metapopulations. We will apply these concepts to real-world problems in conservation biology and restoration ecology.

Math 459: (Spring 2006) Knowledge Discovery
Instructor: Michael Trosset
As used by the data mining community, the phrase "knowledge discovery" encompasses various data-analytic approaches to detecting structure in multivariate data sets. This course will introduce three fundamental topics: (1) techniques for dimension reduction and data visualization (e.g. principal component analysis, multidimensional scaling), (2) cluster analysis (class discovery, unsupervised learning), and (3) classification (class prediction, supervised learning). These techniques are useful in a wide variety of disciplines; I plan to emphasize applications to computational biology, so that there will be a strong bioinformatic flavor to the course; however, no prior knowledge of bioinformatics is assumed.

Math 490-01: (Spring 2006) Topic of mathematics
Instructor: Leiba Rodman
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, subject to instructor's approval, and may reflect particular interests of each student.

Math 490-02: (Spring 2006) Mathematical Biology and Partial Differential Equations
Instructor: Junping Shi
Reaction-diffusion (R-D) systems are some of the most widely used models in situations where spatial dispersal plays significant role. We will learn some theory of reaction-diffusion equations in the context of models in mathematical biology. Applications to be discussed in class include spatial spread of genes and of diseases, random dispersal of population, random and chemotactic motion of microorganisms, cellular maturation, pattern formations in developmental biology and morphogenesis, and animal coat patterns (why zebra has the stripes......). While introducing many biology models, we will also develop related mathematical theory and methods like, diffusion mechanism, waves, bifurcation theory, Turing's instability mechanism. Computation and simulation of solutions will be used throughout the class. (We are going to use software Matlab or/and Maple, but no prior knowledge is required.)
The prerequisites of the course are Math 111, 112 (Calculus I and II), and Math 302 (Differential equations) or Math 410 (Mathematical Models in Biology). Math 211 (multivariable calculus) and 212 (linear algebra) are not required, but suggested.

Math 490-01: (Fall 2005) Teacher seminar on posing questions, solving problems, and doing research in mathematics
Instructor: Chi-Kwong Li and Jinchuan Hou, 2005-06 Freeman Visiting Fellow
Solving problems is important in learning and teaching mathematics. However, teachers and students may not be excited by the problems imposed on them. We discuss how K-12 teachers and students can pose their own questions in elementary mathematics. Studying these problems would require a deeper understanding of their known mathematical knowledge and new techniques. Some of the questions may have open ends leading to research projects.

Math 490-02: (Fall 2005) Problem solving techniques
Instructor: Junping Shi
Pre-requisites: Math 214 (Math 412 Number theory and Math 432 Combinatorics are recommended, but not necessary)
Techniques of solving mathematical problems will be reviewed, and the seminar will also prepare the students for college level mathematical competitions, like Putnam Exam, and Virginia Tech competion. Parallel to a systematic review of knowledge on algebra, combinatorics, number theory, calculus, geometry and other topics, students will also solve problems from selected problem sets, present and discuss their solutions in seminar. Some related material can be found from 2004 problem solving group webpage.

Math 459-01: (Fall 2005) Data Analysis Regression Model
Instructor: Philip Draper DeCamp
Data Analysis and Regression Modeling Simple and mulitple linear regression, inferences and diagnostics, stepwise regression and model selection, advanced regression methods, and Analysis of Variance.

Math 410-01: (Fall 2005) Introduction to Cryptography
Instructor: Moses D Liskov
Students are invited to ask instructor permission to enroll: mliskov@cs.wm.edu. Pending approval of the Educational Policy Committee, this course will be re-numbered. It may be used for 400-level credit in the Computational Mathematics area for the applied concentration in Mathematics. In this course, we will provide a rigorous and in-depth introduction to cryptography. Topics will include public-key cryptography, signatures,one-way functions and permutations, trap-door permutations, pseudorandom functions, block ciphers and modes of operation. A strong grasp of proofs will be required. This course is cross listed with CSCI 420-01.

Math 345: (Fall 2005) Introduction to Mathematical Biology.
Instructor: Sebastian Schreiber
Prerequisite: MATH112 or 132, or permission of instructor.
An introduction to developing, simulating, and analyzing models to answer biological questions. Mathematical topics may
include matrix models, non-linear difference and differential equations, and stochastic models. Biological topics may include ecology, epidemiology, evolution, molecular biology, and physiology.

Advanced math courses 2002-2004

Advanced math courses 2004-2005

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