The special UBM sequence is designed by the participating scientists in the program and will be taught by four UBM faculty members. It will start in the spring semester 06 for the sophomore level undergraduates and continue fall semester 06. During the two academic semesters, it will be a 3 credit sequence, and will be graded on performance in research projects, homework and exams. The UBM supported students are required to register, but the courses are also open to other interested students.
In the short term, this sequence serves as a coherent component to the success of our UBM program: Most of the course content to be covered in the classroom will be closely related to the research projects in the labs (see the detailed description in the lab experience page.) In the long run, it helps to pave the way for the students' future career success. The instruction will emphasize the mathematical reasoning and biological hypotheses behind the quantitative formalism, so the students will not only learn how to apply mathematics in an appropriate way but also to avoid using mathematics inappropriately.
Fall 08 (MTH 370): The first nine weeks will be taught by Prof. Tang, focusing on the mathematical theory of differential equations and its application in chemical and enzyme kinetics. The last six weeks will be taught by Prof. Chiu, focusing on numerical solutions of differential equations and computer simulation. We note that for the second part some computer lab hours will be needed. 1) First order linear and nonlinear ODEs; Logistic growth model; determination of the order and rate constant of a reaction; reaction mechanisms and rate laws; eigenvalues and eigenvectors of 2x2 and 3x3 matrices; characterization of dynamics for system of linear equations; linearization of nonlinear systems; local stability of equilibrium; phase-plane analysis and periodic solutions; sequential reactions and the quasi-steady-state assumptions; derivation of Michaelis-Menten kinetics; competitive and noncompetitive inhibition; analytical solutions of linear scalar reaction and diffusion equations by separation of variables; effect of diffusion and convection on biochemical reactions.
(2) Numerical linear algebra (2) Numerical linear algebra including eigenvalues and eigenvectors of large matrices; numerical solutions of large system of linear ODEs and systems of reaction-diffusion equations (e.g. using MatLab); computer simulation of transient kinetics of an enzyme; steady-state kinetic studies with alternate substrates and inhibitors; computer-assisted kinetic modeling.
Spring 09 (STT 371): This semester will be related to biostatistics and bioinformatics. Prof. Melfi and Prof. Wu will each teach eight weeks, focusing on design and analysis of microarray studies, with a shorter section on modeling and constructing biological networks. Throughout the focus will be on understanding and application rather than on technical details. Students will be instructed in the use of the R statistical computing language and the Bioconductor bioinformatics software. There will be regularly scheduled class meetings in a computer lab for this purpose. Relevant basic concepts in statistics will be reviewed when necessary. icroarray technology; basic design issues of microarrays (simple variance calculations and the relative efficiency of loop, reference, and other designs); analysis of gene expression microarray data (spot recognition, normalization, various methods for assessing differential expression, and multiple comparison issues); clustering and classification algorithms will be covered in the context of gene expression data. In addition, students will be introduced to some online databases such as Gene Ontology and the UCSC Genome Browser. Other microarray-based technologies (for example, ChIP-chip studies, protein binding microarrays) will be introduced briefly. Students will be introduced to basic topics in biological network modeling and construction, including searching for network motifs, network structure, linear model based networks, and Bayesian networks.