Syllabus 

MTH994,  Biological Modeling and Computation I

Fundamentals of biological sciences. (1) Mechanical foundation: Quantum
mechanics of biomolecules. The Schrodinger equation; Interaction potentials; 
Chemical bondings; Intermolecular forces; Classical mechanics and its role 
in biology; Interconnection between classical mechanics and quantum mechanics. 
(2) Structure and catalysis: Protein structure and function; DNA and RNA 
sequences and structures; carbohydrates; Lipids; Enzyme and chemical dynamics; 
Membranes and transport; Biosignaling; (3) Bioenergetics and metabolism: 
Principles of bioenergetics; Glycolysis; Fatty acid catabolism; Carbohydrate 
biosynthesis in plants and bacteria; Metabolic regulations. (4) Information 
pathways: Genes and chromosomes, Metabolism of DNA, RNA and protein; 
Regulation of gene expression. (5) Cellular structure and function; Cellular 
dynamics and transport. 

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MTH994,  Biological Modeling and Computation II

Principles of thermodynamics; Statistical ensembles; Maxwell-Boltzmann 
statistics; Fermi-Dirac and Bose-Einstein statistics; Random work; Stochastic 
process; Markov process; Master equation; Fokker-Planck equation; Brownian 
motion and Langevin equation; Autocorrelation; Density matrix; Liouvelle 
equation; Zwanzig's equation; Linear response theory; Boltzmann equation; 
Theory of liquids; Brownian ratchets; Molecular motor; Biomechanics; Protein
membrane interaction; Evolutionary genomics; mathematical approaches to the 
discovery of gene motifs; Gene regulation; Explanatory and predictive models 
of cellular growth and interaction; Metabolic circuitry and dynamics; Signal 
transduction and enzyme dynamics; Phylogenetic analysis; Biosensors; 
Neuroscience; Electrostatics in metabolic process; Fluid-macromolecule 
interaction and impact to  metabolism; Molecular dynamics and force fields; 
Monte Carlo; Implicit solvent modeling; Poisson-Boltzmann equation.