人才培养
- Fundamental Algebra and Analysis I
- Fundamental Algebra and Analysis II
- Geometry and Topology
- Abstract Algebra I
- Abstract Algebra II
- Ordinary Differential Equations
- Measure Theory and Real Analysis
- Probability Theory
- Functions of One Complex Variable
- Functional Analysis
- Numerical Analysis
- Category Theory
- Number Theory
- Algebraic Topology
- Representation Theory
- Differential Geometry and Differential Manifolds
- Partial Differential Equations
- Stochastic Processes
- Mathematical Modeling
- Numerical Algebra and Optimization
- Numerical Simulation
- Regression and Generalized Linear Models
- Scheme Theory
- Sheaf Theory and Cohomology
- Riemannian Geometry
- Elliptic Curves
- Topics in Several Complex Variables
- Geometric Measure Theory
- Harmonic Analysis
- Analytic Theory of Biological Dynamics
Analytic Theory of Biological Dynamics
Prerequisites:
Differential Equations; Stochastic Processes
Course description:
This is a graduate level course in Applied Mathematics, which introduces a unified theory to biological science via the language of both deterministic dynamics (i.e., nonlinear differential equations) and stochastic dynamics (i.e., stochastic processes). The course emphasizes mechanistic based theories and models in biology. Without prerequisites in life sciences, a wide range of biological systems will be discussed ranging from biochemistry to cell biology, physiology to neuroscience, ecology to evolutionary biology. Biological phenomena also play a fitting role as examples for all other complex systems.
Learning objectives:
Applying the mathematical theories of dynamical systems and stochastic processes to understand biological systems and frame biomedical problems.
Detailed topics covered:
i) population dynamics as a fundamental;
ii) deterministic and stochastic dynamics;
iii) kinetics of chemical species and dynamics of ecological species;
iv) equilibrium vs. nonequilibrium dynamics
v) enzyme kinetics;
vi) preditor-prey and competition;
vii) neural dynamics and neural networks;
viii) central dogma of molecular biology and stochastic gene expression;
ix) emergent phenomena;
x) fundamental theorem of natural selection;
xi) spatial pattern formation;