Math Insight

Thread: Math 2241, Spring 2017

Topics covered in the course Math 2241, Mathematical Modeling of Biological Systems at the University of Minnesota.

  1. Class-structured models
    1. Introduction to one-dimensional discrete dynamical systems
      1. Notes on using R
    2. Introduction to multi-dimensional discrete dynamical systems
      1. Vectors and matrices
      2. Multi-dimensional discrete systems
    3. Linear systems, eigenvectors, and eigenvalues
    4. Analysis of multi-dimensional discrete dynamical systems
      1. Higher dimensional discrete dynamical systems
    5. Sea turtle project
    6. Gut microbiota project
    7. Problems
  2. Two-dimensional continuous dynamical systems
    1. Background: one-dimensional continuous dynamical systems
    2. Two-dimensional linear differential equations
    3. Partial derivatives
    4. Phase plane analysis of nonlinear systems
    5. Infectious disease
      1. One-dimensional equation warmup
      2. A related model for background
      3. The project
    6. Short-term memory
    7. A spiking neuron model
    8. Species competition
      1. One-dimensional equation warmup
      2. Special case of equal competition
    9. Problems
  3. Probabilistic modeling
    1. Probability basics
    2. An introduction to continuous birth-death processes
    3. Neuron decoding
    4. Tumor growth
    5. Problems
  4. Spatial modeling
    1. Discrete space modeling
    2. Continuous space modeling
  5. Modeling philosophy