Math Insight

Thread: Math 5447, Fall 2022

Topics covered in the course Math 5447, Mathematical Neuroscience at the University of Minnesota.

1. Scalar linear differential equations
   • An introduction to ordinary differential equations
   • Ordinary differential equation examples
   • Solving linear ordinary differential equations using an integrating factor
   • Examples of solving linear ordinary differential equations using an integrating factor
   • Online quiz: Scalar linear equation problems
2. Two-dimensional linear equations
   • Visualizing the solution to a two-dimensional system of linear ordinary differential equations
   • Online quiz: Two-dimensional linear problems
3. Higher-dimensional linear equations
   • Online quiz: Oscillations in higher-dimensional linear systems
4. Two dimensional nonlinear equations
   • Online quiz: Two-dimensional nonlinear problems
   • Introduction to visualizing differential equation solutions in the phase plane
   • Online quiz: Two-dimensional neuron problems
   • In-class exam: Midterm
5. Nonlinear oscillations
   • Online quiz: Nonlinear oscillation problems
6. Complex networks
   • An introduction to networks
   • The degree distribution of a network
   1. Random networks
      • One of the simplest types of networks
      • Random networks
      • The absurd high dimensionality of random graphs
      • Evidence for additional structure in real networks
   2. Network types
      • Small world networks
      • Scale-free networks
      • Generating networks with a desired degree distribution
      • Generating networks with a desired second order motif frequency
7. Neural decoding
   • Online quiz: Neural decoding introduction
8. Final exam
   • In-class exam: Final exam

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