Concepts of Mathematics and Computer Science

Calculus

  • Complex numbers

  • Functions

  • Limits

  • Continuity

  • The integral

  • The derivative and linearization

  • Elementary functions

  • Fourier series

  • Multidimensional calculus: linear approximations, integration over multiple variables

Linear Algebra

  • Scalars, vectors, matrices

  • Linear transformations

  • Eeigenvalues and eigenvectors

  • Invariant subspaces

Dynamical Systems

  • Continuous time dynamics—equations of motion and their trajectories

  • Test points, limit cycles, and stability around them

  • Phase plane analysis

  • Cooperativity, positive feedback, and negative feedback

  • Multistability

  • Discrete time dynamics — mappings, stable points, and stable cycles

  • Sensitivity to initial conditions and chaos

Probability and Statistics

  • Probability distributions

  • Random numbers and stochastic processes

  • Covariation, correlation, and independence

  • Error likelihood

Information and Computation

  • Algorithms (with examples)

  • Computability



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