Catalyzing Inquiry at the Interface of Computing and Biology

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338 CATALYZING INQUIRY

Box 10.2
Essential Concepts of Mathematics and Computer Science for Life Scientists

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

  • Eigenvalues 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

  • Optimization in mathematics and computation

  • “Bits”: information and mutual information


Data Structures


  • Metrics: generalized “distance” and sequence comparisons

  • Clustering

  • Tree relationships

  • Graphics: visualizing and displaying data and models for conceptual understanding


SOURCE: Reprinted from National Research Council, BIO2010: Transforming Undergraduate Education for Future Research Biologists,
The National Academies Press, Washington, DC, 2003.
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