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.
