• 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

Additional Quantitative Principles Useful to Biology Students

Rate of Change

  • This can be a specific (e.g., per capita) rate of change or a total rate of change of some system component.

  • Discrete rates of change arise in difference equations, which have associated with them an inherent time-scale.

  • Continuous rates of change arise as derivatives or partial derivatives, representing instantaneous (relative to the units in which time is scaled) rates.

Modeling

  • The process of abstracting certain aspects of reality to include in the simplifications of reality we call models.

  • Scale (spatial and temporal)—different questions arise on different scales.

  • What is included (system variables) depends on the questions addressed, as does the hierarchical level in which the problem is framed (e.g., molecular, cellular, organismal).

  • There are trade-offs in modeling—no one model can address all questions. These trade-offs are between generality, precision, and realism.

  • Evaluating models depends in part on the purpose for which the model was constructed. Models oriented toward prediction of specific phenomena may require formal statistical validation methods, while models that wish to elucidate general patterns of system response may require corroboration with the available observed patterns.



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