Proficiencies

Guidelines for MathBio Minor Proficiencies

The following are intended as benchmarks to help students, advisors, and portfolio readers determine the extent to which a given product demonstrates genuine proficiency in a given area. Few products (if any) will demonstrate all characteristics listed within a proficiency category, but it is expected that most will demonstrate at least 2–3. Students are encouraged to explicitly highlight and discuss the relevant characteristics in both their products and their reflective statements.

• Modeling: To demonstrate proficiency in mathematical modeling, students will typically engage with issues such as the following

1. making and justifying explicit simplifying assumptions;
2. making and justifying decisions about model structure (e.g., discrete vs. continuous, number of discrete categories, etc.);
3. determining appropriate parameter values (through data collection and/or literature review);
4. recognizing the extent to which a model reflects the underlying biological mechanisms, as opposed to simply fitting observed data points;
5. incorporating stochastic factors as appropriate;
6. conducting sensitivity analysis;
7. verifying the model’s internal consistency and/or validating it with additional data sets.

• Computation: To demonstrate proficiency in computation, students will typically engage with issues such as the following:

1.  writing clear and concise pseudocode to summarize the task at hand;
2. planning and implementing flow control through appropriate use of loops, subroutines, conditional statements;
3. making and justifying decisions about the order of steps within a loop (in cases where this makes a difference);
4. managing input and output, including issues re. formatting, filenames, etc.;
5. confronting computational efficiency through runtime, memory requirements, etc.;
6. conducting verification runs and/or line-by-line debugging as needed

• Statistics: To demonstrate proficiency in statistical analysis, students will typically engage with issues such as the following:
  1. choosing appropriate statistical tests for the question at hand, and justifying that choice (e.g., parametric vs. nonparametric);
  2. understanding the assumptions of each statistical test, and testing them where appropriate;
  3. identifying possible outliers in the data set, and assessing the test’s sensitivity to those points;
  4. cross-validating with multiple tests (where appropriate);
  5. assessing the statistical power of a given test;
  6. correcting for multiple comparisons to achieve a desired experiment-wide level of significance.
• Data Acquisition: To demonstrate proficiency in data acquisition, students will typically engage with issues such as the following:
  1. hypothesis development & experimental design;
  2. using pilot studies to test & improve methods;
  3. troubleshooting methods;
  4. strict adherence to exact protocols for maximum repeatability, and/or recognition of variables that could affect repeatability;
  5. devising protocols for objectively handling ambiguous or missing data points;
  6. testing potential systematic biases in the data (e.g., trap avoidance behavior in a mark/recapture study);
  7. data management, cataloging, and formatting (e.g., appropriate processing of digital images).
• Research: To demonstrate proficiency in data acquisition, students will typically engage with issues such as the following:
  1. formulating an informed and testable hypothesis;
  2. searching, reading, and interpreting relevant literature;
  3. writing both a research proposal and a summative technical report;
  4. collaborating with colleagues in both biology and math/computer science;
  5. summarizing and interpreting results;
  6. seriously considering alternative hypotheses and interpretations (and excluding them where possible).