Trustworthy Numerical Computing

These learning modules support the training session Trustworthy Numerical Computing. They develop a practical method for deciding whether a numerical result deserves scientific trust.

The modules are the course’s long-form reading material. The matching files in slides-source/ are teaching aids for instructor-led delivery and deliberately contain less detail.

Learning path

  1. When Correct Code Produces Wrong Answers
  2. Understanding Floating-Point Arithmetic
  3. Measuring And Comparing Numerical Error
  4. Conditioning And Numerical Stability
  5. Common Numerical Failure Modes
  6. Iterative Algorithms And Convergence
  7. Validating Scientific Computations
  8. Reproducibility Across Computing Environments
  9. Communicating Numerical Reliability
  10. Capstone: Investigating A Suspicious Result

The module structure explains the prerequisite order and how the modules fit into a one-day course. Optional advanced topics can be used for a longer course or domain-specific follow-up.

Course through-line

Each module contributes to the same investigation workflow:

  1. State what result is expected and what accuracy is meaningful.
  2. Characterize the problem, its sensitivity to inputs, and the propagation of declared input bounds or uncertainties.
  3. Identify arithmetic and algorithmic failure modes.
  4. Establish independent validation evidence.
  5. Check whether conclusions survive relevant environment changes.
  6. Communicate assumptions, limitations, and evidence.

Status

The complete ten-module core curriculum and matching slide sequence are in place. Modules 1 through 9 contain detailed reading material and executable Quarto activities that generate self-paced Jupyter notebooks. Module 10 provides a guided sensor-inversion capstone with starter code, verification checks, a reference solution, an evidence record, and instructor notes.