Course description
See the detailed syllabus for details. An introduction to scientific computing at the MS level for people interested in practical computing. Covers the main theoretical ideas and fundamental algorithms. Attention paid to good programming practice and scientific computing software. Assignments include theoretical exercises and computing in Python.
Specific topics include sources of error, floating point, finite difference, quadrature, and interpolation formulas. order of accuracy and uses of error expansions, dense linear algebra (conditioning of linear algebra problems, factorizations, uses of SVD), FFT and applications, optimization (gradient descent, Newton's method), ODE solution, basic Monte Carlo.
Prerequisites:
Good linear algebra, multi-variate calculus, some programming (Python preferable). Also helpful: basic probability and differential equations.
Assignments, exams, grading:
The final grade will be based on weekly homework assignments (worth 40% of the grade), a final computing projectassignment (worth 20%) and an in-class written final exam (worth 40%).
Communication:
Please use the Brightspace site for content and homework communications. This way everyone sees and benefits from questions and answers, and there can be class discussion. related comm. Email the instructor for issues that do not involve others such as scheduling appointments, homework extensions, advice, etc.
Academic integrity:
Philosophy. An obvious goal is to make sure that good grades are earned through careful work and mastery of the material. It is unfair to the person who does not cheat if many of the top grades result from cheating. Less obvious is that integrity guidelines help students learn the material. Grades on graduate transcripts normally mean less than skills and knowledge that can be demonstrated through projects and interviews. The most damage from cheating is to the cheater.
Students are encouraged to explore and collaborate widely to understand the material. This includes looking at print and online sources and interacting with experts and each other. Students may receive some help with assignments, but each student must create (write up, code, run) solutions individually. Students may not share ("borrow" or lend) assignment solutions -- all writing must be done individually. Students may not plagairize solutions from other sources such as books or web sites. Violation of these policies may result in grade lowering or more serious penalties, depending on severity.
AI and AI tools:
Students are encouraged to use AI coding tools including copilots, etc. The student is responsible for checking that the code is correct and does the required task. Numerical code produced by AI tools is usually wrong in its mathematical details, though the code logic may be reasonably close to what might work.
Students may not use AI tools to generate answers to written questons. Warning: If you just upload the assignment and ask ChatGPT to do it for you, what you get will look professional until an actual professional (the grader or instructor) reads it.
Students may use AI tools to find web resources. Again, students should be aware that AI generated content, particularly in highly specialized STEM fields, usually includes hallucinations, which are professional looking facts and references that have no basis in reality.