Professor: Jeff Blanchard, Noyce 2516, 269-3304, email prefix: blanchaj
Virtual Office link on our Pioneerweb and Piazza page.
Text: Numerical Analysis by T. Sauer (the first edition). It is important and expected that you read the text, especially the examples. (The second edition is acceptable if you are unable to obtain the first edition.)
This course will study the fundamental ideas and mathematical background for numerical techniques used to solve or approximate the solution to a wide range of scientific problems. The course will cover the application of numerical algorithms to nonlinear equations, linear and nonlinear systems of equations, interpolation, integration, and numerical linear algebra. The primary learning goals for this course are:
- understand and effectively conduct the analysis of numerical algorithms to establish convergence and/or expected error;
- be proficient in implementing numerical algorithms while identifying and understanding the underlying computational costs;
- identify and understand the strengths, weaknesses, and limitations of numerical algorithms in terms of both theoretical analysis and software implementation;
- improve mathematical and technical writing skills;
- improve skills required to master new mathematics.
The College credit hour equivalence for the 7.5 week terms requires us to perform approximately 24 hours of course related work per week. This includes interacting with material via pencast, video lecture, reading, working on problems, implementing algorithms, asking and answering questions on Piazza, writing solutions and papers, studying, project related activities, and our two synchronous meetings each week. The take away message here is that you should expect to dedicate roughly 24 hours per week to the course.
Much of the content delivery for the course will be asynchronous in the form of video lectures, pencasts, notes, and reading assignments. We will use Piazza as our asynchronous discussion board. Importantly, we will meet together twice per week to discuss numerical analysis as a group and learn from each other. These sessions are driven by your questions. Students should post discussion questions in Piazza prior to the meeting. These meetings will take place on Tuesday and Thursday from 10:00 - 11:00 am Central Time (Grinnell Time). All students are expected to participate in these synchronous meetings.
Students will have a wide range of backgrounds in writing code, using python and numpy, managing installations of software, etc. Wednesdays, 10:00 - 11:00 am Central Time (Grinnell Time), are dedicated to issues related to implementation of algorithms and python specific questions. These sessions are optional.
Especially in our online environment, it is critical to your learning, the learning of your peers in class, and the overall experience of everyone that we are engaged with the course. Participation will be a portion of the course grade. You will demonstrate active participation by engaging with class members on Piazza (asking and answering questions in our online discussion board), attending and participating in the Working Sessions (synchronous online discussion sessions), participating in implementation sessions, attending office hours (online meetings with the Professor), completing assignments, etc.
There will be daily assignments consisting of reading, exercises, and computing. Much of this will not be explicitly submitted for grading. There will be a Problem Set consisting of two or three problems to submit each week. These submitted problems must be written using Latex and the template provided for the problem.
- The assignments are already posted in Pioneerweb on our schedule under the syllabus tab. Students are encouraged to work on more problems than those specifically listed.
- The Problem Sets (to turn in) will be posted on Pioneerweb in Assignments and should be submitted via pweb as a pdf.
- Problem Sets must be submitted prior to 12:00 pm CST (noon) on Wednesdays.
To properly understand the numerical algorithms we study, we will implement the algorithms in Python. For each implementation, the code should be properly commented and annotated. You must also maintain a running user guide for your software. It is imperative that you keep up these implementations and ensure they solve the problems given in the test scripts. At the end of the semester you will have written a full numerical software package that will be extended to solve the problem associated with your project. The numerical software package will be submitted as part of your final project.
In place of exams, most chapters will culminate with a writing assignment. These will be posted in Pioneerweb and should be submitted there as a pdf. Writing assignments should be written using LaTex and the template provided. Writing Assignments must be submitted prior to 12:00 pm CST (noon) on the following Friday.
There is a semester project on a topic of your choosing and my approval. Suggested Topics will be provided in Week 2. The final week of class will be entirely dedicated to completing your term long project. This project will have a few check-ins in the first few weeks. You will select a topic in numerical analysis that you would like to study, and write an expository paper on the subject, implement the algorithm in your software package, create an example application, and write a script to solve the problem. This project will also include a short user guide for your numerical software package that has been developed throughout the semester.
All students must be aware of and comply with the Grinnell College Academic Honesty policy. In this course students may collaborate on homework assignments provided they submit their own work and identify their collaborators. All work should be the creation of the student. Students may not copy an algorithm implementation and submit it as their own; they must write their own implementation. Copying a proof from another source or even following the proof so closely as to make your proof indistinguishable from another can be a violation of academic honesty.
If you are in need of specific learning accommodations, please let me know early in the semester so that your learning needs may be appropriately met. If you have not already done so, you will need to provide documentation to the Coordinator for Disability Resources, Autumn Wilke, located on the 3rd floor of the Rosenfield Center (x3702) and discuss your needs with her.
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