Scentific Computing (MATH 164)

Math 164 is a survey course designed to introduce students to a broad range of modern computational techniques through the modeling of real-world problems. Discretization, the importance of linear algebra, and the balance between accuracy and speed are three themes that we'll see frequently during the course.

By the end of this course, I hope that you will be able to carry out the modeling process for real world problems that require numerical computation, meaning that

Topics covered: Limits of computer arithmetic, interpolation, numerical integration, numerical differentiation, root finding, finite difference methods for ODEs and PDEs, numerical linear algebra, spectral methods, optimization.

Suggested texts

There is no required textbook for this course, but you may find some of the books in the list below helpful. I personally own these and many more textbooks and am happy to recommend some to you based on your preferences.

Lecture notes, accompanying files, and videos

Lecture notes are available to students in this class accessing this web site using a computer on the Claremont Colleges.

Topic 13: Misc topics--Spectral differencing and FFTs (spectralderiv.m), finite volume and finite element methods

Handouts and links

Assignments and Final Project

Over the course of the semester, you will complete several computing assignments (worth 60% of your grade) and a final project (worth 40% of your grade). Each of these tasks is also an exercise in written communication. Where indicated, please provide include written explanations along with your calculations. Pay attention to grammar and spelling. Please visit this page for general guidelines about mathematical writing. All of your assignments must be composed on a computer (no hand-written write-ups) unless otherwise noted.

Please keep in mind that Harvey Mudd's honor code is in effect for all students in this course. In particular, remember to acknowledge all sources of help (people, books, websites, etc) that you receive to complete your work.

Assignment #1: First draft due Jan 24; Peer review due Jan 26; Final draft due Jan 31

Assignment #5: First draft due Mar 1; Peer review due Mar 6; Final draft due Mar 8

Your final project will consist of a final paper and oral presentation to the class exploring some computational problem of your own choosing. You can look at projects from 2003, 2004, 2006, 2007, 2008, 2009, 2010, 2011 to get some ideas.

	4	3	2	1
Description of the project	The description of the project is well-motivated, convincing, clearly conveyed, and tailored to the intended audience of the paper.	The project is described well, but is missing one or two things that the audience would need to know to fully understand the problem.	The project is hastily described or is missing significant details.	The project is ill defined.
Problem formulation	The mathematical model is accurately formulated; all assumptions are clearly stated and warranted.	Some unwarranted assumptions were made in the mathematical model.	There are some flaws in the formulation of the mathematical model.	The mathematical model is either largely incorrect or inappropriate for the given problem.
Quality of mathematical work	The computational techniques chosen are well-suited to the problem. The computations performed are thorough, complete and correct.	The computational techniques work well for the problem, but there may be other techniques that are superior. The computations are mostly complete and correct.	The computational techniques chosen are not well implemented or inappropate. Some computations are incorrect.	There are serious mathematical errors that lead to incorrect results.
Insightfulness and depth of understanding	Numerous insightful and thoughtful conclusions from data are presented. It is clear that the author designed the model and computations well to reach these conclusions and that the author learn many thing through the project.	Some insightful conclusions are reached through the computations. There are a few obvious things the author could have done to draw more conclusions from the model.	The author makes a cursory attempt to draw conclusions from the data. The author demonstrates a minimal advancement of technical ability through the project.	The report gives no insights on the original problem or shows no signs of learning on the part of the student.
Grammar and mechanics	Excellent	Few errors	Several errors	Poorly written

I am happy to read drafts of your final paper at any time during the semester, so please get in the good habit of writing via revisions. Remember to structure your final paper in a logical way. Typically, you will begin by describing the problem you are solving. Next, state your objectives in solving this problem. These objectives should then lead to how you formulated your problem mathematically and why you chose the computational techniques that you used. Explain any relevant mathematics behind the problem and how you carried out your computations. Finally, draw appropriate conclusions from your data and summarize what you learned from solving the problem.

Course description

Suggested texts

Lecture notes, accompanying files, and videos

Handouts and links

Assignments and Final Project