Course Summary

In a typical mathematics course, a student learns a combination of theory and computation, with the latter providing concrete examples of how the former is exhibited ``in the real world." Of course, ``the real world" in a mathematics class is the realm of pure mathematics, where real numbers have infinite decimal expansions and there are a continuum of numbers that are as close to zero as you like. In the real world that we experience on a day-to-day basis, however, concepts which rely on infinite precision have a harder time being implemented in a practical way; one simply only has so much memory that one can allocate to storing the decimal digits of $\pi$, for instance. The typical answer to this problem is to allow ourselves to approximate real values in our computations, with the tacit assumption that these approximated values will be sufficient for any ``real" problem we might face. Moreover, if there's some situation where one needs additional precision when doing a certain computation, the assumption is that if one begins with a higher precision approximation to the number in question, then computations with this better approximation should themselves be more precise.

In many ways, numerical analysis is the class in which one investigates whether these assumptions are true. It is a class that is steeped both in practical application (almost by its nature), but also intimately connected to deeply theoretical --- and often philosophical --- considerations. Perhaps the most consistent question we will aim to answer in this class is: how can I approximate a particular mathematical computation, and how well do I understand the error in this approximation? In answering this question we'll consider how computers store and process real numbers, how algebraically equivalent expressions for two quantities can yield dramatically different computed results, and how to effectively compress information to retain only the most important information.

Course Instructor

The professor for this class is Andy Schultz. His office is on the third floor of the Science Center, room S352. His office hours will be Monday from 2-4, Wednesday from 9-10, and Friday from 9:30 to 10:30. You are highly encouraged to attend office hours, and you never need an appointment to do so. If these office hours don't fit with your schedule, contact the instructor so that he can either adjust when ``official" office hours are held or set up an appointment to help you outside of office hours.

You can contact the instructor at . Though he is always happy to receive emails from you with questions or concerns about the course, he can't guarantee that he'll be able to promptly reply to emails late at night or over the weekend. If you do contact the professor by email, please be sure to follow standard email etiquette. In particular, please make sure you include a greeting and signature and avoid abbreviations. If you're contacting him to ask about a problem, please be sure to specify what the problem asks (as opposed to asking something like ``I can't get problem 2 and need your help").