This is an introductory course on numerical linear algebra. The course will present a global overview of a number of topics, from classical to modern to state-of-the-art. The fundamental principles and techniques will be covered in depth but towards the end of the course we will also discuss some exciting recent developments.
Numerical linear algebra is quite different from linear algebra. We will be much less interested in algebraic results that follow from the axiomatic definitions of fields and vector spaces but much more interested in analytic results that hold only over the real and complex fields. The main objects of interest are real- or complex-valued matrices, which may come from differential operators, integral transforms, bilinear and quadratic forms, boundary and coboundary maps, Markov chains, graphs, metrics, correlations, hyperlink structures, cell phone signals, DNA microarray measurements, movie ratings by viewers, friendship relations in social networks, etc. Numerical linear algebra provides the mathematical and algorithmic tools for matrix problems that arise in engineering, scientific, and statistical applications.
Location: Lectures held online through Canvas.
Times: 4:10–5:30pm on Mon and Wed.
Office: Jones 122C
Tel: (773) 702-4263
Office hours: Tue 2:00–4:00 pm.
Course Assistant I: Zhen Dai
Office: Jones 307
Office hours: Wed 7:00–9:00 pm.
Course Assistant II: Zehua Lai
Office: Jones 307
Office hours: Thu 2:00–4:00 pm.
The last two topics we would only touch upon briefly (no discussion of actual algorithms); they would be treated in greater detail in a second course.
Collaborations are permitted but you will need to write up your own solutions and declare your collaborators. The problem sets are designed to get progressively more difficult. You will get about 10 days for each problem set.
Bug report on the problem sets: lekheng(at)uchicago.edu
Grade composition: Five problem sets + one two-hour take-home exam (open book, open notes), with lowest score of the six dropped.
Exam date: Wed, Dec 9, 1:30–3:30pm CST.
We will not use any specific book but the following are all useful references.