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: Ryerson Physical Laboratory, Room 358.
Times: 1:30–2:50pm on Mon/Wed.
Office: Eckhart 122
Tel: (773) 702-4263
Office hours: 2:00–4:00pm, Tue
Course Assistant: Somak
Office: Eckhart 117
Office hours: 6:30–7:30pm, Mon
The last three topics we would only touch upon briefly (no discussion of actual algorithms); they would be treated in greater detail in a second course.
Bug report on lecture notes: lekheng(at)galton.uchicago.edu
Except for the take-home final, collaborations are permitted but you will need to write up your own solutions. The problem sets are designed to get progressively more difficult. You will get at least seven days for each problem set.
Bug report on the problem sets or the solutions: lekheng(at)galton.uchicago.edu
Grade composition: 75% Problem Sets, 25% Final
Any one of the following books, listed in order of increasing sophistication, would be acceptable.
We will use the following references when discussing applications to statistics and economics: