STAT 30900/CMSC 37810. Mathematical Computation I —
Department of Statistics
University of Chicago
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.
- 11/28/17: Office hours today cancelled. Send questions by email.
- 11/26/17: Class on Nov 27 cancelled.
- 11/21/17: Lecture notes 18 posted.
- 11/20/17: Homework 5 and Lecture notes 17 posted.
- 11/13/17: Lecture notes 16 posted.
- 11/08/17: Homework 4 and Lecture notes 15 posted.
- 11/06/17: Lecture notes 14 posted.
- 11/01/17: Lecture notes 13 posted.
- 10/30/17: Homework 3 and Lecture notes 12 posted.
- 10/24/17: Reminder: Quiz I on Wed, Oct 25, in class.
- 10/23/17: Lecture notes 11 posted.
- 10/19/17: Homework 2 and Lecture notes 10 posted.
- 10/16/17: Lecture notes 9 posted.
- 10/13/17: Lecture notes 8 posted.
- 10/12/17: Greg will hold office hours next Wed, Oct 18,
8:30–10:30am, Jones 304.
- 10/11/17: Reminder: Make-up lecture this Fri, Oct 13,
3:00–4:20pm, Stuart 102.
- 10/11/17: Lecture notes 7 posted.
- 10/09/17: Video of first and second make-up lectures
available here (see Sep 30 email for password).
- 10/09/17: Homework 1 and Lecture notes 6 posted.
- 10/06/17: Lecture notes 5 posted.
- 10/05/17: Greg will hold office hours this Fri, Oct 6,
12:00–2:00pm, Jones 304.
- 10/04/17: Reminder: Make-up lecture this Fri, Oct 6,
3:00–4:20pm, Stuart 105.
- 10/04/17: Lecture notes 4 posted.
- 10/02/17: Lecture notes 3 posted.
- 09/30/17: Lecture notes 2 posted. Video of first make-up lecture
- 09/27/17: Lecture notes 1 and Homework 0 posted.
- 09/27/17: First two make-up lectures on Fri, Sep 29 and Oct 6,
3:00–4:20pm, in Stuart 105. Third make-up lecture on Fri, Oct
13, 3:00–4:20pm, in Stuart 102.
- 09/26/17: Class will meet for the first lecture on 3:00pm, Wed, Sep
27, in Stuart 105.
- 09/26/17: Check back regularly for announcements.
Location: Room 105, Stuart
Times: 3:00–4:20pm on Mon and Wed.
Office: Jones 122B
Tel: (773) 702-4263
Office hours: 3:00–5:00pm on Tue.
Course Assistant: Greg
Office: Jones 203/204
Office hours: Two hours on the weekday before a problem set is due
(time/venue to be announced).
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
- Linear algebra over R or C: How this course differs
from your undergraduate linear algebra course.
- Three basic matrix decompositions: LU, QR, SVD.
- Gaussian elimination revisited: LU and LDU decompositions.
- Backward error analysis: Guaranteeing correctness in approximate
- Gram–Schmidt orthogonalization revisited: QR and complete
- Solving system of linear equations in the exact and the approximate
sense: Linear systems, least squares, data least squares, total least
- Low rank matrix approximations and matrix completion.
- Iterative methods: Stationary methods and Krylov subspace
- Eigenvalue and singular value problems.
- Sparse linear algebra: Sparse matrices and sparse solutions.
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:
Grade composition: 50% Problem Sets (six altogether, lowest
grade would be dropped), 50% Quizzes (two altogether, in-class, closed
Exam dates: Quiz I on Wed, Oct 25. Quiz II on Wed, Nov 29.
We will use the 4th edition of Golub–Van Loan.