Notebook

In [1]:

from traitlets.config.manager import BaseJSONConfigManager
#path = "/home/damian/miniconda3/envs/rise_latest/etc/jupyter/nbconfig"
cm = BaseJSONConfigManager()
cm.update('livereveal', {
              'theme': 'sky',
              'transition': 'zoom',
              'start_slideshow_at': 'selected',
              'scroll': True
})

Out[1]:

{'theme': 'sky',
 'transition': 'zoom',
 'start_slideshow_at': 'selected',
 'scroll': True}

Numerical linear algebra, Skoltech, Fall 2018, general course info¶

Lecture access¶

Lectures can be downloaded and viewed on github: https://github.com/oseledets/nla2018

They can also be viewed online using nbviewer: http://nbviewer.jupyter.org/github/oseledets/nla2018/tree/master/

The most comfortable way to navigate through course materials is to use table_of_contents.ipynb file in repo.

Team¶

Course instructor: Ivan Oseledets

TAs:

Marina Mukhoeva
Aleksandr Katrutsa
Daniil Merkulov
Valentin Khrulkov
Talgat Daulbaev
Vitaly Zankin
Gleb Karpov
Leyla Mirvakhabova

Office hours (approximately one hour once a week) for recitation will be announced later.

Feedback system¶

We use Piazza platform for communication with TAs and with each other.

How do we grade¶

50% homework. Includes 3 problem sets with coding in Python and theoretical problems.
15% written midterm test (list of problems from 2017)
20% final oral exam in the traditional manner of Russian oral exams
15% term project. On Piazza you will find more info and you can use it to find teammates.

Problem sets¶

Homework is distributed in Jupyter notebooks
Problem sets contain both theoretical and programming tasks
You can check programming tasks in our Telegram bot . Instructions will be provided later

Problem set rules¶

Solutions must be submitted on Canvas before the deadline
Deadlines are strict . After the deadline Canvas submission is closed. Only the last submission will be graded.
Deadline for every problem set will be announced at the moment of publishing
Problem sets will be checked for plagiarism. If noticed, the score will be divided by a number of similar works

Attendance¶

Attendance is not strict, but do not disappoint us.

Midterm¶

Midterm is planned on week 4
Includes both theoretical questions and practical problems

Exam¶

Classical oral exam with a list of questions (questions from 2017)
If you fail exam, you get zero for the course
We will prepare a list of questions by the end of November such that if you can not answer any question from this list during the final exam, you will automatically get F for this course.

Grades¶

A: 86 - 100 %
B: 70 - 85 %
C: 50 - 70 %
D: 30 - 50 %
E: 15 - 30 %
F: 0 - 15 %

But they can be slightly adjusted.

Course description¶

Numerical linear algebra is the basis for computational science and engineering and data science
Matrices and their decompositions are the key
The tools are different for small-scale and large-scale problems

Learning outcomes¶

Solve medium-scale numerical linear algebra problems

(solve linear systems, compute eigenvalues and eigenvectors, solve linear least squares) using matrix factorizations

Iterative methods for sparse/structured systems
Find which methods are the most appropriate for the particular problem
Find appropriate software

Python 3¶

We will use Python >= 3.6 ecosystem for programming. For those who do not familiar with Python, there will be a Python tutorial practice session this week.

(Approximate) Syllabus¶

Week 1: Floating points arithmetics, matrices, vectors, norms, ranks
Week 2: Matrix decompositions 1: SVD and its applications
Week 3: Matrix decompositions 2: Linear systems and LU, eigendecomposition
Week 4: Matrix decompositions 3: QR and Schur + midterm test
Week 5: Sparse and structured matrices, iterative methods part 1
Week 6: Iterative methods part 2, matrix functions and advanced topic
Week 7: Oral exam
Week 8: Application period

Materials¶

Our materials:

Lecture notes are avaliable online
Matrix decomposition cheat sheet

If you have difficulties with basic linear algebra:

Cheat sheet with basics
Gilbert Strang book "Introduction to Linear Algebra"
Gilbert Strang has recorded lectures on YouTube

Comprehensive NLA books:

Gene H. Golub, Charles. F. Van Loan, "Matrix computations" (4th edition)
Lloyd N. Trefethen and David Bau III, "Numerical Linear Algebra"
Eugene. E. Tyrtyshnikov, "Brief introduction to numerical analysis"
James W. Demmel, "Numerical Linear Algebra"

Many applications of linear algebra you can find in "Introduction to Applied Linear Algebra" by S. Boyd and L. Vandenberghe

In [1]:

from IPython.core.display import HTML
def css_styling():
    styles = open("./styles/custom.css", "r").read()
    return HTML(styles)
css_styling()

Out[1]: