Notes about
Homework Submissions
There will be regular (approximately
bi-weekly) assignments
that will be posted on this webpage and announced via email or
in class. NYU Classes will
only
be used for collecting files from students and grading.
Assignments may be posted before we have covered all the
material, allowing you to start working on some of the
problems early.
Logistics
Please read and follow these rules carefully as we use
automated scripts to process the large number of files.
Submissions that do not conform (e.g., submitting PDF files
directly instead of a zip archive)
will be rejected by the graders.
- Submit a PDF of your
writeup and all
of the source codes. Put all files in a zip archive.
- Do not include
top-level folders/subfolders, that is, when we
unpack the archive it should give a pdf file and matlab
sources, not a directory hierarchy.
- Submit only the
archive file as a solution via NYU Courses. Make sure to complete the
submission as otherwise we cannot access the file.
- Homeworks must be submitted by 8am on the morning after the listed due date. Late
submissions will only be accepted if you send a
justification to the instructor at least two days before
the due date.
- If you use any external source, even Wikipedia, make
sure you acknowledge it by referencing all help. Group work is discouraged:
you may discuss the problems with your colleagues but each
student must do the actual programming and writeup independently.
Organize your files
- Name files sensibly (e.g., not "A.m" or "script.m" but
also not "Solution of Problem 1 by Me.m"). Include your
name in the filename and
in the text of the PDF writeup.
- In general, one should be able to grade without looking
at all the codes. The reports
should be mostly self-contained, e.g., the
figures should be included in the writeup along with
legends, explanations, calculations, etc. Do not include MATLAB codes
in the writeup, only the results.
- Package the files so that the MATLAB codes can be run by
us -- do not put all the sources in one long text file,
for example. Also, we do not need your tex, lyx, Word, svn
files etc., only a PDF of the final product. Please make it easy for us to find
and examine the files quickly.
- If you are using Octave, do not use double quotes for strings, use
single quotes instead for compatibility with MATLAB.
- For pen-and-pencil problems you can submit hand-written
solutions if you prefer.
Present your information effectively
- Plot figures with
thought and care! For example, errors should be
plotted on a logarithmic scale, not linear, so you can see
it going down instead of flat lines. The plots should have
axes labels and be easy
to understand at a glance.
- A picture is worth a
thousand words! Instead of large tables, or
printouts of Matlab matrices, make a plot. Do not submit
pages of numbers unless there is a really good reason --
it is not an effective way to present the information.
- However, a picture by itself is not enough! You must
write a concise explanation of the figure, especially what
you learn from the figure (think of figure captions in
scientific papers).
- If you do print things, use fprintf to format the output nicely
instead of printing large matrices. Also use format compact and
other format commands to control how MATLAB prints things.
Quality over Quantity
- You need to demonstrate, in addition
to a code and plot, that you understand what the
numerical problem is. For example, the roundoff error in
problem 3.1 or 3.2 comes because of cancellation of
significant digits (read the title of the Section
heading!). Just reporting "error is smallest for h=\dots"
without an explanation will not get full points. I do not
expect theorems, but some understanding is crucial.
- Do not substitute true understanding/exploration with
trivial work: Solve a few problems well instead of handing
in quarter solutions to all the problems. Demonstrate that
you are intellectually-curious about the material.
Academic Integrity and Honesty
NYU
academic integrity policies will be strictly enforced
for homework assignments.
- It is encouraged to discuss
with other students the mathematical aspects, algorithmic
strategy, code design, techniques for debugging, and
compare results.
- Each student must write the solutions independently. Copying of any
portion of someone else's solution or allowing others to
copy your solution is considered cheating.
- Code sharing is not
allowed. You must type (or create from things
you've typed using an editor, script, etc.) every
character of code you use.
- The assignments are meant to challenge you: It is not expected that you
will get all of the points. If you spend more than 10-12
hours on an assignment consider talking to the instructor.
These rules not only ensure fairness but will also help you
get the most out of this course. Learning how to apply the
methods we discuss in class in practice is a critical part of
this course and the main component of your grade. Scientific
programming can only be learned by
doing it. What programmers call "debugging" is
an integral part of programming. You type something, and you
think the code does something, but then you run and it does
not run or produces numbers that do not look right. You learn
by fixing it. It is a process that
cannot be replaced by examining someone else's
code.
Assignments
0. (Due ASAP) Questionnaire
Please email me the following information with subject
"Numerical Methods I questionnaire"
- Name, degree, and class, any prior degree(s) or
professional experience.
- List all programming languages/environments that you
have used, when and why, and your level of experience
(just starting, beginner, intermediate, advanced,
wizzard).
- Why did you choose this course? Have you taken or plan
to take any other course in applied mathematics, numerical
analysis, or computing.
- What are your future plans/hopes for activities in the
field of applied and computational mathematics? Is there a
specific area or application you are interested in (e.g.,
theoretical numerical analysis, finance, computational
genomics)?
- Was the first lecture at a reasonable level/pace for
your background?
1. (Due Sept. 19, lecture on Sept. 4 and 11) Numerical Computing
Take a look at
lecture 1
for some examples and possible hints.
2. (Due Oct. 5, lectures on Sept. 11, 18 and 25) Square Linear Systems
Take a look at
lecture 2
and
lecture 3 for
some examples and possible hints.
Take a look at
lecture
4 and
lecture 5
for some examples and possible hints.
Take a look at
lecture
6 and
lecture
7 for some examples and possible hints.
Here is the
MATLAB script to compute
the Gauss-Legendre nodes on [-1,1]. Take a look at
lecture 8,
lecture 9 and
lecture 10, for some
examples and possible hints.
X. (Due Thursday Dec. 18 by 7pm) Take-home final
Will be posted by Dec. 11th.