Mathematical Techniques for Computer Science Applications
Warren Weaver Hall room 312.
Professor Ernest Davis
Office hours: Tue 10:00-12:00, Wed 3:00-4:00
- phone: (212) 998-3123
- office: 329 Warren Weaver Hall
Amos Gilat, MATLAB: An Introduction with Applications, Wiley, 2008.
Note that amazon.com is selling a new copy cheaper ($61.04) than the used
copies at the NYU bookstore ($66), and you can get much cheaper used at
bookfinder.com. For the purposes of this class, it does not matter which
edition you buy. I didn't comparison shop the other books.
Steven Leon, Linear Algebra: With Applications,
7th edition, Pearson, 2005.
Morris DeGroot and Mark Schervish, Probability and Statistics, Addison
Online documentation for MATLAB:
Getting Started with MATLAB
Class email list
Be sure to subscribe to the
class email list
Xin Li. email: lixin @ same host as above. Office: 1009 715 Bway. Office hours
This course gives an introduction to theory, computational techniques, and
applications of linear algebra, probability and statistics. These three
areas of continuous mathematics are critical in many parts of computer
science, including machine learning, scientific computing, computer vision,
computational biology, computational finance,
natural language processing, and computer graphics.
The course will teach a specialized language for mathematical computation,
such as MATLAB, and will discuss how the language can be used for
computation and for graphical output. No prior knowledge of linear algebra,
probability, or statistics is assumed.
Assignment 1 due Sep. 28.
Exercises 1 NOT TO HAND IN.
Assignment 2 due Oct. 12. Postponed to Oct. 19.
Exercises 2 NOT TO HAND IN.
Assignment 3 due Nov. 2.
Sample Output for Assignment 3
Exercises 3 NOT TO HAND IN.
Assignment 4 due Nov. 16. Postponed to Nov. 23
Sample solutions to Assignment 4
Assignment 5 due Nov. 30.
Sample outputs for Assignment 5
Assignment 6 due Dec. 14
Sample outputs for Assignment 6
Monday, December 21, 7:00 PM. 312 WWH.
Provisional syllabus, subject to change
Biweekly assignments (60% of the grade).
Final exam (40% of the grade).
Part I. Introduction:
Week 1.A Introduction to MATLAB. Basic programming language features.
Class Notes Chapter 1: MATLAB. Gilat.
Part II. Linear Algebra:
Week 1.B. Vectors. Basic operations. Dot product. Vectors in MATLAB. Plotting
Class Notes Chapter 2: Vectors.
Week 2. Matrices. Definition, fundamental properties, basic
operations. Linear transformations.
Class Notes Chapter 3: Matrices.
Week 3. Abstract linear algebra: Linear independence, basis,
subspaces, null space.
Class Notes Chapter 4: Vector Spaces.
Week 4. Solving linear equations using Gaussian elimination.
Class Notes Chapter 5: Algorithms
Weeks 5+6. Geometric applications.
Class Notes Chapter 6: Geometry.
Week 7: Basis change and singular value decomposition.
Class Notes Chapter 7: Basis change.
Part III. Probability
Week 8: Introduction. Independence. Bayes's Law.
Week 9: Random variables. Expected value and variance. Discrete and
Application: Machine learning.
Week 10: Information theory and entropy. Maximum entropy technique.
Week 11: Markov chains.
Application: Natural language processing.
Part IV. Statistics.
Week 12: Non-parametric statistics. Computer-based resampling techniques.
Confidence intervals and statistical significance.
Application: Software testing.
Week 13: Distributions. Binomial and normal distributions.
Monte Carlo methods.
Taking care of your health is always a priority, but particularly this year, as
there is a widespread and dangerous flu epidemic. Therefore:
If you have any symptoms of the flu, and especially if you are sneezing or
coughing, PLEASE TAKE CARE OF YOURSELF AT HOME AND DO NOT COME TO CLASS. Going
out in public when you have a communicable illness is not only unwise in terms
of your own health, but it is extremely irresponsible and
unfair to fellow students to put them at risk.
I am not taking attendance, and there is no penalty for missing class. If you
are too ill to come to class, but well enough to work at home, then submit
your assignments by email. If you are too ill to work, I will accept
assignments a week late. If you miss both the regular due date and the late
deadline due to illness, please consult with me promptly about making
up the assignment. If you are too ill to come to the final exam, if at all
possible, let me know in advance by email; if not, then please contact me
as soon as possible.
Please note also:
- A significant fraction of cases of swine flu occur without any fever,
or with a depressed temperature. If you have sneezing, coughing, body aches,
and fatigue, you should assume you have the flu, even if you have no fever.
You remain contagious for some time after you are feeling
better. Please stay home for at least 24 hours after your fever and other
symptoms have gone away.
- The progress of the disease can extremely fast. If you feel seriously ill
(high fever, difficulty breathing, etc.) seek medical attention IMMEDIATELY.
You may discuss any of the assignments with your classmates (or anyone else)
but all work for all assignments must be
entirely your own. Any sharing or copying of assignments will be
considered cheating. By the rules of the Graduate School of Arts and Science,
I am required to report any incidents of cheating to the department.
Department policy is that the first incident of cheating will result in the
student getting a grade of F for the course.
The second incident, by GSAS rules, will result
in expulsion from the University.