# Mathematical Techniques for Computer Science Applications

CSCI-GA.1180-001
Summer 2018

### Teacher:

 Rémi Imbach Email: remi.imbach at nyu.edu Office: Warren Weaver Hall, Room 302. Office hours: Mon 10:00-12:00, Tue 6:00-7:00

### Where/When:

 Warren Weaver Hall, Room 312. (On July, 23 it will be WWH, Room 1302) Monday 6:00-8:20 PM

### Tutoring sessions:

 Warren Weaver Hall, Room 512. Friday 6:00-7:00 PM Tutor: Libin Lu Email: ll1488 at nyu.edu

### Textbooks:

 Ernest Davis, Linear Algebra and Probability for Computer Science Applications, CRC Press, 2012. Please note the List of Errata . Amos Gilat, MATLAB: An Introduction with Applications, Wiley. Online documentation for MATLAB: Getting Started with MATLAB

### Programming language:

 The course will be illustrated with MATLAB. Visit this page to know how to have access to MATLAB as an NYU student. MATLAB is installed on computers of Labs in CIMS.

### Class email list:

 To be announced

 None.

### Description:

 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.

### Schedule:

date subject material due warnings
May 21 Introduction to linear algebra, vectors, and MATLAB Chap. 1,2 of the textbook
June 4 Matrices and linear applications. Chap. 3 of the textbook
Code for the 1-dim signal processing example: signal_processing.m
June 11: Vector spaces and linear subspaces. Chapter 4 of the textbook.
June 18: Vector spaces and linear subspaces (II). Chapter 4 of the textbook. Prog. Ass. 1
June 25: Introduction to the Finite Element method.
Algorithms for solving syst. of lin. eqs. and inverting a matrix.

Chapter 5 of the textbook.
Slightly modified version of the algorithms: Course4_onlyAlgos.pdf
Homework 1
July 2: Affine geometry.
Introduction to ray tracing algorithms.
Chapter 6 of the textbook.
Lecture notes: here!
July 9: Singular Value Decomposition Chapter 7, section 7.7 of the textbook. Prog. Ass. 2
July 16: Basic probabilities Chapter 8 of the textbook
bunch of examples: examples
Homework 2
July 23: Numeric Random variables Chapter 9 of the textbook
bunch of examples: examples
Some exercises on random variables: exercises
Prog. Ass. 3 WWH, Room 1302
July 30: Numeric Random variables: continuous case
Confidence intervals (basic formula)
Monte Carlo algorithms
Chapters 9, 11.1, 12 of the textbook
My lecture slides: here
The Matlab code for computing a confidence inderval: here
The Matlab code for computing an area with Monte Carlo method: here
The Matlab code for computing an integral with Monte Carlo method: here
Homework 3
August 6: Final exam Sample exam: here
Correction: here
Prog. Ass. 4 (optional)

### Homework:

 Problem set for the first course: here Not due! First programming assignment: here . File template.zip . Due for 06/18/2018, 6:00pm. Attach it through the class site, on NYU Classes. Here you will find the perfect work of one of the students. First homework: here . Due for 06/25/2018, 6:00pm. Give it back to me either during a course, or during my office hours, or let it in my mail box in the lobby of WWH during a week day. In the latter case, inform me by email. Answers are here . Second programming assignment: here . Due for 07/09/2018, 6:00pm. Attach it through the class site, on NYU Classes. Here you will find the perfect work of one of the students. Second homework & Third programming assignment: here! . File template_rayTracing.zip: here! . Homework due for 07/16/2018, 6:00pm. Correction of the homework: here! . Prog. ass due for 07/23/2018, 6:00pm. Attach it through the class site, on NYU Classes. Third homework here . Homework due for 07/30/2018, 6:00pm. The solution is here Fourth programming assignment: here . Due for 08/06/2018, 6:00pm. (optional) File sets.m . Attach your work through the class site, on NYU Classes.