Numerical Computing

Numerical Computing, CSCI-UA.0421-001

New York University
Spring Semester 2015

Class meetings: Tues-Thurs, 11am - 12:15pm, in Warren Weaver Hall (CIWW) 517.
Last day of class: Thursday, May 7, 2015.
Final exam: Thursday, May 14, 10-11:50am, in WWH 102.

Instructor: Margaret H. Wright, mhw@cs.nyu.edu

Office: Warren Weaver Hall (CIWW), Room 430

Office Hours: Wed 10-11:45am, or by appointment.

Course Description

Numerical computing is an interconnected combination of computer science and mathematics in which we develop and analyze algorithms for solving important problems in science, engineering, medicine, and business---for example, designing a bridge, choosing a stock portfolio, or detecting tumors in medical images.

This class will cover several topics, including: one-dimensional nonlinear equations; understanding and dealing with sources of error; linear equations and linear least-squares; data fitting; splines; numerical integration; and ordinary differential equations. As much as possible, numerical methods will be presented in the context of real-world applications.

Coursework

The course requirements include class attendance; written and programming homework assignments; and a midterm. In addition, depending on enrollment, there will be either a final examination or a mini-research project. All of these will count in your final grade.

The final grade will be calculated by averaging the three elements (Homework, Midterm, Final Project/Final Examination), with weights of 30%, 30%, 40%, where the weighting for these items will be chosen individually to maximize each student's grade.

Academic Integrity

Academic integrity is a core principle of education at NYU, including five fundamental values: honesty, trust, fairness, respect, and responsibility. For a discussion of academic integrity policy in the Computer Science Department, see on the Computer Science website. In numerical computing, academic integrity includes individual completion of all assignments. If one students shows or gives his/her work to another, both students are considered to be cheating. Students may not use work provided by any person outside the class, or by any external course such as the Web. Students may not solicit other people to do assignments (in whole or in part) for them. External sources, including published materials or materials on the Web, must be explicitly cited if they are involved in any substantive part of an assignment. During an exam, students may not communicate in any way with anyone else, nor use materials or technology not permitted by the instructore. One student may not look at another student's test during an exam. If one student allows another to look at his/her test during the exam, both students are considered to be cheating.

Prerequisites

V22.0102 (introduction to computer science II), V63.0140 (linear algebra), and calculus (preferably V63.0122, Calculus II).

Students without this background should check with the instructor for permission to take the class.

Professor Gilbert Strang's famous linear algebra courses at MIT can be found on the MIT open courseware website or on YouTube, with search terms ``Strang linear algebra MIT''.

Textbook

Primary text: Numerical Methods: Design, Analysis, and Computer Implementation of Algorithms by Anne Greenbaum and Timothy P. Chartier, published by Princeton University Press, available at the NYU Bookstore. Other useful books are A First Course in Numerical Methods by Uri M. Ascher and Chen Greif, published by the Society and Industrial Mathematics (SIAM) and Numerical Computing with Matlab by Cleve Moler, with individual chapters that can be downloaded from the MathWorks website.

Other material will be passed out as notes.

Programming

The instructor will use Matlab, an interactive software package and programming environment, for her own programs. If you prefer another language, this is fine as long as your code is intelligible. Matlab is a product of the Mathworks; a student version costs around $100 at the Computer Store, or you can use Matlab in a Courant computer lab. (You will need a CIMS account, which will be provided after the second class.) You can use Matlab remotely, with a few (solvable) complications if you wish to use its graphics capabilities.

Matlab tutorials are available online from several sites. For example, there is an array of tutorial and other educational resources for students on the MathWorks website .

Homework

HW1, due February 12, 2015.
HW2, due February 19, 2015.
HW3, due February 26, 2015.
HW4, due March 5, 2015.
HW5, due April 2, 2015.
HW6, due April 9, 2015.
HW7, due April 21, 2015.
HW8, due April 30, 2015.
HW9, due May 7, 2015.
Homeworks must be submitted in electronic form, and must be emailed to the instructor no later than 11:59pm on the due date. Without explicit permission from the instructor in advance, late homework will be marked down by 30% for every day of lateness.

Midterm

An in-class, closed-book midterm was given on Tuesday, March 10.