Term:	Spring 2011
Meeting times:	MW 8:55–10:45am (Location TBD)
Instructor:	Dr. Hoai-Minh Nguyen
Office:	CIWW 1009
Office hours:	TBD
Phone:	212-998-3259
Email:	hoaiminh at cims.nyu.edu

Course Description

Systems of linear equations, Gaussian elimination, matrices, determinants, Cramer’s rule. Vectors, vector spaces, basis and dimension, linear transformations. Eigenvalues, eigenvectors, and quadratic forms.

Course Objectives

Upon successfully completing this course students will be able to:

• Formulate, solve, apply, and interpret systems of linear equations in several variables;
• Compute with and classify matrices;
• Demonstrate elementary facts in abstract vector spaces;
• Decompose linear transformations according to their spectra (eigenvectors and eigenvalues)
• Use length and orthogonality in each of the above contexts.

Course Requirements

The course meets for lecture twice a week for 110 minutes each class period. Class will be a mixture of direct instruction (like a lecture) and guided practice (like a recitation).

You are also expected to study outside of class, up to three hours for each hour of class. Studying can be reading the book, reviewing notes, practicing problems, or doing homework.

Resources

Textbook

Linear Algebra and its Applications by David C. Lay. Addison-Wesley, 2005. ISBN 978-0321287137. New and used copies are on sale in the NYU Bookstore and can also be found online. A copy will be put on reserve in Bobst Library.

Calculator Policy

At NYU, undergraduate mathematics is largely conceptual rather than computational. Calculators may be used on homework but do not suffice on problems for which explanation is required. Calculators may not be used on quizzes or exams.

Course Prerequisites

A grade of C or better in V63.0121 Calculus I or equivalent. Linear Algebra does not depend logically on calculus but is conceptually a more challenging course.

Evaluation Plan

There will be regular homework and periodic quizzes. There will be a midterm examination and a final exam. These elements will be combined into a course average using the following weights:

Policy on missed and out-of-sequence assessments

In general, out of fairness to the rest of the students in the class, late homework assignments and makeup quizzes or exams are not possible. We will drop the lowest homework and the lowest quiz to give you one ”free pass” for any reason.

We may approve a rescheduled or makeup exam or quiz in the following cases:

1. A documented medical excuse.
2. A University-sponsored event such as an athletic tournament, a play, or a musical performance. Athletic practices and rehearsals do not fall into this category. Please present documentation from your coach, conductor, or other faculty advisor describing your absence.
3. A religious holiday.
4. Extreme hardship such as a family emergency, again with documentation.

Weddings and other special family events do not qualify as any of the above; the free pass is appropriate here. Nor can we reschedule for purposes of more convenient travel, even if tickets have already been purchased.

Rescheduled exams and quizzes (those not arising from emergencies) must be taken prior to your absence. Otherwise, please contact us before you return to class.

If you require additional accommodations as determined by the Moses Center for Student Disabilities, please let us know as soon as possible.

Grading

The weighted average above will be converted to a letter grade beginning with the following scale:

As for a ”curve,” we may lower these cutoffs to create higher letter grades.

Policy on Academic Integrity

New York University takes plagiarism and cheating very seriously and regards them as a form of fraud. Students are expected to conduct themselves according to the highest ethical standards. These offenses are all considered violations of academic integrity:

• Use of unauthorized resources for completion of assignments (e.g., a solution manual illegally purchased or downloaded or an internet community that provides answers);
• Nondisclosure of collaboration on homework or copying another student’s written solution;
• Discussion of a quiz or exam between someone who has taken it and someone who has not;
• Copying another student’s quiz or exam;
• Forging documentation to justify a makeup quiz or exam or late assignment.

There are of course other possibilities. We expect you to be familiar with your school’s student handbook and its statement of academic integrity. Penalties range from a score of zero on a problem, assignment, quiz, or exam, to a failing grade in the course and notification of the student’s Dean. Multiple violations can result in dismissal from the University.

Schedule of Classes

There are roughly 27 class periods per semester. All of these sections and perhaps some of the optional sections will be covered.

Lecture	Book Section	Description
1	1.1	Systems of Linear Equations
2	1.2	Row Reduction and Echelon Forms
3	1.3	Vector Equations
	1.4	The Matrix Equation Ax = b
4	1.5	Solution Sets of Linear Systems
	1.6	Applications of Linear Systems
5	1.7	Linear Independence
6	1.8	Introduction to Linear Transformations
	1.9	The Matrix of a Linear Transformation
optional	1.10	Linear Models in Business, Science, and Engineering
7	2.1	Matrix Operations
	2.2	The Inverse of a Matrix
8	2.3	Characterizations of Invertible Matrices
optional	2.5	Matrix Factorizations
optional	2.6	The Leontief Input-Output Model
optional	2.7	Applications to Computer Graphics
9	3.1	Introduction to Determinants
	3.2	Properties of Determinants
optional	3.3	Cramer’s Rule, Volume, and Linear Transformations
10	4.1	Vector Spaces and Subspaces
	4.2	Null Spaces, Column Spaces, and Linear Transformations
11	4.3	Linearly Independent Sets; Bases
12	4.4	Coordinate Systems
13	4.5	The Dimension of Vector Space
	4.6	Rank
14	4.7	Change of Basis
15	4.8	Applications to Difference Equations OR
	4.9	Applications to Markov Chains
16	5.1	Eigenvectors and Eigenvalues
	5.2	The Characteristic Equation
17	5.3	Diagonalization
18	5.4	Eigenvectors and Linear Transformations
19	5.5	Complex Eigenvalues
20	5.6	Discrete Dynamical Systems OR
	5.7	Applications to Differential Equations
21	6.1	Inner Product, Length, and Orthogonality
	6.2	Orthogonal Sets
22	6.3	Orthogonal Projections
	6.4	The Gram-Schmidt Process
23	6.5	Least-Squares Problems
24	7.1	Symmetric Matrices
25	7.2	Quadratic Forms