Courant Institute New York University FAS CAS GSAS

# math ua.0140 / V63.140: Linear Algebra

 Term: Fall 2011 Meeting times: TR 11:00 to 12:50 Location TBD Instructor: Esteban Tabak Office: TBA Office hours: TBA Phone: 212-998-3088 Email: Tabak@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:

 Homework 15% Quizzes 20% Midterm 25% Final Exam 40% Total 100 %

#### 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.

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

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

 Cutoff Grade 93% A 90 A- 87 B+ 83 B 80 B- 75 C+ 65 C 50 D

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.

 Week Date Due Section Content 1 Tu Sep. 6 1.1 Systems of linear equations Th 8 1.2+1.3 Solving linear equations, Vectors 2 Tu 13 1.4+1.5 Matrix equations Th 15 HW1 1.6+1.7 Applications, Linear independence 3 Tu 20 Quiz 1 1.8 linear transformations Th 22 HW2 1.9+2.1 Matrix of Lin. Trans., Matrix operations 4 Tu 27 2.2+2.3 Matrix inverses, Characterizations Th 29 HW3 2.4+2.5 Partitioned matrices, LU factorizations, 5 Tu Oct. 4 Quiz 2 2.6-2.7 Leontief I/O model,graphics applications Th 6 HW4 3.1-3.2 Determinants, Properties of Determinants 6 Tu 11 3.3 Cramer’s rule Th 13 Review 7 Tu 18 Midterm Th 20 HW5 4.1-4.2 vector spaces, subspaces 8 Tu 25 4.3-4.4 bases, coordinate systems Th 27 HW6 4.5-4.6 dimension, rank 9 Tu Nov. 1 Quiz 3 4.7 Change of basis Th 3 HW7 4.8-4.9 Applications, Markov chains 10 Tu 8 5.1-5.3 Eigenvectors Th 10 HW8 Eigenvalues 11 Tu 15 5.4-5.6 linear transformations Th 17 HW9 eigenvalue applications 12 Tu 22 Quiz 4 6.1-6.2 inner product Th 24 Thanksgiving Recess (Nov 25-27) 13 Tu Nov. 29 6.3-6.4 orthogonal projection, Gram-Schmidt process Th Dec. 1 HW10 6.5, 6.7 least squares, inner product spaces 14 Tu 6 6.6+7.1 applications, symmetric matrices Th 8 HW11 7.2+7.4 quadratic forms, singular value 15 Tu 13 Last day of classes and Review 16 Tu Dec. 20 Tentative Final Exam: 8:00pm-9:50pm