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:  2129983088 
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. AddisonWesley, 2005. ISBN 9780321287137. 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 outofsequence 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:
 A documented medical excuse.
 A Universitysponsored 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.
 A religious holiday.
 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:


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  2.62.7  Leontief I/O model,graphics applications 

Th  6  HW4  3.13.2  Determinants, Properties of Determinants 






6  Tu  11  
3.3  Cramer’s rule 

Th  13  

Review 






7  Tu  18  Midterm  


Th  20  HW5  4.14.2  vector spaces, subspaces 






8  Tu  25  
4.34.4  bases, coordinate systems 

Th  27  HW6  4.54.6  dimension, rank 






9  Tu  Nov. 1  Quiz 3  4.7  Change of basis 

Th  3  HW7  4.84.9  Applications, Markov chains 






10  Tu  8  
5.15.3  Eigenvectors 

Th  10  HW8  
Eigenvalues 






11  Tu  15  
5.45.6  linear transformations 

Th  17  HW9  
eigenvalue applications 






12  Tu  22  Quiz 4  6.16.2  inner product 

Th  24  
Thanksgiving
Recess
(Nov
2527)








13  Tu  Nov. 29  
6.36.4  orthogonal projection, GramSchmidt 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:
8:00pm9:50pm


