Math 104

Math 104: Applied Matrix Algebra
Fall 2010

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Course Description

This course is a mathematical treatment of linear algebra, but with a view towards numerical applications. The following topics will be covered:

Matrices, vectors and their products (review)

Rank of a matrix, linear independence and the four fundamental subspaces of a matrix

Matrices as linear transformations

Orthogonality and isometries

The QR decomposition

Eigenvalues and the spectral decomposition of symmetric matrices

The singular value decomposition and its applications

The conditioning of a matrix

Least squares problems

Algorithms for solving systems of linear equations and least-squares problems

Iterative methods for solving linear systems: the method of conjugate gradients

A tentative schedule is posted here. It will be updated as the course progresses.

Prerequisites:

Math 51 (or equivalent) and either Math 52 or Math 53. Some familiarity with rigorous (i.e. proof-based) mathematics will be helpful but is not essential.

Location and Time:

The course meets MWF from 2:15-3:05 in 380-380W.

Textbooks

The texts for the course are:

Numerical Linear Algebra by Lloyd N. Trefethen and David Bau III, SIAM (required)

Introduction to Linear Algebra by Gilbert Strang, Wellesley-Cambridge Press, 4th edition (optional)

These books are on reserve at the Math/CS library.

Instructor

The instructor for this course is Jacob Bernstein. His contact information is as follows:

Office: 380-382S (On the second floor next to the printer)

Phone: x3-2204

Email: jbern@math.stanford.edu

Office Hours: M 3-4:30PM, Tu: 9:30-11AM and by appointment.

The Couse Assistant is Sam Nariman. His contact information is as follows:

Office: 380-380U

Phone: TBA

Email: nariman@math.stanford.edu

Office Hours: Tu: 3:30-6PM, F: 2-5PM

Grades

The final course grade will be determined as follows:

40% Homework

20% Midterm Exam

40% Final Exam

Homework Policy

There will be 7 problem sets assigned in total and when assigned will be due the following Wednesday in class. Homework will count for 40% of the final grade with the lowest score dropped. Late work will only be accepted in exceptional circumstances and with prior approval of the instructor.

The homework and solutions will be posted here.

Exams

There will be one midterm exam and a final exam. Please let the instructor know as soon as possible about any conflicts with the date of the midterm.

The midterm exam will be held during class time on Wednesday, October 27 and will count for 20% of the final grade. In order to allow for enough room, the exam will take place in Bldg. 420 Rm. 041

The final exam will be held Friday, December 10, 12:15pm-3:15pm. The final exam will take place in 380-380C. The final exam will count for 40% of the final exam.

Additional Information

Working together is permitted, however it is essential that each student write up his or her own solutions. Use of sources (i.e. other people, books, the internet) without proper attribution will be considered plagarism. Honor Code and Fundamental Standard Statement from the Registrar concerning students with documented disabilities: "Students who may need an academic accommodation based on the impact of a disability must initiate the request with the Student Disability Resource Center (SDRC) located within the Office of Accessible Education (OAE). SDRC staff will evaluate the request with required documentation, recommend reasonable accommodations, and prepare an Accommodation Letter for faculty dated in the current quarter in which the request is being made. Students should contact the SDRC as soon as possible since timely notice is needed to coordinate accommodations. The OAE is located at 563 Salvatierra Walk (phone: 723-1066)."
Honor Code and Fundamental Standard Statement from the Registrar concerning students with documented disabilities: "Students who may need an academic accommodation based on the impact of a disability must initiate the request with the Student Disability Resource Center (SDRC) located within the Office of Accessible Education (OAE). SDRC staff will evaluate the request with required documentation, recommend reasonable accommodations, and prepare an Accommodation Letter for faculty dated in the current quarter in which the request is being made. Students should contact the SDRC as soon as possible since timely notice is needed to coordinate accommodations. The OAE is located at 563 Salvatierra Walk (phone: 723-1066)."
Statement from the Registrar concerning students with documented disabilities: "Students who may need an academic accommodation based on the impact of a disability must initiate the request with the Student Disability Resource Center (SDRC) located within the Office of Accessible Education (OAE). SDRC staff will evaluate the request with required documentation, recommend reasonable accommodations, and prepare an Accommodation Letter for faculty dated in the current quarter in which the request is being made. Students should contact the SDRC as soon as possible since timely notice is needed to coordinate accommodations. The OAE is located at 563 Salvatierra Walk (phone: 723-1066).": "Students who may need an academic accommodation based on the impact of a disability must initiate the request with the Student Disability Resource Center (SDRC) located within the Office of Accessible Education (OAE). SDRC staff will evaluate the request with required documentation, recommend reasonable accommodations, and prepare an Accommodation Letter for faculty dated in the current quarter in which the request is being made. Students should contact the SDRC as soon as possible since timely notice is needed to coordinate accommodations. The OAE is located at 563 Salvatierra Walk (phone: 723-1066)."

Fall 2010 -- Department of Mathematics, Stanford University