Math 235 Introduction to Linear Algebra, Fall 2017

Instructor: Matthew Dobson
Class meeting: MWF 1:25-2:15 in ILC S140
Office hours: T 1p-2p, W 2:30p-3:30p F 9a-10a or e-mail me to make an appointment.
Office: LGRT 1430 (Tower)
e-mail: dobson@math.umass.edu
Office phone: 545-7194
Common Course Website

Overrides

Students needing an override in order to enroll in the course should contact me with the following information: (1) sections of the course which conflict with other courses from your academic schedule, and (2) preferred section of the course. (Unfortunately, in order to keep the sections balanced we cannot guarantee that you will be assigned to your preferred section.)


Textbook and Online homework

The course text is Linear algebra and its applications (5th edition) by David Lay, Steven Lay, and Judi McDonald.

MyMathLab is required for this course. An electronic copy of the textbook is included in your purchase of MyMathLab. Go to My Math Lab and use the Course ID for our section: dobson12536

Online homework will be assigned through MyMathLab.


Syllabus and weekly schedule

This is an introductory course on linear algebra, covering systems of linear equations, matrices, linear transformations, determinants, vector spaces, eigenvalues and eigenvectors, and orthogonality.

The schedule below gives the topics from the course text to be covered each week. (Note: this is a tentative schedule with pacing adjusted as necessary.)



9/5--9/8: 1.1 Systems of linear equations; 1.2 Row reduction and echelon forms; 1.3 Vector equations.

9/11--9/15: 1.3 (continued); 1.4 The matrix equation Ax=b; 1.5 Solution sets of linear systems.

9/18--9/22: 1.7 Linear independence; 1.8 Introduction to linear transformations.

9/25--9/29: 1.9 The matrix of a linear transformation; 2.1 Matrix operations.

10/2--10/6: 2.2 The inverse of a matrix; 2.3 Characterizations of invertible matrices.

10/9--10/13: 3.1 Introduction to determinants; 3.2 Properties of determinants.

10/16--10/20: 3.2 (continued); 3.3 Cramer's rule, volume, and linear transformations; 4.1 Vector spaces and subspaces.

10/23--10/27: 4.2 Null spaces, column spaces, and linear transformations; 4.3 Linearly independent sets and bases.

10/30--11/3: 4.4 Coordinate systems; 4.5 The dimension of a vector space.

11/6--11/10: 4.6 Rank; 5.1 Eigenvectors and eigenvalues.

11/13--11/17: 5.1 (continued); 5.2 The characteristic equation.

11/20--11/24: Thanksgiving break.

11/27--12/1: 5.3 Diagonalization; 5.5 Complex eigenvalues.

12/4--12/8: 6.1 Inner product, Length, and Orthogonality; 6.2 Orthogonal sets.

12/11--12/12: 6.3 Orthogonal projections; 6.4 The Gram--Schmidt process.


Important Dates

Last day to drop with no record is Monday, Sept 18th. Last day to withdraw with a W is Thursday, Oct 19th.


Exams See the common course website for updated exam information: Common Course Website
Grading

Your course grade will be computed as follows: First midterm exam 25%; Second midterm exam 25%; Final exam 25%; Homework 25%.



Netflix Prize In class, I mentioned the Netflix prize, where low-rank approximation (among many other approaches) was applied to a machine-learning algorithm.
Here is a NY Times non-technical writeup about the competition.
The official Netflix Prize site contains more information, including writeups from the top teams.
The BellKor algorithm includes low-rank approximations with many problem-specific improvements (see equation (13)).


Accommodation Policy Statement

UMass Amherst is committed to providing an equal educational opportunity for all students. A student with a documented physical, psychological, or learning disability on file with Disability Services may be eligible for academic accommodations to help them succeed in this course. If you have a documented disability that requires an accommodation, please notify your instructor during the first two weeks of the semester so that we can make appropriate arrangements.