Math 221 - Infinite Dimensional Linear Algebra - Fall 2009

 

General Information

Instructor: Michael Bush
Office: Burton 316
Phone: (413) 585-3644
e-mail: mbush[AT]smith.edu

Class Times: MWF 1:10 - 2:30 pm, Burton 219.
Office Hours: Tu 1:00 - 2:00 pm; W 11:00 - noon; F 10:30 - noon (or by appointment).
Textbook: There is no textbook. All of the course materials will be provided through moodle. Check here during the first week of classes for the first installment.

Syllabus

This course is an honors level version of Math 211. It introduces linear algebra which fundamentally is the study of linear systems of equations. Topics to be covered include solving linear systems, vectors, matrices, determinants, bases, dimension, vector spaces, linear transformations, eigenvalues, eigenvectors, inner products, Hilbert spaces. Despite the title, a lot time will be spent understanding linear algebra in the finite dimensional setting.

Prerequisites: This course is aimed at incoming first year students with one year of calculus (although some older students will be allowed to enrol). The calculus requirement is primarily to ensure that you will be able to handle the level of the material although we will actually make use of some properties of integrals and convergent series in discussing examples of infinite dimensional vector spaces towards the end of the course. If you're not sure you satisfy the prerequisites and want to take this class then please come and talk to me.


Active Learning

The course will be taught using an active learning style called the Cohen method. One of the primary goals is to give undergraduate students exposure to higher level mathematical thinking at an early point in their development. It also aims to help develop good written and oral communication skills. There will be almost no lecturing by me in class (except possibly during review periods). In most classes you will work on problem sets in small groups. These problem sets are self-contained and will introduce you to the relevant material. I will be meeting each group regularly to provide feedback and assistance. At the end of the week, each group will submit a short written paper on their assigned topic/problems and give an oral presentation to the rest of the class.

Here is a more detailed outline of a typical week's activities. Activities in blue take place outside of class:

Friday: Group oral presentations on current week's problems/topic; Start work on next week's topic.
Before class on Monday: Read assignment and work on new problems (2 hours suggested); Make corrections to previous work based on Friday's feedback and review work on other topics by other groups (in preparation for quizzes).
Monday: Group work in class; 15 minute group meetings with me to help resolve problems that are stumping everyone in the group.
Before class on Wednesday: Each individual writes up solutions to the problems.
Wednesday: Each group meets to organize a single final written solution and oral presentation on their topic. I will give you feedback about your initial drafts and assist in resolving any last minute questions.
Before 9 pm on Thursday: Designated group leader (rotates around group) posts final version of paper on moodle for class and myself to access and makes sure group is prepared for presentation; I will post the next week's problems and topics on moodle on Friday morning and bring handouts to class.

The cycle then repeats. You will be probably find it helpful to organize an additional group meeting either over the weekend or between Monday and Wednesday's class. You should expect to spend 5-6 hours working on the course outside of class each week. If you are having difficulties with a problem or topic and these do not get resolved in class you should see me during office hours (or schedule an appointment). There will be regular quizzes (10 minutes) usually in class on either Monday or Wednesday. They will be kept relatively easy and are just meant to check that you are keeping up with work by other groups (as well as your own).

Note: Adjustments to this schedule in certain weeks may be necessary due to events like mountain day. Check moodle regularly for announcements about such changes.

Grading

You grade will be based on group work (written and oral presentations), quizzes, a mid-term exam and a final exam. These will be weighted as follows: Group work 35%, Quizzes 15%, mid-term 20%, Final Exam 30%.

Attendance: Given the nature of the course, attendance is vital. There will not be make-ups for quizzes. Each unexplained absence from class will incur a penalty deduction from your final course total. If on the other hand you have a valid reason for being absent (eg. illness) then you should contact me as soon as you can and no penalty will be assessed.

Late Submission: If submission of a group's weekly written paper is delayed for some reason then I should be contacted with an explanation. Failure to provide an adequate explanation will result in a penalty being assessed against all members of the group.

Honor Code

All students are expected to abide by Smith's Honor code. For group work, please ensure that the names of all people contributing are included on the work. If you receive substantial help from other sources (a book, online, ...) in completing a problem then please include a statement acknowledging this help on your work.

All exams and quizzes must be completed on your own without any help.

Please talk to me in class or email me if you have any questions about the policies above or the course work. Good luck this semester!