Harvard Extension School
Mathematics E-21b - Spring 2020
Recommended Course Textbook
Linear Algebra with Applications, 4th Edition
Linear Algebra with Applications, 3rd Edition
Linear Algebra with Applications, 5th Edition
A key matching HW exercises in different editions is available on request.
A copy of the text will be put on reserve in the Grossman Library in Sever Hall.
AMC Local Walks:
HW #3 problems (PDF) - keyed to 4th Edition (due Thurs, Feb 20 in class or Sat, Feb 22 online via Canvas)
HW #2 problems (PDF) - keyed to 4th Edition (due Thurs, Feb 13 in class or Sat, Feb 15 online via Canvas)
HW #1 problems (PDF) - keyed to 4th Edition (due Thurs, Feb 6 in class or Sat, Feb 8 online via Canvas)
[Multivariable Calculus Notes #1 for vector references]
Classes meet every Thursday evening from 8:00pm to 10:00pm in Maxwell-Dworkin G115 starting January 30, 2020. There will also be optional online weekly problem sessions (conducted by TAs Jeremy Marcq and Renée Chipman). TA Renée Chipman will also meet with individuals and small groups on request. Students are not assigned to sections - any student may attend (online) the sessions by either Jeremy, Renée, or both.
Renee Chipman's online discussion section is scheduled to meet Mondays (starting Feb 3) from 2:00pm to 3:00pm plus an additional half-hour at the end if there are any lingering questions. This session should be accessible via the Canvas site - most likely under Section Meetings (or something similar). You may be asked to download and install an executable file in order to participate.
Jeremy Marcq's online discussion session will take place on Wednesdays (starting Feb 5) from 11:00am to noon. The link will be accessible via the Canvas site.
Needless to say, these section meetings are purely optional and you can participate in either or both of them.
Each week on Thursday evening before class (starting February 13) there will be an optional pre-class Q&A session starting at 7:00pm (or soon thereafter) - currently in Northwest Science Building room B109 (though I hope this will change). The primary purpose of this Q&A session will be to take last-minute questions on the assigned homework problems after you have struggled with them. Robert Winters will conduct the session.
For Thursday, February 6, I will endeavor to arrive early at Maxwell-Dworkin and be available informally for questions at the tables in the area outside our lecture hall. - RW
Important Dates - Harvard University Extension School - Spring 2020
Questions, questions, questions..... and some answers
1) I usually post announcements and assignments initially on the working course website: http://math.rwinters.com/E21b/
2) All of the lectures will be live-streamed and recorded and made available within about one day. All of the lectures will be available via a link on the course's Canvas Site for the duration of the course and for a few weeks thereafter.
3) The main materials of the course are the lectures, the weekly Lecture Notes, the Bretscher text (best to get an inexpensive one online - links for best deals on the course website), and, of course, the homework assignments.
4) People who attend class in person can submit HW on paper in class. Distance students will be able to submit HW as a single scanned PDF (easily readable and with a reasonable file size, i.e. not scanned at an unnecessarily high resolution). Since classes are on Thursday and the recorded lectures are available on Friday (usually), I generally have assignments due no later than the following Saturday night. All students have the option to submit their assignments online, including those who regularly attend the lectures.
5) We will have two midterm exams and a final exam. The Calendar is given at: http://math.rwinters.com/E21b/calendar.htm. Most students who can take exams in person will do so on the scheduled date of the exam. Distance students are responsible for finding a qualified proctor near their home who will administer and monitor them throughout the duration of their exam. The proctor must be approved by the Distance Exams Office at least a week prior to the exam. Proctors scan and send the completed exams to the Exams Office, and they then make them available to the Instructor for grading. Students can find more information at the Extension School website here: https://www.extension.harvard.edu/exams-online-courses
6) Since Linear Algebra is largely independent of the Calculus sequence, any prerequisites other than general mathematical competence are really just recommendations or suggestions. Even the Placement Test is really for your own use to see if you're ready for the course. It is most certainly not required for registration.
7) The "Graduate" credit option is primarily for students enrolled in certain Extension School graduate programs such as the "Math for Teaching" program. All other students (including high school students) should register for the "Undergraduate" option or the Noncredit option (if you will not be submitting homework or taking exams).
The Harvard Extension School is committed to providing an accessible academic community. The Accessibility Office offers a variety of accommodations and services to students with documented disabilities.
Please visit https://www.extension.harvard.edu/resources-policies/resources/disability-services-accessibility for more information.
We prefer that assignments be submitted on paper for those who attend class in person. Other students should submit their assignments as a single scanned PDF file, but this option is also open to local students for any given assignment.
A basic standard is that you should not scan at resolution greater than about 120dpi. Anything beyond that is not necessary for handwritten work and dramatically increases file size. Black & White scans are preferred unless there is a good reason to scan using color. Please also make sure that the contrast is adjusted properly so that all work is clearly legible.
Photographs of assignments will not be accepted - scans only.
Based on class size and practical limits, we will select a subset of each assignment for grading. Solutions to all problems will be posted after the due date.
Homework: Total points and median scores
Academic Integrity Letter from Robert Neugeboren, Dean of Students, Harvard Extension School (2014)
A letter to the New England Courant, dated May 14, 1722, and actually written by Benjamin Franklin under the
posted with the permission of Bill Griffith
A word about calculators:
Though you can do this course without a matrix-capable calculator or mathematical software, it's certainly easier if you have an electronic servant to handle the drudge work. I use a TI-85 (no longer sold, but a good buy if you can find a used one) and I've been very happy with it. Ideally, you'll want a calculator that can find the reduced row echelon form of a matrix (RREF). You might also want one that can calculate determinants, eigenvalues, and eigenvectors, but that's a lesser priority. The TI-83 Plus, the TI-84 Plus, the TI-84 Plus Silver Edition, the TI-86 (also discontinued), and the TI-89 calculators can handle these operations. You don't need anything fancier than this.
One feature that I find very handy is the ability to display fractions and convert a decimal expression (for a rational number) to a fraction. That's useful when translating the results of an RREF calculation into parametric equations for a solution to a system of linear equations.
Here's a link that gives a comparison of the various TI calculators. Other manufactures also produce calculators that will work well with this course.
Linear Algebra Toolkit - an excellent online collection of tools that will not only do the calculations but also walk you through the steps. (The PERL scripts are written by Przemyslaw Bogacki.)
Download your free Adobe Acrobat Reader for reading and printing PDF formatted documents.
Please send comments to Robert Winters.
Last modified: Sunday, February 16, 2020 9:15 PM