Harvard Extension School
Mathematics E-21b - Spring 2018
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:
Course grades will be available online (not via Canvas) on Tuesday, May 22.
HW #14: Read sections 9.1 and 9.2 and the supplement on nonlinear systems and linearization. There are five problems in the nonlinear supplement and solutions are posted for those problems. There is no assignment to be turned in.
The Final Exam will take place on Thursday, May 10 from 7:40pm to 9:40pm in Emerson 105 (not our usual lecture hall).
HW #13 problems (due in class on Thurs, May 3 or online by Sat, May 5, 11:59pm EDT)
Though there are no prepared Lecture #13 notes, all of the necessary information is in sections 9.1-9.2 of the text and in the following supplements:
Sampler of Phase Plane diagrams for uncoupled, coupled, period, and stable sink linear systems and a nonlinear system
You may also want to make use of the following java-based [pplane] tool for showing vector fields and flows: http://math.rice.edu/~dfield/dfpp.html. The current version requires you to download a Java executable file to your own computer and to run it locally on your own machine. You can customize various options. You can also print the graphs.
HW #12 problems (due in class on Thurs, Apr 26 or online by Sat, Apr 28, 11:59pm EDT)
There are no prepared Lecture #12 notes yet, but all of the necessary information is in the Lecture #11 Notes and the appropriate sections of the text on quadratic forms.
HW #11 problems (due in class on Thurs, Apr 19 or online by Sat, Apr 21, 11:59pm EDT)
HW #10 problems (due in class on Thurs, Apr 12 or online by Sat, Apr 14, 11:59pm EDT)
HW #9 problems (due in class on Thurs, Apr 5 or online by Sat, Apr 7, 11:59pm EDT)
Plan ahead: The exam dates for this course are March 1 (~70 minute midterm during latter part of class), April 19 (~70 minute midterm during latter part of class), and May 10 (2 hour Final Exam). 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. Students can find more information at the Extension School website here: https://www.extension.harvard.edu/exams-online-courses
A message was sent to the entire class list on Feb 10 with information about accessing homework solutions. Practice exams and exam solutions will also be found in that same directory when the time is right. If you did not receive the message, (a) check your Spam filter or (b) let me know via email and we'll figure it out. - RW
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.
We are offering this course this semester for the first time with an online option. Some details are being worked out as we go, so check back frequently on this site and on the Canvas site for the course.
Note: 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).
Classes will meet every Thursday evening from 7:40pm to 9:40pm in Harvard Hall 201 (next to Johnson Gate) starting January 25. There will also be an optional weekly problem sessions (conducted by TAs Jeremy Marcq and Renée Chipman) at days and times and locations to be determined. TA Renée Chipman will also meet with individuals and small groups on request. Students are not assigned to sections - any student may attend (in person or online) the sessions by either Jeremy, Renée, or both.
Jeremy's weekly section is scheduled for Tuesdays from 7:40pm to 8:40pm in Maxwell Dworkin G125.
Each week on Thursday evening before class (starting February 1) there will also be an optional pre-class Q&A session starting at 6:40pm (or soon thereafter) - also in Harvard Hall 201. 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.
Important Dates - Harvard University Extension School - Spring 2018
Questions, questions, questions..... and some answers
1) All of the lectures will be recorded and made available within about one day. I don't believe there is any capability for live streaming. 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.
2) 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 Friday or Saturday. All students have the option to submit their assignments online, including those who regularly attend the lectures.
3) Exams for Distance students are handled via the Exams Office. Distance students have to make arrangements for a proctor and this must be approved by the Exams Office. Proctors scan and send the completed exams to the Exams Office, and they then make them available to me for grading. We will have two midterm exams and a final exam. The Calendar is given at: http://math.rwinters.com/E21b/calendar.htm
4) I usually post announcements and assignments initially on this site: http://math.rwinters.com/E21b/
5) The main materials of the course are the lectures, my weekly Lecture Notes, and the Bretscher text (best to get an inexpensive one online - links for best deals on the course website), and, of course, the homework assignments.
6) 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. Students can find more information at the Extension School website here: https://www.extension.harvard.edu/exams-online-courses
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.
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: Wednesday, May 16, 2018 5:51 PM