Linear Algebra and Real Analysis I

If you live near Cambridge, come and take the final exam from 6 PM to 9 PM on Wednesday, December 14 in Science Center 309a.

Otherwise, you will have to arrange an official proctor through the Distance Exams office. As of December 6, many (but far from all) of the "true distance" students have already done this. The expert on distance exams is Jen Crowley at 617-495-7928.

Final Exam format (see blank exam on the quizzes page)

I. 5 of 6 multiple-choice questions on topics from Weeks 9-12
II. Find 3 false statements in a set of 8 and construct an explicit counterexample for each.
III. 7 of 8 problems:
    1-4 are inspired by randomly-chosen section problem topics from Weeks 9-12.
     5-8 fill in the coverage of topics that everyone is anticipating like

  • Differential equations (with patriarchal story line)
  • Diffferentiability
  • Newton's method
  • Implicit function theorem
  • Manifolds and tangent spaces
  • Critical points
  • Lagrange multipliers

IV. 2 of 3 proofs from weeks 9-12

Because of the strict 3-hour time limit, everyone (even those who opted out of proof logging) can omit a proof in the final section.

As with the quizzes, you are allowed a set of executive summaries, but you must print them yourself from the file on the Quizzes tab and bring them to the exam.
There is also a good practice exam on the Quizzes tab. It was written by the course assistants last year, using the format provided by the blank exam.

 

 

Here is an updated syllabus for Fall 2016 : sylE23a-2016.pdf
It explains how you can "opt out" of the problem-solving classes and the proof logging system.

Here is one possible solution to the problem of how to create nice-looking mathematics while presenting a proof online, either in section or for proof logging.

First download and open the finished product: BeamerProof1-1.pdf This works like Power Point if you open the file in Acrobat Reader or TeXworks

To create this file, install MiKTeX and TeXworks (instructions in the syllabus) and then open and typeset this source file:

BeamerProof1-1.tex

This first step will take a while because the Beamer package has to be installed from the Internet.

Here is a template that you can use for your own proofs: BeamerProofTemplate.tex

To learn how to input mathematics in LaTeX, download these files (all on the Week1 page)

Week1-E23a-2016.tex 2-Islands.png 1-WebGraph.png

Now you can typeset the Week1 pdf file. You can look at the .tex file to see how everything, including images, was created.

In your file, include only formulas. There should be almost no text. The file becomes a proof only when you speak the words of explanation.

Official policy: You may cut-and-paste only from the .tex files on the Modules tab. IT IS FORBIDDEN TO CONSULT ANY FILES CREATED BY YOUR CLASSMATES! In creating this sort of proof file, I would prefer that you work alone, but if you collaborate (perhaps to benefit from a classmate's TeX experience, list your collaborators in the file.

 

 

Here is a link to the proof logging software. This will become useful after Sept. 10.

Create and Access Proof Logger accounts HERE (Links to an external site.). 

If you have questions regarding the material outside of section and office hours, there is a thread on the discussions page where anyone can post and respond to questions.  Joe

Getting a head start:

For weeks 1-12, download the "Notes and Problems" and print everything before the lecture outlines (which are still under revision). Then watch Kate's lecture preview videos.

If you enjoy software, watch Paul's R script videos, available for all weeks. If you want to go further, install R and play around with modifying the scripts. If you like this, you will be happy if enrolled for graduate credit, and you may want to pursue R as an extra-credit option even if enrolled for undergraduate credit.

Lecture Notes, Early Section Group Problems, and Problem Sets are all in the Notes and Problems .pdf files under the Modules tab.  It is your responsibility to print them if you prefer hard copies.

Videos of last year's lectures will be posted before next Monday. You might want to watch one as a sample before Tuesday's intor session, but skip over all the administrative issues at the beginning.

There are also scans of Paul's lecture notes on the Modules page.

Posting section problem solutions:

Each week, we create eight pinned discussions on the Discussions page, one for each group problem. After your group has solved the problem, upload it to the appropriate discussion. You can use the built-in editor, which has excellent math capabilities, or you can take a cell-phone picture of the solution from a blackboard or a piece of paper and upload the image. After all sections have met, we will remove the "cannot view without posting" requirement and will add a set of official solutions, quite likely inspired by some of the best ones that were posted.

I have added a discussion thread showing how to enter points, vectors, and matrices into the math editor.

 

Email questions to jgpalin@gmail.com

 

ONLINE SECTION:

Except for Paul's section, online sections will meet in this room: https://zoom.us/j/5050738015

Paul's section will use the room from orientation: https://zoom.us/j/968535870

OFFICE HOURS:

Office hours without a location listed will meet at https://zoom.us/j/5050738015

Alex - Sunday - 5-6pm - Science Center 111 and online

Russell - Sunday - 7:30-9:00pm - online

Giacomo - Monday - 12-2pm - online

Rachel - Monday - 4-5pm (-6pm given demand) - Science Center 322 and online

Paul - Tuesday/Thursday - 1:35-2:20pm - Science Center 322

Joe - Tuesday - 7:40-8:40pm (-9:40 given demand) - Science Center 112 and online

Catherine Li - Wednesday - 9am-11am - online

Proof Party

Saturday - 2-4pm - Science Center 112 and online (https://zoom.us/j/5050738015)

 

Course Summary:

Date Details Due