** Course: ** MATH 2270, Section 002

** Time/Place: ** M,W,F 12:55 - 1:45 PM in ST 208; T 12:55-1:45 PM in LCB 225

** Instructor: ** Thomas Goller

** Course book: ** "Introduction to Linear Algebra (Fourth Edition)", by Gilbert Strang, ISBN: 9780980232714.

** Problem Sessions: ** M 5-6 in JWB 333 and H 12:50-1:50 PM in LCB 225.

** Office Hours: ** By appointment, in JWB 307.

Syllabus

Homework Guide

Summary

Project Guidelines and Ideas

Official final grades are posted in CIS! Thanks for a fun semester!

CIS is producing some errors that are preventing me from entering official final grades. I'll try again tomorrow.

Table of Final Grades: Your first three test scores identify your row in the table. Come to office hours Thursday 10 AM to 4 PM if you have questions or want to discuss your final exam or project. I will post official final grades to CIS on Thursday night.

Please help your instructors improve their teaching by providing anonymous feedback for your courses! You should have received an e-mail with a link taking you to a page where you can review your courses. If you can't find that e-mail, you can log in to your course evaluations by going to http://ctle.utah.edu/scf/index.php and clicking on the "Login" link. Note that you cannot view your official final grades on CIS until you complete your course evaluations.

Final exam week is here! The menu:

Monday 10 AM to 4 PM in JWB 307: office hours - come with questions.

Monday 4-6 PM in JWB 333: review session - come with questions.

Tuesday 1-3 PM in ST 208: final exam.

Wednesday night: I'll post an anonymous table showing scores on the project and final exam as well as (unofficial) final grades.

Thursday 10 AM to 4 PM in JWB 307: office hours - come if you want feedback on the project or if you want to discuss your grade in the course.

Thursday night: I will enter (official) final grades in CIS.

Lost a quiz? Worry not! See all quiz problems here.

We'll have a third and last review session during final exam week: Monday, 4-6 PM, in JWB 333. Come with questions!

Study guide for the final exam . The final exam is on Tuesday, December 16, 1-3 PM, in ST 208 (our usual MWF classroom).

**Overview of the last week of the course:** small group discussions on Monday and Tuesday (worth 1% of your final grade!); optional project help on Wednesday; review on Thursday and Friday. The project is due on Friday!

Enjoy the long weekend! Remember to prepare your project proposal and come to class next Monday or Tuesday to present your project proposal to me.

Table of Grades After Test #5 : Your first three test scores identify your row in the table. Your quiz scores are not shown, but they are being counted. The column "Total %" indicates a percentage of the final grade, not a percentage of the work done so far. 40% of the grade is still to be determined (20% project, 20% final exam).

Peruse these solutions to Test #5 . Please ask me if you have any questions about these solutions or about how I graded your test.

The project weeks are upon us! You can find a link to a detailed write-up about the project guidelines and project ideas above. Read the first two pages carefully. Then browse through the pages detailing six project ideas. I will give an overview of the project guidelines on Monday (24 Nov.), and I will present the six project ideas in class on Monday (24 Nov.) and Wednesday (26 Nov.).

Since I am going into more detail than Strang when it comes to bases and coordinates, I'm posting some notes covering a large part of my lectures on Monday (17 Nov.) and Wednesday (19 Nov.). This material could show up on an upcoming test!

Welcome to the last week of regular lectures! That means we'll begin working on projects the following week. I strongly recommend coming to next Monday's lecture (24 November), in which I'll share a lot of important information about the projects. Also, I will soon post a document detailing some project guidelines and possible topics, so keep your eyes open!

**Recommended problems for test #5** are Section 7.2: 1, 2, 3, 4, 13, 14, 17, 18, 20, 21, 26, 27, 29, 32, 36, 37, 38; Section 7.3: 1, 2, 4. The homework guide has been updated for these sections.

Pore over these solutions to Test #4 ! Please ask me if you have any questions about these solutions or about how I graded your test.

**Recommended problems for quiz #7** are Section 6.6: 1, 3, 6, 12, 13, 20; Section 6.7: 1, 2, 6, 11; Section 7.1: 1, 2, 3, 10, 11, 12, 20, 21, 22, 23, 29, 31. The homework guide has been updated for these sections. There are not many problems in Sections 6.6 and 6.7, but they are tricky, so start them on Wednesday and come to the problem session on Thursday if you would like some help. Section 7.1 is especially important!

Table of Grades After Test #3 : Your three test scores identify your row in the table. Your quiz scores are not shown, but they are being counted. The column "Total %" indicates a percentage of the final grade, not a percentage of the work done so far. For instance, the highest possible percentage so far is (60/72)*.20 + (150/250)*.40 = .407. (Explanation: you've taken six quizzes, one of which is dropped, for a maximum of 5*12=60 quiz points so far, with one quiz still to go. Similarly, the maximum possible test points are 3*50=150 so far, with two more tests to come. I'm multiplying by .20 and .40 because the quiz score is worth 20% of the final grade and the test score is worth 40% of the final grade, as stated in the syllabus.) The reason I'm presenting percentages in this way is to let you know how much of the grade of this course is still to be determined (which means that you still have plenty of opportunity to improve or reduce your grade!). The quiz grade is almost complete, but there are still two tests worth 8% each, a project worth 20%, and the final exam worth 20%. Thus the quiz score is currently heavily overvalued, but it will balance out by the end of the course. You will also note that the listed grades are based on small differences in the total percentage: this is unavoidable because only about 40% of the total grade has been determined. Keep up the hard work and try to score well on the next two tests and on the last quiz!

**Recommended problems for test #4** are Section 6.3: 1, 4, 8, 11, 13, 21; Section 6.4: 3, 4, 8, 11, 18, 21, 24; Section 6.5: 2, 6, 14, 18, 20, 21, 23, 24. The homework guide has been updated for these three sections.

Since we won't be covering Section 6.3 until next Monday, I've removed the problems from Section 6.3 from the list of recommended problems for quiz #6. Also, I've updated the course timeline in the syllabus to reflect the fact that we're spending an extra lecture on Sections 6.1 and 6.2.

Take a careful look at these solutions to Test #3 ! Please ask me if you have any questions about how I graded your test.

**Recommended problems for quiz #6** are Section 6.1: 1, 2, 5, 8, 9, 10, 12, 14, 21, 23, 25, 29, 32; Section 6.2: 1, 2, 4, 8, 11, 12, 18, 20, 26. This is truly a flood of problems, but the only way to become comfortable with eigenvalues and eigenvectors is to work out a lot of examples yourself. Start as early as possible to give yourself time to absorb these crucially important concepts! I highly recommend coming to the Thursday and Monday problem sessions since lectures are too short to cover everything important about eigenvalues and eigenvectors. Be sure to read the book for lots of in-depth examples.

The next five weeks will be hectic: we're covering the most important material (Chapters 5, 6, and 7) and will have a higher frequency of tests (please look at the course timeline in the syllabus). I encourage you to make an extra effort to understand this material because it opens the door to countless applications of linear algebra in many fields of study. We will then have a relatively gentle last three weeks, during which you will be working on a project (I'll tell you more about the projects during the last week of Chapter 7). Your project will most likely involve the concepts in Chapter 6, so be ready to master eigenvalues and eigenvectors!

**Recommended problems for test #3** are Section 5.1: 1, 3, 4, 5, 10, 11, 12, 13, 18, 28, 29; Section 5.2: 1, 3, 4, 11, 12, 16; Section 5.3: 1, 2, 6, 8, 10. The homework guide has been updated for these sections (and for the first three sections of Chapter 6, which you can ignore for now!).

**Recommended problems for quiz #5** are Section 4.2: 1, 2, 3, 11, 12, 13, 16, 21, 22, 23, 31; Section 4.3: 1, 9, 17, 18, 21, 22; Section 4.4: 1, 4, 6, 10, 11, 18, 21. The homework guide has been updated for all of these sections.

Check out these solutions to Test #2 ! Please ask me if you have any questions about how I graded your test.

**Recommended problems for quiz #4** are Section 3.5: 1, 5, 9, 10, 12, 13, 15, 16, 19, 21, 24, 26, 35; Section 3.6: 2, 4, 5, 16, 24; Section 4.1: 3, 4, 9, 11, 22, 24, 25, 28. The homework guide has been updated for these three sections.

The syllabus has been updated with the policy for taking quizzes and exams early or late (please try to avoid this as much as possible because it is a lot of extra work for me!). Also, a summary of major things to know for test #2 is posted above. This summary is extensive, but I make no guarantee that it is complete.

**Recommended problems for test #2** are Section 3.2: 1, 2, 3, 9, 11, 12, 21; Section 3.3: 1, 2, 8, 9, 10, 28; Section 3.4: 1, 2, 3, 16, 17, 22, 28, 34. Get started early and get help if you need it! There are two problem sessions, and you can e-mail me if you'd like to meet at a different time. The homework guide has been updated, but you should try the problems on your own first.

**My response to your feedback:** (1) The Homework Guide, for which you can find a link above, will be updated weekly. (2) The Monday problem session will be from 5-6 PM in JWB 333. (3) You will have 20 minutes for each future quiz. (4) I will drop your lowest quiz score.

**Warning: Increase in difficulty!** Friday's lecture will kick off Chapter 3. Beware! Be ready for a challenge!

**Recommended problems for quiz #3** are Section 2.6: 1, 2, 5, 6, 7, 9, 11, 15; Section 2.7: 1, 2, 6, 7, 20, 22; Section 3.1: 1, 4, 9, 10, 12, 13, 19, 24, 26. Again, there are a lot of problems, so start Sections 2.6 and 2.7 as early as possible and come to the problem session on Thursday with questions so that you can be ready for the transition to more difficult (abstract!) material in Chapter 3. You will definitely want to come to Friday's lecture, and be sure to think carefully about all the problems from Section 3.1 because we are beginning to view vectors the way mathematicians view vectors!

Here are solutions to Test #1 ! Please ask me if you have any questions about how I graded your test.

**Recommended problems for quiz #2** are Section 2.3: 1, 2, 3, 4, 6, 16, 24; Section 2.4: 1, 2, 3, 5, 7, 11, 14, 26; Section 2.5: 1, 2, 6, 7, 8, 21, 22, 23, 27. I know this is a lot of problems, but it will be vital for the remainder of the course that you are comfortable multiplying matrices. Many of the problems are quick, straightforward computations. Be sure to spend plenty of time on the Section 2.5 problems; the last three recommended problems ask you to perform an important task, namely computing inverse matrices. Get started early and come to the problem sessions if you have questions!

**Problem sessions** will be held 12:50-1:50 on Thursdays in LCB 225 and 4-5 on Mondays in JWB 333. Before coming to the Thursday problem sessions, please work on the problems for the sections that were covered on Monday and Wednesday of that week. During the Monday problem sessions, any problems from the previous week's list of recommended problems may be discussed, as well as questions about the upcoming Tuesday quiz or test. Bring any questions you may have about the material and expect me to work through problems with you instead of presenting complete solutions.

**Recommended problems for test #1** are Section 2.1: 1, 2, 5, 15, 17, 22, 26, 31; Section 2.2: 1, 2, 3, 4, 5, 8, 11, 13, 21. Be sure to review the recommended problems from Chapter 1. Pay particular attention to the concepts that I emphasized in class, be able to give examples of those concepts, and solve additional problems in the book if time permits.

Reminder: the first quiz is at the start of class on Tuesday, September 2, in LCB 225. The quiz will be based on the recommended problems from Sections 1.1, 1.2, and 1.3.

**We're moving!** Starting this Friday, we'll be in ST 208 on all Mondays, Wednesdays, and Fridays. We'll meet in LCB 225 on Tuesdays.

**Warning!** I'm trying to move us to a different classroom in order to raise the course limit from 42 to 50 students. We will meet in the usual room on Wednesday, but we'll hopefully have more spacious accommodations on Friday. Please keep checking this webpage for updates!

**Recommended problems for quiz #1** are Section 1.1: 1, 3, 4, 6, 26, 29, 30; Section 1.2: 1, 2, 4, 8, 13, 16, 19, 27; Section 1.3: 1, 2, 6.

Welcome!