## Navigation

- Canvas: important announcements, grades, calendar, etc.
- Ed (Discussion Boards).
**Homework Problems**- Instructor Contact and General Info:
- Course Information
- Course Policies
- Legal Issues
- LaTeX
- Links
- Handouts
- Homework Problems

## Instructor Contact and General Information

Instructor: |
Luís Finotti |

Office: |
Ayres Hall 251 |

Phone: |
974-1321 (don't leave messages! -- e-mail me if I don't answer!) |

e-mail: |
lfinotti@utk.edu |

Office Hours: |
By appointment only. Over Zoom or in person. |

Textbook: |
K. Hoffman, R. Kunze, "Linear Algebra" 2nd Edition, Pearson, 1971. (Out of print!) |

Prerequisites: |
One semester of undergraduate basic linear/matrix algebra. |

Class Meeting Time: |
TuTh 9:45-11:00 at Ayres 406. |

Exams: |
Midterm: 03/21 (Thu). Final: 3:30-5:30, May 10 (Fri). |

Grade: |
30% for HW, 30% for the Midterm, 40% for the Final. See here for letter grade ranges. |

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## Course Information

### Course Content

This course is a one-semester course in Linear Algebra, at a first-year graduate level. It will give students the necessary background for the Diagnostic Exam in Linear Algebra.

### Chapters and Topics

We will follow the official textbook (Hoffman and Kunze’s *Linear Algebra*), with digressions for applications and extra topics as needed (and as time allows). We should cover Chapters 2 to 8, although we will go over Chapter 4 only briefly. Note that **Chapter 1 is a prerequisite**, and thus I only will go over it *very* quickly. (Students should also be familiar with the contents of the appendix.)

If time allows, I will also show how to use the computer to perform some of the computations using either Sage or Python (with NumPy).

### Additional Bibliography

Here are some other books, besides our text, that you might find helpful:

- S. Garcia and R. Horn "Matrix Algebra: A Second Course in Linear Algebra", 2nd Edition, 2023, Cambridge University Press.
- D. Damiano, "A Course in Linear Algebra", 2011, Dover.
- B. Noble and J. Daniel, “Applied Linear Algebra”, 3rd Edition, 1987, Pearson. (Out of print!)
- K. Nomizu, “Fundamentals of Linear Algebra”, 2nd Edition, 1979, Chelsea. (Out of print!)

I *do not* recommend Axler’s “Linear Algebra Done Right”. In fact, Treil’s "Linear Algebra Done Wrong" (freely available) might be a good reference as well.

## Course Policies

### Homework Policy

Homework will be assigned weekly and it will usually be due on Wednesdays. The official due dates will be posted in Canvas (as an Assignment). The problems will be those from the Homework Problems section below.

Here is how it will work: the sections we cover in a week are due in the next Wednesday. For example, if in week 4 we cover Sections 3.1 and 3.2, the problems for those sections in Homework Problems will be due in the Wednesday of week 5. Although I will post the corresponding due dates on Canvas, these will only come on Fridays, when I know exactly what was covered. Therefore, **do not wait for me to post the due dates**! As soon as I finish a section, start working on the problems from that section. If you leave it all to start Friday (after I post the assignment), you won’t have as much time to do all the problems.

Although you can work in groups, each student should write and turn in their own solution.

Here is some additional information:

**You should not search for solutions online!**If you need help, ask me (or a colleague), e.g., on Ed.- Not all problems turned in will be graded.
*You will not know in advance which problems will be graded before you turn them in!*Therefore, you must turn in all assigned problems.- Each question will receive a grade between 0 and 2 points.
- The homework should be turned in Canvas
*as a PDF*file. - They do not need to be typed, but they
*must be clear and legible*! If I cannot understand the handwriting or if the solution is to messy to follow, the problem in question will receive zero points. - The lowest HW score will be dropped in the grade computation.
- The HW average will account for 30% of the grade.

### Exams

We will only have one midterm (on 03/21) and a *comprehensive* final (on 05/10). Each will contain questions that could appear on a diagnostic exam. In particular, the final exam should be very close to a diagnostic exam.

The midterm accounts for 30% of your grade (same as the HW) and the final accounts for 40%.

### Statements

I *strongly recommend* you write in a separate sheet of paper all definitions and statements of important theorems (lemmas, corollaries, propositions, etc.), and perhaps even a few more important examples that illustrate some technique. I recommend you do it before you start your HW on the corresponding section!

There are two main reasons for doing so: firstly, the act of writing helps you review and remember the main tools to solve problems in your HW. Secondly, having them on a separate sheet of paper makes it quicker to find what you need when doing your HW. (Hopefully by now you are aware that it is impossible to solve problems without knowing the relevant definitions and theorems!)

I would also recommend you write the definitions and theorems covered in class *before the following class*. This will help you follow better the new lecture.

If you (the students) want to collaborate in producing a single document in LaTeX with these, I could facilitate it. (Just let me know.)

### Curve

In principle there will be no curve for this course. The letter grade cut offs can be found here. (Basically 90 and above is an A, 80 and above is a B, etc.)

In *special circumstances* I might curve the final course averages before submitting the letter grades, but this *should not be expected*. On the other hand, a curve can only help with the grades.

### How to Be Successful in this Course

*Study hard and do as many problems as you can!*- Write statements of main theorems and results for quick reference (and to help you memorize them).
- Review the material before classes.
- Work on
*all*the HW problems. Don’t look at the solutions until you’ve tried for a while. You will only learn by working on problems! - Don’t let a HW problem “pass”. You should always try to find how to solve every problem.
- Look for help if you are having trouble: post questions on on Ed or come see me.
- If you can’t do a problem and do get help on it:
- Look for what you were missing! (Did you forget a theorem? Were you missing a particular idea?) Seeing the solution won’t help if you don’t get anything out of it .
- Go back to the problem a couple of days later and redo it by yourself.

- Ask questions in class.

A couple more things to keep in mind:

- Studying a little every day is better than cramming before the exam.
- Reviewing your class notes shortly after class will help you retain what you’ve learn.
- It’s a lot easier to remember procedures and statements of theorems if they make sense. So try to understand what we are doing instead of just memorizing it.

### Ed (Discussion Board)

We will use Ed for online discussions. The advantage of Ed (over other discussion boards) is that it allows us (or simply me) to use math symbols efficiently and with good looking results (unlike Canvas) and to post (and run!) formatted code. It also allows anonymous posts (also unlike Canvas).

To enter math, you can use LaTeX code. (See the section on LaTeX below.) Even if you don’t take advantage of this, I can use it making it easier for you to read the answers.

You can access Ed through here: https://edstem.org/us/courses/51210/discussion/. (There is also a link at the “Navigation” section on the top of this page and on the Links section.)

To keep things organized, I’ve set up a few different categories for our discussions:

*Lectures:*Questions about something I’ve done in class.*Homework:*Questions about the HW.*Exams:*Questions about the exams.*Course Structure:*Ask questions about the class, such as “how is the graded computed”, “when is the final”, etc. in this category. (Please read the Syllabus first, though!)*Feedback:*Give (possibly anonymous) feedback about the course using this category.*Computer:*I might post some notes on how to do some computations using a computer. Or you can ask about LaTeX as well.*Other:*In the unlikely event that your question/discussion doesn’t fit in any of the above, please use this category.

I urge you to use Ed often for discussions! (This is specially true for *Feedback*!) If you are ever thinking of sending me an e-mail, think first if it could be posted there. That way my answer might help others that have the same questions as you and will be always available to all. (Of course, if it is something personal (such as your grades), you should e-mail me instead.)

Note that you can post anonymously. *(Just be careful to check the proper box!)* But please don’t post anonymously if you don’t feel compelled to, as it would help me to know you, individually, much better.

Students can (and should!) reply to and comment on posts on Ed. Discussion is encouraged here!

Also, please don’t forget to choose the appropriate category for your question. And make sure to choose between *Question* and *Post*.

When replying/commenting/contributing to a discussion, please do so in the appropriate place. If it is an answer to the question, use the *Answer* area. If you have a comment, question, or suggestion, you can use the *Comment* area.

You can also use Ed for *Private Posts*, by checking the corresponding box. Posts marked as private will be only viewed by the student who posted and me. Only use this what you have to ask cannot be shared with all, e.g., if you are sharing something from your HW. Otherwise, don’t make it private, as other students might have the same questions as you.

You should receive an invitation to join our class in Ed via your “@vols.utk.edu” e-mail address before classes start. If you don’t, you can sign up here: https://edstem.org/us/join/ebrPdN. If you’ve register with a different e-mail (e.g., @tennessee.edu) you do not need to register again, but you can consolidate your different e-mails (like @vols.utk.edu and @tennessee.edu) in Ed, so that it knows it is the same person. (Only if you want to! It is recommended but not required as long as you have access to our course there!) Just click on the *Account* icon on the top right of Ed, select *Emails*, and then *Add email address*.

### Communications and E-Mail Policy

You are *required* to set up notifications for Ed and for Canvas to be sent to you *immediately*.

On Ed, click on the *Account* icon on the top left, then *Settings*. In the new page click on *Notifications*. Under *New Thread Digest*, set the drop down box to *Instant*. *I will consider a post in Ed official communication in this course, I will assume all have read every single post there!*

For Canvas, check this page and/or this video on how to set your notifications. *Set notifications for Announcements to “right away”!* (Basically: click on the the profile button on left, under UT’s “T”, then click “Notifications”. Click on the check mark ("notify me right away") for Announcements.)

Moreover, I may send e-mails with important information directly to you. I will use the e-mail given to me by the registrar and set up automatically in Canvas. (If that is not your preferred address, please make sure to forward your university e-mail to it!)

**All three (notifications from Ed, notifications from Canvas, and e-mails) are official communications for this course and it’s your responsibility to check them often!**

### Feedback

Please, post all comments and suggestions regarding the course using Ed. Usually these should be posted as *Post* and put in the *Feedback* category. These can be posted anonymously (or not), *just make sure to check the appropriate option*. **Other students and myself will be able to respond and comment.** If you prefer to keep the conversation private (between us), you can send me an e-mail (not anonymous), or a private message in Ed (possibly anonymous).

## Legal Issues

### Conduct

All students should be familiar with
Hilltopics’ Students Code of
Conduct and
maintain their *Academic Integrity*: from
Hilltopics
Academics:

Integrity

Study, preparation, and presentation should involve at all times the student’s own work, unless it has been clearly specified that work is to be a team effort. Academic honesty requires that the student present their own work in all academic projects, including tests, papers, homework, and class presentation. When incorporating the work of other scholars and writers into a project, the student must accurately cite the source of that work. For additional information see the applicable catalog or the UT Libraries site.See also the Student Code of Conduct and Honor Statement (below).

All students should follow the *Honor Statement* (also from
Hilltopics
Academics):

Honor Statement

"An essential feature of the University of Tennessee, Knoxville, is a commitment to maintaining an atmosphere of intellectual integrity and academic honesty. As a student of the university, I pledge that I will neither knowingly give nor receive any inappropriate assistance in academic work, thus affirming my own personal commitment to honor and integrity."

You should also be familiar with the Classroom Behavior Expectations.

*We are in a honor system in this course!*

### Disabilities

Students with disabilities that need special accommodations should contact the Student Disability Services and bring me the appropriate letter/forms.

### Campus Syllabus

Please, see also the Campus Syllabus.

## LaTeX

**This is not necessary to our class!** I leave it here in case someone
wants to learn how type math, for instance to type their HW. But again,
you can ignore this section if you want to.

LaTeX is the most used software to produce mathematics texts. It is quite powerful and the final result is, when properly used, outstanding! Virtually all professional math text you will ever see is done with LaTeX, or one of its variants.

LaTeX is freely available for all platforms.

The problem is that it has a steep learning curve at first, but after the first difficulties are overcome, it is not bad at all.

One of the first difficulties one encounters is that it is not WYSIWYG ("what you see is what you get"). It resembles a programming language: you first type some code and then this code is processed to produce a nice document (a non-editable PDF file, for example). Thus, one has to learn how to “code” in LaTeX, but this brings many benefits.

I recommend that anyone with any serious interest in producing math texts to learn it! On the other hand, I don’t expect all of you to do so. But note that there are processors that can make it “easier” to create LaTeX documents, by making it “point-and-click” and (somewhat) WYSIWYG.

Here are some that you can use online (no need to install anything and files are available online, but need to register):

- Cocalc (Previously known as “Sage Math Cloud”. This one is much more than just LaTeX, and will be used in our course.)
- Overleaf

The first one, Cocalc, is more than just for LaTeX, as you can also run Sage, which can do computations with the objects we will study in this course.

If you want to install LaTeX in your computer (so that you don’t need an Internet connection), check here.

A few resources:

- Here is a video I’ve made where I talk about LaTeX and producing documents with it: Introduction to LaTeX and Sage Math Cloud. (Again, note that “Sage Math Cloud” is simply the old name for Cocalc. The video does not show it in great detail, but might be enough to get you started.) Note it was done for a different course, so disregard any information not about LaTeX itself.
- TUG’s Getting Started: some resources, from installation to first uses.
- A LaTeX Primer by D. R. Wilkins: a nice introduction. Here is a PDF version.
- Art of Problem Solving LaTeX resources. A very nice and simple introduction! (Navigate with the links under “LaTeX” bar on top.)
- LaTeX Symbol Lookup: Draw a symbol and the app will try to identify it and give you its LaTeX code.
- LaTeX Wikibook: A lot of information.
- LaTeX Cheat Sheet.
- Cheat Sheet for Math.
- List of LaTeX symbols.
- Comprehensive List of Math Symbols.
- Constructions: a very nice resource for more sophisticated math expressions.

## Links

- Canvas.
- Ed (Math Related Forum).
- Linear Algebra Diagnostic Exam Page
- UT Knoxville Home
- UTK’s Math Department.
- Services for Current Students and MyUTK (registration, view your grades, etc.).
- Office of the Registrar
- Academic Calendars, including dates for add and drops, other deadlines, final exam dates, etc.
- Hilltopics.
- Students Disability Services
- Office of Equity and Diversity (includes sexual harassment and discrimination).
- My homepage

## Handouts

- Campus Syllabus (Fall 2023).
- Using Sage for Computations in Linear Algebra
- Using Python and NumPy for Computations in Linear Algebra
- Midterm and its solutions.
- Final and its solutions.

## Homework Problems

*Due dates and (partial) solutions will be posted in Canvas.*

**Section 1.2:** 2, 3.

**Section 1.3:** 4, 5.

**Section 1.4:** 1, 2, 4, 8.

**Section 1.5:** 1, 4, 5.

**Section 1.6:** 1, 3, 7.

**Section 2.1:** 3, 4, 5.

**Section 2.2:** 1, 3, 4, 6(b), 7.

**Section 2.3:** 7, 9, 11(a), (b). (Do *not* turn in, but you should know how to do 2, 3, and 4.)

**Section 2.4:** 2, 4, 5, 7.

**Section 2.6:** 2(a), 3.

**Section 3.1:** 1, 3, 5, 8, 10.

**Section 3.2:** 2, 5, 6, 8, 11.

**Section 3.3:** 2, 6, 7.

**Section 3.4:** 2, 3, 6, 12. (Do not turn in, but make sure you know how to do 1 and 5.)

**Section 3.5:** 4, 5, 9, 11, 12, 14. (You should know how to do 1, 2, 7, and 8!)

**Section 3.6:** 1, 2.

**Section 3.7:** 1, 5, 6, 7. (You should also know how to do 2, 3.)

**Section 6.2:** 4, 6, 7, 12 (use 11 without proof), 13.

**Section 6.3:** 2, 3, 4, 5, 7,

**Section 6.4:** 1, 2, 4, 5, 6, 8.

**Section 6.5:** 1, 3, 5.

**Section 6.6:** 1, 2, 3, 6, 7.

**Section 6.7:** 1, 2, 3, 6 (Problem 6 should say “Example **5** from Section 6.3”, not Example 6.

**Section 6.8:** 1, 2, 5, 6, 10. (**Turn in only:** 2, 6.)

**Section 7.1:** 2, 3, 4, 7. (**Turn in only:** 3, 7.)

**Section 7.2:** 3, 4, 7, 8, 9, 10, 12, 13. (**Turn in only:** 4, 7, 8, 13.)

**Section 7.3:** 1, 2, 3, 4, 5, 11. (**Turn in only:** 1, 3, 4, 5.)

**Section 8.1:** 1, 5, 7, 10, 12. (**Turn in only:** 1, 12.)

**Section 8.2:** 1, 2, 3, 5, 6, 11, 12, 13, 14. (**Turn in only:** 2, 5, 11.)

**Section 8.3:** 1, 3, 4, 5. (**Turn in only:** 1, 4.)

**Section 8.4:** 1 (*Hint:* look at Example 8.27), 6, 7. (**Turn in only:** 1, 6.)

**Section 8.5:** 1, 9, 11. (**Turn in only:** 9, 11.)