GO TO:
(04/27 - 5:10am) The room for the review session (today at 10am) is Aconda Court 113 (at the corner of Volunteer and Cumberland, beside the University Center).
(04/24 - 10:00am) Here is some info about the final:
(04/24 - 9:00am) I posted (yesterday) solutions to all the HWs. (Note that the solutions include also problems which have not been assigned.) See the section Solutions to Selected HW Problems below. I also posted the final from the last time I taught 251. It is on the section Final of my Fall 2007 M251 web page.
(01/02 - 1:00pm) Please, check this section often. I will put announcements and important info here.
(01/02 - 1:00pm) Please, hit the ``Refresh'' or ``Reload'' button on your web browser every time you visit this page, so that you can see the most recent updates.
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Instructor: Luís Finotti
Office: Aconda Court 211-H
Phone: 974-1321 (please do not ask me to call back -- leave your e-mail)
Office Hours: M 3:30pm-4:30pm and W 11:00am-12:00pm or by appointment (subject to change!!)
Textbook: H. Anton, ``Elementary Linear Algebra'', 9th Edition. Wiley, 2004. (The ``Applications Version'' of this book is also OK, but more expensive and unnecessary.)
Prerequisite: Math 142 or Math 148.
Class: TTh 9:40-10:55 at HSS 56. (Section 4.)
Exams: Midterms: 02/17 (Tue) and 03/31 (Tue), in regular classroom and time; Final: 04/28 (Tue) from 10:15am to 12:15pm, also in our regular classroom.
Grade: 25% for quizzes + 20% for each Midterm + 35% for the Final. Note the weight of the HWs!
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Here is the Midterm I and the Midterm I with solutions.
The exams were graded and will be returned in class on Thursday (02/19). (You can check your grades in Blackboard.) If you are not in class that day, you have to come by my office to pick up yours. (I will not take them to class anymore.) The average was 69.24, the median was 81 and the highest grade was 98. I am happy with the results, but keep in mind that this was an easy exam.
Here is how I would curve these grades and the number of people with each grade:
Grade | Range | # of people |
A | 90-100 | 10 |
A- | 87-89 | 2 |
B+ | 83-86 | 0 |
B | 79-82 | 1 |
B- | 77-78 | 2 |
C+ | 73-76 | 2 |
C | 68-72 | 4 |
C- | 66-67 | 0 |
D+ | 63-65 | 1 |
D | 60-62 | 1 |
D- | 57-59 | 0 |
F | < 57 | 1 |
Note: This curve is just to give you an idea of how I curve. In the end I will not even look at this curve, I will just curve all the final averages.
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Here is the Midterm II and the Midterm II with solutions.
The exams were graded and will be returned in class on Thursday (04/02). (You can check your grades in Blackboard.) If you are not in class that day, you have to come by my office to pick up yours. (I will not take them to class anymore.)
The results of the exam, as expect, were not as good as the previous exam. The average was 64.6 and the median was 69.5. The highest score was 95. (You can see more statistics in Blackboard.)
Here is how I would curve these grades and the number of people with each grade:
Grade | Range | # of people |
A | 90-100 | 2 |
A- | 87-89 | 0 |
B+ | 81-86 | 3 |
B | 78-80 | 2 |
B- | 72-77 | 3 |
C+ | 65-71 | 1 |
C | 60-64 | 3 |
C- | 57-59 | 0 |
D+ | 53-56 | 1 |
D | 50-52 | 0 |
D- | 47-49 | 0 |
F | < 47 | 4 |
As you can see, the grades were very spread out...
Note: This curve is just to give you an idea of how I curve. In the end I will not even look at this curve, I will just curve all the final averages.
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Here is the final: Final, Final Solution.
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This is a first course on Linear Algebra. We will study matrix algebra, system of linear equations, vector spaces, linear transformations, and eigenvalues/eigenvectors.
The first two of these topics are of computational nature, while the latter topics will be more theoretical, and hence usually considered harder by the students. Therefore, the initial plan is to go rather fast through the computational material, so that we can go over the most challenging topics on a better pace.
We will likely cover the following:
The first three chapters will be covered in a faster pace. Chapter 4 might also be covered superficially and briefly. The last three chapters should be the more challenging ones, I hope to have enough time to cover them in a slower pace.
Also, note that this outline is subject to change slightly without prior notice.
Homeworks will be assigned after every class and will be posted at the section Homework of this page. No paper copy of the HW assignments will be distributed in class. It is your responsibility to check this page often! Besides HW assignments, other important information will be posted here. (Check the section Important Notes often!)
The HWs will be collected on Thursdays. Each HW will have problems from the previous week (Tuesday and Thursday lectures). The problems to be turned in, as well as due dates, will be clearly posted here. The homework turned in will NOT be graded (unless it will replace a quiz -- see below) I will look through them and keep comments for myself which will affect only border line cases when deciding the final grade for the course. (Again, unless it will be counted as a quiz, as explained below.) Borderline students who do not turn in HWs consistently will always receive the lower grade.
Since the HW will not be graded, we will have HW Quizzes every Thursday, at the beginning of the class. You will not have extra time if you are late. The quizzes will consist entirely of HW questions. You will have only ten or fifteen minutes, and so if you hadn't already solved it, you might not have enough time to come up with a solutions. Points will be taken from messy solutions, and you need to show work in all questions (unless stated otherwise)! The same applies to exams and all graded work!
Every once in a while I might grade two or three HW questions instead of giving a quiz. (So, there will be no quiz that day in class.) This will be done whenever I need the extra time or want to better check how well you are doing your HW. The questions will be graded as a quiz (you need to write the solution properly and show work) and will count as a quiz. I will not tell you in advance when that will happen! So, be always prepared.
Calculators will not always be allowed! You will need to know how to perform some computations. Later in the course you might be allowed to use calculators, but you should never depend on it. You can only use your calculator if I explicitly say so! (This includes HW, quizzes, and exams!)
I will do my best to post solutions to the most difficult problems. If I do, they will be posted in this page.
In my opinion, doing the HW is one of the most important parts of the learning process, so the weight for them is greater than the weight of a single midterm, and I will assume that you will work very hard on them.
Also, you should try to come to my office hours if you are having difficulties with the course. I will do my best to help you. Please try to come during my scheduled office hours, but feel free to make an appointment if that would be impossible.
Finally, it is your responsibility to keep all your graded Quizzes and Midterms! It is very important to have them in case there is any problem with your grade. You can check all your scores at Blackboard. (Blackboard will be used only for scores. This is the official site for the course.)
There will be no make-up quizzes or exams. If you miss a quiz or exam and have a properly documented reason, your final will be used to make-up your score.
You will have to check your e-mail at least once a week, preferably daily. I will use your e-mail (given to me by the registrar's office) to make announcements. (If that is not your preferred address, please make sure to forward your university e-mail to it!) I will assume that any message that I sent via e-mail will be read in a week or less, and it will be considered an official communication.
I have an On-line Feedback Form where you can anonymously send me your comments and suggestions. I will consider your comments and try to do whatever I can to resolve possible problems before it is too late. So, please, feel free to use it whenever you have any constructive comment or suggestion. (In fact, I would greatly appreciate it.) If you don't want you comments to be anonymous, just send me an e-mail or come by my office and we can discuss the problem.
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Academic 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 his or her 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.
All students should follow the Honor Statement: from Hilltopics 2008/2009, pg. 11:
Honor Statement
``An essential feature of The University of Tennessee 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.
Students with disabilities that need special accommodations should contact the Office of Disability Services and bring me the appropriate letter/forms.
For Sexual Harassment and Discrimination information, please visit the Office of Equity and Diversity.
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Wednesday, January 7 - Classes begin.
Friday, January 16 - Last day to add, change grade options, or drop a full semester course without a "W".
Monday, January 19 - Martin Luther King, Jr. Day. (No class.)
Tuesday, February 17 - Midterm I.
Tuesday, March 10 - Last day to drop a full term course with a "W".
Monday-Friday, March 16-20 - Spring Break. (No class.)
Tuesday, March 31 - Midterm II, Last day to drop with a WP/WF.
Friday, April 10 - Spring Recess. (No class.)
Friday, April 24 - Last Class Day.
Tuesday, April 28 - Final.
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This list is subject to change without prior notice. The official assignments will be posted below.
Section 1.1: 1, 2, 3(a), (b), 4(a), (c), 5(a), (c), 6, 11, 12, 13.
Section 1.2: 1, 3, 5(a), (c), 6(b), (d), 7(b), 8(b), 10(b), 12, 14(a), (b), 17, 21, 22.
Section 1.3: 1, 2, 3(g), (j), (k), 5(a), (b), (d), (h), (j), 7(a), (d), (e), 8, 12(b), 13(a), 14(a), 18(a), 21.
Section 1.4: 1(b), (d), 3(d), 4(b), 5(b), 6(a), 7(c), (d), 9(b), 13, 14, 17, 20(b), 21, 29.
Section 1.5: 1, 3, 5, 7(a), (d), 9, 14, 15.
Section 1.6: 2, 7, 11 (you can use any method here), 15, 16, 17, 23.
Section 1.7: 1, 2, 4, 5, 11, 12, 13 (only matrix A), 15, 18.
Section 2.1: 3(a), (d), 4, 7, 12, 13, 17.
Section 2.2: 1(b), 2, 3, 4, 6, 9, 12, 14(a).
Section 2.3: 2, 4, 5, 6, 7, 12, 14(a), (b), 15(a), (b) (this means use only (a) and (b) from 14 in 15), 16.
Section 3.1: 6, 7, 8, 9, 10, 11.
Section 3.2: 1(a), (e), 2(a), (c), 3, 4, 7.
Section 3.3: 1(a), (d), 2(a), (d), 3, 4(a), (c), 5(a), (c), 9, 12, 16.
Section 4.1: 3, 7, 9(d), 11(c), 14(d), (e), 16, 18(b), 20.
Section 4.2: 1, 3, 5, 7, 9, 12, 16, 20.
Section 4.3: 1, 2(b), (c), 4, 5(b), 6(b), 7, 8, 11, 13, 15, 19(a), (c), 22.
Section 5.1: 1, 5, 6, 7, 9, 11, 12, 15, 18.
Section 5.2: 1, 2(b), (c), 3(c), (d), 4(a), (b), (c), 5(b), (c), 7, 8(a), 10(c), (d), 11(a), (b), 13.
Section 5.3: 1, 3(a), (c), 5, 6(a), (b), 8, 9, 11, 13, 15.
Section 5.4: 1, 3(a), (c), 4(a), (c), 7(b), (c), 8(c), 9(b), 10(b), 14, 16, 18(b), (c), 19, 23.
Section 5.5: 2(c), (d), 3(b), (c), 5(b), 6(c), 7, 8(c), 9(c), 11(b), (c), 12(c), 13.
Section 5.6: 2(b), (c), 3(b), (c), 4, 5, 7, 8, 9, 12, 13.
Section 6.1: 3(a), 4(a), 6, 8(b), 9(a), (d), 10(c), 11, 13(a), 14, 16(c), (f).
Section 6.2: 2, 4, 6(a), 8(a), 11, 15, 18(b), (c), 21.
Section 6.3: 3, 4, 6, 8, 9, 11, 13, 14.
Section 6.5: 2, 4, 5, 6, 9, 11.
Section 7.1: 4(a), (c), (f), 6(a), (c), (f), 7, 9, 10, 11, 20.
Section 7.2: 1, 2, 6, 7, 9, 13, 16, 17, 19.
Section 7.3: 1(b), (c), (e), 3, 5, 7, 9.
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Please read: I will try to post here a few solutions. The new solutions will be added to this same file. They might come with no explanation, just the ``answer''. If yours do not match mine, you can try to figure out again. (Also, read the disclaimer below!) You can come to office hours if you want explanations for the answers. Be careful that just because our ``answers'' were the same, it doesn't mean that you solved the problem correctly (it might have been a ``fortunate'' coincidence), and in the exams what matters is the solution itself. I will do my best to post somewhat detailed solutions to the harder problems, though.
Disclaimer: I will have to put these solutions together rather quickly, so they are subject to typos and conceptual mistakes. (I expect you to be a lot more careful when doing your HW than I when preparing these.) You can contact me if you think that there is something wrong and I will fix the file if you are correct.
Solutions to Selected HW Problems (Click on ``Refresh'' or ``Reload'' if you don't see the changes!)
CHANGE LOG:
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HW1 - Due on Thursday 01/22:
Section 1.1: 1, 2, 3(a), (b), 4(a), (c), 5(a), (c), 6, 11, 12, 13.
Section 1.2: 1, 3, 5(a), (c), 6(b), (d), 7(b), 8(b), 10(b), 12, 14(a), (b), 17, 21, 22.
Section 1.3: 1, 2, 3(g), 5(a), (b), (d).
HW2 - Due on Thursday 01/29:
Section 1.3: 3(j), (k), 5(h), (j), 7(a), (d), (e), 12, 13(a), 14(a), 18(a), 21.
Section 1.4: 1(b), (d), 3(d).
HW3 - Due on Thursday 02/05:
Section 1.4: 4(b), 5(b), 6(a), 7(c), (d), 9(b), 13, 14, 17, 20(b), 21, 29.
Section 1.5: 1, 3, 5, 7(a), (d), 9, 14, 15.
Section 1.6: 2, 6, 11, 15.
HW4 - Due on Thursday 02/12:
Section 1.6: 16, 17, 23.
Section 1.7: 1, 2, 4, 5, 11, 12, 13 (only matrix A), 15, 18.
Section 2.1: 3(a), (d), 4, 7, 9, 12, 13, 17.
HW5 - Not to be turned in! Just work on them to prepare for the exam:
Section 2.2: 1(b), 2, 3, 4, 6, 9, 12, 14(a).
Section 2.3: 2, 3, 4, 5, 6, 7, 12, 16.
HW6 - Due on Thursday 02/26:
Section 3.1 6, 7, 8, 9, 10, 11, 13.
Section 3.2: 1(a), (e), 2(a), (c), 3, 4, 5(a), 7.
HW7 - Due on Thursday 03/05:
Section 3.3: 1(a), (d), 2(a), (d), 3, 4(a), (c), 5(a), (c), 9, 12, 16.
Section 4.1: 3, 7, 9(d), 11(c), 14(d), (e), 16, 18(b).
HW8 - Due on Thursday 03/12:
Section 4.2: 1, 3, 5, 7, 9, 12, 16, 19, 20.
Section 4.3: 1, 2(b), (c), 8, 11, 13, 15, 22.
HW9 - Due on Thursday 03/26:
Section 4.3: 4, 5(b), 6(b), 7, 19(a), (c).
Section 5.1: 1, 5, 6, 7, 9, 11, 12, 15, 18.
HW10 - Do not turn in!:
Section 5.2: 1, 2(b), (c), 3(c), (d), 4(a), (b), (c), 5(b), (c).
HW11 - Due on Thursday 04/09:
Section 5.2: 7, 8(a), 10(c), (d), 11(a), (b), 13.
Section 5.3: 1, 3(a), (c), 5, 6(a), (b), 8, 9, 11, 13, 15.
HW12 - Due on Thursday 04/16:
Section 5.4: 1, 3(a), (c), 4(a), (c), 7(b), (c), 8(c), 9(b), 10(b), 14, 16, 18(b), (c), 19, 22(a), 23.
Section 5.5: 2(c), (d), 3(b), (c), 5(b), 6(c), 7.
HW13 - Not to turn in (practice for the final):
Section 5.5: 8(c), 9(c), 10(c), 11(b), (c), 12(c), 13.
Section 5.6 2(b), (c), 3(b), (c), 4, 5, 7, 8, 9, 12, 13.
Section 6.1: 16(c), (f).
Section 6.2: 2, 4, 11, 15, 18(b), (c), 21.
Section 6.3: 3, 4, 9, 11, 13, 14.
Section 6.5: 2, 3, 5, 6, 9, 11.
Section 7.1: 4(a), (c), (f), 6(a), (c), (f), 7, 9, 10, 11, 20.
Section 7.2: 1, 2, 6, 7, 9, 13, 16, 17, 19.
And that's all!!
PLEASE, HIT ``REFRESH'' (OR ``RELOAD'') IN YOUR BROWSER WHEN VISITING THIS PAGE!!!!!!! I usually get messages asking for the update in the HW when it has already been updated. Since I change this page often, some times the browser don't see the changes. But, if you hit refresh and there is still problems missing, feel free to write me.
If it is already Friday afternoon and there still is a ``More to come'' after the HW assignment due on the coming Monday, write me an e-mail at lfinotti@utk.edu, and I'll update it and let you know.
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