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(04/26 - 5:00pm) I have written (a first draft for) the final exam. Here is some info about it:
(04/04 - 3:15pm) I will allow you to make corrections to your Midterm 2. Here is how this works:
(03/21 - 7:50pm) I have written (a first draft for) the second exam. Here is some info about it:
(02/20 - 12:05pm) I've posted some information about our first midterm below: Midterm 1.
(02/18 - 12:40pm) I've posted solutions for HW5 below (in the section Handouts). Please read the disclaimer!
(02/15 - 5:30pm) I have written (a first draft for) the first exam. Here is some info about it:
(01/05 - 5:00pm) Please, check this section often. I will put announcements and important info here.
(01/05 - 5:00pm) 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: Ayres Hall 243
Phone: 974-1321 (please do not ask me to call back -- leave your e-mail)
Office Hours: M, W 10am-11am or by appointment (subject to change!!)
Textbook: D. J. Velleman, ``How to Prove It: A Structured Approach'', 2nd Edition. Cambridge University Press, 2006.
Prerequisite: Math 142 or Math 148.
Class: Tu, Th 9:40am to 10:55pm at Ayres 110. (Section 001.)
Exams: Midterms: 02/19 (Tu) and 04/02 (Tu), in regular classroom and time; Final: 05/02 (Thu) from 8:00am to 10:00am also in our regular classroom.
Grade: 25% for quizzes/HW + 20% for each Midterm + 35% for the Final. Note the weight of the Quizzes/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 (02/21). (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 69.44, the median was 69.5, and the highest grade was 100 (two of them). (You can see more statistics at Blackboard.)
The results were not very good, although we had some good grades. If I were to curve these grades, roughly, an A would be 90 and above, a B would be 80 and above and a C could be either 65 or 60 and above. (I'd have a hard time actually deciding. I don't think 60 is a grade good enough for an exam like this, but maybe I would consider it.) Note that this is just to give you an idea on how I curve grades. In the end I will just curve (if necessary) your final averages, and will not even consider this curve given here.
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Here is the Midterm II and the Midterm II with solutions.
The exams and corrections were graded and will be returned in class on Thursday (04/11). (You can check your grades in Blackboard.) Your official Midterm II grade will be the one with the points from corrections added. 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 74.96, the median was 80 and the highest grade was 100.
If I were to curve these grades, roughly, an A would be 89 and above, a B would be 80 and above and a C would be 65 and above. Note that this is just to give you an idea on how I curve grades. In the end I will just curve (if necessary) your final averages, and will not even consider this curve given here.
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Here is the final: Final, and Final Solution.
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Math 300/307 is a basically a course on mathematical proofs. A proof is a series of logical steps based on predetermined assumptions to show that some statement is, beyond all doubt, true. Thus, there are two main goals: to teach you how think in a logical and precise fashion, and to teach how to properly communicate your thoughts. Those are the ``ingredients'' of a proof.
So, the topics of the course themselves play a somewhat secondary role in this course, and there are many difference possible choices. On the other hand, since these will be your first steps on proofs, the topics should be basic enough so that your first proofs are as simple as possible. Therefore, you will be dealing at times with very basic mathematics, and will prove things you've ``known'' to be true for a long time. But it is crucial that you do not lose sight of our real goal: do you know how to prove those basic facts? In fact, the truth is that you don't really know if something is true until you see a proof of it! You might believe it to be true, based on someone else's word or empirical evidence, but only the proof brings certainty.
In any event, the topics to be covered in this course are: logic, set theory, relations and functions, induction. We will use also basic notions of real and integer numbers.
This course is clearly crucial to mathematicians, as our job is to prove things (and find things to be proved). But, this is a course also required for computer scientists, not only here at UT, but virtually everywhere. The most obvious reason is that computer programs are written using formal logic. Another relevant connection is Artificial Intelligence, where you basically have to ``teach'' a machine to come up with its own proofs.
Moreover, the skills taught in this course are universally important, and their benefits cannot be overstated! Everyone should be able to think clearly and logically to make proper choices in life, and you should be able to communicate your thoughts clearly and concisely if you want to convince, teach, or explain your choices to someone else. In particular, Law Schools are often interested in Math Majors, as the ability to think logically and clearly develop an argument is (or should be) the essence of a lawyer's job.
The goal is to cover the whole text. Chapter 7 is not crucial but would be interesting to cover it. Some sections might eventually be skipped or only briefly discussed if we are pressed on time, though. In particular, I might go over Chapter 3 (on proof strategies) quickly, leaving to discuss the corresponding strategies as they appear in a more natural context.
Homeworks will be assigned after every class and the selected problems and due dates 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 due on Tuesdays, when you will either turn in your HW or take a quiz on problems taken directly from the HW set due on that day. In the former case, two or three problems will be graded and count the same as a quiz. In the the latter, the HW will not be collected at all. You will not know in advance if the HW will be collected or if there will be a quiz, and hence you should be prepared for either one.
The quizzes will take place at the beginning of the class. You will not have extra time if you are late. You will have only ten or fifteen minutes to take a quiz, and so if you hadn't already solved the HW problems, you might not have enough time to come up with a solutions.
Note that you will also be graded on how well it is written, not only if it is correct! (Remember, how to communicate your proofs is part of the course.) The same applies to exams and all graded work!
Calculators will not be allowed! (This includes HW, quizzes, and exams!) As you will see, you won't miss them either.
I will do my best to post solutions to the most difficult problems. If I do, they will be posted in this page.
If you like to do your HW early, you can do problems in the list of Problems Likely To Be Assigned below, even before I assigned them. I might change a problem or two for the actual assignment, but that is not very likely. I will try to update it early enough for those who would like to start before we covered the material.
Also, some times I might get too ambitious in posting problems, i.e., I might think we will cover a section during the week, put exercises from it in the next assignment, and then end up not being able to finish it. In this case I might have to take a few problems off the assignment. The bottom line is the following: the assignment is not final until I remove the "More to come" from it. (If you've done problems which were removed, just saved them for the following week.)
Finally, if there is still a "More to come" in an assignment on a Thursday, please write me right away so that I can update it. If I only realize on Monday (or Tuesday morning!) that an assignment was not complete (with the "More to come" still there) and nobody tried to contact me, I may add new problems just then, giving you little time to finish the assignment. (If I delay in replying, you can proceed with the Problems Likely To Be Assigned.)
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, HW, 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.
I will assume you check your e-mail at least once a day. 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 less than twenty four hours, 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
The university expects that all academic work will provide an honest reflection of the knowledge and abilities of both students and faculty. Cheating, plagiarism, fabrication of data, providing unauthorized help, and other acts of academic dishonesty are abhorrent to the purposes for which the university exists. In support of its commitment to academic integrity, the university has adopted an Honor Statement.
All students should follow the Honor Statement: from Hilltopics 2012/2013, pg. 16:
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.
Please, see also the Campus Syllabus.
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This list is subject to change without prior notice. The official assignments will be posted below.
Section 1.1: 1, 3, 6, 7.
Section 1.2: 2, 3, 8, 9, 12, 17.
Section 1.3: 2, 4, 6, 8.
Section 1.4: 2, 6, 7, 9, 11, 15.
Section 1.5: 3, 4, 5, 9.
Section 2.1: 3, 5, 6, 9.
Section 2.2: 2, 5, 7, 10.
Section 2.3: 2, 5, 6, 9, 12.
Section 3.1: 2, 3, 6, 8, 10, 15, 16.
Section 3.2: 2, 3,4, 7, 9, 12.
Section 3.3: 2, 4, 10, 13, 15, 18, 21, 24.
Section 3.4: 3, 8, 10, 16, 24.
Section 3.5: 3, 6, 9, 13, 17, 21, 24.
Section 3.6: 2, 3, 7, 10.
Section 4.1: 3, 7, 9, 10.
Section 4.2: 2, 3(a), 5, 6(b), 8.
Section 4.3: 2, 4(a), (c), 9(a), 12, 14, 16, 21.
Section 4.4: 2, 3, 6, 9, 15, 20, 22.
Section 4.6: 4, 8, 13, 20, 22.
Section 6.1: 2, 4, 9, 16.
Section 6.2: 5, 6 (use the triangle inequality from Problem 12(c) of section 3.5; you don't need to do that exercise, just refer to it), 10.
Section 6.3: 5, 9, 16.
Section 6.4: 7(a), (b), (c).
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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.
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HW1 - Due on Tuesday 01/15:
Section 1.1: 1, 3, 6, 7.
HW2 - Due on Tuesday 01/22:
Section 1.2: 2, 3, 8, 9, 12, 17.
HW3 - Due on Tuesday 01/29:
Section 1.3: 2, 4, 6, 8.
Section 1.4: 2, 6, 7, 9, 11, 15.
HW4 - Due on Tuesday 02/05:
Section 1.5: 3, 4, 5, 9.
Section 2.1: 3, 5, 6, 9.
HW5 - Due on Tuesday 02/12:
Section 2.2: 2, 5, 7, 10.
Section 2.3: 2, 5, 6, 9, 12.
HW6 - Due on Tuesday 02/26:
Section 3.1: 2, 3, 6, 8, 10, 15, 16.
Section 3.2: 2, 3,4, 7, 9, 12.
Section 3.3: 2, 4, 10, 13, 15, 18, 21, 24.
HW7 - Due on Tuesday 03/05:
Section 3.4: 3, 8, 10, 16, 24.
HW8 - Due on Tuesday 03/12:
Section 3.5: 3, 6, 9, 13, 17, 21, 24.
Section 3.6: 2, 3, 7, 10.
HW9 - Due on Tuesday 03/19:
Section 4.1: 3, 7, 9, 10.
Section 4.2: 2, 3(a), 5, 6(b), 8.
HW10 - Not to be turned in! Just practice for the exam:
Section 4.3: 2, 4(a), (c), 9(a), 12, 14, 16, 21.
HW11 - Due on Tuesday 04/09:
Section 4.4: 2, 3, 6, 9, 15.
HW12 - Due on Tuesday 04/16:
Section 4.4: 20, 22.
Section 4.6: 4, 8, 13, 20, 22.
HW13 - Due on Tuesday 04/23:
Section 6.1: 2, 4, 9, 16.
HW14 Not to be turned in! Just practice for the final:
Section 6.2: 5, 6 (use the triangle inequality from Problem 12(c) of section 3.5; you don't need to do that exercise, just refer to it), 10.
Section 6.3: 5, 9, 16.
Section 6.4: 7(a), (b), (c).
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 Thursday afternoon and there still is a ``More to come'' after the HW assignment due on the coming Tuesday, write me an e-mail at lfinotti@utk.edu, and I'll update it and let you know.
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