Math 300: Introduction to Abstract Mathematics - Fall 2008

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## Important Notes

• (11/27 - 6:25pm) I've just posted the solutions for HW12. I strongly recommend that you first try to solve the problems, and only then check the solutions! (I cannot stress this enough!) Otherwise you will not know if you are capable of solving problems on the final or realize what are your difficulties (on which you should work before the final).

• (11/27 - 5:15pm) There will be no HW due on Tuesday (12/02) and no quiz in class.

• (11/27 - 5:15pm) Here is some info about our final:

• It is this coming Thursday (12/04) from 10:15am to 12:15am in our regular classroom.
• No calculators, notes, book, etc., will be allowed.
• It covers all sections we covered. More precisely, Chapters 1, 2, 3 (except ``Odd and Even Functions''), 4 (except ``Finite Sets''), and the first three sections of Chapter 5. (``Roots and Irrationals'' will not be in the exam.)
• The exam has 10 questions: two from Chapter 1, one from Chapter 2, one from Chapter 3, three from Chapter 4, three from Chapter 5. (In total, four questions cover the material since the last midterm.) All questions are worth the same (10 points). Of course, expect lots of proofs.
• You will be graded on how well you write your proofs! It is not enough to have the correct idea, you have to be able to communicate it clearly, precisely, and concisely.
• To study, I recommend:
• Review your notes and read the book. The most important parts is to review the definitions and theorems. If necessary, write those in a different sheet of paper so that you don't have to browse your book every time you need to refresh your memory.
• Look at all examples and solved problems. In particular, look over the examples from your notes carefully, as sometimes they are a bit different from the book and something like that can show up in the test.
• Review your old HWs and midterms. Redo all problems that you've missed. (You should always learn from your mistakes!) Always look for exactly what went wrong so that you do not repeat the same mistake!
• Look in solutions of solved problems for ideas that can make a proof shorter or simpler.
• Do as many problems as possible from the book.
• When you first start studying, you can look at the book or notes, but by the end, you should be able to do problems without looking.
• Try to choose about 10 problems to work on as if you were in the exam: no notes, allow only two hours, etc. This might give you an idea if you are prepared.
• Solutions for problems from Chapter 5 are being posted. Keep checking it.

• (08/18 - 12:00pm) Please, check this section often. I will put announcements and important info here.

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### Instructor Contact and General Information

Instructor: Luís Finotti

Office: Ayres Hall 212-D

Office Hours: MW 11:00am-12:00pm or by appointment (subject to change!!)

Textbook: W. Wade, ``Math 300: Introduction to Abstract Mathematics''. Printed by Graphic Creations.

Prerequisite: Math 142 or Math 148.

Class: TTh 9:40-10:55 at Ayres Hall 320. (Section 4.)

Exams: Midterms: 09/30 (Tue) and 11/04 (Tue), in regular classroom and time; Final: 12/04 (Thu) from 10:15am to 12:15pm, also in our regular classroom.

Grade: 25% for HW (quizzes and board work) + 20% for each Midterm + 35% for the Final. Note the weight of the HWs!

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### Exams:

#### Midterm I

The exams were graded and will be returned in class on Thursday (10/02). (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 average was 69.24, the median was 61 and the highest grade was 97. So, the results were OK, but I thought they'd be better as the exam was easy. (Just check the solutions.)

Here is how I would curve these grades and the number of people with each grade:

 Grade Range # of people A 90-100 3 A- 86-89 2 B+ 82-85 3 B 77-81 0 B- 74-76 1 C+ 70-73 2 C 66-69 2 C- 60-65 5 D+ 57-59 2 D 53-56 0 D- 50-52 3 F < 50 2

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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#### Midterm II

The exams were graded and will be returned in class on Thursday (11/06). (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 exam might have been too long, so I considered the grade out of 80 instead of out 100 to compensate. On the other hand, most of what was in the exam you had seen before and so it should not have taken you as long. In any case, the average was 65.51 (out of 100, or 54.9 out of 80), the median was 64.38 (out of 100, or 52 out of 80) and the highest grade was 125 (out of 100, or 100 out of 80, i.e., a perfect score). The next highest grade was 98.75 (out of 100, or 79 out of 80).

Here is how I would curve these grades and the number of people with each grade:

 Grade Range # of people A 90-125 5 A- 87-89 0 B+ 83-86 0 B 77-82 1 B- 70-76 3 C+ 65-69 2 C 60-64 3 C- 57-59 0 D+ 53-56 0 D 50-52 0 D- 47-49 4 F < 47 3

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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#### Final

Here is the final and the final with solutions.

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### Course Information

#### Course Description

Math 300 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, and properties of the real 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.

#### Course Structure

We will try to cover as much as possible of the text, but I'd like to cover at least the first 5 chapters. On the other hand, I might, and likely will, deviate from the book. I might just change the order of things a bit, but I might even change some topics, in which case your class notes would be quite important.

#### Homework and Quizzes

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. I will look through them and keep comments for myself which will affect your final course grade from minus 5 points to plus 5 points (out of 100 points). People that do not turn HWs will have five points deducted from their final grades!

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. 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!

We will also have board work some Thursdays. I will ask for volunteers to do HW problems at the board for extra-credit. But, you will have to explain your solution to the class, not just write it down, and I will ask questions about it. It will count up to half of the points of a single quiz.

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.)

#### Missed Work

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.

#### E-Mails

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, write me an e-mail letting me know ASAP. 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.

#### Feedback

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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### Legal Issues

#### Conduct

All students should be familiar and maintain their Academic Integrity: from
Hilltopics 2008/2009, pg. 40:

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.

#### Disabilities

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

#### Sexual Harassment and Discrimination

For Sexual Harassment and Discrimination information, please visit the Office of Equity and Diversity.

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### Important dates:

Wednesday, August 20 - Classes begin.

Friday, August 29 - Last day to add, change grade options, or drop a full semester course without a "W".

Monday, September 01 - Labor Day Holiday. (No class.)

Tuesday, September 30 - Midterm I.

Thursday-Friday, October 09-10 - Fall Break. (No class.)

Tuesday, October 21 - Last day to drop a full term course with a "W".

Tuesday, November 04 - Midterm II.

Tuesday, November 11 - Last day to drop with a WP/WF.

Thursday-Friday, November 27-28 - Thanksgiving. (No class.)

Tuesday, December 02 - Last Class Day.

Thursday, December 04 - Final.

More dates.

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### Homework

HW1 - Due on Thursday 09/04:

Pg. 8: 1, 2, 3, 4, 5, 7.

HW2 - Due on Thursday 09/11:

Pg. 12: 8(a), 9(a), 10, 12, 15, 16, 17.

HW3 - Due on Thursday 09/18:

Pg. 17: 22(a), 24(c) (you should also do 24(a) and (b), but do not turn them in), 25(b), 26, 28(a), (b), (c).

Pg. 20: 29, 31, 32, 33, 36, 37.

HW4 - Due on Thursday 09/25:

Pg. 24: 1, 2, 3(a), (b).

Pg. 28: 4, 5(d), (e), 6.

HW5 - NOT to be turned in:

Pg. 28: 7, 9, 10.

HW6 - Due on Thursday 10/16:

Pg. 33: 1(a), (b), (c), 2, 3, 4(a), 5, 6(b).

HW7 - Due on Thursday 10/23:

Pg. 38: 8(a), (c), (e), (f), 9, 10.

HW8 - Due on Thursday 10/30:

Pg. 44: 1, 3, 4, 5.

HW9 - NOT to be turned in:

Pg. 46: 7, 9, 10, 12, 13.

Pg. 49: 14, 16, 17, 19.

HW10 - Due on Thursday 11/13:

Pg. 53: 39, 40, 41, 44, 45.

HW11 - Due on Thursday 11/20:

Pg. 56: 46, 47, 48, 49, 50, 52.

HW12 - Not to be turned in:

Pg. 60: 1 to 8.

Pg. 64: 10, 11, 12, 15, 17, 25, 27.

Pg. 66: 29(a), (c), (d), 30, 33, 35, 41, 43.

THAT'S ALL FOLKS!

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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