Math 300: Introduction to Abstract Mathematics - Fall 2009

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Important Notes

• (12/09 - 11:05am) Your average will be computed in the following way. I will drop your lowest HW/Quiz score when computing your Quiz/HW average. Then, if you did not miss more than a two HWs/Quizzes, then your course average will be the greatest value between 0.25*HW + 0.20*(Mid1 + Mid2) + 0.35*Final (the way made explicit in the syllabus) and (0.20*(Mid1 + Mid2) + 0.35*Final)/0.75 (so, the HW are not considered). The bottom line is that the HW can only help you. On the other hand if you missed more than two Quizzes/HWs, your course average will be computed as in the syllabus (i.e., 0.25*HW + 0.20*(Mid1 + Mid2) + 0.35*Final).

If you did not turn in your HW/Quiz for health reasons (and I told you that I would replace your score with your final), then this score will count (as usual), i.e., you will not be penalized.

• (12/01 - 9:00am) I have just written the final exam. Here is some info about it:

• It is on 12/09 (Wednesday), from 12:30pm until 2:30pm, 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 five sections of Chapter 5 (except ``Absolute Values''). ``Roots and Irrationals'' will be in the exam.
• The exam has 9 questions: two from Chapter 1, one from Chapter 2, one from Chapter 3, three from Chapter 4, and two from Chapter 5. (In total, four questions cover the material since the last midterm.) The first 4 questions are worth 10 points, while the last 5 are worth 12 points. (Of course, expect lots of proofs.)
• There are questions straight from the HW, and from book/notes (like examples). There are questions that are also the same, but with numbers changed.
• 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.
• It is essential that you know all definitions (and terminology), and how to start all the kinds of proofs.
• To study, I recommend:
• Work on HW12. The solutions are posted, but try to solve the problems before looking at them.
• Quickly 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. 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. Also, they might help on writing proper proofs.
• Look at all solved exams in my Fall 2008 Math 300 web page. In particular, look at the final. The material for our final is slightly different, as we did not cover ``Absolute Value'' and did cover ``Roots and Irrationals''. (So, question 10 is not relevant to us.)
• 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 around 9 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. (You can also work on my old final, but remember to exclude question 10 and maybe add one from ``Roots and Irrationals''.)
• (09/09 - 7:40am) Change in make up work policy: As recommended by the university administration, I will not require a doctor's note in order to make up for missed work anymore. The change was suggested to avoid encouraging sick students to come to class while still contagious, and to prevent the Student Health Center to receive more appointments that necessary.

• (08/16 - 7:00pm) 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: Aconda Court 211-H

Office Hours: MW 9:00am-10:00am 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: MWF 11:15-12:05 at HBB 103. (Section 1.)

Exams: Midterms: 09/30 (Wed) and 11/04 (Wed), in regular classroom and time; Final: 12/09 (Wed) from 12:30pm to 2:30pm, also in our regular classroom.

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

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Exams:

Midterm I

The exams were graded and will be returned in class on Friday (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 61.18, the median was 56 and the highest grade was 91. So, the results were not good.

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

 Grade Range # of people A 89-100 2 A- 80-88 1 B+ 77-79 1 B 75-76 1 B- 65-74 2 C+ 55-64 1 C 50-54 1 C- 47-49 2 D+ 45-46 0 D 43-44 0 D- 40-42 0 F < 40 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 Friday (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 results were mostly OK. This was the sort of exam that shows who are working on the class, as all the problems were very similar to HW. So, the grades were distributed among very good and very bad grades, with just a few in between. In any case, the average was 75.87, the median was 78, and the highest grade was 100. You can see the statistics at Blackboard.

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

 Grade Range # of people A 90-100 6 A- 87-89 0 B+ 83-86 0 B 80-82 0 B- 77-79 1 C+ 70-76 1 C 65-69 1 C- 63-64 0 D+ 60-62 2 D 55-59 2 D- 50-54 0 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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Final

Here is the final: final and 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 due on Wednesday, 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 known 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!

Points will be taken from messy solutions in all assignments, and you need to show work in all questions (unless stated otherwise)! (This same applies to quizzes, HWs, 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.

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.)

Missed Work

There will be no make-up quizzes or exams. If you miss a quiz or exam and have a properly documented reason or due to sickness, 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.

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 2009/2010, pg. 40:

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 2009/2010, 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 19 - Classes begin.

Friday, August 28 - Last day to add, change grade options, or drop a full semester course without a "W".

Monday, September 07 - Labor Day Holiday. (No class.)

Wednesday, September 30 - Midterm I.

Thursday-Friday, October 15-16 - Fall Break. (No class.)

Tuesday, October 20 - Last day to drop a full term course with a "W".

Wednesday, November 04 - Midterm II.

Tuesday, November 10 - Last day to drop with a WP/WF.

Thursday-Friday, November 26-27 - Thanksgiving. (No class.)

Tuesday, December 01 - Last Class Day.

Wednesday, December 09 - Final.

More dates.

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Problems Likely To Be Assigned

This list is subject to change without prior notice. The official assignments will be posted below.

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

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

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.

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

Pg. 28: 4, 5(d), (e), 6, 7, 9, 10.

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

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

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

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

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

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

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

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.

(And maybe more!)

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Solutions to Selected HW Problems

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:

• (11/29 - 10:30am) Added solutions for HW11 and HW12.
• (11/18 - 5:30pm) Added solutions for HW10.
• (11/12 - 9:20am) Added solutions for HW9.
• (10/30 - 12:40pm) Added solutions for HW7 and HW8.
• (10/21 - 4:10pm) Added solutions for HW6.
• (10/14 - 9:30am) Added solutions for HW5.
• (09/25 - 9:20am) Added solutions for HW4.
• (09/18 - 12:40pm) Added solutions for HW3.
• (09/14 - 8:45am) Added solutions for HW2.
• (09/03 - 10:50am) Posted solutions for HW1.

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Homework

HW1 - Due on Wednesday 09/02 (note it was postponed!):

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

HW2 - Due on Wednesday 09/09:

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

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

HW3 - Due on Wednesday 09/16:

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

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

HW4 - Due on Wednesday 09/23 (note that some problems were postponed):

Pg. 28: 4, 5(d), (e), 6, 8, 9.

HW5 - Due on Wednesday 10/07 (note it was postponed!!!):

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

HW6 - Due on Wednesday 10/21 (note it was postponed):

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

HW7 - Due on Wednesday 10/28:

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

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

HW8 - Do not turn in, just practice for the exam:

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

HW9 - Due on Wednesday 11/11:

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

HW10 - Due on Wednesday 11/18:

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

HW11 - Due on Wednesday 11/25:

Pg. 60: 1 to 8.

Pg. 62: 10, 11, 12(b), 13(a), 17, 18.

HW12 - Do not turn in, just practice for the final:

Pg. 64: 20, 21, 22(a), 25, 25, 26.

Pg. 68: 46 (you can use 44 and 45 if you need), 47, 50.

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 Wednesday, write me an e-mail at lfinotti@utk.edu, and I'll update it and let you know.

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