Math 421: Combinatorics - Spring 2014

Math 421: Combinatorics - Spring 2014



Important Notes


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Instructor 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!)


Office Hours: MW 9-10 or by appointment.


Textbook: M. Bona, ``A Walk Through Combinatorics: An Introduction to Enumeration and Graph Theory'', 3rd Edition, World Scientific Publ., 2011.

Prerequisite: Math 300/307.

Class: TuTh 3:40pm-4:55pm at Ayres 111. (Section 001, CRN 27657.)

Exams: Midterms: 02/25 (Tuesday) and 04/08 (Tuesday); Final: 05/05 (Monday) from 12:30pm to 2:30pm.

Grade: 25% for HW (lowest score dropped) + 20% for each Midterm + 35% for the Final. Note the weight of the HWs!


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Course Information

Course Content

In this course we will study Combinatorics, more precisely, Enumerative Combinatorics.

It is very important that you already have some practice with writing proofs (which was covered in Math 300/307), as well as the topics in set theory usually covered in this course (sets, inclusion, unions, intersections, relations, functions, etc.). In particular, you should be familiar with the contents of Part I (called Basic Methods and covering Chapters 1 and 2) in the text. It might be worth looking over those chapters to see if you are prepared for what is to come. (I would gladly try to help you with that if you come to my office hours.)


Chapters and Topics

The goal is to cover Part II (called Enumerative Combinatorics and covering Chapters 3 to 8). My initial intention is to follow the text closely, but I might take slight detours as we go.

Note that this outline is subject to change slightly without prior notice.


Homework Policy

Homework problems and their 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!)

Since the text has solutions to all exercises, you will not turn in these HW sets, but instead take quizzes in class. (I do urge you to only look at solutions after you took a considerable time thinking about the problem and perhaps talked to me or a friend to get some help. If you constantly look at solutions, you won't be able to do the exams and will likely fail...) The problems on the quiz will be either straight from the HW set or perhaps with numbers changed (not in any significant way).

So, to each HW set assigned below, there will be a quiz in class at the due date. The due date will (most likely) be the class after I finish the corresponding section(s). Since sometimes I might not be able to finish the section(s) when I thought I would, the due dates will initially be marked as "tentative date". So, as long as you see "tentative date" in the assignment, it is not final. If the tentative date is the date of next class, then please write me immediately to see if there will be a change or not.

The quiz will take place at the beginning of class and should not take more than 15 minutes (probably less). I won't give extra time for those who come late, so please try to be on time (at least when we are having a quiz). I recommend you review your HW shortly before class, so that the ideas are fresh in your mind and you don't have to spend time actually figuring out how to do the problems. In fact, I will assume you've seen already how to do the problems, so the time I will give you will not be enough to figure things out on the spot!

You should not wait to start the HW only after the date is set, or you might not have enough time to do all the problems properly. (Again, looking at solutions without giving yourself time to think about the problems is a very bad idea!) You can always start doing problems that it seems to be from the material already covered in class.

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 hope to be able to keep this list ahead of the class, so that you can always start early. It will also be useful if I, for some reason, delay to post problems.

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 HWs 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 and feedback. This is the official site for the course.)


Missed Work

There will be no make-up exams or quizzes. If you miss an exam or quiz and have a properly documented reason, your final will be used to make-up your score.

The way this works is as follows: imagine you missed a midterm (and had a documented excuse). The points from the problems on the final involving the sections of the corresponding midterm will make your midterm grade. For example: let's say that you missed Midterm 1, which, say, involved Sections 2.1-9 and 3.1-4. If questions 1 to 3 of the final (which is comprehensive!) are the questions from those sections and you get 24 out of 30 in those questions, your Midterm 1 grade will 80 out of 100 (as 24 is 80% of 30).


E-Mail Policy

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.


Blackboard and Feedback

Blackboard will be used mainly for grades and feedback. The main content will be posted in this page.

There you can post an introduction (a blog post that all enrolled in the class can read) and post questions, both math related or about the course structure. (I've created a different forum for each. Please use the appropriate one!) The former is moderated by me (your post has to be approved by me before appearing), while the second is not. Again, all students will be able to read these and offer help.

Lastly, there is also a link for (general) Feedback. Please, post all comments and suggestions there as often as you want. (I really appreciate your input.) These can be posted anonymously (or not). Just make sure to check the option before posting. Others 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, but then, of course, it won't be anonymous.


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Legal Issues


All students should be familiar and maintain their Academic Integrity: from Hilltopics 2013/2014, pg. 46:

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.

We are in a honor system in this course!



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.


Campus Syllabus

Please, see also the Campus Syllabus.


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Here is a video about class policy for the first day of class (when I will be out of town). DISCLAIMER: It is hard to make perfect videos. And this is quite far from perfect. But I hope it will be helpful, despite some awkward pauses, English mistakes, mistatements, stutering, etc. If I had more time, I would probably edit it, redo a few parts or even rerecord from scratch, but alas, I didn't. Again, try to overlook (and forgive) the problems and concentrate on content.


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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.


Chapter 3: 1, 2, 3, 4, 7, 8, 11, 13, 14, 19.

Chapter 4: 3, 4, 5, 7, 8, 9, 11, 14, 17, 26, 27.

Chapter 5: 1, 2, 5, 7, 11, 15, 16.

Chapter 6: 26, 27, 29, 30, 31, 42(a), 46, 47.

Chapter 7: 16, 18, 22, 25, 31, 36.

Chapter 8: 1, 4, 7, 34.


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HW1 - Due on Tuesday 01/28:

Chapter 3: 1, 2, 3, 4, 7, 8, 11, 13, 14, 19.


HW2 - Due on Thursday 02/06:

Chapter 4: 3, 4, 5, 7, 8, 9, 11, 14, 17, 26, 27.


HW3 - To prepare for the exam on Tuesday 02/25:

Chapter 5: 1, 2, 5, 7, 11, 15, 16.


HW4 - Due on Wednesday 04/02 by 12pm:

Chapter 6: 26, 27, 29, 30, 31, 42(a), 46, 47.


HW5 - Due on 04/22:

Chapter 7: 16, 18, 22, 25, 31, 36.


HW6 - To prepare for the final:

Chapter 8: 1, 4, 7, 34.


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 Thursday, write me an e-mail at, and I'll update it and let you know.


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