Discrete Mathematics Projects

The main goals of the course project are to allow students to choose a topic of personal interest for in-depth

study and research provide experience in reading technical literature provide experience in self-directing a partnered project provide practice at presenting technical information (orally and

written) provide a meaningful culminating experience for every student

Guidelines:

1. Choose a topic and group: You must choose a topic that interests you and appropriately challenges you. The topic should build upon knowledge you gained in this course. You will decide on a project topic in consultation with your partner(s). (Most of you will work in groups of 3, some in groups of 2.) The end of this document contains a list of suggested topics, but you are encouraged to propose your own topic.

2. Background research: Each person in the group must research the chosen topic. We suggest starting with web-searches, looking for scientific articles, and using interlibrary-loan as necessary to procure books (plan ahead!). Your bibliography should not rely solely on websites – you need to use some published documents (available online or off).

3. Prepare informal project proposal: The informal project proposal, due in class on Thursday Nov 15, should be an approximately ½- to 1-page outline of the project goals (what do you hope to accomplish?), an explanation of why the chosen topic is appropriate* given your backgrounds, and a list of your preliminary references (which may or may not wind up in your final bibliography). *Do not propose to learn about algorithm complexity if you already know about algorithm complexity. Do propose to learn about algorithm complexity if you have no idea what this means but it sounds interesting.

4. Prepare project outline: The formal project outline, due on Thursday Nov 29 by 9am, should be a more fleshed out version of the informal project proposal. Enough detail should be provided concerning your project goals (What exactly are you doing? What do you hope to learn/accomplish?) and progress (What is done so far? What is left to do?) for the professor to

determine if the scope of work is appropriate. Feedback will be provided in class on Thursday Nov 29.

5. Prepare presentation: a. Written: Each pair will write a roughly 8 page paper

using the provided IEEE style files. The paper should be professionally written and should (in most cases) include sections such as:

i. Abstract – Give a short, self-contained description of the project. This will be archived for future reference.

ii. Introduction - Give a brief introduction to your chosen topic and outline what you will do in the balance of the paper (ie. Explain the goals of the paper). Indicate why this topic is exciting/useful.

iii. Background - Introduce any new definitions, notation, or other background information necessary for understanding the rest of the paper.

iv. Main Section(s) - Describe the heart of your project. What did you learn? What theorems did you prove or results did you discover? What examples did you find/invent? How did you advance your learning? Show off the new stuff that you now know. Your paper must include some original, creative thought. For example, you might come up with a new result, a novel example, an original comparison of different systems, or a new proof of an old result. Clearly indicate what is original and what was found in references. You can (and should) use references to guide your write-ups of the examples, theorems, and proofs, but you must explain the details in your own words. Proofs and examples should not be copied, but rather explained as your group has grown to understand them.

v. Conclusions - Wrap things up. Remind us what new knowledge your project produced and remind us why your project is exciting/useful. You might also draw connections among the new stuff you learned or perhaps draw connections to another aspect of the course.

vi. Bibliography.vii. Proof-read, proof-read, proof-read. This is one of the

reasons why we do it in pairs. Use writing tutors.b. Oral: Each pair will deliver a 15 minute presentation on

their project. The oral presentation will essentially give an overview of the content of the paper to the class. Usually, the oral presentation will not contain formal proofs. Remember, the goal here is to explain new knowledge to

your classmates. Structure your presentation as you would hope others would structure theirs! Make it interesting and easy to understand. Practice, practice, practice. This is why you have friends and/or stuffed animals.

Evaluation: Please see the “Presenting Mathematics” document for criteria for effective papers and oral presentations. These criteria will be used in the grading process. Each student will also evaluate every other presentation.

Project Ideas Graph theory and the channel assignment problem: L(2,1) graph

labelings (opportunity to continue research in the future) Space-time block codes (opportunity to continue research in the

future) Error-control codes (opportunity to learn more in ECE elective

MTH 3140) Cryptosystems/hash functions Symmetry Groups Group theory and advanced counting techniques Graph algorithms Group theory and connections to Rubic's cube Magic squares – combinatorial analysis Latin squares – combinatorial analysis Ramsey Numbers Combinatorial designs Catalan Numbers Rook polynomials Algorithm complexity Continuation of Mini-Project Idea sparked from Enrichment Reading articles For more ideas, see

http://www.mathpages.com/home/icombina.htm . One student based a project on “The coin in 3 fountains,” which turned into a research project.

For basic definitions of different areas of discrete math, see http://mathworld.wolfram.com/topics/DiscreteMathematics.html