Cryptology and Coding Theory Projects

 

 

The main goals of the course project are to

 

Guidelines:

 

  1. Choose a topic and partner:   You must choose a topic that interests you and appropriately challenges you.  You will decide on a project topic in consultation with your partner.   (You will work in pairs.)  The end of this document contains a list of suggested topics, some of which require more mathematics background than others.  These ideas are broad so that you can narrow your exact focus based on your interests.  You may also 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 must eventually contain at least four references, two of which must be published documents (so a website does not count as a published document but a journal article accessed through an online journal subscription does count as a published document).  You have to have read the documents (or noted portions of the documents) for them to go into the bibliography!
  3. Preliminary ideas:  A document summarizing your preliminary ideas should be prepared for Thursday, November 9th.  During class that day, you will have an opportunity to share ideas with classmates, to help focus your plans and to choose a partner.
  4. Prepare project outline:  The project outline is (tentatively) due Monday November 27th.  This will count towards your project grade and should be professionally written. It should include
    1. A brief description of the chosen area of study.
    2. A statement of the specific goals of the project. (What do you hope to accomplish? What exactly will you investigate?)
    3. An explanation of why the chosen topic is appropriate* given your strengths, backgrounds, and interests. *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. A detailed outline of the planned paper/oral presentation.
    5. Brief descriptions (2-3 sentences) of your preliminary references (which may or may not wind up in your final bibliography).  
  5. Prepare presentation: 
    1. Written:  Each pair will write a roughly 10-page double-spaced (12pt font, one inch margins) paper describing the chosen project.  Diagrams, tables, and figures do not count in the page limit. You should work to fit high quality mathematics and exposition within the page limitation.  The paper should be professionally written and should (in most cases) include sections as follows:

                                                              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?  Show off the new stuff that you now know.

                                                            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 why we do it in pairs.

Note on Written Presentation: 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.  Your paper must include some original thought.  For example, you might come up with a new example, an original comparison of different systems, or a new proof of a result. Be sure to indicate your use of references, and be sure to indicate which parts represent original thought.  See guidelines hand-out for more information.

    1. 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! See guidelines hand-out for more information.

 

Evaluation:  Please see the “Presenting Mathematics” document (linked from daily schedule) for criteria for effective papers and oral presentations.  Keep these criteria in mind as you proceed with your project.  These criteria will be used in the evaluation of your work.  Each student will also evaluate every other presentation.

 

 

Project Ideas