Final Project Guidelines

This is to be an individual project, which will be turned in (in various stages) as a preliminary bibliography and abstract, a preliminary organizational plan, and a presentation and a final annotated bibliography. Graduate students will also turn in a written report. The topic choices will be limited on a first-come-first-served basis, so get them approved by Dr. Sarah by posting a message to the WebCT bulletin board (NOT email!)

Preliminary Bibliography and Oral and Electronic Abstract - Tuesday April 24th Final project abstract and preliminary bibliography due by 11am to the WebCT bulletin board (NOT email!) as an attachment that I can read and post to the main web page (latex, text, Word, rtf, or Maple) and you should be prepared to present your abstract orally in class.

Writing an abstract is an important part of giving a talk. An abstract for a talk should be thought of as an advertisement of the talk content that others can read in order to decide whether they wish to attend. At conferences, there are often many talks that occur at the same time. Hence, people use abstracts to decide which talk to attend from among possibly many talks that they are interested in at the given time. Conference abstracts are usually due many months before a conference. Hence, it is not imperative that you follow the abstract exactly when presenting the talk, since many people find that by the time they prepare their talk, related but new material is of interest. An abstract should be your best guess of what you will talk about in the allowed space. It should also include some big picture ideas that discuss the importance and relevance of your talk content and place it into the bigger context of related fields. Abstracts are usually a few paragraphs long, and sometimes have space limitations on the number of characters or words. Your abstract will be less than 250 words. While the final talk may well be different, the abstract should be at least loosely adhered to since otherwise talk attendees will be confused and sometimes angry that the talk was unrelated to what you said it would be. After all, attendees are giving their valuable time to you, and might instead have chosen a different talk. The first step in writing an abstract is to choose a title. The title should be chosen carefully to summarize the content of your talk. Some people may not read the abstract (it is sometimes published in a separate book from the schedule), and may use only the title in order to decide whether they will attend.

Here is an example of one of my abstracts: Good News Everyone! Mathematical Morsels from The Simpsons and Futurama

Here is an example of an abstract by Robert Ghrist on Barcodes: The Persistent Topology of Data

Your preliminary organizational plan - Friday April 27th must explain how you will present your project and must contained a detailed talk outline. You will post this to the WebCT bulletin board and I will respond to your message with comments and suggestions for improvement. Your final project will be a 15-20 minute presentation. You may present your project on the blackboard, on transparencies, or as a powerpoint, pdf, or other digital presentation.

The Presentation - Monday April 30th If you are doing a digital presentation, you must turn it in as an attachment on WebCT by 11am. In addition, bring a printed copy with you to give to Dr. Sarah at the start of your talk. If you are presenting your project on transparencies, bring a paper copy of them to give to Dr. Sarah at the start of your talk. If you are presenting your project on the blackboard, create detailed notes of what you will write, and bring a copy to give to Dr. Sarah at the start of your talk. In addition, everyone will create and turn in a final list of references with a summary of what is in each reference and how you used the reference. If you use index cards on what you will say during the presentation, turn those in when you are finished. Talks are 12-2:30 on Monday. Part of your final project grade will be determined by the quality of the peer review you fill out for each other. Your presentation needs to be in your own words. If you take a quote from somewhere, then you need to give reference where it is due. Your presentation will be 15-20 minutes in length total - practice the length carefully!
Speaker Guidelines A quote: Oral presentations my be summed up as follows: "Tell them what you're going to tell them. Tell them. Then tell them what you told them". In the Introduction you tell them what you are going to tell them. In the Body and Technicalities you tell them. In the Conclusion you tell them what you told them. Don't be scared of this repetition. Sometimes repetition is the only way to clarify misconceptions. Naturally, this means that you should repeat things in different ways, and not quote yourself verbatim. Practice, practice, practice! Practice in front of others. Practice in front of a mirror. Time your talk to be sure it fits into the time frame allotted. Use visual aids if they help make the talk clearer. Be sure to go very slowly since others will not have seen the material before. Do not flip through slides or transparencies quickly - instead, leave them up for a while to give the audience a chance to read them and let the material sink in.

Your presentation should include the following:

Introduction Your introduction must explain what your final project is about, and summarize the contents of the rest of the presentation.
Background Material You should explain any background material that is necessary. You should also review and summarize important ideas from class that are related.
The Body of Your Talk
Conclusion This might also contain questions / ideas for further exploration.
Graduate Student Written Report - Monday April 30th The written report may take the form of a paper, a demo, a classroom worksheet, a computer program, the beginning of a more extensive research project... I encourage you to be creative. It must be a product that you create yourself in your own words, and it must look professional and flow well. You will turn in your report attached as a message to the WebCT bulletin board (be sure to include the file extension!) Your project will be posted to the main web page, so you must give it to me in a form that I can read and post (for example, Word.doc, Tex.tex,, html.html, pdf.pdf...)
Grading and Final Annotated References - Monday April 30th The project will be graded based on the depth of the mathematics, the creativity of your work, the clarity of the explanations and presentation, and your peer reviews. Your project must be in your own words and it must exhibit effort that is appropriate for your background and major. Also turn in a list of annotated references, ie after each reference, you need to summarize (in your own words) what is contained within each reference and how you used it. You should spend a reasonable amount of time on your final project, but you should not spend excessive time on your project. For example, you might find that your original goal is unobtainable. That is ok. The purpose of this report is for you to research an area that is interesting and related to topology, and report back to us on what you were able to find in your own words. Depth of content and topological ideas does matter, but you should not feel as if your project needs to contain everything there is to say on the subject (this would be impossible to do for many of the topics). You might wish to include a section on what you thought you might find before you started out, and how it differed from what you actually ended up doing.

Project Ideas I have many topology books and articles in my office. Come browse in office hours! Some additional ideas (you'll need to narrow these topics down):
Topics from the books we have not covered in class
Non-orientable surfaces - Projective space, Klein bottle...
Classification of closed orientable surfaces
Euler's formula and topological invariants
Knots and links
Topology in biology
Topology in chemistry
Topology and economics
Topology and electric circuit design
Topology of the internet
Topology and robotics
Topology and the shape of the universe
The Poincare conjecture
Barcodes: The Persistent Topology of Data

I am happy to give you feedback if you bring your work into office hours.