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
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
Here is an example of one of my abstracts:
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!
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
Your presentation should include the following:
Your introduction must explain what your final project is about, and summarize the contents of the rest of the presentation.
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
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, Maple.mw,
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.
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.