Objectives. MATH 491 Senior Project I and MATH 492 Senior Project II are each a 3 credit required course for seniors completing their mathematical degree. The courses are used to assess the students independent thinking skills and ability to understand, write, and present formal mathematics, as well as to develop a sense of individual research and of mathematical creativity. Senior projects in mathematics are evaluated according to depth of mathematical content, clarity of exposition, effort, and originality.
Organization.
These courses are developing
approximately the same way. The courses involve a course
coordinator and project advisers.
The
Course Coordinator keeps record of the projects, project
advisers, collects the final written essays, organizes occasional
meetings with students and the oral presentations, evaluates the
written projects, and submit the final letter grades.
The
Project Adviser: At the beginning of each semester,
each student has to choose a project adviser and the topics. The
student works individually with the faculty adviser on a project. In
order to facilitate an efficient dialog between the students and
their project advisers, no more than two students can be advised by
each of our faculty members. During the semester, each student sets
up a regular schedule of meetings with the project adviser, at least
once per week: failure to do so may result in disqualification.
Choosing the Project: At the beginning of each semester, the students should have available a list with proposed topics, two titles from each faculty member. The first semester course should be concerned more on establishing the background for the more advanced problems to be considered during the second semester, and for the strongest students this may lead to original contribution at the undergraduate research level. This should be reflected in the proposed topics and keeping the same adviser for both semesters (if possible), viewing the two courses as two sequential parts of the same course.
Mathematical Typesetting: The students have access to a platform for mathematical editing with available computers equipped with the necessary software, a clear and easy accessible tutorial, and documentation, that is, books that introduce the TeX, LaTeX, AMSTeX, and especially AMSLaTeX.
Meetings with the Course Coordinator: Several times during the semester, there are meetings in the Mathematics Seminar Room. Each meeting and its topics are announced in advance. The students are required to attend these meetings.
Weekly Meetings with the Project Adviser: The student and her/his project adviser should schedule a meeting time, preferably once per week. The main part of the course relies on this relation and how it unfolds over the semester. This implies that the adviser has the possibility to gradually evaluate the progress. Flexibility in evaluating the potential of the student is necessary because the original topics may be in some cases too difficult and it must be adjusted on the way.
Project Presentation: During the second half of the semester it is preferable that each student present her/his work as an 1/2 hour part of a mathematics seminar. All senior students are required to attend the presentations of their colleagues. The dates of these presentations are arranged after consultation between the faculty adviser, the students, and the course coordinator. The students that do not have earlier presentation have to present their work during one day, organized as a session, before the final exams session. The students are encouraged to use their creativity and originality to get their ideas across. The common tools for presentations are whiteboard and overhead projectors. The presentation may not refer to the whole amount of information contained in the final paper and it must be pitched at a level that allows the peers to follow the contents. The student should have a clear understanding of what is supposed to talk about in such a way to enable the student to be confident in her/his ability of answering questions from the audience; spending some time at the beginning of the talk to orient the audience about the topics, by making sure that almost everybody understands the material, its importance and difficulty; clearly stating the main results and the ideas of the proofs; connecting the material with other research problems. Preferably, the presentations should be done before the final exam sessions, in order to avoid a difficult and overcrowded period.
Written Project: By the end of the semester each student has to submit three copies to the course coordinator (one for each member of the grading panel) of the written project, edited using TeX or the like. The written project has to be presented in final form to the adviser at least one week before and it should carry the adviser's signature, for approval. The written project is supposed to be done in the ``scientific article style'', that is, having a small abstract, a comprehensive introduction, a core presentation (preferably in the definitiontheoremproof style) accompanied by graphics if necessary, and a bibliography.
According to the MerriamWebster Online Dictionary,
to "plagiarize"
means
to steal and pass the ideas or words of another as one's own
to use another's production without crediting the source
to commit literary theft
to present as new and original an idea or product derived from an existing source.
Plagiarism is an act of fraud and it really means to steal someone else's work and/or ideas and, more than that, to lie about it. You have to note that "lying by omission" is still a lie. Plagiarism can be avoided by citing sources, for example, acknowledging that certain material has been borrowed and clearly providing the information necessary to find that source. However, copying most of the words or ideas from a source, whether you give credit or not, is still a plagiarism.
Modern mathematical editing uses TeX, a programming
media designed by Donald Knuth during the 1980's, to produce high
printing quality of articles and books. The TeX evolved to very
sophisticated versions: AMSTeX, LaTeX, LaTeX2e, and AMSLaTeX. We
recommend the usage of AMSLaTeX that has the most capabilities and
high flexibility. The students should study independently and be able
to write their project using one of these versions. There are
different textbooks available for this, among which we recommend
Guide to LaTeX. 4th edition, by H. Kopka,
P.W. Daly, AddisonWesley 2004 that can be found in the
bookshop.
You can use on any computer from the BCC the MikTeX
environment by using the
path:
Programs>Applications>TeXnicCenter>TeXnicCenter
and
then a window will open. After a short configuration you will be able
to type your LaTeX file. Please note that there are at least three
stages before producing your written pages:
Editing your file (that with extension .tex).
Compiling (building out) to produce your .dvi file that can be previewed.
Printing, that is, producing your .pdf or .ps files that can be printed.
If you have a personal computer or a laptop, other distributions of the TeX are available: MikTeX is freely available from the Internet to be downloaded and installed under Windows operating system, teTeX is part of any Linux operating system, TeXShop is freely available for MacIntosh operating systems, etc. Here you can download an Example file in AMSLaTeX, and the corredsponding Example file in PDF.
This should reflect the overall activities associated
with this course, following a combination of grades: the adviser
evaluation (50%), course coordinator evaluation of the written
project (20%), and a panel of three independent graders of the oral
presentation (30%).
Each partial grade will be done on a scale
0100. In the following table we give general guidelines for the
correspondence with lettergrades:
Points 
Lettergrade 
90100 
A 
8089 
A 
7579 
B+ 
7074 
B 
6569 
B 
6064 
C+ 
5559 
C 
5054 
C 
4549 
D+ 
4044 
D 
039 
F 
The following criteria for evaluation may be used
as guidelines:
Advisor (50%):
 level of understanding of the material;
 weekly
attendance (missing for more than 25% of the weekly appointments
implies an automatic FX grade);
 visible progress over the semester;

originality expressed as new ideas of proofs, new connections or
applications, or new results are not a must, but if any of these
exists at a relevant level it should be reflected in the
evaluation.
Independent Graders
(Panel of at least three) of the Oral Presentation (30%):

clearly stating the background and the problems;
 clearly
presenting the main results and the ideas of proofs;

capability of answering questions on the details, ideas, and
connections with related problems;
 timing of the oral
presentation;
 earlier presentation should be appreciated.
Course Coordinator
(20%):
 quality
of the written project expressed by the abstract, introduction,
sections and presentation of the results, conclusions and open
problems, bibliography;
 clarity of the written project;
 level of mastering the TeX commands;
 attendance and in class participation at the
meetings and oral presentations;
 timing in submitting the
written presentations.
The following syllabus
might be used:
MATH 491 Senior Project I
Week
0: Each faculty member proposes two topics for this course. The
course coordinator collects and makes this information available to
students.
Week 1: Time to choose the topics and the
adviser, by direct contact and discussions.
Week 2  Week
5: Independent study closely monitored by the advisers through
weekly meetings; understanding TeX and its capabilities.
Week
6  Week 9: Independent study monitored by the advisers through
weekly meetings; typing the written presentation; preparation of the
material for the oral presentation.
Week 10  Week 14:
Finishing the written project and submitting it; finishing the
preparation for the oral presentation; holding the oral presentation
of the project.
Week 15: Correcting and improving the
final project and submitting it as a PDF file.
MATH 492
Senior Project II
Week 1: Time to discuss the
choice of the topics, by direct contact and discussions with the
adviser.
Week 2  Week 9: Independent study monitored
by the advisers through weekly meetings; typing the written
presentation; preparation of the material for the oral
presentation.
Week 10  Week 14: Finishing the written
project and submission; finishing the preparation for the oral
presentation; holding the oral presentation of the project.
Week
15: Correcting and improving the final project and submitting it
as a PDF file .
Page maintained by
Aurelian Gheondea (course coordinator);
last update October 24th, 2011.