Guidelines for the Senior Comprehensive Paper
The Senior Comprehensive Paper is a record of the student's work on her
topic of study for the Senior Comprehensive Project. As such, it is a piece
of work which should give personal satisfaction as well as reflect what
the student has learned about writing mathematics during her four years
at Saint Mary's. On a practical level, one could show it to a future employer
as an example of one's ability to communicate well. One should keep these
goals in mind while preparing this paper. This paper is also the final addition
to the Advanced W portfolio. For general style information, see the book Stephen B. Maurer,
Undergraduate Guide to Writing Mathematics, available through the deartment which serves
as a style manual for the department.
The paper is to be addressed to one's peers. There is a standard background for all seniors (specifically, the material in the first two years), which you can assume the reader knows. Some of these ideas you may want to recall merely to refresh the memory of the reader. These aspects need not be covered in great detail; however those ideas or concepts which are new to classmates should be developed carefully and clearly.
The Senior Comprehensive paper is to be typed in
proper (formal) style (including page numbers, headings, etc.); see the
document "General Guidelines in Writing a Mathematical Paper"
for information on this style.
It must contain the following sections:
1. Cover page
This shows the title of the paper, the author's name, the advisor's name, and the date the paper is completed.
2. Table of contents
List the contents (introduction, chapters, appendices, references) with page numbers. Use descriptive titles for the chapters. (This list gives the reader a brief idea of the topics covered.)
3. Introduction
This section would include some of the following;
-a statement of the problem or topic to be discussed,
-some historical background or some perspective on the problem,
-an explanation of the structure of the paper - what topics will be covered in each chapter, how the discussion will develop (for example:, a special case is considered first followed by a discussion of the general theory and applications; or history and then theory and applications, etc.),
-a discussion of the labeling systems and special notation,
-assumptions about the background of the reader (for example: "a familiarity with statistics (or topology, or basic algebra) is assumed")If the bulk of the material comes from a single source, this source should be credited in the introduction, so that only page references for specific statements need be given in the text.
4. Preliminary material
The chapter (or chapters) dealing with the first two talks will be expository in nature, and quite terse. This part of the paper will summarize the material presented in the first two talks. Contents should include major theorems and definitions that werd (formally written - including numbering) and text that will provide the reader with a good overview of the material covered, including the reason for the theorems, definitions, concepts included (why are they necessary? what is the connection to other areas? what are the natural questions that arise?)
Material (theorems, definitions, explanations) quoted from any reference must be credited in the proper form.5. Content of the final (formal) talk
The content of the third talk is covered in greater detail, but this section will not usually be more than twenty pages in length. The writer includes the proofs of the theorems and must also be conscious of the reader, providing examples and exposition between the definitions and theorems.
As a guide to writing this exposition, consider answering one or more of the following questions:a) what is the purpose of this definition?
b) what does this theorem or definition really mean?
c) what is the power of this theorem?
d) what is the crux of the proof of the theorem?
e) how is a certain lemma used to prove this theorem?
f) is this theorem a step towards a major result or is it the major result?
g) how does one apply this theorem?
h) why are the hypotheses of this theorem so important?
i) is this theorem the strongest possible result?
j) does the converse of this theorem hold?Material (theorems, definitions, explanations, diagrams, etc.) quoted from any reference must be credited in the proper form.
Include a conclusion in which you summarize the contents of the paper or the major result. If possible, indicate some consequences of the major result or areas of investigation which would follow your work.6. References (bibliography)
All references used in the preparation of the material are to be cited (whether or not there are specific citations in the paper). See Maurer's book and the templates provided for the appropriate format.
7. Appendix of all presented definitions
As indicated, all definitions presented in the paper should be listed in an appendix, with numbers and page references.
8. Appendix of all presented theorems
As indicated, all theorems presented in the work are to be listed in an appendix, with numbers and page references.
9. Other appendices, if appropriate
If there are many special symbols used in your paper, it may be appropriate to have an list as an appendix; similarly, there may be relevant other data - tables, charts, computer printouts - that should accompany the paper but are not part of the main text.
1. Prepare the paper using a TeX. Use the Tex tamplate for the comprehensive provided at (with more information on writing) at the Mathematics Departement Advanced Wrtiting Page:
More information (with formatiing examples that can be copied and adapted)on using TeX
The descriptive document with explanations, examples
The TeX source of the descriptive document with copyable commands
The basic frame document (with preamble, settings)
Proofread!!!! Use a spell checker, but also check technical words and usage yourself.
2. Prepare four copies of the paper - one for yourself and one for each of the three readers. Attach a small note with the paper indicating to the readers where the material for the final talk is found.
3. You are to turn in a complete draft of the paper to your advisor at least 21 days prior to your scheduled final talk. The readers must have the final paper in hand at least one week before the final talk. Typing, revising and correcting will probably take longer that you expect. Allow for this.
4. Type the early chapters (introduction, preliminaries, etc.) as you prepare the seminar talks. Then revisions are easily made later. Keep backup copies on at least one additional disk, and keep them current.
5. After your presentation, there will usually be revisions and corrections to the paper recommended by yuor committee. You need to submit an electronic copy of the correctd/revised paper to your advisor within a week of your presentation.
Description of the Senior Comprehensive Project
Proseminar and Student Comprehensive in Mathematics Student Guide
Mathematics Department Home Page
Last update 1/15/2010/strong>
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