# Guidelines for Mathematics Senior Comprehensive Paper

## Proseminar and Senior Comprehensive Student Guide

### 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 references (especially Maurer's book) and the style templates on the Advanced W Resources Page.

### Audience

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.

### Format for the Senior Comprehensive Paper

The Senior Comprehensive paper is to be typed in proper (formal) style (including page numbers, headings, etc.); see see the references and the style templates on the Advanced W Resources Page. It must contain the following sections:

- Cover page

This shows the title of the paper, the author's name, the advisor's name, and the date the paper is completed. - 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.) - 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.

- Preliminary material

The chapter (or chapters) dealing with the preliminary talk will be expository in nature, and quite terse Contents should include major theorems and definitions (formally presented - 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. - Content of the final (formal) talk

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:

- what is the purpose of this definition?
- what does this theorem or definition really mean?
- what is the power of this theorem?
- what is the crux of the proof of the theorem?
- how is a certain lemma used to prove this theorem?
- is this theorem a step towards a major result or is it the major result?
- how does one apply this theorem?
- why are the hypotheses of this theorem so important?
- is this theorem the strongest possible result?
- 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.

- 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. - Appendix of all presented definitions

As indicated, all definitions presented in the paper should be listed in an appendix, with numbers and page references. - 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. - 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

### Procedure Comments

- Prepare the paper using TeX. Use the template provided:

- The template for the Senior Comprehensive Paper. Use this template to type your paper in order to have the correct sections, formatiing, table of contents, etc.
- The TeX source (.tex document) type your text in the sections of this document
- Typeset version (.pdf document) showing the results

For assistance in working with TeX, see: - 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. - 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.
- You are to turn in the final draft of the paper to your advisor at least 17 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.
- 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.