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2021-22 Math Thesis Handbook
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Mathematics

                                

                        

        

                

                                

                                        

Thesis Capstone Handbook

                                

                                                        

2021-2022

                                

                        

                

The Thesis Capstone Program

Objectives                        

The principal objective of the Math Department’s Senior Thesis program is to help you develop intellectually and improve your written and verbal communication skills. Meeting that goal requires you to achieve several essential objectives during the course of your project:                                

  1. Conduct a thorough independent study and exposition of a body of mathematical or mathematically related scholarship.
  2. Write a comprehensive professional thesis document reflecting your focused study and effort.
  3. Present your work in various informal and formal settings.                         

To this end, the department of mathematics has established a number of obligations that students engaging in research—whether working on a Clinic project or an individual thesis—are required to meet. Some of these obligations follow from the fact that both Clinic and Thesis are official, graded courses worth three units of credit each semester, and therefore fit into the larger curricular framework. Other obligations follow from the nature of the enterprise of research itself.

The Senior Thesis program affords you the opportunity for an in-depth intellectual exploration not normally available in other courses. The process culminates in a written document that we print on archival paper and hard bound for you and the department. By understanding the history, background, current state of affairs, and any new insights for your topic and writing it up in your own words, you are making an original contribution to the mathematics community. While some thesis projects lead to publishable research, it is not a goal of the thesis program. It is our sincere hope that your experience engaging in a literature review, managing independent research and mathematics exposition, giving oral presentations, and developing a finished written product, will have a lasting positive impact on your educational and professional future.

Thesis Project Requirements                        

Thesis projects generally take place during the fall and spring semesters of your senior year. A successful project will meet all of the following requirements by the end of this period:                

The following are traditionally part of Thesis but may have to be modified this year:

Many of these requirements have specific deadlines associated with them. The Thesis Coordinator will share a calendar with this calendar year’s deadlines.                                 

Double Majors and Interdisciplinary Theses                                

If you are a double major, you may choose to have a thesis advisor in another department but still participate in the mathematics senior thesis program. You may also choose to complete a thesis in an external department and petition to substitute it for the math department’s requirements.

                                        

In general, this process requires substantial cooperation between the two departments. If you are considering either of these options, we suggest you to talk to the thesis coordinators for both departments, as well as become familiar with the particular requirements of each department.

                                        

If your thesis is interdisciplinary in nature, it must still contain significant mathematical content to satisfy the requirements of the mathematics major. In particular, your midyear report and final must include at least one separate chapter dedicated to detailing the mathematical aspects of your research. A member of the HMC mathematics department (typically your second reader) and the mathematics thesis coordinator must approve the mathematical content of both the midyear report and the final thesis.

                                        

Joint Math–Physics majors can fulfill their capstone requirement with a thesis from either the mathematics or the physics department, and do not need to petition for approval.                

Substituting a Thesis from Another Department                

If you want to fulfill the thesis requirements for the mathematics major with work completed in another department under the supervision of a faculty advisor from that department, you must meet the following requirements:

                                        

1. You must obtain, via petition, the approval of the Math Department Curriculum Committee (MDCC) by no later than the spring semester of your junior year. Your petition to the MDCC should include an explanation of the anticipated mathematical content of your thesis.

                                        

Note that an approved petition does not guarantee that your thesis will be accepted as a mathematics capstone, since your final work must satisfy the department’s requirements for significant mathematical content to qualify.

                                        

  1. Enroll in Math 197 and complete its requirements. Participation in the thesis seminar is a vital part of the mathematics capstone experience, providing you with exposure to the work of your fellow mathematics thesis students and giving you the opportunity to improve your presentation and writing skills while helping your peers with their own.                        
  2. Have an advisor (or joint advisor) or second reader from the mathematics department. Your mathematics advisor or reader will be primarily responsible for determining whether the mathematical content of your work satisfies the requirements for a mathematics capstone project.                                                                                                
  3. Submit both printed and electronic (PDF) copies of your final thesis to the mathematics department’s thesis coordinator that include the mathematics thesis signature page with all appropriate signatures.

Your Thesis Committee                                

Your thesis committee will have at least two members—a faculty advisor and a second reader. At least one member should be from the Harvey Mudd College mathematics department; the other may be from another department at Mudd or even from another college or university.

                                        

Typically the department will assign an advisor prior to your registering for Math 197. We expect that you will have found a second reader by the third week of the fall semester.

                                        

In special circumstances, your thesis advisor may be from an external department. In these cases, you must identify a second reader from the HMC math department before the beginning of the academic year.

Required External Presentation or Poster Session                        

During the course of the year you will be expected to give a number of presentations about your topic and your progress to various groups of people, including your fellow thesis students, the college community, and the general public during Presentation Days at the end of the spring semester.

                                        

You are also required to give a talk or show a poster at one or more conferences or other professional meetings. Some typical venues are the regional Mathematical Association of America (MAA) meetings in the fall (student talks) or spring (poster session). Other options will be announced by the Thesis Coordinator.

                                        

Your advisor will also have advice on suitable venues for your external presentation.

                                        

In addition to the posters and talks for Presentation Days, there is a poster session on Alumni Weekend that students are expected to attend. If you have a poster from your external presentation, you may use that poster or revise it to reflect new work since that presentation.

Copyright and Fair Use                        

Under US copyright law, your thesis is automatically copyrighted by you. We ask you for the right to “publish” your thesis on the department’s website as well as on the Scholarship@Claremont site.

                                        

Copyright cuts both ways, of course, and you must cite resources you rely on properly. You also need to be aware of restrictions on the use of significant quotations from others’ work, graphs, diagrams, or other illustrations that you have not created yourself but want to include in your document. Although “fair use” might apply to some of these uses, it’s generally better to err on the side of caution.

                                        

If possible, obtain permission from the copyright holder (usually the author or publisher, but you might need to do some digging). In some cases, you can redraw or adapt a diagram or graph, but you must credit the original source.

                                        

Some materials may be available under Creative Commons licenses or “in the public domain”, but you should still credit the creator whenever possible (even if the license doesn’t require attribution, providing it is always a good thing to do).

                                        

Copyright issues are complicated and not always entirely clear—for example, the legal definition of fair use is not so precise that you can be sure that your use falls under those provisions (or, more importantly, that the rights holder might dispute your usage). The Claremont Colleges Library has some resources on its website that should be helpful, as well as experts who specialize in copyright and digital publication issues. We encourage you to take advantage of these resources.                

Publication of Your Thesis Work                

If you and your advisor decide that your work could be published, we encourage you to do so. Your advisor can help you select an appropriate journal. Since the thesis document is quite different than a typical publication you will be expected to make suitable modifications to develop a research paper that meets the expectations of the intended journal (this work is optional and not part of the Senior Thesis class).

                                        

Note that publication of your work does not substitute for an external presentation, although giving a talk or presenting a poster about your paper would.

        

Publication also raise potential copyright issues affecting your final report—consult with your advisor and the thesis staff to ensure that we all understand the copyright requirements of the particular journal you’re publishing in.                                

Writing Your Mathematics Thesis                                

The thesis process requires you to write two documents during the course of the year.

The first document is a midyear report, due at the end of the first semester. This document serves several roles: it is a means of updating your advisor on your results to date; an initial draft of your final report; and an introduction to the tools, skills, and outlook required when writing professional reports.

                                        

Although your midyear report serves as a draft of your final thesis, the final report will probably still require a great deal of additional work to complete, so you will need to plan ahead to avoid collisions with all of the other activities (final exams, other papers and projects) that typically crowd up at the end of the year (especially for graduating seniors).

                                        

The department has several resources with more information on formatting your reports with LaTeX.        

What is a Thesis?

Your thesis will be a professional document that represents your best effort to capture the essence of your year-long independent study and explain the salient points in a readable format that an interested reader can benefit from.  It is a highly personal document reflecting the nature and scope of your work and therefore hard to prescribe formally.  

What it is not:

What it is:

The Thesis Coordinator will review sample theses in Math 197 to help you better understand the scope and format of a final thesis report.                                                                 

Getting Started                                                                

Your thesis may be the longest and most complex document that you’ve ever worked on. But tackling the report is a lot easier if you look at it as a series of smaller tasks whose results combine to create the final document.

                                        

The best way to write your thesis is to do so incrementally—adding elements as they become available. This includes writing pieces of your report while you’re doing your research. You can also dedicate some time to setting up the formal components of the document (discussed below) and making sure it compiles correctly.

                                                                                

You will be reviewing and collecting several key publications related to your project. For each reference, you should write a brief discussion of its central themes and how they relate to your project and other papers in your (annotated) bibliography. It is important that your descriptions be written in your own words (i.e., not just copying the synopsis/abstract).

                                        

By working on your thesis incrementally throughout the course of the year, by the time it’s due you will be able to concentrate most on the chapters and sections that detail your results.

                                        

Your faculty advisor is an important resource while you’re writing your thesis. Keep your advisor involved as you work on drafts to assist you with matters of style as well as content. It will be useful  to also solicit comments and suggestions from your reader(s), other interested faculty, and your peers.

Formal Components of a Thesis                                

The Front Matter                                

The front matter generally corresponds to the parts of the book that are numbered using roman numerals. In the front matter of your thesis, you should have the following elements:

Title Page

Formatted for you by the document class.

Copyright Page

Formatted for you by the document class.                                

Abstract

A brief  high-level description of the main thrust of your report. You want to explain what the problem is, how you went about solving it, and perhaps have a very brief summation of your solution.                                

Table of Contents, List of Figures, List of Tables

These elements are produced by LaTeX’s automatic numbering system and their placement is specified using the commands \tableofcontents, \listoffigures, and \listoftables, respectively.

Acknowledgments

A place to thank individuals, organizations, or even things that were particularly helpful in completing your project. You should also thank anyone who read your draft(s) and made suggestions for improving them.                                

The Main Matter                                

The main matter is where the real content of your report is found. For a report of this significance, we expect to see several chapters (discussed below) dealing with the key elements of your project.

The Introduction                                

You should start with an introductory chapter (usually just called “Introduction”) that explains the problem, talks briefly about previous research, and then sketches out the remainder of your report with references to the in-depth discussions.

                                        

To the extent possible,  your introduction should be written using non-technical language. Write for an intended audience of non–math-major HMC juniors or seniors, without assuming any specific knowledge of the area of your thesis work.                                        

Other Chapters                                        

You should then have chapters covering topics such as

                                        

The Conclusion                                

The conclusion is an important chapter in your thesis. Many readers will only read your introduction and conclusion. Some might even skip the introduction, which means that your conclusion is even more important.

                                        

Your conclusion shouldn’t be just another summary of the whole process. You need to say what it is that you accomplished over the course of the year, and what new insights it yields about your topic of study. It is not uncommon to also include some criticisms of your work in light of what you’ve learned.                                

Future Work                                        

You should talk about some of the possibilities for future research based on the work that you’ve done. For your midyear report, this section will be the place to talk about the work that is currently in progress and where you expect it to lead in the next semester. For your final thesis, this section might grow to be its own chapter, outlining several possible future approaches to your problem and why they might be worth pursuing.                                

Appendices                                

Appendices are extra bits of information that aren’t necessary for understanding the key ideas of your report, but that may be interesting for people who are especially interested in a particular topic.

                                        

Good uses for appendices can be derivations that are not essential to the flow of a given chapter, clarifications for why an algorithm was constructed one way and not another, and/or sharing background material about your project that may provide some additional insight.                

Source Code and Algorithms                                                        

By and large, people don’t read printed source code. If you have source code that you think people will find useful, we can make it available through the website that we will maintain for your thesis.

                                        

If you want to describe one or more algorithms in detail, especially if they are too complex to easily handle within the normal flow of your implementation and results chapters, you may do so in one or more appendices.                        

Back Matter                                

The back matter comprises elements such as your bibliography, an index, a glossary, and so on. Of these, the only one you’re likely to need is the bibliography..

                                        

If you’re interested in including one or more of the other commonly seen back-matter components, please talk to your advisor and the department’s IT Analyst about the best way to do so.

Presentations and Posters                        

A major component of your thesis experience is continued practice in the art of giving oral presentations on technical material for a variety of audiences. The department views this component of Math 197 as an extension of the skills and growth you experienced in Math Forum.

                                        

You will be giving at least three talks as part of your thesis work.

                                        

  1. An introductory talk (typically 12 - 15 minutes) during the fall semester in Math 197;
  2. During the spring semester you will give a second talk in Math 197, present a poster, or otherwise share your work with the mathematics community during a conference or other mathematics meeting;
  3. During Presentation Days, you will give a third talk about your research to a general audience composed of the college community and the general public.

                                        

Depending on how you fulfill the public presentation component of your thesis work, you may be giving additional formal talks or poster presentations at a professional meeting. You will also present a poster on your work during Alumni Weekend.

                                                                        

Remember that your presentations are aimed at a general audience. Therefore, your choice of language and use of technical details should reflect this.

                                        

You should work closely with your advisor when preparing your talks. Your advisor should review your slides, and, if possible, attend your practice presentations and provide feedback. You may also want to practice your talk in front of peers to get added feedback.

Slides should act as reinforcements or illustrations of what you’re saying rather than as a distraction. Keep the textual content of your slides brief and to the point. You want your audience to listen to your talk not read your slides. Your slides act as supplements, illustrating complex ideas or allowing you to summarize information.

        

You may want to include some slides that cover some of the more advanced material that you didn’t include in your talk, but that you think people might ask questions about. (Hint: Figuring out what questions you might want to cover is best done by giving practice presentations and paying attention to the questions that people ask you during the practice sessions!)                                                

The talks you give in class are meant to encourage critiques on your presentations from your peers. During each talk we encourage you to think of good questions that you can ask during the Q&A session. By asking (and being asked) questions, you will learn about things that you may have left out of, underemphasized, or glossed over in your presentation. This information will help you adjust your presentation for future talks.

                                        

If you have an insight or question about someone’s topic, share it! You may help your classmate gain new insight or find a new way of exploring their problem that they might not have done without your question.                                         

Creating Research Posters                                                

Research posters have to balance the goal of communicating your work with that of having a visually appealing poster that encourages people to take a closer look. You should work closely with your advisor in the development of your poster.

                                        

The department has a LaTeX poster class, hmcposter, that handles many of the basic decisions you might otherwise need to make, and also happens to produce posters that we can easily print.         

Completing Your Thesis                                

There are a number of final tasks that must be completed so that you can receive a grade for your thesis and we can print, archive, and mail the final copies of your thesis. This chapter explains what those tasks are, how to perform them, and where to look for more information.

Due Dates                        

The exact due dates for the components of your thesis are specified in the calendar.

Address Form                        

We need to have an address to which we can send your copy of your bound thesis. The bound theses will be ready sometime in mid- to late summer or early fall, so be sure that the address you give us will be valid for that period. If your address changes during that time, please notify us.

                                

If your address changes, please send the changes to DruAnn Thomas at dthomas@g.hmc.edu as soon as you can.

                                

Signed Signature Pages                                

You must deliver four (4) copies of the signature page of your thesis to the thesis capstone coordinator by the deadline listed in the calendar.

                                        

Each signature page must be

                                        

                                        

You may need to start the signature-gathering procedure early if one or more of your advisors or readers is not a local resident. The signature pages will be used for your copy and the department’s library copy.                                

Obtaining the Signature Pages                                

The current version of the hmcthesis class file does not generate the signature page by default to facilitate the creation of ready-to-use copies of your thesis. To get a signature page, you should temporarily modify your master LaTeX document by adding the sigpage document-class option to the \documentclass command in the preamble of your document using:

                                        

\documentclass[sigpage,mathematics]{hmcthesis}

                                        

The easiest way to have the signature pages printed on the correct paper is to submit a pdf file containing only your signature page to the mathematics department’s capstone coordinator, DruAnn Thomas.                        

Mathematics Subject Classification                                        

The CCDL takes part in a larger indexing effort for online materials, and part of its metadata is a keyword field. For theses, having up to three (3) classifications from the Mathematics Subject Classification (MSC) will make your thesis more easily findable and categorizable.

                                        

The Mathematics Subject Classification is available online at http://www. ams.org/mathscinet/msc/msc2010.html.                        

Scholarship@Claremont

                                        

Theses are made available both from the department’s website and the Claremont Colleges Library’s Scholarship@Claremont site (http://scholarship. claremont.edu).

                                        

You will need to fill out the thesis submission form, which records a bunch of metadata about your thesis. More information on this is provided in a separate handout.

Grading/Reference Copy                        

You must submit a Portable Document Format (pdf) file containing your complete thesis, typeset by you, which can be used by your advisor and the department for grading and during its awards process.                                

Copies for Binding                        

We will print at least three copies of your thesis on archival paper and have those copies bound. Printing is usually done sometime during the summer.

                                        

Once we have the bound theses back from the bindery, we will distribute the copies as follows:

                                        

If your thesis is chosen for one of the department awards, we will also print and bind a fourth copy for the award collection.                                

Official Faculty Names                        

Our faculty use particular arrangements of their names for publications, which makes it easier to keep track of their publications across different journals, books, and so on. Please use the official names from this list for your faculty advisor and second reader as well as for any bibliographic references to their work. If your advisor or reader isn’t listed here, then check with them to find out what name they use for publications.

Arthur T. Benjamin

Andrew J. Bernoff

Alfonso Castro

Lisette G. de Pillis

Weiqing Gu

Jamie Haddock

Jon Jacobsen

Dagan Karp

Haydee Lindo

Susan E. Martonosi

Mohamed Omar                                        

Michael E. Orrison                                

Nicholas Pippenger

Francis Edward Su

Talithia D. Williams

Darryl H. Yong

Heather Zinn-Brooks

Acknowledgments

The Harvey Mudd College mathematics thesis handbook is based on the work of many thesis coordinators and Clinic directors (as some parts of the handbook are based on similar parts of the Clinic handbook). Substantial contributions to this document were made by (in alphabetical order) Andrew J. Bernoff, Claire M. Connelly, Lisette de Pillis, Weiqing Gu, Jon Jacobsen, Kerry Karukstis, Nicholas Pippenger, Michael Raugh, Molly Reeves, Barbara Schade, and Lesley Ward.