thesis math definition

Writing Your Thesis

The thesis should be the heart of your graduate school career. It will certainly be the most involved and difficult thing you do while in grad school.

Of course, before writing the thesis, one needs to have research to report. To make things easier on yourself, it’s a good idea to record your results as you work. Don’t rely on your memory to save you when you need to write everything down in your thesis! While you needn’t have everything written in final draft, having a detailed account of your research progress is a great idea. When you start your research, you and your advisor should try to establish a goal for your thesis as soon as possible. Performing research without a goal can be very difficult and even more frustrating.

When one does mathematical research, one rarely knows exactly where they are going. Gaining mathematical intuition comes from lots of hard work, not simply being very smart. A tried and true method for doing research is to do lots of examples, and make simplifying assumptions when needed. Before you can prove a theorem, you need a conjecture; these aren’t going to just fall in your lap! The idea is that after seeing enough examples, one can make a general conjecture and then hopefully prove it.

It’s a good idea to find out who else in the community (both in and out of the department) thinks about your field. You may find it useful to contact these people from time to time. This serves multiple purposes: you’ll lessen the chance of duplicating someone else’s research; you’ll find multiple sources of advice. While your advisor will likely be the single biggest source of help in writing your thesis, they needn’t be your only source. Talking to many people about your work will give you several different perspectives on the same thing. Seeing the same thing in different ways can be invaluable in understanding something.

When you have enough results such that you and your advisor are satisfied, you need to organize your work into one coherent document. This can be a highly non-trivial task! Make sure that your problem is stated clearly, along with why it is important, and how you solved it. Your thesis shouldn’t simply be a list of definitions, theorems, and proofs; there should be quite a bit of prose to explain the mathematical ambiance of your work. What is the motivation for even thinking about this problem? The more people that find your research interesting, the better.

Please refer to this manual for guidelines on formatting your thesis:  http://grad.ucsd.edu/_files/academics/BlueBook%202017-18%20updated%204.13.18.pdf

Defending Your Thesis

Setting a time to defend your dissertation can be frustrating. Contact your committee members well in advance in order to check availability and schedule a date/time.

You would think that finding a time for 6 people to meet would be an easy task. However, it can be exceedingly difficult. You may need to be very flexible and accommodating in order to make things work. You may also need to be persistent about asking if you have a non-responsive committee member.

Please carefully review these guidelines regarding committee attendance:

Department  Policy on Graduate Examination  Format:

Effective Fall 2022, the default format of a graduate examination in the Mathematics Department is  in person , i.e.,  all the committee members and the student are physically present in the same room for a scheduled examination . (This is set by the Division of GEPA.) However, when an unexpected situation arises and affects a committee member’s ability to participate in the examination synchronously, and when the student agrees, a remote or hybrid examination is allowed and can be decided by the committee chair or co-chairs. The following guidelines should be followed to arrange a remote or hybrid, synchronous examination:

• In forming the committee, the student needs to provide different examination options, in person, remote, or hybrid, to potential faculty committee members, and based on the conversation, the student can decide whether or not they want the faculty member on their committee. If such conversation did not take place, and if an unexpected situation arises, the faculty committee member can request remote examination, and can be released from the committee duty should the student refuse the request.
• In general, the graduate student is not allowed to opt for a remote examination unless there are extenuating circumstances, such as illness, travel difficulties related to visa problems, or a graduation deadline. Under such circumstances, the committee chair can decide to reschedule an in-person examination, or have a remote or hybrid examination.
• According to the Division of GEPA, there must be sufficient expertise among present members to examine the student. If a committee member must be absent for the scheduled exam, it is permissible for one absent committee member to examine the candidate on a separate date. The committee chair, or one co-chair, must participate synchronously in the scheduled exam.

Make sure to inform the PhD staff advisor in advance if any of your committee members will not be physically present.

During this scheduling phase, you also want to schedule your “Preliminary Appointment” with Graduate Division:  https://gradforms.ucsd.edu/calendar/index.php  – this appointment is optional but highly recommended! The purpose of this appointment is for them to check the margins and the formatting of your dissertation. While the above information should get you through this part without any problem, sometimes there are minor issues that arise and must be confronted (for example, published work that shows up in your dissertation has some extra requirements associated to it). The meeting should last about 30 minutes and you’ll receive a couple questionnaires to complete before your final appointment. You will also be required to schedule a Final Appointment with Graduate Division – allow at least a few days between your defense and your final appointment in order to finalize department paperwork.

In addition, the following information is critical to you completing your thesis, defending it, and completing your PhD:

• The university requires that your committee members each have a good readable draft of your dissertation at least FOUR WEEKS before your final defense.
• It  is your responsibility  to make arrangements with each committee member for the date and time of your defense.  Room reservations should be made at the Front Desk (in person or email to  [email protected])
• The  Final Report  form must have the original signatures of all members of the doctoral committee; the  Final Report  must also be signed by the program chair. (The  Final Report  form is initiated by the graduate coordinator and signatures are obtained from each faculty member through DocuSign.). Proxy signatures are not accepted.
• After your examination, committee chair emails PhD staff advisor confirming the passing of the defense. PhD staff advisor prepares Final Report through DocuSign.
• The final version of the thesis must conform to procedures outlined in the " Preparation and Submission Manual for Doctoral Dissertations and Master's Theses "
• The student submits the final approved dissertation to the Graduate Division  at the final document review  (the  Final Report  form is routed electronically from the program’s graduate coordinator via DocuSign). Final approval and acceptance of the dissertation by the Dean of the Graduate Division (on behalf of the University Archivist and Graduate Council) represents the final step in the completion of all requirements for the doctoral degree.

A few other suggestions:

About a week before you defend, you should send an email to your committee to remind them that your defense is coming, and you might even want to send a day-before or day-of reminder.

You should discuss the details of your defense with your advisor, but it’s basically a 50-minute talk where you highlight the main results of your dissertation. The audience is usually your committee plus a few graduate students.

Once Graduate Division has signed off on your thesis, it is time to submit your thesis online to Proquest/UMI. When you do this, they give you an option to purchase bound copies of your thesis from them. This is not particularly appealing for three reasons:

• They are rather pricey, about $40-$60 per copy
• They will print it exactly as you submitted it, according to Graduate Division standards: double-spaced, 8.5×11, etc, which doesn’t make for an attractive book. (How many of the math books on your shelf are 8.5×11 double-spaced?)

Fortunately, another option is available: self-publishing services. Originally these were intended for authors who had written a book, but couldn’t find a publisher for it, so they’d have it printed at their own expense. Nowadays, there are online sites filling this market, where you submit your manuscript and design the book yourself through their site. They can print on demand, so there is no minimum number of copies to order, and they can be quite inexpensive. A former graduate student, Nate Eldredge, chose to go with Lulu, so this article will describe that service.

You can begin by creating an account on Lulu’s site, which is pretty self-explanatory. They have several different book types available. I decided to go with a 6×9 “casewrap hardcover”, which is a pretty standard size and style for a book. If you have a yellow Springer book on your shelf, that’s a pretty good facsimile of what we’re talking about here.

The main issue, then, is reformatting the thesis into a 6×9 format. Fortunately, LaTeX makes this pretty easy. Pretty much, you just need to swich from the UCSD thesis class to the standard LaTeX book class and make a few other changes. Here is a modified version of the UCSD thesis template, modified to fit this format. Nate put comments in various places indicating the relevant changes and choices he made. In several places he took advantage of the fact that he no longer had to conform to OGS’s awkward requirements to make the thesis more “book-like” and remove some things that wouldn’t appear in a book. It shouldn’t take you more than an hour or two to convert your thesis file, depending how fastidious you are. (If you don’t want to go to this trouble, Lulu will also print 8.5×11 books. You could use your existing PDF without change. It may not look as pretty, but it will still be cheaper than UMI.)

Note that you should check carefully for overfull \hbox’es when you compile the thesis, because changing the paper size may have caused things to run outside the margins or off the page. You may have to manually break up long equations or reword paragraphs. Also, the book class will insert several apparently blank pages; these relate to the fact that the book will be printed double-sided, and guarantee that certain things always appear on the left- or right-hand side of a spread. If you want a book-like effect, you should not try to defeat this.

Once you’ve generated an appropriate 6×9 PDF file and uploaded it to Lulu, you can design a cover for it. They have a couple of different interfaces. For his thesis, Nate created a pretty simple cover with a UCSDish blue color scheme, and the abstract and a graduation photo on the back cover.

When you are all finished, Lulu creates a page where you or anyone else can buy copies of the book. (You have the option of keeping this private, so that only people you share it with can find it.) Then you can buy as many copies as you want to keep or give away, and you can also send the link to your parents if they want to buy lots of copies for all the relatives. (In this case, Lulu’s “revenue” option may be useful, where you select an amount to add to the price of the book, which Lulu passes along to you after each sale. The page remains up indefinitely if you want more copies later.

If you want to see what a finished product looks like, Nate Eldredge’s thesis Lulu page is located at http://www.lulu.com/content/7559872.

The book turned out quite nice looking, with quality and appearance comparable to commercially published math books. And they were only $15.46 per copy (plus tax and shipping). Overall that is a vast improvement over UMI.

Also, Nate uploaded the template as a Lulu project. It can be found at http://www.lulu.com/content/7686303.

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Guidelines for writing a thesis

These guidelines are intended for students writing a thesis or project report for a  Third Year Project Course ,  Honours year  or  Postgraduate Coursework Project . Postgraduate research students should see  Information about Research Theses  for postgraduate research students.

Before you start your Honours or Project year, you should speak to members of staff about possible thesis topics. Find out who works in the areas that you are interested in and who you find it easy to talk mathematics with. If at all possible, settle on a topic and supervisor before the start of the first semester of your Honours or Project year.

Most students see their supervisor about once a week, although this is usually open to negotiation between the student and the supervisor. Even if you haven't done much between visits it is a good idea to have a regular chat so that your supervisor can keep track of how you are going. You can expect your supervisor to:

• Help you select - and modify - your topic.
• Direct you to useful references on your topic.
• Help explain difficult points.
• Provide feedback on the direction of your research.
• Read and comment on drafts of your thesis.
• Help prepare you for your talk.
• Give general course advice.

Your thesis or project report is an overview of what you have been studying in your Honours or Project year. Write it as if you were trying to explain the area of mathematics or statistics that you have been looking at to a fellow student.

• Include an introduction that explains what the project is all about, and what its contents are. (It is sometimes better to leave writing this part to the end!) For many reports, a conclusion or summary is appropriate.
• Your thesis should be a coherent, self-contained piece of work.
• Your writing should conform to the highest standards of English. Aim at clarity, precision and correct grammar. Start sentences with capital letters and end them with full-stops. Don't start sentences with a symbol.
• Take great care with bibliographic referencing. Wherever some material has an external source, this should be clear to the reader. Don't just write in the introduction: 'This report contains material from [1],[2] and [3]' - give the references for the material wherever it is used. Don't gratuitously pad your reference list with references that are not referred to in the text. Check current journals for acceptable referencing styles.
• Be careful not to plagiarise. What constitutes plagiarism is perhaps a little different in mathematics and statistics compared to some other subjects since there is a limit to how different you may be able to make a proof (at least in its basic structure). We do, however, expect the report to be written in your own words. A basic rule is: if you put a fact or an idea in your report which is not your own, the reader should be able to tell where you got this fact or idea.
• The University has  policies on academic honesty and plagiarism  which all students should familiarise themselves with.

Generally, mathematics reports and theses are almost always typed in LaTeX. If you are going to type it yourself, you should allow a certain amount of time to become familiar with this software. Indeed, starting to learn LaTeX well before you actually want to write is a very good idea.

You should not underestimate the time it takes to produce a polished document. You will almost certainly need several drafts. It is very difficult to concentrate on getting the mathematics, spelling, grammar, layout, etc., all correct at once. Try getting another student to proofread what you have written - from their different viewpoint they may pick up on lots of things that you can't see.

P R Halmos (1970) in  How to write mathematics, Enseignement Math.  ((2) 16, 123-152) has the following advice: "The basic problem in writing mathematics is the same as in writing biology, writing a novel, or writing directions for assembling a harpsichord: the problem is to communicate an idea. To do so, and to do it clearly:

• you must have something to say (i.e., some ideas), and you must have someone to say it to (i.e., an audience)
• you must organize what you want to say, and you must arrange it in the order you want it said in
• you must write it, rewrite it, and re-rewrite it several times
• and you must be willing to think hard about and work hard on mechanical details such as diction, notation, and punctuation.

That's all there is to it."

His other advice includes:

• Say something: "To have something to say is by far the most important ingredient of good exposition---so much so that if the idea is important enough, the work has a chance to be immortal even if it is confusingly misorganized and awkwardly expressed..... To get by one the first principle alone is, however, only rarely possible and never desirable."
• Audience: "The second principle of good writing is to write for someone. When you decide to write something, ask yourself who it is that you want to reach." Your broad audience will be fellow Masters and Honours students, who may not be experts in your thesis topic. "The author must anticipate and avoid the reader's difficulties. As he(/she) writes, he(/she) must keep trying to imagine what in the words being written may tend to mislead the reader, and what will set him(/her) right."
• Organise: "The main contribution that an expository writer can make is to organize and arrange the material so as to minimize the resistance and maximize the insight of the reader and keep him(/her) on the track with no unintended distractions". 
• Think about the alphabet: "Once you have some kind of plan of organization, an outline, which may not be a fine one but is the best you can do, you are almost ready to start writing. The only other thing I would recommend that you do first is to invest an hour or two of thought in the alphabet; you'll find it saves many headaches later. The letters that are used to denote the concepts you'll discuss are worthy of thought and careful design. A good, consistent notation can be a tremendous help".
• Write in spirals: "The best way to start writing, perhaps the only way, is to write on the spiral plan. According to the spiral plan the chapters get written in the order 1,2,1,2,3,1,2,3,4 etc. You think you know how to write Chapter 1, but after you've done it and gone on to Chapter 2, you'll realize that you could have done a better job on Chapter 2 if you had done Chapter 1 differently. There is no help for it but to go back, do Chapter 1 differently, do a better job on Chapter 2, and then dive into Chapter 3... Chapter 3 will show up the weaknesses of Chapters 1 and 2".
• Write good English: "Good English style implies correct grammar, correct choice of words, correct punctuation, and, perhaps above all, common sense."

More information on how to write mathematics:

• Lee, K. A guide to writing mathematics
• Lee, K. Some notes on writing mathematics 
• Jackson, M. Some notes on writing in mathematics
• Reiter, A. Writing a research paper in mathematics
• Honours thesis
• Postgraduate Coursework Project
• Third Year Project Courses

• More from M-W
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Definition of thesis

Did you know.

In high school, college, or graduate school, students often have to write a thesis on a topic in their major field of study. In many fields, a final thesis is the biggest challenge involved in getting a master's degree, and the same is true for students studying for a Ph.D. (a Ph.D. thesis is often called a dissertation ). But a thesis may also be an idea; so in the course of the paper the student may put forth several theses (notice the plural form) and attempt to prove them.

Examples of thesis in a Sentence

These examples are programmatically compiled from various online sources to illustrate current usage of the word 'thesis.' Any opinions expressed in the examples do not represent those of Merriam-Webster or its editors. Send us feedback about these examples.

Word History

in sense 3, Middle English, lowering of the voice, from Late Latin & Greek; Late Latin, from Greek, downbeat, more important part of a foot, literally, act of laying down; in other senses, Latin, from Greek, literally, act of laying down, from tithenai to put, lay down — more at do

14th century, in the meaning defined at sense 3a(1)

Dictionary Entries Near thesis

the sins of the fathers are visited upon the children

thesis novel

Cite this Entry

“Thesis.” Merriam-Webster.com Dictionary , Merriam-Webster, https://www.merriam-webster.com/dictionary/thesis. Accessed 5 Jul. 2024.

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Thesis and Completing your Studies in Mathematics

In order to successfully complete a Bachelor's or Master's degree program in the area of Mathematics, students must write a scientific work: the Bachelor’s thesis or Master's thesis. Here, you will find an overview of everything you need to know, from planning to submission:

General Information

Registration, when and where.

It is possible to register your thesis on the 1st and 15th of each month. 

All final theses starting from  1st February 2024 onwards in the PP Mathematics at the School of Computation, Information and Technology will be managed via the CIT portal .

Once you have found a topic and a supervising chair for your thesis, you will be registered by the supervising chair . You will receive an e-mail asking you to confirm your thesis registration. Only after you have confirmed your registration the Academic Programmes Office will be able to check the admission requirements and you will receive an email confirming your binding registration for your thesis.

For more information, see  Thesis and Completing your Studies .

Further documents?

If you have completed extracurricular activities or a stay abroad during your studies, these can be included in the Diploma Supplement. To do this, we need the  Route Card for the Diploma Supplement   by the end of your studies at the latest. Please send the completed form as a PDF or photo/scan (readable) to  bachelor(at)ma.tum.de  or  master(at)ma.tum.de . We recommend you to hand in the Route Card when registering your thesis or shortly afterwards. Please also note the Information on the Diploma Supplement .

For more information, see  Thesis and Completing your Studies

Note: The  Diploma Supplement  is an English-language supplement to the university diploma and describes the qualifications linked to the study program. Under the heading “Additional Information” in this document, you can request the incorporation of specific details of extracurricular activities completed within the framework of your degree course.

Composition

The thesis can be written in German or English language. The Bachelor's thesis muss be prefaced with an abstract in the other language, not the one in which it is written.

Formal considerations

Cover page and page 1

Here you indicate the topic of the work as well as your name and that of the supervisor. In addition, you indicate the date of submission (see example).

Example of a cover page

Here you make the following declaration: 

“I hereby declare that this thesis is my own work and that no other sources have been used except those clearly indicated and referenced.” (Place, date, signature either on a tablet or as a scan of your original signature).

If you do not wish to use a digital signature, you may alternatively submit a separate page with the declaration and your original signature at the Infopoint.

Change of title

Please write an e-mail containing the new thesis title to  bachelor(at)ma.tum.de  or  master(at)ma.tum.de  and CC your supervisor and co-supervisor.

Submisson and extension of theses starting until and including 15.01.2024

Digital submission.

The Bachelor's or Master's thesis has to be submitted digitally. Please submit the thesis as a PDF file to  bachelor(at)ma.tum.de  or  master(at)ma.tum.de   within the deadline . If you have to hand in code or other files, please e-mail all files collected in a zip folder. Printed copies and USB sticks will no longer be accepted.

Should the submission date fall on a weekend or a public holiday, submission on the subsequent workday is also possible. Theses can of course also be submitted prior to the planned submission date. 

In the event that you need more time to work on your thesis, you must submit an application to  bachelor(at)ma.tum.de  or  master(at)ma.tum.de  for an extension, at least seven days prior to the planned submission date. This application must have been signed by your thesis supervisor (or you have to send the consent of the supervisor in electronic form). In the event of a second extension, the Chair of the Examination Board must sign the application as well as the thesis supervisor.

Bachelor's Thesis: Application for an extension Master's Thesis: Application for an extension

Submisson and extension of theses starting from 01.02.2024 onwards

Theses registered from 01.02.2024 onwards are managed entirely via the CIT portal . This portal is also used for submission within the deadline (including all required files, such as codes). If necessary, you can also apply for an extension of the submission deadline.

Tools and tips

The typesetting system  LaTeX  is the standard program worldwide for the compilation of theses that contain mathematical formulas. It is recommended that you familiarize yourself with LaTeX as early as possible during the course of your studies. It is a good exercise to prepare sheets for seminar presentations using LaTeX. 

You can find further information, templates and helpful advice on our  LaTeX info page .

Corporate design and use of  TUM logos

Thesis Templates for LaTeX

LaTeX-Template Bachelor / Master

The  TUM Library  does not only offer outstanding access to a wide range of books, newspapers, and electronic media, it also offers courses on, for example, bibliographical research and how to correctly cite works. 

Please also note subject-specific practices when citing works.

Further seminar papers and tools specific to mathematics

For licensing and contractual reasons, some of these databases are only accessible via domains belonging to the TUM Departments of Mathematics and/or Informatics. Please address queries where applicable to your supervisor or the TUM Library:

• MathSciNet  – Mathematical reviews on the web
• JADE  – Journal Articles Database
• ERAM  – Electronic Research Archive for Mathematics
• Online database at  Zentralblatt MATH

English theses

The  English Writing Center  offers all TUM members free one-to-one advice on writing English texts and helps you to enhance your writing skills.

Any questions?

For questions relating to the content of your Bachelor's or Master's thesis, please contact your thesis supervisor as defined in the General Academic and Examination Regulations (APSO), co-supervisor or the Student Advisory Office responsible.

Bachelor's Thesis Details

When to start.

Do you have at least 8 credits in Advanced Courses? Then it is the right moment to commence your Bachelor’s thesis. By the eighth semester of enrollment in your current degree program, at the latest, you must commence your thesis as long as there are no reasonable grounds preventing you from doing so in accordance with section 10 (6) of the  APSO .

Time frame & length

You have three months in which to complete your Bachelor’s thesis. This period begins on the date of registration. During this period, you should spend an average of at least 30 hours per week on the Bachelor's thesis – an effort equivalent to 12 credits.

The Bachelor’s thesis should not exceed 35 pages.

Choice of topic

In order to reduce the time needed to familiarize yourself with the topic, it is recommended to choose a topic for your Bachelor's thesis which corresponds to the theme of the Advanced Seminar taken.

Examiner and assessment

The Bachelor’s thesis must be evaluated by someone who is authorized to do so (thesis supervisor as defined in the APSO) at the TUM School of CIT. You will find an overview of other eligible persons outside the School of CIT in the list below. It is the written work that is assessed. The talk you give concerning the content does not affect the grading.

Persons outside the School of CIT who are authorized to examine theses

Master's Thesis Details

You have six months to complete your Master’s thesis. This period begins on the date of registration. You normally complete the Master’s thesis in the fourth semester of your Master’s program after you have fulfilled all other academic and exam requirements.

Examiners and assessment

The Master’s thesis must be approved and evaluated by someone who is authorized to do so (thesis supervisor as defined in the APSO) at the TUM School of CIT. You will find an overview of other eligible persons outside the School of CIT in the list below:

Completing your Studies

Release of final certificate.

Once you have completed all the requirements for your degree, we will contact you by email and ask for the approval to issue your diploma certificate.

Graduation documents and preliminary certificates

After you have given us the approval for the generating of your diploma certificate, your graduation documents will be generated within 4 - 6 weeks at the Graduation Office and Academic Records Campus Garching . You will be notified by post as soon as your certificate has been issued. Please make sure that your current study address in TUMonline is up to date.

If required, you can also apply to the Graduation Office and Academic Records Campus Garching for a preliminary certificate .

Transition Bachelor – Master

If you have applied for a consecutive mathematics Master's program at our school after completing your TUM mathematics Bachelor's degree, please let us know (at bachelor(at)ma.tum.de ). It is possible to forward your Bachelor's degree to the Admissions and Enrollment Office for enrollment (not for the application!). The graduation documents are therefore not necessary for enrollment. A green checkmark will then appear in the online application portal for your degree certificate and diploma ( Application Status ). Please note that it may take a few days until the documents are updated in the portal. If you do not see these two green check marks one week before the enrollment deadline, please contact bachelor(at)ma.tum.de as soon as possible.

Diploma Supplement

If you have completed extracurricular activities or a stay abroad during your studies, these can be included in the Diploma Supplement. To do this, we need the  Route Card for the Diploma Supplement   by the end of your studies at the latest. Please send the completed form as a PDF or photo/scan (readable) to  bachelor(at)ma.tum.de  or  master(at)ma.tum.de . Please also note the Information on the Diploma Supplement .

Please find more information under  graduation .

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[ thee -sis ]

He vigorously defended his thesis on the causes of war.

Synonyms: proposal , contention , theory

• a subject for a composition or essay.
• a dissertation on a particular subject in which one has done original research, as one presented by a candidate for a diploma or degree.
• Music. the downward stroke in conducting; downbeat. Compare arsis ( def 1 ) .
• a part of a metrical foot that does not bear the ictus or stress.
• (less commonly) the part of a metrical foot that bears the ictus. Compare arsis ( def 2 ) .
• Philosophy. Hegelian dialectic

/ ˈθiːsɪs /

• a dissertation resulting from original research, esp when submitted by a candidate for a degree or diploma
• a doctrine maintained or promoted in argument
• a subject for a discussion or essay
• an unproved statement, esp one put forward as a premise in an argument
• music the downbeat of a bar, as indicated in conducting
• (in classical prosody) the syllable or part of a metrical foot not receiving the ictus Compare arsis
• philosophy the first stage in the Hegelian dialectic, that is challenged by the antithesis
• The central idea in a piece of writing, sometimes contained in a topic sentence .

Discover More

Word history and origins.

Origin of thesis 1

Example Sentences

“The Saudis have been proving the thesis of the film — they do in fact have an army,” said Thor Halvorssen, founder and chief executive of the nonprofit Human Rights Foundation, which funded the movie.

It’s a hypothesis that Bush pursued in her master’s thesis, and last year she began attending virtual Goth parties in a final round of field work before defending her doctoral thesis later this year.

While this partnership was planned prior to the coronavirus outbreak, co-founder Jordana Kier said the pandemic instantly proved out the expansion thesis.

They’ve had to defend that thesis for a very, very long time in front of a variety of different customers and different people.

Over the past decade, In-Q-Tel has been one of the most active investors in the commercial space sector, with a broad investment thesis that touches many aspects of the sector.

In “Back Home,” Gil also revisits the nostalgia for the South explored in his Johns Hopkins thesis, “Circle of Stone.”

At least father and son were in alignment on this central thesis: acting “gay”—bad; being thought of as gay—bad.

Her doctoral thesis, says Ramin Takloo at the University of Illinois, was simply outstanding.

Marshall McLuhan long ago argued the now accepted thesis that different mediums have different influences on thinking.

He wrote his Master's thesis on the underrepresentation of young people in Congress.

And indeed for most young men a college thesis is but an exercise for sharpening the wits, rarely dangerous in its later effects.

It will be for the reader to determine whether the main thesis of the book has gained or lost by the new evidence.

But the word thesis, when applied to Systems, does not mean the 'position' of single notes, but of groups of notes.

This conclusion, it need hardly be said, is in entire agreement with the main thesis of the preceding pages.

Sundry outlying Indians, with ammunition to waste, took belly and knee rests and strengthened the thesis to the contrary.

Related Words

• proposition
• supposition

What Is The Plural Of Thesis?

Plural word for  thesis.

The plural form of thesis is theses , pronounced [ thee -seez ]. The plurals of several other singular words that end in -is are also formed in this way, including hypothesis / hypotheses , crisis / crises , and axis / axes . A similar change is made when pluralizing appendix as appendices . 

Irregular plurals that are formed like theses derive directly from their original pluralization in Latin and Greek.

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How do I cite a mathematical definition replicated verbatim?

I am writing a paper, in which I must include a definition of a particular mathematical structure. It's a structure with which very few people would be familiar, thus I wish to include it verbatim, as opposed to citing it. Rewriting it in my own words would only obscure the meaning. Putting a long mathematical definition (perhaps half a page) in quotes looks bizarre and messes up the type setting. Is there a standard way to indicate the definition is cited, whilst avoiding any appearance of plagiarism?

• mathematics

• 1 Read other papers in your field of mathematics - some of them must run into similar problems. –  Oswald Veblen Commented Sep 3, 2014 at 1:35

3 Answers 3

Immediately before the definition, you could say "Quoting verbatim from [source], we define a [whatever-it-is] as follows:"

That is, in general, thinking in terms of honesty/forthrightness is an excellent guide.

• Thanks, just a follow-up. Would you say this behaviour is common / standard practise? And how closely do I have to stick to the original before it's a misquote (i.e. can I change formatting, the order of the arguments, fix typos)? –  jhoyla Commented Sep 2, 2014 at 21:56
• 5 If you fix typos and change format, then say "essentially verbatim", rather than "verbatim". And, yes, the behavior I recommend is common practice, not to mention inescapable. –  paul garrett Commented Sep 2, 2014 at 22:17
• Beware if you later put the paper on the arXiv, though. It might say "substantial text overlap with..." –  Flounderer Commented Sep 3, 2014 at 1:15
• 9 In my experience it is not common to see math papers state "quoting verbatim from ...". One simply references the definition, as if it was not a direct quote, with an attribution to the paper where the definition originated. This is not considered plagiarism in mathematics. –  Oswald Veblen Commented Sep 3, 2014 at 1:33
• 1 @Flounderer: if quoting a few definitions leads to the " substantial text overlap " warning, one should rethink whether the entire paper is worthwhile. Also, I wish more people would read the arXiv help document linked above to see what that automatically generated comment really is intended to mean. –  Willie Wong Commented Sep 3, 2014 at 11:00

This is common practice in mathematics. Definitions are not normally thought of as containing creative content, and if you need to use exactly the same definition as the previous paper, you use the same words. As far as I know, no mathematician considers this to be plagiarism of any kind, provided an appropriate citation is given. Quotation marks or block quotes are not used, because, as you say, it would look weird.

Some phrases you might use:

We define, as in [4]: The following definition is taken from [4]: We follow [4] by defining: We use the definition from [4], which we include here for the reader's convenience:

Then format the definition as you normally would. Minor paraphrases and spelling/grammar fixes that do not change the meaning are also fine. If you fix a typo that makes a mathematical difference (e.g. the original author wrote 2 but from context obviously meant 4) then you should point it out explicitly, but this is more for mathematical correctness than citation practice.

Note that if you are publishing in a non-mathematics journal, standards might vary, and you might have to use quotes or otherwise format in some way that would look weird to a mathematician.

• 4 Another common practice is that one usually only cites unfamiliar or recent definitions. Definitions that "everyone knows" are often stated with no citation at all. –  Oswald Veblen Commented Sep 3, 2014 at 1:34
• 8 It might be an over-statement to claim that definitions have no creative content. In some situations, finally coming to an apt definition can be a large part of the work, depending how one couches things. –  paul garrett Commented Sep 3, 2014 at 12:09

If you define terms in a "Definition" environment, then you may state the reference after the heading. For example:

Definition 2 (Noche, 2014). A real number x is said to be small if 0 < x < 1.

• A minor point: I think it would be more typical to omit the `and only if' in a mathematical definition like this. –  Shane O Rourke Commented Sep 3, 2014 at 19:51
• I agree. I've edited the post. –  JRN Commented Sep 4, 2014 at 0:26

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Mathematics PhD theses

A selection of Mathematics PhD thesis titles is listed below, some of which are available online:

2023   2022   2021 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996 1995 1994 1993 1992 1991

Reham Alahmadi - Asymptotic Study of Toeplitz Determinants with Fisher-Hartwig Symbols and Their Double-Scaling Limits

Anne Sophie Rojahn –  Localised adaptive Particle Filters for large scale operational NWP model

Melanie Kobras –  Low order models of storm track variability

Ed Clark –  Vectorial Variational Problems in L∞ and Applications to Data Assimilation

Katerina Christou – Modelling PDEs in Population Dynamics using Fixed and Moving Meshes  

Chiara Cecilia Maiocchi –  Unstable Periodic Orbits: a language to interpret the complexity of chaotic systems

Samuel R Harrison – Stalactite Inspired Thin Film Flow

Elena Saggioro – Causal network approaches for the study of sub-seasonal to seasonal variability and predictability

Cathie A Wells – Reformulating aircraft routing algorithms to reduce fuel burn and thus CO 2 emissions  

Jennifer E. Israelsson –  The spatial statistical distribution for multiple rainfall intensities over Ghana

Giulia Carigi –  Ergodic properties and response theory for a stochastic two-layer model of geophysical fluid dynamics

André Macedo –  Local-global principles for norms

Tsz Yan Leung  –  Weather Predictability: Some Theoretical Considerations

Jehan Alswaihli –  Iteration of Inverse Problems and Data Assimilation Techniques for Neural Field Equations

Jemima M Tabeart –  On the treatment of correlated observation errors in data assimilation

Chris Davies –  Computer Simulation Studies of Dynamics and Self-Assembly Behaviour of Charged Polymer Systems

Birzhan Ayanbayev –  Some Problems in Vectorial Calculus of Variations in L∞

Penpark Sirimark –  Mathematical Modelling of Liquid Transport in Porous Materials at Low Levels of Saturation

Adam Barker –  Path Properties of Levy Processes

Hasen Mekki Öztürk –  Spectra of Indefinite Linear Operator Pencils

Carlo Cafaro –  Information gain that convective-scale models bring to probabilistic weather forecasts

Nicola Thorn –  The boundedness and spectral properties of multiplicative Toeplitz operators

James Jackaman  – Finite element methods as geometric structure preserving algorithms

Changqiong Wang - Applications of Monte Carlo Methods in Studying Polymer Dynamics

Jack Kirk - The molecular dynamics and rheology of polymer melts near the flat surface

Hussien Ali Hussien Abugirda - Linear and Nonlinear Non-Divergence Elliptic Systems of Partial Differential Equations

Andrew Gibbs - Numerical methods for high frequency scattering by multiple obstacles (PDF-2.63MB)

Mohammad Al Azah - Fast Evaluation of Special Functions by the Modified Trapezium Rule (PDF-913KB)

Katarzyna (Kasia) Kozlowska - Riemann-Hilbert Problems and their applications in mathematical physics (PDF-1.16MB)

Anna Watkins - A Moving Mesh Finite Element Method and its Application to Population Dynamics (PDF-2.46MB)

Niall Arthurs - An Investigation of Conservative Moving-Mesh Methods for Conservation Laws (PDF-1.1MB)

Samuel Groth - Numerical and asymptotic methods for scattering by penetrable obstacles (PDF-6.29MB)

Katherine E. Howes - Accounting for Model Error in Four-Dimensional Variational Data Assimilation (PDF-2.69MB)

Jian Zhu - Multiscale Computer Simulation Studies of Entangled Branched Polymers (PDF-1.69MB)

Tommy Liu - Stochastic Resonance for a Model with Two Pathways (PDF-11.4MB)

Matthew Paul Edgington - Mathematical modelling of bacterial chemotaxis signalling pathways (PDF-9.04MB)

Anne Reinarz - Sparse space-time boundary element methods for the heat equation (PDF-1.39MB)

Adam El-Said - Conditioning of the Weak-Constraint Variational Data Assimilation Problem for Numerical Weather Prediction (PDF-2.64MB)

Nicholas Bird - A Moving-Mesh Method for High Order Nonlinear Diffusion (PDF-1.30MB)

Charlotta Jasmine Howarth - New generation finite element methods for forward seismic modelling (PDF-5,52MB)

Aldo Rota - From the classical moment problem to the realizability problem on basic semi-algebraic sets of generalized functions (PDF-1.0MB)

Sarah Lianne Cole - Truncation Error Estimates for Mesh Refinement in Lagrangian Hydrocodes (PDF-2.84MB)

Alexander J. F. Moodey - Instability and Regularization for Data Assimilation (PDF-1.32MB)

Dale Partridge - Numerical Modelling of Glaciers: Moving Meshes and Data Assimilation (PDF-3.19MB)

Joanne A. Waller - Using Observations at Different Spatial Scales in Data Assimilation for Environmental Prediction (PDF-6.75MB)

Faez Ali AL-Maamori - Theory and Examples of Generalised Prime Systems (PDF-503KB)

Mark Parsons - Mathematical Modelling of Evolving Networks

Natalie L.H. Lowery - Classification methods for an ill-posed reconstruction with an application to fuel cell monitoring

David Gilbert - Analysis of large-scale atmospheric flows

Peter Spence - Free and Moving Boundary Problems in Ion Beam Dynamics (PDF-5MB)

Timothy S. Palmer - Modelling a single polymer entanglement (PDF-5.02MB)

Mohamad Shukor Talib - Dynamics of Entangled Polymer Chain in a Grid of Obstacles (PDF-2.49MB)

Cassandra A.J. Moran - Wave scattering by harbours and offshore structures

Ashley Twigger - Boundary element methods for high frequency scattering

David A. Smith - Spectral theory of ordinary and partial linear differential operators on finite intervals (PDF-1.05MB)

Stephen A. Haben - Conditioning and Preconditioning of the Minimisation Problem in Variational Data Assimilation (PDF-3.51MB)

Jing Cao - Molecular dynamics study of polymer melts (PDF-3.98MB)

Bonhi Bhattacharya - Mathematical Modelling of Low Density Lipoprotein Metabolism. Intracellular Cholesterol Regulation (PDF-4.06MB)

Tamsin E. Lee - Modelling time-dependent partial differential equations using a moving mesh approach based on conservation (PDF-2.17MB)

Polly J. Smith - Joint state and parameter estimation using data assimilation with application to morphodynamic modelling (PDF-3Mb)

Corinna Burkard - Three-dimensional Scattering Problems with applications to Optical Security Devices (PDF-1.85Mb)

Laura M. Stewart - Correlated observation errors in data assimilation (PDF-4.07MB)

R.D. Giddings - Mesh Movement via Optimal Transportation (PDF-29.1MbB)

G.M. Baxter - 4D-Var for high resolution, nested models with a range of scales (PDF-1.06MB)

C. Spencer - A generalization of Talbot's theorem about King Arthur and his Knights of the Round Table.

P. Jelfs - A C-property satisfying RKDG Scheme with Application to the Morphodynamic Equations (PDF-11.7MB)

L. Bennetts - Wave scattering by ice sheets of varying thickness

M. Preston - Boundary Integral Equations method for 3-D water waves

J. Percival - Displacement Assimilation for Ocean Models (PDF - 7.70MB)

D. Katz - The Application of PV-based Control Variable Transformations in Variational Data Assimilation (PDF- 1.75MB)

S. Pimentel - Estimation of the Diurnal Variability of sea surface temperatures using numerical modelling and the assimilation of satellite observations (PDF-5.9MB)

J.M. Morrell - A cell by cell anisotropic adaptive mesh Arbitrary Lagrangian Eulerian method for the numerical solution of the Euler equations (PDF-7.7MB)

L. Watkinson - Four dimensional variational data assimilation for Hamiltonian problems

M. Hunt - Unique extension of atomic functionals of JB*-Triples

D. Chilton - An alternative approach to the analysis of two-point boundary value problems for linear evolutionary PDEs and applications

T.H.A. Frame - Methods of targeting observations for the improvement of weather forecast skill

C. Hughes - On the topographical scattering and near-trapping of water waves

B.V. Wells - A moving mesh finite element method for the numerical solution of partial differential equations and systems

D.A. Bailey - A ghost fluid, finite volume continuous rezone/remap Eulerian method for time-dependent compressible Euler flows

M. Henderson - Extending the edge-colouring of graphs

K. Allen - The propagation of large scale sediment structures in closed channels

D. Cariolaro - The 1-Factorization problem and same related conjectures

A.C.P. Steptoe - Extreme functionals and Stone-Weierstrass theory of inner ideals in JB*-Triples

D.E. Brown - Preconditioners for inhomogeneous anisotropic problems with spherical geometry in ocean modelling

S.J. Fletcher - High Order Balance Conditions using Hamiltonian Dynamics for Numerical Weather Prediction

C. Johnson - Information Content of Observations in Variational Data Assimilation

M.A. Wakefield - Bounds on Quantities of Physical Interest

M. Johnson - Some problems on graphs and designs

A.C. Lemos - Numerical Methods for Singular Differential Equations Arising from Steady Flows in Channels and Ducts

R.K. Lashley - Automatic Generation of Accurate Advection Schemes on Structured Grids and their Application to Meteorological Problems

J.V. Morgan - Numerical Methods for Macroscopic Traffic Models

M.A. Wlasak - The Examination of Balanced and Unbalanced Flow using Potential Vorticity in Atmospheric Modelling

M. Martin - Data Assimilation in Ocean circulation models with systematic errors

K.W. Blake - Moving Mesh Methods for Non-Linear Parabolic Partial Differential Equations

J. Hudson - Numerical Techniques for Morphodynamic Modelling

A.S. Lawless - Development of linear models for data assimilation in numerical weather prediction .

C.J.Smith - The semi lagrangian method in atmospheric modelling

T.C. Johnson - Implicit Numerical Schemes for Transcritical Shallow Water Flow

M.J. Hoyle - Some Approximations to Water Wave Motion over Topography.

P. Samuels - An Account of Research into an Area of Analytical Fluid Mechnaics. Volume II. Some mathematical Proofs of Property u of the Weak End of Shocks.

M.J. Martin - Data Assimulation in Ocean Circulation with Systematic Errors

P. Sims - Interface Tracking using Lagrangian Eulerian Methods.

P. Macabe - The Mathematical Analysis of a Class of Singular Reaction-Diffusion Systems.

B. Sheppard - On Generalisations of the Stone-Weisstrass Theorem to Jordan Structures.

S. Leary - Least Squares Methods with Adjustable Nodes for Steady Hyperbolic PDEs.

I. Sciriha - On Some Aspects of Graph Spectra.

P.A. Burton - Convergence of flux limiter schemes for hyperbolic conservation laws with source terms.

J.F. Goodwin - Developing a practical approach to water wave scattering problems.

N.R.T. Biggs - Integral equation embedding methods in wave-diffraction methods.

L.P. Gibson - Bifurcation analysis of eigenstructure assignment control in a simple nonlinear aircraft model.

A.K. Griffith - Data assimilation for numerical weather prediction using control theory. .

J. Bryans - Denotational semantic models for real-time LOTOS.

I. MacDonald - Analysis and computation of steady open channel flow .

A. Morton - Higher order Godunov IMPES compositional modelling of oil reservoirs.

S.M. Allen - Extended edge-colourings of graphs.

M.E. Hubbard - Multidimensional upwinding and grid adaptation for conservation laws.

C.J. Chikunji - On the classification of finite rings.

S.J.G. Bell - Numerical techniques for smooth transformation and regularisation of time-varying linear descriptor systems.

D.J. Staziker - Water wave scattering by undulating bed topography .

K.J. Neylon - Non-symmetric methods in the modelling of contaminant transport in porous media. .

D.M. Littleboy - Numerical techniques for eigenstructure assignment by output feedback in aircraft applications .

M.P. Dainton - Numerical methods for the solution of systems of uncertain differential equations with application in numerical modelling of oil recovery from underground reservoirs .

M.H. Mawson - The shallow-water semi-geostrophic equations on the sphere. .

S.M. Stringer - The use of robust observers in the simulation of gas supply networks .

S.L. Wakelin - Variational principles and the finite element method for channel flows. .

E.M. Dicks - Higher order Godunov black-oil simulations for compressible flow in porous media .

C.P. Reeves - Moving finite elements and overturning solutions .

A.J. Malcolm - Data dependent triangular grid generation. .

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This subreddit is for discussion of mathematics. All posts and comments should be directly related to mathematics, including topics related to the practice, profession and community of mathematics.

What exactly is a hypothesis/thesis?

The idea of a thesis/hypothesis in mathematics like the Church-Turing thesis or the continuum hypothesis sort of confuses me. What is a hypothesis? It's not just a theorem that we haven't proved or disproved yet, like P = NP or something, right?

Is the continuum hypothesis essentially saying something like "well, we'd like to know if | R | = ℵ1, but our set theory axioms aren't 'good enough' to tell us if that's true or not (like defining a table as something with three or four legs that you don't sit on, and then asking 'can tables be made of wood?' 'well, I don't know, that question doesn't make much sense give our definition of table'), but since we'd like to think that | R | is ℵ1 (ie, this makes sense to us), we'll hypothesize that this is the case, and make it sort of axiom of a new kind of set theory"?

Is that close to what a hypothesis is? An axiom that we define because we'd like to have it in retrospect, as opposed to defining it as part of our system from the get-go?

Dissertations

Most Harvard PhD dissertations from 2012 forward are available online in DASH , Harvard’s central open-access repository and are linked below. Many older dissertations can be found on ProQuest Dissertation and Theses Search which many university libraries subscribe to.

Home > College of Natural Sciences > Mathematics > Mathematics Theses, Projects, and Dissertations

Mathematics Theses, Projects, and Dissertations

Theses/projects/dissertations from 2024 2024.

On Cheeger Constants of Knots , Robert Lattimer

Information Based Approach for Detecting Change Points in Inverse Gaussian Model with Applications , Alexis Anne Wallace

Theses/Projects/Dissertations from 2023 2023

DNA SELF-ASSEMBLY OF TRAPEZOHEDRAL GRAPHS , Hytham Abdelkarim

An Exposition of the Curvature of Warped Product Manifolds , Angelina Bisson

Jackknife Empirical Likelihood Tests for Equality of Generalized Lorenz Curves , Anton Butenko

MATHEMATICS BEHIND MACHINE LEARNING , Rim Hammoud

Statistical Analysis of Health Habits for Incoming College Students , Wendy Isamara Lizarraga Noriega

Reverse Mathematics of Ramsey's Theorem , Nikolay Maslov

Distance Correlation Based Feature Selection in Random Forest , Jose Munoz-Lopez

Constructing Hyperbolic Polygons in the Poincaré Disk , Akram Zakaria Samweil

KNOT EQUIVALENCE , Jacob Trubey

Theses/Projects/Dissertations from 2022 2022

SYMMETRIC GENERATIONS AND AN ALGORITHM TO PROVE RELATIONS , Diddier Andrade

The Examination of the Arithmetic Surface (3, 5) Over Q , Rachel J. Arguelles

Error Terms for the Trapezoid, Midpoint, and Simpson's Rules , Jessica E. Coen

de Rham Cohomology, Homotopy Invariance and the Mayer-Vietoris Sequence , Stacey Elizabeth Cox

Symmetric Generation , Ana Gonzalez

SYMMETRIC PRESENTATIONS OF FINITE GROUPS AND RELATED TOPICS , Samar Mikhail Kasouha

Simple Groups and Related Topics , Simrandeep Kaur

Homomorphic Images and Related Topics , Alejandro Martinez

LATTICE REDUCTION ALGORITHMS , Juan Ortega

THE DECOMPOSITION OF THE SPACE OF ALGEBRAIC CURVATURE TENSORS , Katelyn Sage Risinger

Verifying Sudoku Puzzles , Chelsea Schweer

AN EXPOSITION OF ELLIPTIC CURVE CRYPTOGRAPHY , Travis Severns

Theses/Projects/Dissertations from 2021 2021

Non-Abelian Finite Simple Groups as Homomorphic Images , Sandra Bahena

Matroids Determinable by Two Partial Representations , Aurora Calderon Dojaquez

SYMMETRIC REPRESENTATIONS OF FINITE GROUPS AND RELATED TOPICS , Connie Corona

Symmetric Presentation of Finite Groups, and Related Topics , Marina Michelle Duchesne

MEASURE AND INTEGRATION , JeongHwan Lee

A Study in Applications of Continued Fractions , Karen Lynn Parrish

Partial Representations for Ternary Matroids , Ebony Perez

Theses/Projects/Dissertations from 2020 2020

Sum of Cubes of the First n Integers , Obiamaka L. Agu

Permutation and Monomial Progenitors , Crystal Diaz

Tile Based Self-Assembly of the Rook's Graph , Ernesto Gonzalez

Research In Short Term Actuarial Modeling , Elijah Howells

Hyperbolic Triangle Groups , Sergey Katykhin

Exploring Matroid Minors , Jonathan Lara Tejeda

DNA COMPLEXES OF ONE BOND-EDGE TYPE , Andrew Tyler Lavengood-Ryan

Modeling the Spread of Measles , Alexandria Le Beau

Symmetric Presentations and Related Topics , Mayra McGrath

Minimal Surfaces and The Weierstrass-Enneper Representation , Evan Snyder

ASSESSING STUDENT UNDERSTANDING WHILE SOLVING LINEAR EQUATIONS USING FLOWCHARTS AND ALGEBRAIC METHODS , Edima Umanah

Excluded minors for nearly-paving matroids , Vanessa Natalie Vega

Theses/Projects/Dissertations from 2019 2019

Fuchsian Groups , Bob Anaya

Tribonacci Convolution Triangle , Rosa Davila

VANISHING LOCAL SCALAR INVARIANTS ON GENERALIZED PLANE WAVE MANIFOLDS , Brian Matthew Friday

Analogues Between Leibniz's Harmonic Triangle and Pascal's Arithmetic Triangle , Lacey Taylor James

Geodesics on Generalized Plane Wave Manifolds , Moises Pena

Algebraic Methods for Proving Geometric Theorems , Lynn Redman

Pascal's Triangle, Pascal's Pyramid, and the Trinomial Triangle , Antonio Saucedo Jr.

THE EFFECTIVENESS OF DYNAMIC MATHEMATICAL SOFTWARE IN THE INSTRUCTION OF THE UNIT CIRCLE , Edward Simons

CALCULUS REMEDIATION AS AN INDICATOR FOR SUCCESS ON THE CALCULUS AP EXAM , Ty Stockham

Theses/Projects/Dissertations from 2018 2018

PROGENITORS, SYMMETRIC PRESENTATIONS AND CONSTRUCTIONS , Diana Aguirre

Monomial Progenitors and Related Topics , Madai Obaid Alnominy

Progenitors Involving Simple Groups , Nicholas R. Andujo

Simple Groups, Progenitors, and Related Topics , Angelica Baccari

Exploring Flag Matroids and Duality , Zachary Garcia

Images of Permutation and Monomial Progenitors , Shirley Marina Juan

MODERN CRYPTOGRAPHY , Samuel Lopez

Progenitors, Symmetric Presentations, and Related Topics , Joana Viridiana Luna

Symmetric Presentations, Representations, and Related Topics , Adam Manriquez

Toroidal Embeddings and Desingularization , LEON NGUYEN

THE STRUGGLE WITH INVERSE FUNCTIONS DOING AND UNDOING PROCESS , Jesus Nolasco

Tutte-Equivalent Matroids , Maria Margarita Rocha

Symmetric Presentations and Double Coset Enumeration , Charles Seager

MANUAL SYMMETRIC GENERATION , Joel Webster

Theses/Projects/Dissertations from 2017 2017

Investigation of Finite Groups Through Progenitors , Charles Baccari

CONSTRUCTION OF HOMOMORPHIC IMAGES , Erica Fernandez

Making Models with Bayes , Pilar Olid

An Introduction to Lie Algebra , Amanda Renee Talley

SIMPLE AND SEMI-SIMPLE ARTINIAN RINGS , Ulyses Velasco

CONSTRUCTION OF FINITE GROUP , Michelle SoYeong Yeo

Theses/Projects/Dissertations from 2016 2016

Upset Paths and 2-Majority Tournaments , Rana Ali Alshaikh

Regular Round Matroids , Svetlana Borissova

GEODESICS IN LORENTZIAN MANIFOLDS , Amir A. Botros

REALIZING TOURNAMENTS AS MODELS FOR K-MAJORITY VOTING , Gina Marie Cheney

Solving Absolute Value Equations and Inequalities on a Number Line , Melinda A. Curtis

BIO-MATHEMATICS: INTRODUCTION TO THE MATHEMATICAL MODEL OF THE HEPATITIS C VIRUS , Lucille J. Durfee

ANALYSIS AND SYNTHESIS OF THE LITERATURE REGARDING ACTIVE AND DIRECT INSTRUCTION AND THEIR PROMOTION OF FLEXIBLE THINKING IN MATHEMATICS , Genelle Elizabeth Gonzalez

LIFE EXPECTANCY , Ali R. Hassanzadah

PLANAR GRAPHS, BIPLANAR GRAPHS AND GRAPH THICKNESS , Sean M. Hearon

A Dual Fano, and Dual Non-Fano Matroidal Network , Stephen Lee Johnson

Mathematical Reasoning and the Inductive Process: An Examination of The Law of Quadratic Reciprocity , Nitish Mittal

The Kauffman Bracket and Genus of Alternating Links , Bryan M. Nguyen

Probabilistic Methods In Information Theory , Erik W. Pachas

THINKING POKER THROUGH GAME THEORY , Damian Palafox

Indicators of Future Mathematics Proficiency: Literature Review & Synthesis , Claudia Preciado

Ádám's Conjecture and Arc Reversal Problems , Claudio D. Salas

AN INTRODUCTION TO BOOLEAN ALGEBRAS , Amy Schardijn

The Evolution of Cryptology , Gwendolyn Rae Souza

Theses/Projects/Dissertations from 2015 2015

SYMMETRIC PRESENTATIONS AND RELATED TOPICS , Mashael U. Alharbi

Homomorphic Images And Related Topics , Kevin J. Baccari

Geometric Constructions from an Algebraic Perspective , Betzabe Bojorquez

Discovering and Applying Geometric Transformations: Transformations to Show Congruence and Similarity , Tamara V. Bonn

Symmetric Presentations and Generation , Dustin J. Grindstaff

HILBERT SPACES AND FOURIER SERIES , Terri Joan Harris Mrs.

SYMMETRIC PRESENTATIONS OF NON-ABELIAN SIMPLE GROUPS , Leonard B. Lamp

Simple Groups and Related Topics , Manal Abdulkarim Marouf Ms.

Elliptic Curves , Trinity Mecklenburg

A Fundamental Unit of O_K , Susana L. Munoz

CONSTRUCTIONS AND ISOMORPHISM TYPES OF IMAGES , Jessica Luna Ramirez

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Bibliometrics & citations, view options, recommendations, approximating minimum-size k -connected spanning subgraphs via matching.

An efficient heuristic is presented for the problem of finding a minimum-size k-connected spanning subgraph of an (undirected or directed) simple graph G=( V, E). There are four versions of the problem, and the approximation guarantees are as follows: ...

Forbidden Subgraphs and Weak Locally Connected Graphs

A graph is called H-free if it has no induced subgraph isomorphic to H. A graph is called $$N^i$$Ni-locally connected if $$G[\{ x\in V(G): 1\le d_G(w, x)\le i\}]$$G[{x?V(G):1≤dG(w,x)≤i}] is connected and $$N_2$$N2-locally connected if $$G[\{uv: \{uw, vw\...

Finding densest k-connected subgraphs

Dense subgraph discovery is an important graph-mining primitive with a variety of real-world applications. One of the most well-studied optimization problems for dense subgraph discovery is the densest subgraph problem, where given an ...

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Elsevier Science Publishers B. V.

Netherlands

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• Approximation algorithms
• Color-avoiding connectivity
• Spanning subgraphs
• Research-article

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