how to write a master's thesis in mathematics

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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Senior Thesis Guidelines

A senior thesis can form a valuable part of a student's experience in the  Mathematics Major . It is intended to allow students to cover significant areas of mathematics not covered in course work, or not covered there in sufficient depth. The work should be independent and creative. It can involve the solution of a serious mathematics problem, or it can be an expository work, or variants of these. Both the process of doing independent research and mathematics exposition, as well as the finished written product and optional oral presentation, can have a lasting positive impact on a student's educational and professional future.

Supervision

Supervision by a qualified member of the field of mathematics at Cornell is the normal requirement for a senior thesis. Other arrangements are possible, however, provided they are made with the assistance of the student's major advisor, and with the approval of the Mathematics Major Committee.

Finding a supervisor/Encouraging students.  

It should be emphasized that both the writing and the supervising of a senior thesis are optional activities, both for students and faculty. Students interested in doing this will need to find a suitable supervisor — perhaps with the aid of their major advisor or another faculty member whom they know. Advisors and other faculty who encounter students whom they think would benefit from this activity are invited to mention this option to them and assist them in finding a supervisor.

Standard venues for senior theses . 

One obvious way in which a senior thesis can be produced is through an independent research course (MATH 4900); another way is through an REU experience, either at Cornell or elsewhere. (If the REU work was accomplished or initiated elsewhere, a "local expert" will still be needed to supervise or "vouch for" the work as a senior thesis.) In yet a third way, a student may present a faculty member with a solution or partial solution to an interesting problem. In such cases, this could form the core of a senior thesis. Faculty are invited to encourage such work from their students.

Public Lecture

A public lecture in which the results of the senior thesis are presented is welcome but optional. This should be arranged by the thesis supervisor in conjunction with the undergraduate coordinator and adequately advertised. Department faculty and graduate students are encouraged to attend these presentations.

Submission Deadlines

The supervisor must approve the student's thesis. The student will submit a completed first draft of the thesis to the thesis supervisor. If the supervisor asks the student to make changes, the student will have two weeks to do so and submit a PDF copy of the thesis in final form. The thesis will be posted on the department's web site.

For students graduating in December 2024 , the deadline for the first draft is Friday, November 22 and the final submission is due to the thesis supervisor and the undergraduate coordinator on Friday, December 6.

For students graduating in May 2025 , the deadline for the first draft is Friday, April 18 and the final submission is due to the thesis supervisor and the undergraduate coordinator on Friday, May 2.

Format of the Thesis

Ideally, the final document should be TeXed or prepared in some equivalent technical document preparation system. The document must have large left margins (one and one-half inches or slightly larger). The title page should contain:

The student's name and graduating class.

The title of the senior thesis.

The name of the faculty supervisor. (If there is more than one supervisor, list both. If one of the supervisors is not in the Mathematics Department, list the department and institution.)

The date of completion of the thesis.

This information will be used to produce a standard frontispiece page, which will be added to the document in its library copies.

Judgment as to the merit of a senior thesis will be based largely on the recommendation of the faculty member supervising the thesis. The Mathematics Major Committee will use this recommendation both in its determination of honors and in its decision on whether to place the thesis in our permanent library collection.

The senior thesis will automatically be considered by the Mathematics Major Committee as one of the ingredients for deciding on an  honors  designation for the student. Students may receive honors without a thesis and are not guaranteed honors with one. However, an excellent senior thesis combined with an otherwise excellent record can elevate the level of honors awarded.

Library Collection

Meritorious senior theses will be catalogued, bound, and stored in the Mathematics Library.

Master thesis

Goal of a master thesis.

The master thesis project is the final step in your studies before graduation. As such its intention is to show what you have learned in your studies by applying your knowledge and capabilities in an independent scientific work. In that sense, the master thesis project becomes the crown of your academic career so far and will lay the first cornerstone for your future career.

More formally, the master thesis project is a course like any other with the only distinction that you are working independently, most often as part of a larger team or research group. The aims of the master thesis project are described in detail at the corresponding course plans. Generally, you should show that you can independently plan and carry out a project in Mathematics and present the results, in a written report and orally at a presentation, including a discussion of the prerequisites, methodology, approach and results of the work.

Components of a master thesis project

The main outcome is a project report (master thesis). Here, you will present the findings and results of your project in a scientific manner. However, the goals of a master thesis project are much broader than that: You shall show a number of capabilities, knowledge and attitudes indispensable for a scientist or engineer. Thus, further activities are required where you must show your abilities in mathematical communication. This consists of an oral presentation and discussion of your work and of being an opponent at other thesis presentations.

How to find a project

Once you are eligible for starting a master thesis project you can begin to search for a suitable project. Projects can be carried out at KTH, most often at the Department of Mathematics, or at other collaborating departments at KTH. But many projects are done at a company or other external institutions or authorities. It is also possible that you are carrying out your master thesis project abroad. It is recommended to start the search well ahead of time. Remember, you will not be the only one looking for a project! Also keep in mind that the project must have sufficient scientific level and scope. Before starting the administrative process (master thesis project application, signing of necessary agreements, and much more), you need to submit a project proposal and get it approved by your examiner.

In order to find a project proposal you may consult KTH’s Degree Project Portal . You may also look at company web sites where you will often find proposals, too. Another source of information are your professors. Often, they will have offers or can guide you to colleagues who might have interesting proposals.

More details and the administration

For each of the programs and study tracks, certain special rules apply. Before you start it is important you keep the following in mind:

• The project is 30 credits — usually 5 months of full-time work.
• You need to have at least 60 credit points on advanced level before you can start your project.
• You need an advisor and an examiner. The examiner should normally be from KTH.
• Before you start you and the examiner need to fill out a form. This form can be downloaded here (link to be added).
• The grading is generally Pass/Fail. Exceptions may apply.
• Link to latex style file .

More information specific to the various directions can be found at the following webpages:

Mathematics (TMAKM)

• Applied Mathematics, Scientific Computing (COMA)
• Applied Mathematics, Mathematics of Data Science (DAVE)
• Applied Mathematics, Financial Mathematics (FIMA)
• Applied Mathematics, Optimization and Systems Theory (OPSY)

Examples of typical master theses

Scientific computing (coma), mathematics of data science/statistics (dave), financial mathematics (fima), optimization and systems theory (opsy).

MS and MA Requirements

Master’s degree requirements.

This page sets out the requirements for Master’s degrees in Mathematics.

It is expected that each graduate student who is a U.S. citizen or permanent resident should begin the process of establishing North Carolina residency during the first semester of graduate study. Detailed information can be found here.

A candidate for a master’s degree must satisfy each of the following requirements:

Time and residency Requirements

Time and residency requirements, course-requirements, course requirements.

A Master’s student must perform satisfactorily in 30 hours of graduate work in a program approved by the Director of Graduate Studies. Fifteen of these hours must be in graduate level courses numbered 600 and above in the Department of Mathematics.

• Candidates for either the M.S. or M.A. are required to complete 30 semester hours of approved course work. Programs of course work must be approved by the Director of Graduate Studies. Two semesters prior to the date that the student expects to receive a Master’s degree the student should submit the remainder of the course list for final approval.
• When reading for the Master’s thesis or project students should sign up for the section of Math 920 that corresponds to their adviser. When writing the Master’s thesis or project students should sign up for at least three hours of Math 992, Master’s Project, or Math 993, Master’s Thesis. Signing up for Math 992 or 993 is normally done in the semester prior to completing the Master’s degree. Signing up for at least three credits of Math 992 or Math 993 guarantees full time student status, but this is not true for Math 920.
• Fifteen hours must be in graduate level mathematics courses numbered 640 or above in the Department of Mathematics. These fifteen hours may not include Math 920, 992 or 993; however, these courses may be counted toward the 30 hour requirement.
• Advanced undergraduate mathematics courses approved by the Director of Graduate Studies. These should be at the level of 521, 577 or 578.
• Graduate level courses in the Department of Statistics and Operations Research.
• Courses numbered at least 400 in the Department of Computer Science with an approved level of mathematical content.
• Graduate level courses from other science departments at UNC which have an approved level of mathematical content.
• An approved computer science course at UNC that is used to satisfy the computer language requirement for the Master’s degree may not be used to satisfy the requirement for 30 semester hours.

Any incomplete grades must be resolved within one year (ideally within one semester).

Computer Language Requirement

A Master’s student must pass a computer language requirement by demonstrating a certain level of programming ability. Please note the following guidelines:

• Computer language requirements are the same for Ph.D. and Master’s students.
• Passing the following courses at UNC will be sufficient to satisfy the computer language requirement: MATH 565, MATH 566, MATH 661, MATH 662, MATH 761, MATH 762, COMP 110, COMP 116, COMP 121, COMP 401
• Any computer science course which lists one of these courses as a prerequisite is also acceptable.
• A Master’s or Ph.D. student may also satisfy the computer language requirement by passing an approved one semester undergraduate course on computer programming at any university.
• If the course title title on the transcript is not self-explanatory, then a syllabus, text or other information may be required. In all cases where there is some question about whether a course fulfills the requirement the Graduate Director will decide in consultation with the Graduate Committee.

Examinations

Students entering at the Master’s level must pass one of the written Ph.D. qualifying exams. Master’s candidates must also pass an oral exam conducted by the the student’s Master’s Committee after the completion of the thesis or project.

Written Examinations

• Candidates for either the M.S. or M.A. degree are required to pass at the Master’s level one of the written Ph.D. qualifying examinations. The committee which writes and grades a Ph.D. qualifying exam shall determine what constitutes a Master’s level pass.
• The written exams will be administered to Master’s and Ph.D. candidates at the same time and place. Exams are offered twice each year, near the beginning of classes in August and January.
• A Master’s candidate must pass the written qualifying exam by the beginning of the sixth semester to stay in the Master’s program.
• A Ph.D. candidate who passes one or more of the written Ph.D. qualifying exams will be given credit for passing the written Master’s qualifying exam.

Oral Examination

Candidates for either of the two Master’s degrees are also required to pass an oral examination to be taken near the end of the student’s program of study but after the completion of the Master’s thesis or project. In this examination the student will be expected to discuss with the committee the thesis or project. The student should also be prepared to answer questions on the courses in his or her program.

Master’s Thesis or Project

Difference between the master’s thesis and the master’s project.

• Candidates for the Master of Arts degree are required to write a Master’s Thesis while candidates for the Master of Science degree have a choice between either a Master’s Thesis or a Master’s project.
• The Master’s Project is a substitute for the more formal Master’s Thesis. Both Master’s degrees require a written report of comparable effort and character. The Master’s Thesis is subject to strict composition guidelines enforced by the University while the Master’s Project is subject to the current standards of mathematical presentation.

Master's Thesis or Project

Guidelines for the for a master’s thesis or project.

• The Master’s Thesis is traditionally a written expository work on some area of mathematics. The Master’s Project can range from a Master’s Thesis to a substantial written report on a research project in some applied area. The nature of the Master’s Thesis or Project is determined in consultation with the student and the Master’s Committee of the student.
• Students should sign up for at least 3 credits of Math 992 for the Master’s Project or at least 3 credits of Math 993 for the Master’s Thesis. This guarantees full time student status for that semester. Students should normally sign up for 992 or 993 in the semester prior to the date they expect to receive the Master’s degree.
• Students who are reading for a Master’s Project or Thesis may sign up for the adviser’s section of Math 920. Note that 3 credits of Math 920 does not confer full time student status for that semester.

Composition of the Master’s Committee

The Master’s Committee consists of three people: the adviser of the student, who is also Chair of the Committee, and two readers.

For Additional Information Contact

Ann Van Elsue Graduate Student Services Manager Phillips Hall 331A 919-962-4178 [email protected]

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COLLEGE OF LIBERAL ARTS AND SCIENCES

Department of Mathematics

Thesis formatting, introduction.

If you write a Ph.D. thesis, you have to follow the  specifications  of the graduate school.

Additional information and answers to frequently asked questions can be found the graduate school’s Doctoral Degree Programs page.

A thesis in mathematics is invariably written in some form of LaTeX. It is usually quite a large LaTeX project, so it should not be your first attempt at typesetting. This implies that you should have typed a couple articles, quizzes, homeworks or exams in LaTeX before embarking on this. Below, two options have been created that conform to the guidelines set forth by the graduate school. The first is a minimal option that builds on the familiar book class that comes standard with any LaTeX distribution, while the second is a class file to be used in place of the book class, but contains extra content not suitable for all users. You may choose the option that works best in your case.

Below are a few of the well-done thesis variants from our department.

• Thesis class by Waseet Kazmi – 2023
• Thesis class by Ben Salisbury – 2012
• Thesis class by Marc Corluy – 2000

After unzipping put files into  one  directory. Some browsers (e.g. Safari on the Macs in the department) will put the files on your desktop. In this case create a new folder and put them all in there. In any case, make this move before you start compiling, because LaTeX generates a multitude of files when compiling and your desktop will turn into a (more?) disorderly mess.

Also make sure that the extensions are preserved. Some browsers have a tendency to slap on “.txt” at the end.

Open a text editor or a dedicated LaTeX editor,  such as TeXShop  (installed on department Macs).  When you are typing LaTeX code, it is usually clearer to use a fixed width font so that you have a clear view of your indentations and matrices (should there be any). In TeXShop, a good choice is “Courier Bold 14pts”. This font also has different characters for “|” and lowercase L. This is particularly important if you are trying to typeset tables where both “|” and lowercase L are used in the declaration.

You will now have to open some of the files that you downloaded and edit them. Here are descriptions of the set of files prepared by Ben Salisbury, listed (as best as possible) in order of priority.

• macros.tex  This file is the heart of your personalization. If you have been using LaTeX for your other manuscripts and have developed your own set of user-defined commands, then you should put them in this file. If you are importing text into one of the later files from an older LaTeX file with predefined commands, you will want your personal macros to be loaded already before fumbling with LaTeX error messages.

so those who prefer to use, say,

• thesis.tex  Lines 8 through 17 of this file require the user to input their personal data; i.e., name, degrees, year of graduation, advisory committee, and title. Further down in the file, you’ll notice the command \input{ch1.tex} . This imports the text from  ch1.tex  to the current position in this file. By copying the command and changing ch1 to ch2 (and so on), you will be able to link all chapters of your work to this file. Essentially, this file is the glue that holds the whole project together. This is also the file on which the TeX engine is run to obtain the desired output.
• abstract.tex ,  acknowledgments.tex , and  ch1.tex  should be self-explanatory. Of course, you should have more than one chapter to their thesis. The challenge of creating LaTeX files for the subsequent chapters is left to the user. Good luck!
• thesis.bib  This is a standard BibTeX file to be used as the source for your bibliography output. This may take some time to learn, so the file comes preloaded with a sample  .bib  file. Your best bet is find some literature on BibTeX to tackle this beast. Of course, one could simply replace the bibligraphy declarations in the  thesis.tex  with a manual bibliography, as Marc Corluy does in his setup below. To each his own.
• frontmatter.tex  Simply put: don’t touch it. If you need to make changes here, you should probably consider using Marc Corluy’s template (unless you are familiar enough to make the appropriate changes).

Here are comments on the files prepared by Marc Corluy.

• bibliography.tex  is not your first concern. The references that are listed in there are there to give you an idea about the exact format in which a book or article should be entered into this file.
• chapter1.tex ,  chapter2.tex , and  introchapter.tex  are almost empty; they are merely there to show you how to use titles and sections.
• The file  definitions.tex  you can completely ignore if you want to. It contains (re)definitions of some symbols and a fairly long list of basic mathematical symbols and functions. It can be handy to get a certain feel for how to use “def” in LaTeX and you can also add whatever you end up using often in your thesis.
• Most of the static data (title of the thesis, your previous degrees, your advisors, acknowledgment etc.) are entered in  front_matter.tex . The comments in this file will explain you what to put where.
• If you want to explain some of the notation that you use in your thesis, you should do so in notationpage.tex . It is technically part of the front matter of the thesis, but it is a separate file because this is probably the only part of the front matter data that changes as the thesis evolves.
• You will probably not change much to  settings.tex . This file loads a lot of the extensions to LaTeX and defines the elements of the  amsthm.sty  package, as is explained in the comments in  settings.tex .
• As you can guess,  thesis.tex  is the file where it all comes together. The includeonly command will allow you to compile only parts of your thesis if you prefer to do so. Note that you should compile the thesis twice to make sure that all the labels are set correctly.
• In principle, you should never change anything to  uconnthesis.cls .

Write your thesis. Good Luck.

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Applied and Computational Mathematics Master's Thesis - 625.803

This is the first in a two-course sequence (EN.625.803 and EN.625.804) designed for students in the master’s program who wish to work with a faculty advisor to conduct significant, original independent research in the field of applied and computational mathematics. (Each course is one semester.) A sequence may be used to fulfill two courses within the 700-level course requirements for the master’s degree; only one sequence may count toward the degree. For sequence 625.803 and 625.804, the student is to produce a bound hard-copy thesis for submission to the JHU library and an electronic version of the thesis based on standards posted at https://www.library.jhu.edu/library-services/electronic-theses-dissertations/. (The student is also encouraged to write a technical paper for publication based on the thesis.) The intent of the research is to expand the body of knowledge in the broad area of applied mathematics, with the research leading to professional-quality documentation. A full description of the guidelines (which includes the list of approved ACM research faculty) and the approval form can be found at https://ep.jhu.edu/current-students/student-forms/.

Course Prerequisite(s)

Completion of at least six courses towards the Master of Science, including EN.625.601 Real Analysis and/or EN.625.609 Matrix Theory, EN.625.603 Statistical Methods and Data Analysis, and at least one of the following three two-semester sequences: EN.625.717–EN.625.718 Advanced Differential Equations: Partial Differential Equations and Nonlinear Differential Equations and Dynamical Systems, EN.625.721– EN.625.722 Probability and Stochastic Processes I and II, or EN.625.725– EN.625.726 Theory of Statistics I and II. It is recommended that the sequence represent the final two courses of the degree.

Course Offerings

There are no sections currently offered, however you can view a sample syllabus from a prior section of this course.

Universität Bonn

Preparation of the Final Thesis

The mathematics degree programs conclude with a Bachelor's or Master's thesis, in which independent work on a mathematical topic is to be demonstrated. The Examination Board has compiled the most important requirements for theses and some assessment criteria as guidelines.

• Please read the document carefully before you register your thesis.
• When registering the thesis, you confirm with your signature that you have taken note of the requirements in the document.

The teacher training programs also end with a final thesis. This can be completed in the subject mathematics.

Rules for Theses in the Subject-Specific Study Programs

Here you will find the regulations for registering and submitting final theses that apply to both mathematics programs. Specific deadlines and rules are listed under the respective degree program.

As a rule, students find a supervisor for their thesis on their own initiative.

• Every professor of mathematics in Bonn can of course assign topics for theses.
• Many other doctoral lecturers at Bonn Mathematics have been appointed by the Examination Board to supervise theses. You can enquire about this with the person concerned.
• One of the two reviewers must always be a professor of mathematics at Bonn University.
• If you have not found a supervisor yourself, you can also have one assigned to you by the Examination Board . In this case, please contact the Bachelor-Master Office Mathematics.

The thesis must be registered using the form Registration of the Thesis .The form must be signed by both you and the supervisor of the thesis.

• The form must state the topic of the thesis and your first supervisor.
• You also confirm that you have taken note of the requirements for the final theses of your degree program.
• At the same time, you will be registered for the seminar accompanying your thesis.
• The registration form must be submitted to the Bachelor-Master Office Mathematics immediately after the topic has been assigned and within four weeks of the supervisor's signature.
• If the registration form is received in February or August, the thesis can still be assessed in the semester in which it is submitted.
• For the accompanying thesis seminar you earn 6 credit points. It is registered for the semester in which your thesis is due for submission.
• During the time you are working on your thesis, there are usually three presentations in the thesis seminar on the topic of the thesis and the results achieved.
• The examination of the thesis seminar consists of a graded (final) presentation, which should be held shortly before or shortly after the submission of the thesis. 
• The day on which you give the graded presentation is an examination date and is therefore relevant for your degree.
• Therefore, please make sure that the presentation takes place before the end of the semester in which you wish to graduate.
• The deadline for submitting your thesis is calculated from the signature date of your supervisor plus the working time.
• You can see the submission date of your thesis in BASIS.
• The deadline for submitting your thesis is strict. If you submit the thesis after this date, it will be failed.
• Please note that you are responsible for meeting the submission deadline. Your supervisors are not necessarily aware of your submission deadline, and in no case could they change the deadline for you, as this is set by the examination regulations.
• In the event of illness , the deadline can be extended by up to six weeks.

The thesis must be submitted on time in the required number of copies together with the form Submission of the Thesis at the Bachelor-Master Office Mathematics . On the submission form, you confirm that you have written the paper independently and have not used any sources or aids other than those specified and that you have indicated any quotations.

Requirements:

• DIN A4, printed on both sides, with cover page
• in a bound version (no spiral bindings please!)
• If programming code or similar is available, it must be attached to each copy of the work on a CD or a USB stick that is as flat as possible (do not send it by e-mail). The CD or stick must be glued to the last page of a copy.
• A single copy of the submission form must be submitted separately.

Options for submitting the thesis:

• personal delivery during office hours
• personal delivery after making an appointment outside office hours
• by post to the Bachelor-Master Office Mathematics The date of the postmark is decisive for the submission.

The thesis is evaluated by two assessors.

• The first assessor is the person who provided the topic of the thesis.
• The second assessor must be proposed by you when you submit your thesis. You are therefore responsible for finding a suitable second reviewer. On request, the supervisor can of course help you with this.
• Both reviewers must be noted on the title page of the thesis (see templates for the title page).

As a rule, the candidate is notified of the thesis' evaluation six to eight weeks after the submission date.

Bachelor's Thesis (B.Sc. Mathematik)

• The topic of the Bachelor's thesis is usually assigned towards the end of the fifth semester.
• You need to have earned at leat 90 credit points in order to register the Bachelor's thesis.

The working period of a Bachelor's thesis is five months.

• The Bachelor's thesis is estimated to require a workload of 360 hours.
• Therefore it earns 12 credit points.

The text part of the Bachelor's thesis must be between 5 and 50 pages long.

• Deviations from this require the approval of the Examination Board.
• In this case, please obtain the consent of both your advisors.
• Then send an application by e-mail to the Bachelor-Master Office Mathematics .

The language of the Bachelor's degree program is German. You can write your Bachelor's thesis in English if

• your supervisor agrees with it and
• the thesis contains a summary in German.

There is a coursework for the Bachelor's thesis seminar, the training in subject-specific literature research . It will be noted in BASIS when you register your Bachelor's thesis and it is a prerequisite for passing the Bachelor's thesis seminar.

The training courses are offered by the University and State Library in the form of a one-off two-hour course. The course imparts knowledge that is very useful for academic work, especially when writing a Bachelor's thesis, for example the use of the relevant academic online archives.

• The courses are held in the MNL departmental library in the training room on the 1st floor.
• Usually three dates are offered every semester, each on a Monday or Wednesday from 16.15 to 18.00 hrs.
• You can register for a date via an online form.

After you have taken part in a course, we will enter the coursework as passed in BASIS.

• You must complete this training shortly before or during the time you are working on your Bachelor's thesis.

The title page of your Bachelor's thesis must be agreed with your supervisor.

• In particular, make sure that you name the correct institute to which your supervisor belongs.
• Please use our LaTeX-template for the title page of your Bachelor's thesis.

The submission deadline for the Bachelor's thesis is 5 months after the date on which the supervisor signed the application.

• Three copies of the Bachelor's thesis must be submitted.

Master's Thesis (M.Sc. Mathematics)

• The topic of the Master's thesis is usually assigned towards the end of the second semester.
• You need to have earned at leat 30 credit points in order to register the Master's thesis.

The working period of a Master's thesis is twelve months.

• The Master's thesis is estimated to require a workload of 900 hours.
• Therefore it earns 30 credit points.

The text part of the Master's thesis must be between 10 and 100 pages long.

The language of the Master's degree program is English. You can write your Master's thesis in German if

• the thesis contains a summary in English.

The title page of your Master's thesis must be agreed with your supervisor.

• Please use our LaTeX-template for the title page of your Master's thesis.

The submission deadline for the Master's thesis is 12 months after the date on which the supervisor signed the application.

• Four copies of the Master's thesis must be submitted. One copy will be made available to the Mathematics Library.

If you would like to apply for a PhD position at BIGS Mathematics you should find out about the application process at the beginning of the third Master's semester.

Reimbursement of the Printing Costs for the Thesis

The printing costs for the required copies of your thesis can be reimbursed upon application. This also applies to theses in the teacher training programs that were written in mathematics.

• Please fill out the application form and hand it in at the Bachelor-Master Office Mathematics.
• The enclosed original receipt must show the number of copies printed.
• Please attach the receipts to the separately printed page 2 of the form using a glue stick.

Please submit the form promptly, as the original receipts are only valid for 6 months.

Examination Office Mathematics

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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 .

How to write a great Mas­ter thes­is

09.06.2021  |  EIM-Nachrichten ,  CS-Nachrichten

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Im Rahmen der Vortragsreihe "Scientific Working“ der Matiker ( https://matiker.de/ ) hält am Montag, dem 14. Juni, ab 19 Uhr Stefan Krüger einen Vortrag "How to write a great Master thesis" in englischer Sprache. Der Vortrag findet in Big Blue Button unter der Adresse  https://open-bbb.uni-paderborn.de/b/har-tz9-i7y-hy4  statt.

As part of the Matiker series with talks on „Scientific Working“, Stefan Krüger will be giving a talk on "How to write a great Master thesis“. The talk will be given in English and will be broadcast in Big Blue Button at   https://open-bbb.uni-paderborn.de/b/har-tz9-i7y-hy4 .

The final thesis concludes every Bachelor's and Master's program. It is usually the first time students work systematically for a longer time on their own on a single topic and write up the results of this work in a scientific manner. Consequently, it is widely considered a huge and important part of any curriculum and grants up to 1/3 of all credit points a student may earn during their studies. Yet, curricula tend to focus on other topics, often leaving students feeling unprepared for this unique challenge. In this talk, I will share my insights on how to write a good master thesis, based on my experience from supervising more than a dozen student theses. I will discuss what, in my experience, works and what does not. In specific, I will discuss how to find a suitable thesis and supervisor and why finding a suitable supervisor is actually important for any student. I will also address how to approach scientific work as well as how to structure and write the thesis itself, and prepare the final presentation. After my talk, there will be time for questions. The talk will take place online on June 14th at 7pm local time (UTC+2), at  https://open-bbb.uni- paderborn.de/b/har-tz9-i7y-hy4and  will be given in English. The talk will also be recorded for those who cannot attend. Speaker's bio: Stefan Krüger has received a Ph.D. in software security from Paderborn University in 2020. They are most well-known from their work on the developer-assistant tool for cryptographic APIs CogniCrypt. In August 2020, Krüger joined CQSE GmbH as a Software Engineer. In their time at UPB and CQSE, Krüger has supervised more than a dozen seminar, bachelor, and master theses, covering a wide range of software-engineering topics.

• Ph.D. in Mathematics
• Ph.D. in Atmosphere Ocean Science

M.S. in Mathematics

• M.S. in Scientific Computing
• M.S. in Mathematics in Finance
• Non-Degree Study
• M.S. at Tandon School of Engineering
• Current Students

The Master's degree in mathematics encompasses the basic graduate curriculum in mathematics, and also offers the opportunity of some more specialized training in an area of interest.  A typical Master's course of study will involve basic courses in real analysis, complex analysis and linear algebra, followed by other fundamental courses such as probability, scientific computing, and differential equations. Depending on their mathematical interests, students will then be able to take more advanced graduate courses in pure and applied mathematics.  Information about admission on a non-degree basis is  here .

See frequently-asked questions regarding the impact of the Covid-19 pandemic on MS programs.

Degree Requirements

A candidate for the Master's degree in mathematics must fulfill a number of departmental requirements .

The Written Comprehensive Examinations

Master’s students who choose the Written Comprehensive Examinations option must pass with an overall grade of B. The three-part Written Comprehensive Examination is administered by the department twice a year in early September and early January. Most Master's students tend to take the exam toward the end of their graduate studies.

Students are permitted to take the written examinations twice with no special permission.  A third and final attempt may be granted by the Department on a case-by-case basis.

The examinations, in advanced calculus, complex variables and linear algebra, may include some of the following material:

Advanced Calculus:  Real numbers. Functions of one variable: continuity, mean-value, differentiability, maxima and minima, integrals, fundamental theorem of calculus, inequalities, estimation of sums and integrals, elementary functions and their power series. Funtions of several variables: partial derivatives, chain rule, MacLaurin expansion, critical points, Lagrange multipliers, inverse and implicit function theorems, jacobian, divergence and curl, theorems of Green and Stokes.

Complex Variables:  Complex numbers, analytical functions, Cauchy-Riemann equations, Cauchy's integral and applications, power series, maximum principle, Liouville's theorem, elementary functions and their conformal maps, bilinear transformation, classification of singularities, residue theorem and contour integration, Laurent series, Rouche's theorem, number of zeros and poles. 

Linear Algebra:  Vector spaces, linear dependence, basis, dimension, linear transformation, inner product, systems of linear equations, matrices, determinants, ranks, eigenvalues, diagonalization of matrices, quadratics forms, symmetric and orthogonal transformations.

Cooperative preparation is encouraged, as it is for all examinations. Students may also find the following books helpful:

Buck,  Advanced Calculus ; Courant and John,  Introduction to Calculus and Analysis ; Strang,  Linear Algebra ; Churchill,  Complex Variables and Applications .

Master's Thesis

Students who have earned a GPA of 3.7 or higher and taken at least 18 credits in the program have the option to write a Master's thesis under the supervision of a Mathematics faculty member. In certain cases involving interdisciplinary research, a second advisor outside the Department of Mathematics may be approved by the Director of Graduate Studies. All students must submit the Thesis Proposal and Advisor Approval form, outlining the research plan for the thesis which has been approved by the thesis advisor, to the Program Administrator at least four months prior to the graduation date. The completed Master's thesis must be approved by two readers -- the thesis advisor and a second reader. At least one of the readers must be a full-time Courant Mathematics faculty member. You can find more detailed information in the Thesis Guidelines FAQ.

Academic Standards

To continue registering for courses in the Department of Mathematics, a student must be in a good academic standing, fulfilling the following requirements:

• Students must maintain an average of B or better (3.0) in their first 12 credits. Students failing to achieve this will not be permitted to continue in the program. Students cannot obtain an M.S. degree unless they have maintained an overall average of at least B
• Students will be allowed no more than four no-credit grades, withdrawals, or unresolved incomplete grades during their academic tenure, and no more than two such grades in the first six courses for which they have registered.
• Credit will be given for up to two core courses taken elsewhere, subject to the normal GSAS restrictions on transfer of credit and the approval of the Program Coordinator. At least 24 course points must be taken at New York University.

For any questions contact us at:

Office of Admissions and Student Affairs Department of Mathematics Courant Institute of Mathematical Sciences 251 Mercer Street New York, NY 10012-1185 Phone (212) 998-3238 Fax (212) 995-4121 [email protected]

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How to write Master's thesis summary for PhD application

I am currently applying for several PhD programs (in mathematics) and for many of them, it is required to write a short (approx. 2 pages; no more than 10.000 characters) summary of my Master's thesis. It should contain the motivations of the thesis and research, the methods used as well as the results obtained in my research.

Now, the application commitee is probably less interested in the precise topic of my research or in the project itself, but I guess that the aim of this writing in my application is more for them to examine my ability of writing and explaining my research to others, as the latter is one of the key abilities a scientist should probably have, in my opinion.

My questions are now the following:

(1) How detailed should such a writing be? In my specific case, I am appliying for a math PhD and many things which I did in my thesis, which lied in the border of math and physics, are very abstract, so it not always easy to explain them in simple, non-technical, terms (and I guess, this applies for most of the projects done in pure mathematics). So, should I aim in writing this text in a more "popular" science way, or should I "confront" them with full technical details (the middle way is, as written above, hardly possible, as the things are kind of abstract).

(2) Should I aim in writing this stuff more formally, or more from a personal point of view? So, should I, for example, write about my personal reasons for chosing this particular problem, or should I more concentrate on the scientific reasons of why this type of questions are interesting?

• graduate-admissions
• application

• 2 A thesis I'd have supervised (not in math, admittedly) would have a summary/an abstract in the beginning which could be used just like it is for your purpose. Does your thesis not contain an abstract/a short summary? –  Snijderfrey Commented May 16, 2022 at 15:05
• 1 Hi, yes my thesis does contain an abstract, but this is rather small (half a page) and really just contains the technical contents and result.... So its written similar in spirit as an abstract of a paper... –  B.Hueber Commented May 16, 2022 at 16:19
• 1 @Snijderfrey I'm not sure that's a good advice in generality. Many job applications I see which contain the abstract of the thesis don't look very convincing - this might just be correlations, but just putting the abstract makes a very un-excited impression. And who wants to hire unexcited students? –  user151413 Commented May 17, 2022 at 19:17

2 Answers 2

Note that your essay will be read by other mathematicians, but most of them won't be in your specialty. An overly detailed presentation, such as you might present to your advisor won't be the best.

You are probably correct that they are looking for a writing sample, so focus on the writing at least as much as the math.

A personal view of "why" you chose this path is probably not the right focus, though a sentence might be fine.

First, though, what is the most important result in your thesis? It might be a theorem, but it might also be an interesting (thought provoking) proof technique. Talk about that result primarily, and situate it within the mathematical literature. Talk about why it is an important result. If possible, talk about what it might lead to, though you may not yet be sophisticated enough to understand that.

If the work gave you any special "insights" into the wider world of your specialty (or math in general) include a few words about that. Is there follow up research that is indicated?

As to the level, think about how you would explain the thesis to a good upper level undergraduate class. I'm guessing that such a level might be the best, of course, but all of your readers (various mathematicians) would be able to understand it.

The details are in the thesis, of course, and the committee will probably have access to that as well, so a higher level (or lower level, if you like) presentation is probably enough.

• Thanks a lot! Yes indeed, I also uploaded the full thesis in the application. –  B.Hueber Commented May 16, 2022 at 16:23
• I join this answer to ask If it could be a good idea to write the MSc thesis summary in the form of a scientific article. Consider the following template provided by springer as a possible example: overleaf.com/latex/templates/… –  g_don Commented Aug 13, 2023 at 19:29

Make it in 3 parts

• Synopsis: This is what you have written at the start of your Master's thesis.
• Brief description of your work: Describe what (and how) you did in your Master's project.
• Results: What new goals you achieved in your work.

The whole language is slightly technical, without many complex formulas and equations.

You must log in to answer this question.

Not the answer you're looking for browse other questions tagged phd graduate-admissions thesis application ..

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Whether you’re thinking about pursuing an advanced degree in education or are already in such a program, one thing you will need to be prepared for is writing a thesis or dissertation. In most graduate-level education programs, a thesis or dissertation is the culmination of years of challenging work, serving as your own independent research that marks the final step before earning your graduate degree.

If writing a dissertation or thesis sounds like a daunting task, it does not have to be. With a little preparation and some best practices in mind, you can approach writing a thesis or dissertation with confidence.

Understanding the Thesis and Dissertation Process

Before writing a thesis or dissertation, it’s important to understand their general scope and purpose, along with some key differences between a thesis and a dissertation. After all, while there are some similarities between the two, a dissertation and a thesis are not the same thing.

Defining the Scope and Purpose

The primary purpose of a thesis or dissertation in an education graduate program is for students to demonstrate what they have learned in their respective programs while applying their own research, theory, analysis and synthesis. Ultimately, the author of a thesis or dissertation should successfully contribute something new to the existing topic. In dissertations specifically, students may also be required to articulate, discuss and defend their research orally in front of professors or other faculty members. This oral defense is not required for a master’s thesis.

Differences Between Thesis and Dissertation

When it comes to writing a thesis or a dissertation, the terms “dissertation” and “thesis” are sometimes used interchangeably. That said, it is crucial to understand that these are two different things. Generally, a dissertation is primarily focused on filling a gap in existing literature or extending upon current research regarding a specific topic. The goal is to analyze literature to the point of saturation and determine where there is a need for further research. In a dissertation, a doctoral student will then explain where the problem exists given current research and develop a research study to explore or evaluate the problem, thus filling the gap and contributing meaningfully to the field.

On the other hand, a thesis is more of a presentation of information that’s already out there with no obligation to conduct additional research.

Choosing the Right Topic

One of the most important aspects of drafting a great thesis or dissertation begins with choosing the right topic. Here, it is paramount to select a topic that not only interests you but is relevant to your future professional goals and aspirations. After all, there’s a good chance you may use your thesis or dissertation as a basis for future work or further research.

Considering Current Research Trends

In selecting a topic, you will also want to consider current research trends in your field. What is trending in the realm of education and what could you contribute to existing research? There are research gaps or questions that remain unanswered about certain educational topics that could be addressed through your research.

Research and Proposal Development

In most graduate programs, you will need to write and present a research proposal before you can really get started on your thesis or dissertation. Most research proposals are reviewed and approved by a professor or other faculty.

Conducting a Literature Review

A literature review is to discover the research available on your research topic. This review should detail each source you plan to use in your own research with plenty of detail. More specifically, a literature review is a comprehensive summary of the current literature on a given topic that demonstrates the need for additional research to be conducted. Literature reviews comprise a major portion of a proposal, including a summary of each source as it relates to the need for additional research.

Finding Reliable Sources

Quality is vital when it comes to selecting literature for your research or literature review. Ideally, your literature review should include plenty of recent and reputable sources that come from academic journals, books, articles and even other dissertations.

Developing a Research Proposal

Once you have a better understanding for what is already out there, you can craft a research proposal that discusses your specific research topic, the current problem, the purpose behind your research, the methodology you plan to use and the relevant literature that further defends a need for your topic to be investigated.

Methodology Selection

An important part of your research proposal will be your methodology selection, which will explain exactly how you plan to go about your research. For example, will your research be qualitative, quantitative or a mix of both and why? How will the methodology you choose answer your research questions?

Writing and Structuring Your Thesis or Dissertation

After your research proposal is approved, you will have the green light to begin working on your thesis or dissertation. You will receive feedback or thesis guidance from the faculty member who reviewed your proposal. It is important to reflect on the feedback and make revisions as needed.

Creating an Outline

One of the most helpful things you can do as you get started with your dissertation or thesis is to create an outline. This allows you to develop the most critical aspects of your final project that include your thesis, your main points and other key details to ensure that they flow logically.

For reference, an outline for a dissertation will typically include the following:

• Introduction of existing research
• Review of literature
• Conceptual framework
• Methodology
• Results or findings
• Interpretations, conclusions or recommendations for future research

Structuring Arguments

In creating an outline, include designated sections for each of your main points with specific research, statistics, or other data to support it. This will ensure that your arguments are made clearly and that your thought process is clear.

Writing Tips and Strategies

Even if writing is not necessarily your strong suit, you will need to be able to put together a cohesive document for your thesis or dissertation. There are some basic strategies worth keeping in mind to help you get started.

First, it can be helpful to write your introduction and conclusion paragraphs last once you have completed all your research. While it might seem counterintuitive to do it this way, it can help set the tone for the rest of your writing. Likewise, this strategy ensures that you include your main points while preparing your readers for the information to come.

Additionally, meet with your advisor or faculty sponsor regularly to gain valuable feedback and keep your project on track.

Data Collection and Analysis

Whether you are writing a thesis or dissertation, you will need to do a fair amount of your own qualitative or quantitative research. It’s important to understand the various data collection methods available to you, plus the best practices for analyzing and interpreting data.

Choosing Data Collection Methods

There are two main types of data collection:

• Quantitative data  - Refers to hard data that is numerical in nature, such as statistics and percentages.
• Qualitative data  - Refers to information that is non-numerical, such as interviews and focus groups.
• Mixed methods – Refer to a combination of both quantitative and qualitative data.

Analyzing and Interpreting Data

Once you have all the data you need to write your thesis or dissertation, the challenging part is often analyzing and interpreting the data to apply to your own research. The most important thing to keep in mind when looking at hard data is how it relates back to your research and specific research questions.

When working with quantitative data, it can also be helpful to look for specific trends and correlations that you can share in your research.

Reviewing and Editing Your Work

Once you have completed the first draft of your thesis or dissertation, the process of reviewing, revising and editing your work before submission is important to ensure that the document is free of errors and that it effectively communicates your main points to the reader.

Peer Review and Feedback

One of the best ways to improve upon the first draft of your dissertation or thesis is through peer review and feedback. By having others read your draft and provide feedback, you can gain some valuable insights into how your arguments are being interpreted. Even if the person you ask to read your draft is not familiar with the subject matter, they can still provide useful feedback on the organization of the information, structure and grammar/spelling.

Proofreading and Final Edits

It may take several rounds of revisions before your dissertation or thesis is approved. Even when you feel like the entire thing is ready to submit, it is important to complete another round of proofreading and editing to be sure that the entire document is polished and in the best shape possible. This includes not just running a basic spell check but taking the time to read your paper word for word.

Formatting Guidelines

In most education programs, you will be instructed to use the  American Psychological Association (APA) style when writing and formatting your thesis or dissertation. It is important to follow all formatting guidelines here, especially as they relate to citations or references.

Preparing for the Defense

In many doctorate programs and some graduate programs, students will also be expected to defend their dissertations in front of other scholars, usually professors or other faculty from the department. This process can be daunting, even for those who know their research well and have crafted thoughtful dissertations.

Crafting Your Presentation

In preparing for a dissertation defense, it is imperative to craft a presentation that covers the basics of your dissertation topic, how you researched it and what your findings were. Following your presentation, you can expect to be asked questions by those in attendance about your topic and other aspects of your research.

Practicing Your Defense

The best way to prepare for a dissertation defense is to practice as much as possible. This way, you will be prepared for the kinds of questions that may be asked, and you will feel a little more confident when completing your defense.

Mock Sessions

Mock defense sessions can be especially helpful for practicing your presentation and answering questions from a real crowd. Do not hesitate to ask your fellow students or even some trusted professors to practice with you to provide feedback or ask questions.

Handling Questions

One of the most difficult aspects of defending a dissertation is often answering questions from the audience. One important tip to keep in mind here is to prepare some answers in advance to some of the questions you think might be asked during your dissertation defense. This way, you will be completely prepared to knock these out of the park.

Ready to Pursue an Advanced Degree?

As you can see, there is a lot that goes into writing a dissertation or thesis as part of your graduate education program. With this dissertation guidance in mind, you will be prepared to craft and even defend your thesis or dissertation with success.

Still looking for the right graduate education program to suit your interests and professional goals? Keiser University is proud to offer a number of advanced degrees in education, including our  Master of Science in Education, Teaching and Learning  program. If you’re interested in earning your doctorate degree, we also offer a  Doctor of Education  and a  Doctor of Philosophy in Educational Leadership .

Learn more about any of the graduate programs offered at Keiser University by  contacting a graduate admissions counselor today, or get started with your online application  for enrollment.

Jessica Kircher

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Aug 23 – Master of Science Thesis Defence – Clement Frimpong Osei

Tuesday, August 13, 2024 | By jtitone

Master of Science thesis defence in Computer Science

Clement Frimpong Osei, a Master of Science candidate in the Department of Computer Science, will defend his thesis titled “Application of L-Fuzzy Relation to Social Choice Theory” on Friday, Aug. 23 at 11 a.m.., in Plaza building room 600F.

The examination committee includes Melanie Pilkington, Chair; Michael Winter, Supervisor; Ke Qiu, External Examiner (Brock University); and Beatrice Ombuki-Berman; and Renata Queiroz Dividino, Committee Members.

Tags: Computer Science , FMS , Thesis defence Categories: News

FMS News and Events

• Aug 21 – PhD Thesis Defence – Alicia Martin
• Aug 19 – Master of Science Project Presentation – Samiha Tasmin
• Aug 2 – Master of Science Thesis Defence – Fardad Pirri
• July 23 – PhD Thesis Defence – Gregory Foran
• July 15 – Master of Science thesis defence – Abhishek Kumar
• May 31 – Master of Science Thesis Defence – Pierre Simiganoschi
• May 29 – Master of Science Thesis Defence – Quanjian Li
• May 21 – Doctor of Philosophy Thesis Defence – Frank Betancourt
• May 16 – Master of Science Thesis Defence – Georgina Louise Gardner

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