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Is it common for an undergraduate thesis in pure mathematics to prove something new?
What do undergraduate students in mathematics do for their thesis, if they have done one, besides expository or applied math?
I was thinking that the kind of research they do is something applied, say using math in social sciences or a problem in one of the less rigorous natural sciences, or discussing such a problem (that's what expository is, right?).
To me it seems something non-expository or non-applied is an original contribution to mathematics, something that PhD students do.
I attended some pure math undergraduate thesis presentations. I was quite surprised: Did they prove anything new? Never bothered to ask due to fear of looking stupid. Would it be out of the ordinary to expect an undergraduate proves something new? If they did not prove anything new, what the heck are they talking about?
It seems like if it's not new, they are giving a lecture. If it's new, that seems like a PhD-level accomplishment.
I mean, do math undergraduates frequently prove new things?
- mathematics
- research-undergraduate
- 6 "Anything new" is rather broad. I myself proved "something new" in by bachelors thesis, in the sense that nobody answered that particular question rigorously before. Was it deep? Probably not. Could I have published it? I don't think so. Still, it was new . – Raphael Commented Jul 30, 2015 at 8:05
- Depending on the country and the quality of the teaching, yes it is possible. If you have a Professor who gives you an actual problem knowing you have been taught the right modules/topics to investigate it, yes. If you have little teaching and then are told to pick a topic (as it happens in some places) then the chance is significantly lower. – DetlevCM Commented Jul 30, 2015 at 12:03
- 1 @DetlevCM I'm guessing there may be 1 for every dozens or hundreds. I was actually wondering about the average batch of undergrad math majors whose thesis is in pure math. My guess is in the first place not many math majors will do pure math in their thesis. So what about those who do? They actually try to prove something? What happens if they cannot prove that particular conjecture in a month after they come up with the proposal after a month? 2 months left in the semester. So what happens? – BCLC Commented Jul 30, 2015 at 16:09
- 1 @JackBauer Yes, that Enigma - I only covered the rotors and left out the switchboard but the switchboard is the trivial part. Heck, I suspect I could write an implementation fairly easily nowadays having gotten better at programming since. (Side note, its not cracking Enigma, its encoding and decoding which is really trivial.) – DetlevCM Commented Jul 30, 2015 at 17:05
- 1 @JackBauer Something like that. Some researchers claimed a property of the things they worked with; it was crucial for their method to work, but they did not provide a proof. (I don't know if they could have.) I filled that gap. My advisor found it, and I had the luck that it was a reasonably scoped task that took mostly undergrad stuff plus some tinkering. (I think he (and I) hoped I'd happen upon a case where they were wrong, but they weren't.) – Raphael Commented Jul 30, 2015 at 21:28
5 Answers 5
I'm going to disagree with Oswald. In my experience, undergraduate students do not often prove new things in pure math. I wouldn't even say master's theses often contain new results. There are a few main reasons for this.
Firstly, pure mathematics operates at a level that is not very accessible for most undergraduates, even those doing research. Undergraduates doing research are often well out of their depth and holding on for dear life. This can mostly be attributed to just not having enough time to get up to speed with what is considered modern mathematics. Most courses in mathematics at the undergraduate level are about math from 50-100 years ago (if not older).
Secondly, undergraduates do not often have the mathematical experience to know what the right plan of attack is when faced with an abstract and new problem and they may not know how to check their work thoroughly to make sure there are no major oversights or blunders. A lot of mathematics involves lateral thinking and it takes a lot of time to build those connections. The hardest part of a pure math PhD (in my opinion) is learning how to attack a problem no one has considered before. Standard techniques that others used may not be useful at all to you for one reason or another. An undergraduate won't have the creativity to navigate this kind of issue because the kind of creativity that is needed comes with a lot of experience. Even when an undergraduate student thinks they've proved something, the nuances of their argument likely will not be apparent to them. (This is especially true when it comes to functional analytic/measure theoretic arguments - the devil is in the details.) Thus a proposed proof may not even be close to being right.
Lastly, not many undergraduates in pure math do research because the gap they have to overcome between coursework and modern mathematics is pretty substantial. Those that make contributions in pure math are those that are very, very talented and have very thorough backgrounds (backgrounds that rival master's/PhD students).
Undergraduates in pure math are not expected to make contributions. That is not what research is about for them. Introducing an undergraduate to research serves a couple of different purposes: it introduces them to more advanced topics and it gives them a taste of what research is like so that they can make an informed decision about whether or not graduate school is right for them. As such, the theses are more like surveys of a specialized topic in mathematics. There is a lot of independent learning involved and there may be some unique examples, insights, and connections contained therein. They may not be presenting "original" work, but poster sessions are there to present what they've learned regardless of whether or not it was original. So yes, it is kind of like a lecture. They are undergraduates and far from being experts in their field.
Note that I am not saying that no undergraduate ever produces new results in pure math (there are some high school students that are better than most PhDs), but it is not a common occurrence and is not expected or considered the norm.
- 27 Bingo. Exactly. Further, I think it is bad to promote the mythology that "undergrads can do meaningful research in mathematics" if only because it sets of unrealistic expectations, so that "everyone fails". That is, it does not help anyone to "assure" them that "they can do research while undergraduates", because most likely they will not, and this is not failure. And so on. For that matter, many graduate students misunderstand the degree of "originality/creativity" that will actually play a role in their thesis, since the bulk of the work is assimilation of known techniques... – paul garrett Commented Jul 29, 2015 at 21:09
- 8 I think a large part of the difference here is subfield. It is very rare for an undergraduate to make a substantial contribution anywhere, or any contribution to a subfield requiring a large amount of background. On the other hand, it's not so unusual for undergraduates to be able to prove new results in many areas of combinatorics, even if these results are unlikely to be interesting to anyone except other undergraduates working on follow-up projects. – Alexander Woo Commented Jul 29, 2015 at 22:15
- 2 I fully agree with @AlexanderWoo (and, perhaps counter-intuitively, Cameron's Answer): I think undergrads can definitely do bona fide research, in combinatorics if nowhere else. But, it is probably is likely that most undergrads don't do original research. – pjs36 Commented Jul 29, 2015 at 22:24
- 8 @Alexander Woo - I think it is important to distinguish between undergraduates working alone (who are indeed unlikely to produce much publishable work) versus undergraduates working in collaborations with faculty. For example, the well-known Duluth REU run by Gallian states they have over 200 published papers, in professional journals. These papers seem to be no more likely to be "uninteresting to anyone" than all the other papers in those journals :) See d.umn.edu/~jgallian/progbib.html – Oswald Veblen Commented Jul 29, 2015 at 22:31
- 3 @JackBauer - see the link that OswaldVeblen provided. All those papers were written by undergrads. Personally I coauthored an REU paper as an undergraduate, and my undergraduate thesis also had original results in graph theory, but I went into computer programming for a couple years and didn't publish before those results ended up (completely independently) as part of someone else's PhD dissertation. If you want details, e-mail me; I'm using my real name and can be easily found by Google. – Alexander Woo Commented Jul 30, 2015 at 22:49
The answers so far contain a yes and a no, so let me add a yes-and-no.
Undergraduates can - and often do - prove new things, but hardly ever anything of importance. It is up to the advisor to find an interesting question which is simple enough to serve as the topic of a thesis, but not yet dealt with in the literature. Different from a Ph.D., a bachelor or master thesis is heavily constrained in time, so as an advisor you should only give a topic if you are pretty certain that something can be done by an unexperienced researcher in short time. On the other hand just repeating the literature is boring for the student. One way to find good topics is to look at what is often referred to as folklore: Every textbook contains the theorem that X implies Y, and every expert knows that quasi-X already suffices, but noone bothered to write it up. This will most probably not be worth a publication, but proving a theorem not yet contained in the literature is motivating. Another simple method is looking at all the things you excluded from your own papers. If you worked out an example, but did not include it in a publication, you can let the student generalize it.
What you should not do is ask a student a problem you are really interested in. First the student will be frustrated, because the problem is too hard for him, then you will be frustrated, because you will spend much more time explaining things to him then you would need to find the results for yourself, and finally everyone is frustrated, because you find an answer and have to explain it to the student.
- 3 "Every textbook contains the theorem that X implies Y, and every expert knows that quasi-X already suffices, but noone bothered to write it up." Are there a lot of things like that just lying around? For example? – BCLC Commented Jul 30, 2015 at 16:03
- 1 If someone proves a result, which only serves as a tool, the conditions are quite often too restrictive. For example, Hilbert space is used where reflexive Banach space suffices, or compact can often be replaced by countably compact. In number theory you can look at older paper using exponential sums, and see what improvements for the latter yield in the application. – Jan-Christoph Schlage-Puchta Commented Jul 31, 2015 at 16:59
- Jan-Christoph Schlage-Puchta, "the conditions are quite often too restrictive", do you mean it wouldn't be of interest to many mathematicians anyway? – BCLC Commented Aug 5, 2015 at 12:04
- 3 When talking about topics for a Bachelor or Master thesis, I think about problems which are open in the sense that they are not published, but solved in the sense that every expert in the area could immediately write down a proof. So I don't think these questions are interesting to other people. – Jan-Christoph Schlage-Puchta Commented Aug 10, 2015 at 7:51
- 1 @JackBauer Most of the work is in figuring out what these things are. If I had an example which I knew well enough to cite it here, probably somebody would have proved it. – Ben Webster Commented Aug 11, 2015 at 17:17
Yes, undergraduates frequently prove new things, in the sense that every year there are new, publishable results proved by undergraduates. So, although a relatively small number of undergraduate math students participate in true "research", there are certainly students who are able to make nontrivial discoveries as undergraduates, and more than one might initially think. I have been at prestigious research schools and at anti-prestigious regional universites in the U.S.A. At every school I have been, there were undergraduates in mathematics with the aptitude for publishable research. The talent needed may not be "common", but it is certainly not "rare". The obstacles are primarily cultural, not intellectual.
The topic of undergraduate research has also been the subject of a question on MathOverflow , which makes for good reading.
For an example from personal experience: I recently published a peer-reviewed paper in what I consider to be a high-quality journal (and which is not in any way a "student" journal), with an undergraduate student co-author, who discovered the proof of one of the main theorems on his own between two of our research meetings.
Another example is the journal Involve , which is devoted to genuine student research. From their self-description :
Involve showcases and encourages high-quality mathematical research involving students from all academic levels. The editorial board consists of mathematical scientists committed to nurturing student participation in research. Submissions in all mathematical areas are encouraged. All manuscripts accepted for publication in Involve are considered publishable in quality journals in their respective fields, and include a minimum of one-third student authorship. Submissions should include substantial faculty input; faculty co-authorship is strongly encouraged. In most cases, the submission (and accompanying cover letter) should come from a faculty member. Involve, bridging the gap between the extremes of purely undergraduate-research journals and mainstream research journals, provides a venue to mathematicians wishing to encourage the creative involvement of students.
One thing that undergraduates are unlikely to have is the breadth of knowledge that is expected for PhD recipients. Particularly in mathematics, PhD students are examined in a range of subjects, and are expected to have mastered large parts of the undergraduate curriculum. Undergraduate research often involves learning enough about one particular area to prove new theorems. The student still needs to spend time learning other areas to have the knowledge expected of a PhD.
The real key for undergraduates who are looking to do publishable research is to find a collaboration with a good faculty mentor. Independent research by undergraduates is indeed quite rare (in fact, the majority of mathematics papers currently published have two or more authors - even experts benefit from collaboration). The MathOverflow thread linked above has more advice from other mathematicians.
- 1 Thanks Oswald. Your example is kind of strange. WOuld your undergraduate co-author even have the opportunity to do such if not for knowing you? – BCLC Commented Jul 29, 2015 at 18:41
- 1 Perhaps I should have said: I heard a PhD is like an original contribution or something. Doesn't proving something new kind of amount to an original contribution? Again, I understand this may seem stupid. – BCLC Commented Jul 29, 2015 at 18:42
- 5 I wouldn't say undergraduates frequently prove new things, especially not in pure math. A small number of math undergraduates do serious research and even fewer make major contributions to the work. Most undergraduates hardly have the mathematical chops and insight to make major contributions simply due to lack of enough exposure. – Cameron Williams Commented Jul 29, 2015 at 19:06
- 2 I respectfully disagree. I'm saying that you're way over-inflating how successful undergraduate students are and my guess is that it's because you've worked with some very successful ones. My point is that on average, so very few that actually do research make contributions. Hell, successful PhD students maybe end up with only one or two papers by the time they're finished. – Cameron Williams Commented Jul 29, 2015 at 19:47
- 5 So far, I've worked with three (sets of) students at a non-selective school, resulting in three peer-reviewed papers that, in their journals, are indistinguishable from any other research. The students all met the usual standards for co-authorship. (This record is partially because, as a researcher, I know enough to pick math problems where we are likely to find publishable contributions.) When I was at prestigious research schools, I saw even more math majors who would have been able to work on publishable research as undergrads. As I wrote, the issue is much more culture than aptitude. – Oswald Veblen Commented Jul 29, 2015 at 21:51
I can tell you my experience as I am currently writing an undergraduate thesis (though as a summer project).
I am an undergraduate student in mathematics currently doing a summer « introduction to research » internship. I'm studying probability theory.
As a first year student, about half of my time was spent solidifying my mathematical background in probability, measure theory and analysis. I also spent quite a lot of time studying specialised articles, and finally I applied the general theory I studied to a specific problem, where I did prove something « new », while very closely following other published results. On the way there, I also proved a few lemmas, that, while not of general interest, are « new » and interesting to me.
Clearly, undergraduate students are not expected to find groundbreaking results of general interest. However, they can contribute to mathematics by summarising and gathering related results from multiple articles, applying new theories, finding examples, etc.
A word of advice.
You should not aim for great discoveries, but rather simply try to do your own mathematics. Ask yourself a lot of « stupid » questions and find their answers. That's how you'll end up with a few small new results. Make sure you can grasp the big picture of your field of study, that you look at it from a critical standpoint and that you understand the issues that motivate it.
Do math undergraduates frequently prove new things?
Yes. But not great things, and sometimes things that might already be known to experts (but not widely accessible). I think that it is good enough for an undergrad to prove things that are new to him/her and her classmates/advisor/etc.
Some of the implicit premises of these sorts of questions, or the implicit premises in responses to the question, are really the issue. I would heartily agree that undergrads of all "calibers" should "be in the room" when something resembling "live" mathematics is being discussed. But/and this is most meaningful when we look at the falseness, artificiality, and sterility of the typical undergrad curriculum: it's fake and moribund, with no immediate room for anyone to do anything at all, and no hints about reality, either. Ghastly, yes. But that does not immediately entail a sort of "opposite", that novices need know very little to make meaningful contributions. Raw cleverness has already been exercised, quite systematically, for some hundreds of years (thousands?). People have learned useful things, and to not know these is to not know how to change a tire, or a light bulb, or a furnace filter, or open the door. Not that the usual curriculum helps much, either, I agree! But that does not mean that basic operational skills (involving occasionally subtle mathematics, literally, here) are irrelevant. Getting outside the degenerate "school math" thang is excellent... but thinking that that means "we don't need to know anything!" is obviously silly... even if appealing. "Complicated".
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Do All Degrees Have a Dissertation?
In General , University by Think Student Editor February 5, 2023 Leave a Comment
When thinking about university and the work you have to do, dissertations can often come to mind. As they’re an extended piece of writing, they can often feel long, hard, and simply too much of a hassle. Due to this, it’s entirely naturally to wonder if you must do one at all. That’s exactly what you’ll find out in this article.
In short, at undergraduate level, not all degrees will require you to have a dissertation. Whether you have to do a dissertation or not will generally depend on what you study and what university you study at.
However, at master’s degree level, you will need to do a dissertation to gain the full master’s degree. It may be possible for you to start the master’s degree and then to switch to a postgraduate certificate or diploma, which would not require you to do a dissertation.
Continue reading to learn more about dissertations and when you may need to do one. This article will tell you all you need to know about whether you have to do a dissertation and what the point of one is at all.
Table of Contents
Does everyone at university have to do a dissertation?
While university is often associated with traditional degrees, there are many other options for what you can study at university. These will generally be forms of higher education, meaning that they will be qualifications done after completing sixth form or college at level 4 or above. For more on higher education, check out this Think Student article .
The options of what you can study at a university can range from higher national certificates (HNCs) to foundation degrees and many more. For more on these, check out this UCAS guide .
Due to the wide range of qualifications that you can get at university, the answer is no, not everyone at university will have to do a dissertation . This is primarily due to how these higher education qualifications have different structures to the traditional bachelor’s or master’s degrees and so will often not require a dissertation.
For example, a HNC is equivalent to the first year of a bachelor’s degree. As a dissertation would generally be done in the final year of the degree, a dissertation couldn’t fit into its structure at all. For more on HNC qualifications, check out this article by University Compare.
Can you get a degree without doing a dissertation?
University can be hard to navigate, and it can be even harder trying to get your head around all of the terms and trying to figure out what a degree actually involves. Dissertations are a notorious part of the degree process, and you may wonder if they’re also an essential part.
In the UK, most degrees will require you to do a dissertation. However, this doesn’t apply to all degrees and will likely depend on where you go and what you study . To learn more about this, check out this article by Unite Students.
This means that it is entirely possible for you to get a degree without doing a dissertation as long as it’s not a compulsory part of your course. If the dissertation is something you feel strongly about not doing, then it can be worth fully looking at whether the courses you are interested in will make it compulsory in the modules section of course information pages.
For more insight into which subjects at undergraduate degree level are likely to require you to do a dissertation as well as if dissertations are compulsory at master’s degree level, check out the following headings.
Which degrees require a dissertation?
As mentioned above, in the UK, the majority of degrees will require you to do a dissertation. Otherwise, a dissertation or some other kind of research project may be an optional module that you can choose whether or not to take in your third year.
To find out more specific information about whether or not a specific course will require you to do a dissertation, it is best to look at the course information provided on the university’s website.
However, as a rule of thumb, it’s safe to assume that subjects that are based in both researching and writing will likely require you to do a dissertation . For example, history degrees are very likely to require you to do one.
Especially as at some universities they are considered a key part of the degree due to enabling you to put the skills you have developed into practice. For more on this, check out this page on the University of Southampton’s website.
Whereas more practical subjects, such as engineering, may instead get you to do a research or design project instead of a dissertation. In the same way, doing this kind of project instead will enable students to best apply the skills that they have learnt and developed during the course of their degree.
Do all master’s degrees require a dissertation?
During a master’s degree, students will typically learn about their subject area in greater depth to the extent that they pretty much become a “master” of it by the end of the degree. At level 7 (or level 11 in Scotland), master’s degrees are the second highest level of qualification you can get in the UK. To learn more about master’s degrees, check out this Think Student article .
Due to this, it’s no wonder that a range of high-level academic skills are involved and that you will have increased independence in your studies. As both of these are also traits that dissertations give you, you may be wondering if the master’s dissertation is essential.
The answer is yes, it is. In the UK, a master’s degree will require you to do a dissertation in order to complete your full master’s qualification.
However, if you start a master’s degree and are unable to do the dissertation, some universities will allow you to switch to a shorter postgraduate course, where you won’t have to do the dissertation. This may be a postgraduate certificate (PG Cert) or a postgraduate diploma (PG Dip).
To learn more about all of this, check out this guide by the University of York.
What is the point of a university dissertation?
In the UK, a dissertation is a massive research project and extended piece of writing that students undertake typically at the end of their degree, whether it is an undergraduate or master’s. To learn more about dissertations, check out this article by Think Student.
A dissertation allows a student to study the specific area of their subject that they are most interested in. This enables them to get more in-depth knowledge and to specialise in this element of their subject area. This can be especially great if you want to break into a specific career, related to this subject or if you want to study further.
Also, as a dissertation is done independently, it allows students to develop a wide range of skills from problem solving to time management to organisation. This means that a dissertation can enable students to come out of their studies not only with the degree and specialist knowledge in their subject area but also transferable skills that can improve their career prospects. To learn more about how doing a dissertation can improve your employability, check out this article by LSE.
While a dissertation can leave you will some valuable, transferable skills that can greatly enhance your career prospects and make it easier for you to integrate into a working environment, the dissertation alone may not be enough to secure you the graduate job you’re looking for. However, you can look at this Think Student article , which will give you some useful tips on how to find the right job for you after you graduate.
Guide to Graduate Studies
The PhD Program The Ph.D. program of the Harvard Department of Mathematics is designed to help motivated students develop their understanding and enjoyment of mathematics. Enjoyment and understanding of the subject, as well as enthusiasm in teaching it, are greater when one is actively thinking about mathematics in one’s own way. For this reason, a Ph.D. dissertation involving some original research is a fundamental part of the program. The stages in this program may be described as follows:
- Acquiring a broad basic knowledge of mathematics on which to build a future mathematical culture and more detailed knowledge of a field of specialization.
- Choosing a field of specialization within mathematics and obtaining enough knowledge of this specialized field to arrive at the point of current thinking.
- Making a first original contribution to mathematics within this chosen special area.
Students are expected to take the initiative in pacing themselves through the Ph.D. program. In theory, a future research mathematician should be able to go through all three stages with the help of only a good library. In practice, many of the more subtle aspects of mathematics, such as a sense of taste or relative importance and feeling for a particular subject, are primarily communicated by personal contact. In addition, it is not at all trivial to find one’s way through the ever-burgeoning literature of mathematics, and one can go through the stages outlined above with much less lost motion if one has some access to a group of older and more experienced mathematicians who can guide one’s reading, supplement it with seminars and courses, and evaluate one’s first attempts at research. The presence of other graduate students of comparable ability and level of enthusiasm is also very helpful.
University Requirements
The University requires a minimum of two years of academic residence (16 half-courses) for the Ph.D. degree. On the other hand, five years in residence is the maximum usually allowed by the department. Most students complete the Ph.D. in four or five years. Please review the program requirements timeline .
There is no prescribed set of course requirements, but students are required to register and enroll in four courses each term to maintain full-time status with the Harvard Kenneth C. Griffin Graduate School of Arts and Sciences.
Qualifying Exam
The department gives the qualifying examination at the beginning of the fall and spring terms. The qualifying examination covers algebra, algebraic geometry, algebraic topology, complex analysis, differential geometry, and real analysis. Students are required to take the exam at the beginning of the first term. More details about the qualifying exams can be found here .
Students are expected to pass the qualifying exam before the end of their second year. After passing the qualifying exam students are expected to find a Ph.D. dissertation advisor.
Minor Thesis
The minor thesis is complementary to the qualifying exam. In the course of mathematical research, students will inevitably encounter areas in which they have gaps in knowledge. The minor thesis is an exercise in confronting those gaps to learn what is necessary to understand a specific area of math. Students choose a topic outside their area of expertise and, working independently, learns it well and produces a written exposition of the subject.
The topic is selected in consultation with a faculty member, other than the student’s Ph.D. dissertation advisor, chosen by the student. The topic should not be in the area of the student’s Ph.D. dissertation. For example, students working in number theory might do a minor thesis in analysis or geometry. At the end of three weeks time (four if teaching), students submit to the faculty member a written account of the subject and are prepared to answer questions on the topic.
The minor thesis must be completed before the start of the third year in residence.
Language Exam
Mathematics is an international subject in which the principal languages are English, French, German, and Russian. Almost all important work is published in one of these four languages. Accordingly, students are required to demonstrate the ability to read mathematics in French, German, or Russian by passing a two-hour, written language examination. Students are asked to translate one page of mathematics into English with the help of a dictionary. Students may request to substitute the Italian language exam if it is relevant to their area of mathematics. The language requirement should be fulfilled by the end of the second year. For more information on the graduate program requirements, a timeline can be viewed at here .
Non-native English speakers who have received a Bachelor’s degree in mathematics from an institution where classes are taught in a language other than English may request to waive the language requirement.
Upon completion of the language exam and eight upper-level math courses, students can apply for a continuing Master’s Degree.
Teaching Requirement
Most research mathematicians are also university teachers. In preparation for this role, all students are required to participate in the department’s teaching apprenticeship program and to complete two semesters of classroom teaching experience, usually as a teaching fellow. During the teaching apprenticeship, students are paired with a member of the department’s teaching staff. Students attend some of the advisor’s classes and then prepare (with help) and present their own class, which will be videotaped. Apprentices will receive feedback both from the advisor and from members of the class.
Teaching fellows are responsible for teaching calculus to a class of about 25 undergraduates. They meet with their class three hours a week. They have a course assistant (an advanced undergraduate) to grade homework and to take a weekly problem session. Usually, there are several classes following the same syllabus and with common exams. A course head (a member of the department teaching staff) coordinates the various classes following the same syllabus and is available to advise teaching fellows. Other teaching options are available: graduate course assistantships for advanced math courses and tutorials for advanced undergraduate math concentrators.
Final Stages
How students proceed through the second and third stages of the program varies considerably among individuals. While preparing for the qualifying examination or immediately after, students should begin taking more advanced courses to help with choosing a field of specialization. Unless prepared to work independently, students should choose a field that falls within the interests of a member of the faculty who is willing to serve as dissertation advisor. Members of the faculty vary in the way that they go about dissertation supervision; some faculty members expect more initiative and independence than others and some variation in how busy they are with current advisees. Students should consider their own advising needs as well as the faculty member’s field when choosing an advisor. Students must take the initiative to ask a professor if she or he will act as a dissertation advisor. Students having difficulty deciding under whom to work, may want to spend a term reading under the direction of two or more faculty members simultaneously. The sooner students choose an advisor, the sooner they can begin research. Students should have a provisional advisor by the second year.
It is important to keep in mind that there is no technique for teaching students to have ideas. All that faculty can do is to provide an ambiance in which one’s nascent abilities and insights can blossom. Ph.D. dissertations vary enormously in quality, from hard exercises to highly original advances. Many good research mathematicians begin very slowly, and their dissertations and first few papers could be of minor interest. The ideal attitude is: (1) a love of the subject for its own sake, accompanied by inquisitiveness about things which aren’t known; and (2) a somewhat fatalistic attitude concerning “creative ability” and recognition that hard work is, in the end, much more important.
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Mathematics Graduate Projects and Theses
Theses/dissertations from 2023 2023.
Association of Lockdown Policies with COVID-19 Early Case Growth Rates in the United States , Anna Barefield
A History of the Hurwitz Problem Concerning Branched Coverings , James Alexander Byars
Theses/Dissertations from 2022 2022
Relationships Between COVID-19 Infection Rates, Healthcare Access, Socioeconomic Status, and Cultural Diversity , MarGhece P. J. Barnes
The Matrix Sortability Problem , Seth Cleaver
Cognitive Demand of Teacher-Created Mathematics Assessments , Megan Marie Schmidt
Waring Rank and Apolarity of Some Symmetric Polynomials , Max Brian Sullivan
Security Analysis of Lightweight Cryptographic Primitives , William Unger
Regression Analysis of Resilience and COVID-19 in Idaho Counties , Ishrat Zaman
Theses/Dissertations from 2021 2021
Tukey Morphisms Between Finite Binary Relations , Rhett Barton
A Data Adaptive Model for Retail Sales of Electricity , Johanna Marcelia
Exploring the Beginnings of Algebraic K-Theory , Sarah Schott
Zariski Geometries and Quantum Mechanics , Milan Zanussi
Theses/Dissertations from 2020 2020
The Directed Forest Complex of Cayley Graphs , Kennedy Courtney
Beliefs About Effective Instructional Practices Among Middle Grades Teachers of Mathematics , Lauren A. Dale
Analytic Solutions for Diffusion on Path Graphs and Its Application to the Modeling of the Evolution of Electrically Indiscernible Conformational States of Lysenin , K. Summer Ware
Theses/Dissertations from 2019 2019
Dynamic Sampling Versions of Popular SPC Charts for Big Data Analysis , Samuel Anyaso-Samuel
Computable Reducibility of Equivalence Relations , Marcello Gianni Krakoff
On the Fundamental Group of Plane Curve Complements , Mitchell Scofield
Radial Basis Function Finite Difference Approximations of the Laplace-Beltrami Operator , Sage Byron Shaw
Formally Verifying Peano Arithmetic , Morgan Sinclaire
Theses/Dissertations from 2018 2018
Selective Strong Screenability , Isaac Joseph Coombs
Mathematics Student Achievement in the Context of Idaho’s Advanced Opportunities Initiative , Nichole K. Hall
Secure MultiParty Protocol for Differentially-Private Data Release , Anthony Harris
Theses/Dissertations from 2017 2017
A Stable Algorithm for Divergence-Free and Curl-Free Radial Basis Functions in the Flat Limit , Kathryn Primrose Drake
The Classification Problem for Models of ZFC , Samuel Dworetzky
Joint Inversion of Compact Operators , James Ford
Trend and Return Level of Extreme Snow Events in New York City , Mintaek Lee
Multi-Rate Runge-Kutta-Chebyshev Time Stepping for Parabolic Equations on Adaptively Refined Meshes , Talin Mirzakhanian
Investigating College Instructors’ Methods of Differentiation and Derivatives in Calculus Classes , Wedad Mubaraki
The Random Graph and Reciprocity Laws , Spencer M. Nelson
Classification of Vertex-Transitive Structures , Stephanie Potter
Theses/Dissertations from 2016 2016
On the Conjugacy Problem for Automorphisms of Trees , Kyle Douglas Beserra
The Density Topology on the Reals with Analogues on Other Spaces , Stuart Nygard
Latin Squares and Their Applications to Cryptography , Nathan O. Schmidt
Solution Techniques and Error Analysis of General Classes of Partial Differential Equations , Wijayasinghe Arachchige Waruni Nisansala Wijayasinghe
Numerical Computing with Functions on the Sphere and Disk , Heather Denise Wilber
Theses/Dissertations from 2015 2015
The Classical Theory of Rearrangements , Monica Josue Agana
Nonlinear Partial Differential Equations, Their Solutions, and Properties , Prasanna Bandara
The Impact of a Quantitative Reasoning Instructional Approach to Linear Equations in Two Variables on Student Achievement and Student Thinking About Linearity , Paul Thomas Belue
Student Understanding of Function and Success in Calculus , Daniel I. Drlik
Monodromy Representation of the Braid Group , Phillip W. Hart
The Frobenius Problem , Anna Marie Megale
Theses/Dissertations from 2014 2014
Pi-1-1-determinacy and Sharps , Shehzad Ahmed
A Radial Basis Function Partition of Unity Method for Transport on the Sphere , Kevin Aiton
Diagrammatically Reducible 2-Complexes , Tyler Allyn
A Stochastic Parameter Regression Model for Long Memory Time Series , Rose Marie Ocker
Theses/Dissertations from 2013 2013
The Assignment Packet Grading System , Sarah Nichole Bruce
Using Learner-Generated Examples to Support Student Understanding of Functions , Martha Ottelia Dinkelman
Computing Curvature and Curvature Normals on Smooth Logically Cartesian Surface Meshes , John Thomas Hutchins
Schur's Theorem and Related Topics in Ramsey Theory , Summer Lynne Kisner
Theses/Dissertations from 2012 2012
On the Geometry of Virtual Knots , Rachel Elizabeth Byrd
A Stochastic Parameter Regression Approach for Time-Varying Relationship between Gold and Silver Prices , Birsen Canan-McGlone
Uncertainty Analysis of RELAP5-3D© , Alexandra E. Gertman and George L. Mesina
A Statistical Method for Regularizing Nonlinear Inverse Problems , Chad Clifton Hammerquist
Perfect Stripes from a General Turing Model in Different Geometries , Jean Tyson Schneider
Stability and Convergence for Nonlinear Partial Differential Equations , Oday Mohammed Waheeb
Regular Homotopy of Closed Curves on Surfaces , Katherine Kylee Zebedeo
Theses/Dissertations from 2011 2011
Coloring Problems , Thomas Antonio Charles Chartier
Modules Over Localized Group Rings for Groups Mapping Onto Free Groups , Nicholas Davidson
How Do We Help Students Interpret Contingency Tables? A Study on the Use of Proportional Reasoning as an Intervention , Kathleen M. Isaacson
A Fictitious Point Method for Handling Boundary Conditions in the RBF-FD Method , Joseph Lohmeier
Theses/Dissertations from 2010 2010
Developmental Understanding of the Equals Sign and Its Effects on Success in Algebra , Ryan W. Brown
The Inquiry Learning Model as an Approach to Mathematics Instruction , Michael C. Brune
Galois Theory for Differential Equations , Soheila Eghbali
Stably Free Modules Over the Klein Bottle , Andrew Misseldine
Combinatorics and Topology of Curves and Knots , Bailey Ann Ross
Theses/Dissertations from 2009 2009
Concept Booklets: Examining the Performance Effects of Journaling of Mathematics Course Concepts , Todd Stephen Fogdall
Effective Sample Size in Order Statistics of Correlated Data , Neill McGrath
Transparency in Formal Proof , Cap Petschulat
Weight Selection by Misfit Surfaces for Least Squares Estimation , Garrett Saunders
The Effects of a Standards-Based Mathematics Curriculum on the Self-Efficacy and Academic Achievement of Previously Unsuccessful Students , Cindy Chesley Shaw
Analytical Upstream Collocation Solution of a Quadratic Forced Steady-State Convection-Diffusion Equation , Eric Paul Smith
Solvability Characterizations of Pell Like Equations , Jason Smith
Theses/Dissertations from 2008 2008
Tube-Equivalence of Spanning Surfaces and Seifert Surfaces , Thomas Glass
Simple Tests for Short Memory in ARFIMA Models , Timothy A. C. Hughes
Incomparable Metrics on the Cantor Space , Trevor Jack
Richards' Equation and Its Constitutive Relations as a System of Differential-Algebraic Equations , Shannon K. Murray
Theses/Dissertations from 2007 2007
Theorem Proving in Elementary Analysis , Joanna Porter Guild
An Investigation of Lucas Sequences , Dustin E. Hinkel
A Canonical Countryman Line , William Russell Hudson
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Home > Computational, Mathematical, and Physical Sciences > Mathematics Education > Theses and Dissertations
Mathematics Education Theses and Dissertations
Theses/dissertations from 2024 2024.
Rigorous Verification of Stability of Ideal Gas Layers , Damian Anderson
Documentation of Norm Negotiation in a Secondary Mathematics Classroom , Michelle R. Bagley
New Mathematics Teachers' Goals, Orientations, and Resources that Influence Implementation of Principles Learned in Brigham Young University's Teacher Preparation Program , Caroline S. Gneiting
Theses/Dissertations from 2023 2023
Impact of Applying Visual Design Principles to Boardwork in a Mathematics Classroom , Jennifer Rose Canizales
Practicing Mathematics Teachers' Perspectives of Public Records in Their Classrooms , Sini Nicole White Graff
Parents' Perceptions of the Importance of Teaching Mathematics: A Q-Study , Ashlynn M. Holley
Engagement in Secondary Mathematics Group Work: A Student Perspective , Rachel H. Jorgenson
Theses/Dissertations from 2022 2022
Understanding College Students' Use of Written Feedback in Mathematics , Erin Loraine Carroll
Identity Work to Teach Mathematics for Social Justice , Navy B. Dixon
Developing a Quantitative Understanding of U-Substitution in First-Semester Calculus , Leilani Camille Heaton Fonbuena
The Perception of At-Risk Students on Caring Student-Teacher Relationships and Its Impact on Their Productive Disposition , Brittany Hopper
Variational and Covariational Reasoning of Students with Disabilities , Lauren Rigby
Structural Reasoning with Rational Expressions , Dana Steinhorst
Student-Created Learning Objects for Mathematics Renewable Assignments: The Potential Value They Bring to the Broader Community , Webster Wong
Theses/Dissertations from 2021 2021
Emotional Geographies of Beginning and Veteran Reformed Teachers in Mentor/Mentee Relationships , Emily Joan Adams
You Do Math Like a Girl: How Women Reason Mathematically Outside of Formal and School Mathematics Contexts , Katelyn C. Pyfer
Developing the Definite Integral and Accumulation Function Through Adding Up Pieces: A Hypothetical Learning Trajectory , Brinley Nichole Stevens
Theses/Dissertations from 2020 2020
Mathematical Identities of Students with Mathematics Learning Dis/abilities , Emma Lynn Holdaway
Teachers' Mathematical Meanings: Decisions for Teaching Geometric Reflections and Orientation of Figures , Porter Peterson Nielsen
Student Use of Mathematical Content Knowledge During Proof Production , Chelsey Lynn Van de Merwe
Theses/Dissertations from 2019 2019
Making Sense of the Equal Sign in Middle School Mathematics , Chelsea Lynn Dickson
Developing Understanding of the Chain Rule, Implicit Differentiation, and Related Rates: Towards a Hypothetical Learning Trajectory Rooted in Nested Multivariation , Haley Paige Jeppson
Secondary Preservice Mathematics Teachers' Curricular Reasoning , Kimber Anne Mathis
“Don’t Say Gay. We Say Dumb or Stupid”: Queering ProspectiveMathematics Teachers’ Discussions , Amy Saunders Ross
Aspects of Engaging Problem Contexts From Students' Perspectives , Tamara Kay Stark
Theses/Dissertations from 2018 2018
Addressing Pre-Service Teachers' Misconceptions About Confidence Intervals , Kiya Lynn Eliason
How Teacher Questions Affect the Development of a Potential Hybrid Space in a Classroom with Latina/o Students , Casandra Helen Job
Teacher Graphing Practices for Linear Functions in a Covariation-Based College Algebra Classroom , Konda Jo Luckau
Principles of Productivity Revealed from Secondary Mathematics Teachers' Discussions Around the Productiveness of Teacher Moves in Response to Teachable Moments , Kylie Victoria Palsky
Theses/Dissertations from 2017 2017
Curriculum Decisions and Reasoning of Middle School Teachers , Anand Mikel Bernard
Teacher Response to Instances of Student Thinking During Whole Class Discussion , Rachel Marie Bernard
Kyozaikenkyu: An In-Depth Look into Japanese Educators' Daily Planning Practices , Matthew David Melville
Analysis of Differential Equations Applications from the Coordination Class Perspective , Omar Antonio Naranjo Mayorga
Theses/Dissertations from 2016 2016
The Principles of Effective Teaching Student Teachershave the Opportunity to Learn in an AlternativeStudent Teaching Structure , Danielle Rose Divis
Insight into Student Conceptions of Proof , Steven Daniel Lauzon
Theses/Dissertations from 2015 2015
Teacher Participation and Motivation inProfessional Development , Krystal A. Hill
Student Evaluation of Mathematical Explanations in anInquiry-Based Mathematics Classroom , Ashley Burgess Hulet
English Learners' Participation in Mathematical Discourse , Lindsay Marie Merrill
Mathematical Interactions between Teachers and Students in the Finnish Mathematics Classroom , Paula Jeffery Prestwich
Parents and the Common Core State Standards for Mathematics , Rebecca Anne Roberts
Examining the Effects of College Algebra on Students' Mathematical Dispositions , Kevin Lee Watson
Problems Faced by Reform Oriented Novice Mathematics Teachers Utilizing a Traditional Curriculum , Tyler Joseph Winiecke
Academic and Peer Status in the Mathematical Life Stories of Students , Carol Ann Wise
Theses/Dissertations from 2014 2014
The Effect of Students' Mathematical Beliefs on Knowledge Transfer , Kristen Adams
Language Use in Mathematics Textbooks Written in English and Spanish , Kailie Ann Bertoch
Teachers' Curricular Reasoning and MKT in the Context of Algebra and Statistics , Kolby J. Gadd
Mathematical Telling in the Context of Teacher Interventions with Collaborative Groups , Brandon Kyle Singleton
An Investigation of How Preservice Teachers Design Mathematical Tasks , Elizabeth Karen Zwahlen
Theses/Dissertations from 2013 2013
Student Understanding of Limit and Continuity at a Point: A Look into Four Potentially Problematic Conceptions , Miriam Lynne Amatangelo
Exploring the Mathematical Knowledge for Teaching of Japanese Teachers , Ratu Jared R. T. Bukarau
Comparing Two Different Student Teaching Structures by Analyzing Conversations Between Student Teachers and Their Cooperating Teachers , Niccole Suzette Franc
Professional Development as a Community of Practice and Its Associated Influence on the Induction of a Beginning Mathematics Teacher , Savannah O. Steele
Types of Questions that Comprise a Teacher's Questioning Discourse in a Conceptually-Oriented Classroom , Keilani Stolk
Theses/Dissertations from 2012 2012
Student Teachers' Interactive Decisions with Respect to Student Mathematics Thinking , Jonathan J. Call
Manipulatives and the Growth of Mathematical Understanding , Stacie Joyce Gibbons
Learning Within a Computer-Assisted Instructional Environment: Effects on Multiplication Math Fact Mastery and Self-Efficacy in Elementary-Age Students , Loraine Jones Hanson
Mathematics Teacher Time Allocation , Ashley Martin Jones
Theses/Dissertations from 2011 2011
How Student Positioning Can Lead to Failure in Inquiry-based Classrooms , Kelly Beatrice Campbell
Teachers' Decisions to Use Student Input During Class Discussion , Heather Taylor Toponce
A Conceptual Framework for Student Understanding of Logarithms , Heather Rebecca Ambler Williams
Theses/Dissertations from 2010 2010
Growth in Students' Conceptions of Mathematical Induction , John David Gruver
Contextualized Motivation Theory (CMT): Intellectual Passion, Mathematical Need, Social Responsibility, and Personal Agency in Learning Mathematics , Janelle Marie Hart
Thinking on the Brink: Facilitating Student Teachers' Learning Through In-the-Moment Interjections , Travis L. Lemon
Understanding Teachers' Change Towards a Reform-Oriented Mathematics Classroom , Linnae Denise Williams
Theses/Dissertations from 2009 2009
A Comparison of Mathematical Discourse in Online and Face-to-Face Environments , Shawn D. Broderick
The Influence of Risk Taking on Student Creation of Mathematical Meaning: Contextual Risk Theory , Erin Nicole Houghtaling
Uncovering Transformative Experiences: A Case Study of the Transformations Made by one Teacher in a Mathematics Professional Development Program , Rachelle Myler Orsak
Theses/Dissertations from 2008 2008
Student Teacher Knowledge and Its Impact on Task Design , Tenille Cannon
How Eighth-Grade Students Estimate with Fractions , Audrey Linford Hanks
Similar but Different: The Complexities of Students' Mathematical Identities , Diane Skillicorn Hill
Choose Your Words: Refining What Counts as Mathematical Discourse in Students' Negotiation of Meaning for Rate of Change of Volume , Christine Johnson
Mathematics Student Teaching in Japan: A Multi-Case Study , Allison Turley Shwalb
Theses/Dissertations from 2007 2007
Applying Toulmin's Argumentation Framework to Explanations in a Reform Oriented Mathematics Class , Jennifer Alder Brinkerhoff
What Are Some of the Common Traits in the Thought Processes of Undergraduate Students Capable of Creating Proof? , Karen Malina Duff
Probing for Reasons: Presentations, Questions, Phases , Kellyn Nicole Farlow
One Problem, Two Contexts , Danielle L. Gigger
The Main Challenges that a Teacher-in-Transition Faces When Teaching a High School Geometry Class , Greg Brough Henry
Discovering the Derivative Can Be "Invigorating:" Mark's Journey to Understanding Instantaneous Velocity , Charity Ann Gardner Hyer
Theses/Dissertations from 2006 2006
How a Master Teacher Uses Questioning Within a Mathematical Discourse Community , Omel Angel Contreras
Determining High School Geometry Students' Geometric Understanding Using van Hiele Levels: Is There a Difference Between Standards-based Curriculum Students and NonStandards-based Curriculum Students? , Rebekah Loraine Genz
The Nature and Frequency of Mathematical Discussion During Lesson Study That Implemented the CMI Framework , Andrew Ray Glaze
Second Graders' Solution Strategies and Understanding of a Combination Problem , Tiffany Marie Hessing
What Does It Mean To Preservice Mathematics Teachers To Anticipate Student Responses? , Matthew M. Webb
Theses/Dissertations from 2005 2005
Fraction Multiplication and Division Image Change in Pre-Service Elementary Teachers , Jennifer J. Cluff
An Examination of the Role of Writing in Mathematics Instruction , Amy Jeppsen
Theses/Dissertations from 2004 2004
Reasoning About Motion: A Case Study , Tiffini Lynn Glaze
Theses/Dissertations from 2003 2003
An Analysis of the Influence of Lesson Study on Preservice Secondary Mathematics Teachers' View of Self-As Mathematics Expert , Julie Stafford
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COMMENTS
OMMS and Part C students are required to undertake a dissertation worth two units as part of their degree programme. This can be either a mathematics dissertation or a statistics dissertation. The dissertation will entail investigating a topic in an area of the Mathematical Sciences under the guidance of a dissertation supervisor. This will ...
Lastly, not many undergraduates in pure math do research because the gap they have to overcome between coursework and modern mathematics is pretty substantial. Those that make contributions in pure math are those that are very, very talented and have very thorough backgrounds (backgrounds that rival master's/PhD students).
Department of Mathematics. Science Center Room 325. 1 Oxford Street. Cambridge, MA 02138 USA. Tel: (617) 495-2171 Fax: (617) 495-5132. Department Main Office Contact. Web Site Contact. Digital Accessibility. Legacy Department of Mathematics Website.
The answer is yes, it is. In the UK, a master's degree will require you to do a dissertation in order to complete your full master's qualification. However, if you start a master's degree and are unable to do the dissertation, some universities will allow you to switch to a shorter postgraduate course, where you won't have to do the ...
For this reason, a Ph.D. dissertation involving some original research is a fundamental part of the program. The stages in this program may be described as follows: ... Non-native English speakers who have received a Bachelor's degree in mathematics from an institution where classes are taught in a language other than English may request to ...
The Department of Mathematics offers Bachelor's degrees in Mathematics, Applied Mathematics, and Secondary Education Mathematics. In addition to mastering specific mathematical content, mathematics majors develop excellent general skills in problem solving and precise analytical thinking. Graduates of the program are prepared for more ...
The Department of Mathematics offers Bachelor's degrees in Mathematics and Mathematics with Secondary Education option. A student's course of study can be tailored to suit a particular interest in pure mathematics, applied mathematics, mathematics teaching, or statistics. ... Theses/Dissertations from 2022 PDF. Relationships Between COVID ...
Theses/Dissertations from 2020. Mathematical Identities of Students with Mathematics Learning Dis/abilities, Emma Lynn Holdaway. Teachers' Mathematical Meanings: Decisions for Teaching Geometric Reflections and Orientation of Figures, Porter Peterson Nielsen. Student Use of Mathematical Content Knowledge During Proof Production, Chelsey Lynn ...
Summary. This course is compulsory for MMath students in Year 5. It may also be taken in Year 4 by BSc/MA students who wish to undertake a challenging dissertation at masters level. It may only be taken once and so should NOT be taken in Y4 by MMath students. The Mathematics dissertation is an opportunity to research a subject in depth under ...
History of Mathematics. Students wishing to do a dissertation based on the History of Mathematics are asked to contact Brigitte Stenhouse at [email protected] by Wednesday of week 1 with a short draft proposal. All decisions will be communicated to students by the end of week 2.
A selection of PhD theses and MSc dissertations are available for you to read: mathematics PhD theses. statistics PhD theses. mathematics MSc dissertations. Department of.
In the UK, the typical entry requirements for a Maths PhD is an upper second-class (2:1) Master's degree (or international equivalent) in Mathematics or Statistics [1]. However, there is some variation on this. From writing, the lowest entry requirement is an upper second-class (2:1) Bachelor's degree in any math-related subject.
As a guide, most MSc dissertations are between 30 and 50 A4 pages, double spaced, with normal font size and margins. Longer dissertations are not necessarily better, and the marks obtained depend much more on the quality of the content (especially the mathematics) than on the number of words. It is essential that the dissertation is well presented.
Our department offers Masters degrees in Mathematics, Applied Mathematics, and Statistics as well as a Ph.D. Degree in Mathematics, which can have an emphasis in any of the three areas mentioned. ... The M.S. in Data Science (MSDS) program is a professional, non-thesis degree that is jointly offered by the Mathematics and Computer Science ...
The dissertation must be word-processed and have a font size of 12pt. The text may be single spaced. The dissertation should have a title page which includes the following: { the title of the dissertation, { the candidate's examination number, { the title of the candidate's degree course, { the term and year of submission.
See the top 10 universities for Mathematics. What do you need to get onto a Mathematics degree? Must have. Entry requirements for a Mathematics degree range from 96-165 UCAS points. This could include the qualifications below: A Levels: A*A*A-CCC (Further Maths is sometimes an essential requirement) BTECs: D*D*D*-MMM
Dissertation in mathematics. This module enables you to carry out a sustained, guided, independent study of a topic in mathematics. There's a choice of topics, for example: algebraic graph theory; aperiodic tilings and symbolic dynamics; advances in approximation theory; history of modern geometry; interfacial flows and microfluidics ...
A selection of dissertation titles are listed below, some of which are available online: 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996 1995 1994 1993 1992 1991. 2014: Mathematics of Scientific and Industrial Computation. Amanda Hynes - Slow and superfast diffusion of contaminant species through porous ...
The advanced topics you'll cover and the extensive research training make this course great preparation for a PhD. Sheffield maths graduates have secured postgraduate research positions at many of the world's top 100 universities. Mathematics graduates also develop numerical, problem solving and data analysis skills that are useful in many careers.
Say "I taught myself Python in order to do the following for my thesis." The latter is more accurate, more informative, and not self-deprecating. ... If you have a degree in pure mathematics you shouldn't find it too hard to acquire skills in applied mathematics, statistics, and computer science. The biggest advantage a pure mathematician ...
All master's degrees have a research component. There are postgraduate diplomas which do not have a research component (i.e. just the taught part of the master's degree), but ultimately the entire purpose of higher education is the development of independent critical thought, no matter what the discipline (i.e. getting a doctor to the required level so they can practice safely on their own or ...
Hope this has made sense, thanks. (edited 12 years ago) Reply 1. 12 years ago. River85. No, not all students take a dissertation module in their final year, though most do. Other options including extended essays or short dissertations are common alternatives, particularly in Joint Honours programmes.
A. Blou17. Most named degrees have a compulsory project module. Doing a named OU degree not an easy way out of writing a dissertation.m If you want an "Open" degree then I guess you could skip the project component, but most level 3 courses will involved writing with a significant word count, in essay subjects. Reply 7.
Most do, but they're not always mandatory. Maths often doesn't. In STEM a lot of ppl don't depending on ur degree. For example I do a straight science and most ppl did an investigative honours project (experiment and then write up in scientific paper style) but u could do a diss if u wanted.