THESIS

Introduction:

Writing a thesis is time consuming and hard work; your supervisor will encourage you to start writing up early in your final year. These notes are intended to help you produce your thesis.
The thesis will, of course, contain your account of the new results you have obtained in your research. It should not, however, be merely a catalogue of these results and their proofs. Your work should be put into context. A clear description of the topics you have worked on and the questions you have tried to answer is essential. You must also show that you are aware of existing work in the subject and so your thesis should contain a review of such work. According to the University you are also supposed to be have a "a good general knowledge of the field of study". Writing the thesis gives you one opportunity to demonstrate that you do know something more than your own results and their proofs.

It is usually a good idea to write a plan setting out the expected chapters of the thesis and giving a very brief outline of the contents of each chapter. Normally you would discuss your plan with your supervisor and when agreement has been reached, you proceed with the writing.
Your thesis will be produced using LaTeX with which you will be familiar long before you come to writing up.

Structure
Every thesis has an introduction which tells the reader what it is about. It will briefly summarise the problems you have worked on, explain how these problems arose from existing work and perhaps give an overview of the main results of the thesis. An introduction often finishes with a description of the contents of each chapter. Although it comes first, the introduction is usually written last.

The introduction is followed by a chapter giving background information. Remember that the thesis will be read by people who have not been immersed for two years in your research problems. Usually you will give all the basic definitions which are not in standard textbooks and often some which are. It is best to make life easier for the reader by including too much rather than too little.

You will also want to give a review of the state of the art relevant to your thesis. This may be included in the final sections of the chapter on background material or may form a separate chapter.

Next, the bulk of the thesis is taken up with an account of your research. Here you should describe what you are doing, state the results carefully and clearly and write proofs so that they can be followed by a reader who is not an expert on the particular topic. Do not make the readers work too hard. Remember that you are trying to show that you can communicate mathematical ideas as well as demonstrating that you can solve problems. It is impossible to be too clear.
Theses often finish with a short section on future research. This will be a brief account of questions which arise from your results, and directions for further work on the thesis topic.
At the end of the thesis you list the references relevant to your research. Details of how they should be set out are given in the University regulations.

Style
Your thesis must be written in English. This implies that it must not be in the form of rough notes or contain sequences of unexplained formulae. It must be written in grammatically correct sentences. There are also several points of style which are peculiar to writing mathematics. Here is a list of some of them.

1. Do not start a sentence with a symbol. Bad: x2+1 is irreducible over R. Good: The polynomial x2+1 is irreducible over R.

2. The symbols , , , etc. should not be used; replace them by appropriate words. Bad: m N primes p1 pk such that m=p1 pk . Good: Every natural number can be written as a product of primes.

3. Be careful not to use the same symbol for two different things. For instance, if a proof starts with "Let x " do not introduce a vector x later in the proof.

4. When referring to a result or section which is numbered, use a capital letter. For example, ... follows by Theorem 1 and in Section 4 we discuss ....

5. Symbols in different formulae should be separated by words. Bad: If x+y=z , x y , then ... Good: If x+y=z where x y , then ....

6. Quantifiers should be clear. Bad: f(x)=g(x) (x X ).Does this mean "for all x X " or "for some x X "? Good: f(x)=g(x) for all x X .

Returning to the issue of clarity, when writing a long proof you must think how to structure it so that a reader can follow it. When a proof is longer than a couple of pages, you should explain the strategy of the proof at the beginning. Then make clear when each stage of the proof is complete and what you are going to do next. These points can sometimes be met by giving a series of lemmas and then explaining how the theorem is a consequence of the lemmas. Try to ensure that at all times the reader knows what you are doing, why you are doing it and what you are aiming for.

Revision and proofreading
Once you have written a chapter you should read it with a critical eye and make revisions as appropriate. You will want to ensure that you have made a good job of organizing the material of the chapter and that what you have written makes sense, is correct and reads well. You should also check the spelling and grammar, and correct any typos. To achieve a polished finished product you will have to read the chapter carefully several times. You may also find that when you write Chapter n you will be forced into making changes to some or all of Chapters 1 to n -1. You must be prepared to do this several times.

You are responsible for proofreading your work; your supervisor is not your proofreader. When you print a portion of your thesis you must read the printout and correct mistakes before handing it to your supervisor.

Plagiarism

Plagiarism is defined by the University to be incorporating within your work without appropriate acknowledgement material derived from the work (published or unpublished) of another. Thus, for example, if you are explaining the basics of a topic, you must present it in your own words and not simply copy several sections of a textbook. By writing it yourself, as well as avoiding plagiarism, you demonstrate that you actually understand the material. When you quote results from a paper or a book you should make clear where the result comes from. Similarlyif someone has proved but not published a result you need, then you should acknowledge this fact when you use the result.

Guidelines for Graduation with Honors in Mathematics:

Every graduate of the College of Liberal Arts and Sciences with an upper-division
grade-point average (GPA) of 3.5 or better receives at least a cum laude (honors) designation
on his or her diploma; students not meeting this GPA criterion are ineligible
for honors designations. (\Upper-division GPA" is de ned as the the GPA computed
from all non-S/U courses taken at UF starting with the rst semester in which the
student enrolls after he/she has completed 60 hours. The courses themselves may
be at any level.) To be eligible for the designation magna cum laude (high honors)
or summa cum laude (highest honors), mathematics majors must write a thesis in
addition meeting the GPA criterion. The Undergraduate Coordinator will make the
nal decision on the honors designation after consulting with the student's supervisor.
Eective fall 2005, only students meeting the requirements listed in the
latest Undergraduate Catalog will be eligible for the designation summa
cum laude. (The highest designation available to students meeting the then-current
Bachelor of Arts requirements but not the then-current Bachelor of Science requirements
will be magna cum laude.)

General thesis guidelines:
The thesis must be neatly typed and formatted. The Graduate School's thesisstyle requirements should be a target for the quality of the format, though not a requirement. The thesis should be grammatically correct and without spelling errors. The thesis must be mathematically correct, and must represent independent work by the student, even though the results need not be original. Subject to the approval of the Undergraduate Coordinator, an article authored solely by the student may be submitted as the thesis if the article has already been accepted by a standard research journal aimed at experts in a mathematical eld. In all other cases, the thesis should be written at at such a level that it would be understandable to other students who have successfully completed an appropriate undergraduate course. The content of the thesis must adhere to the University's Academic Honesty Guidelines as they appear on the website http://www.dso.ufl.edu/judicial/honestybrochure.htm. Students whose theses fail to meet these general guidelines but who graduate with an upper-division GPA of at least 3.5 GPA will receive a cum laude designation. Students who start working with a faculty mentor early enough in their academic careers are encouraged to apply for the Undergraduate Scholars Program (USP). The application deadline is usually in February, and only students who will
no earlier than spring of the next calendar year are eligible. Each student in the USP receives a stipend over the next summer and fall, as well as some travel money. The same project may serve simultaneously for the student's thesiswork and Undergraduate Scholars project. Information on the USP is available at http://www.scholars.ufl.edu.
1. Students working on an honors thesis may wish to sign up for MAT 4905, Individual Work. The Undergraduate Coordinator, in consultation with the student's supervisor, will decide how many credits to give (1, 2, or 3 in a given semester). However, under no circumstances will Individual Work count towards the math-major requirements; e.g. it cannot substitute for one of the student's four math-major electives. Individual work in general, and honors-thesis work in particular, is done over and above the basic math-major requirements, not in partial ful llment of them.

Length of thesis:
It is up to the student's supervisor to set an appropriate length for the thesis. However, typically, theses are in the 10{20-page range. Theses should not be shorter than this unless they represent new research that happens to be presentable in a shorter format. Expository theses may be longer.

Guidelines for the designation magna cum laude:
For a magna designation, an undergraduate thesis need not be a standard researchjournal- style mathematics paper, or work that could be rewritten as such a paper. Listed below are some acceptable general categories into which the thesis may fall. Other categories are possible, but the supervisor should confer with the Undergraduate Coordinator (who, in turn, may wish to confer with the Undergraduate Committee) before directing the student into a category not listed below. Among the categories into which the thesis may fall are:

1. Proof. The student should independently arrive at and write up the proof of a theorem. The result need not be entirely original, but the work is expected to be beyond normal course work. For example, the student might ll in the gaps of a proof in the literature.

2. Applied-mathematics model. The student should provide more than a routine solution of a system of equations intended to model a real-world problem. There should also be an argument for the appropriateness of the model to the problem and some analysis of the role of the problem's parameters.

3. Data analysis. The student should demonstrate more than an elementary application of statistical methods. The analysis should be general enough to be transferable to other data-sets that would originate from a similar source or sampling technique.

4. Computer program. The student should correctly program a problem and argue for the correctness of the code. If the program is a computer simulation intended to model a real-world problem there should be an analysis of the behavior of the code for an interesting and broad variety of parameters.

5. History of mathematics. Preferably, the student should read a paper or papers by an original author. The student's writing should show a clear understanding of the basic problem being addressed, the author's approach, the methods available to the author, the impact at the time of the writing and the present, and possibly how the problem would be approached today.

Guidelines for the Designation summa cum laude:

This designation is reserved for only a few excellent students who show genuine promise as mathematicians (and, starting fall 2005, who meet the then-current requirements for a Bachelor of Science in Mathematics). The thesis should display originality in the solution of an acknowledged open problem, provide a proof of a new result, or provide a new proof of a known result. The quality of the work should be exceptional for an undergraduate and should carry the possibility of being published in a peer-reviewed journali.e. one that is refereed by mathematiciansalthough the thesis itself need not be written in journal-ready form.

Submitting the thesis:

By the deadlines below, the student should hand in one copy of the thesis to the Academic Advising Center, one copy to the student's supervisor, and one copy to the Undergraduate Coordinator (who will maintain an archive of theses so that future students and supervisors can see what has been done in the past).

1. No later than the last day of classes of the semester in which the student is graduating, an unbound copy of the thesis must be turned in at 105 Academic Advising Center, along with a typed thesis-submission form (available under \QuickLinks" at www.honors.ufl.edu).

2. Several weeks before the last day of classes the student should give at least a rst draft of the thesis to the supervisor. For the nal draft of the thesis, the supervisor will set a deadline no later than two or three weeks before the end of classes. Once the supervisor is satis ed, he or she will communicate a recommended honors-designation to the math department's Undergraduate Coordinator, who will set the nal designation. If the student feels he or she deserves a higher designation, he or she may make an appeal to the Undergraduate Coordinator, provided the thesis is handed in early enough (see below).

3. As soon as the student has a draft that the supervisor accepts as nal, but no later than the last day of classes, the student should turn in a copy to the Undergraduate Coordinator. The Undergraduate Coordinator will consider an appeal of the recommended designation only if a nal draft of the thesis is turned in to him or her no later than one week before the end of classes.

THESIS

Thursday, July 3, 2008

Bank Vacant in India

Saturday, June 28, 2008

MATHS THESIS INTRODUCTION

MATHEMATICS THESIS TOPICS

Blog Archive

About Me