Literature review. The goal of the literature review is to give a broad view of the topic on your dissertation and locate your work in the existi

Guide to writing a dissertation

Sara Merino-Aceituno https://saramerinoaceituno.wordpress.com/

This short guide has been specially designed for students in the MSc Financial Math- ematics and MSc Corporate and Financial Risk Management, University of Sussex.

1 Structure and contents of the dissertation

1.1 Structure

The dissertation must contain the following:

• Title (title-page)

• Abstract

• Table of contents

• Table of figures (where applicable)

• Introduction

– Description of the project (questions and objectives)

– Literature review and results

– Contributions/ personal work

– Structure of the document

• Main body

– Data-set: description (if you are using data)

– Methods (specially if you are doing numerics)

– Main results. Analysis of main results and their proofs

• Conclusions o What has been accomplished. Future works. Open questions.

• Appendices (if necessary)

• Bibliography

In the following sections we describe in more detail the content of each one of these parts.

1

1.2 Contents

1.2.1 Abstract

Describe succinctly the topic and goal of the project, the methods used and the results obtained. It should be a short summary of less than a page.

1.2.2 Introduction

The introduction must contain the following parts:

1. Description of the project. In this section include:

• description of the topic of the dissertation; • goals of the project; • motivation, i.e., why is the problem important/relevant (add references to jus-

tify your statements);

• which methodologies/strategies will be used to tackle the problem in consider- ation.

Do not assume that the reader has any previous knowledge on the subject.

2. Literature review. The goal of the literature review is to give a broad view of the topic on your dissertation and locate your work in the existing literature.

• Describe previous works and methods related to your problem, explain how they relate to your work (what do you do new or different with respect to these works? Do you reach new/different conclusions? Did they have different goals/used different methodologies?).

• You do not need to have read all the documents that you reference. You just need to know what they are about and what is their message (this typically amounts to reading the title, abstract and taking a quick look at the introduc- tion and body of the document).

• Don’t just copy-paste a sequence of abstracts: (a) first, it is plagiarism;

(b) second, it shows no critical thinking (no capacity to assimilate new infor- mation, process it, compare it with your own work, and express it in a coherent way);

(c) third, it is impossible for the reader to understand as there is no logical underlying structure in the document.

• Tools: I recommend to use Google Scholar for your search of research papers (and then look at the introduction of relevant papers to find further references). It has also the advantage that it gives you directly the citation.

2

– Don’t just pick the first 10 papers that are listed on Google Scholar, re- member: show critical thinking! Choose which papers are more relevant than others. Go to those papers and look at their introduction as it already should contain a literature review.

• You can get inspired on the introduction of the paper ’Continuum dynamics of the intention field under weakly cohesive social interaction’ by Degond et. al. Beware though! The introduction of a paper is always shorter than a literature review, so take this example just to understand the style, but your literature review should be longer and more detailed.

• Aim to have at least 25 references. If you have less, it typically means that your literature search is poor. But beware!, do not pick just 25 papers just vaguely related to your subject just to get 25 references.

3. Contributions/ personal work. Any paper or report is always a mixture of known things and new things. It is important that you clearly separate which are the new things from the rest, stating them in a clear and concise way. In this section you can add:

(a) What have you produced that is new (e.g., analysis of a particular set of data with a given method; comparison of different methods to analyse a particular data set; developing new code; reaching different conclusions from the existing ones in the literature or reinforcing the existing results;…).

(b) What have you learned (e.g., you have learned a new method that was not explained in class; or you mastered one method explained in class by taking it into practice; or you had to learn a new theory,…).

(c) What have been the challenges of the project (what difficulties did you have to overcome).

State clearly the contributions in the introduction using bullet points and referring to the corresponding sections in the report (i.e., in which section of the document appears that contribution).

4. Structure of the document. Describe clearly the structure of the document: enumer- ate each section of the main body and explain what is covered in that section.

1.2.3 Main body

The main body must contain the following information:

1. Description of the data-set (where applicable).

• Presentation of the data. Do not add large tables of raw data (it will be incomprehensible), represent your data using graphs.

• Critical analysis of the data. Describe the data-set and analyse how com- plete/good/relevant is the data-set in relation to the question that you want to investigate. Would extra data be desirable?, in that case what type of data? May there be biases in the data?…

3

2. Methods. Explain the methods used and the strategy to investigate the ques- tion/problem of your dissertation.

• Show that you understand the advantages and limitations of each method and on which assumptions they are build. Why are they good to analyse the data available and study the question at hand?

• Do not assume previous knowledge by the reader – Derive (shortly) the formulas that you use (specially if not learned at

lectures) or give a reference.

– Give the definition of any mathematical object or tool before using them, even if they are basic (e.g. the definition of VaR, the student-t distribution, etc.).

• State the software and libraries used. Describe the code developed.

3. Main results. The conclusions of your data analysis or investigations must be clearly stated. Do not just write the output of the code, you must make an analysis of the output and explain the results. This critical thinking is crucial. What do the results mean? Which conclusions can be reached? Which is the range of validity of these results? How conclusive are these results and how could they be improved…).

1.2.4 Figures/graphs/tables

If you add a figure/graph/table, it must have an explanatory caption (describing the meaning of the figure) and must be referred in the main text. It must also appear in the list of figures.

Also, make sure that graphs and plot have axes properly labelled and with units. Make sure that they are readable (as sometimes the font may be too small).

1.3 Once again: show critical thinking!

Your capacity for critical thinking is crucial (and what employers look for). You must show critical thinking in the following sections:

• Literature review (selection of relevant papers and comparison between them and your work).

• Analysis of the data set (i.e., how good/ incomplete is the data).

• Methodology/strategy used to investigate the topic of your dissertation (explain your choices, advantages, limitations and assumptions of the methods).

• Analysis of the results (what can be gathered from the graphs and tables that you present and the outcome of your project?).

4

2 Some golden rules

• Writing takes A LOT of time: do not leave it for the last two weeks, start writing immediately, keeping track of your work. Writing and editing do not happen at the same time. You have to polish your text many times to make it good.

• Use a spelling checker.

• All statements must be precise and justified (by references or data).

• Use bold and italics to make important information stand out.

• Plagiarism is a serious offence. Avoid it!

• For coherence and clarity:

– Label each section and refer to it explicitly. Example: In Sec. 3…, do not write ’in the section above’.

– Establish a notation before starting to type. Keep notation coherent and con- sistent. For example, do not use the same symbol for two different concepts. Or two different symbols for the same concept.

– Define immediately every new symbol/notation that you introduce. Or, in other words, you should not write a formula containing unexplained symbols.

– Always refer to which equation you are talking about: do not write ’on the right hand side of the equation we have…’ or ’we encounter this kind of equation’; write instead ’on the right hand side of Eq. (4) we have…’, ’we encounter equations of the form (X)’.

• Avoid giving an evaluation of your own work, i.e, things like ’It is remarkable…’, ’It is interesting….’, ’It is ugly…’, ’it proves to be quite significant…’. Write directly WHY it is remarkable/interesting/ugly/significant (without saying that it is, that is for the reader to judge).

• Do not write a reasoning that takes place in your head, sort of ’Now I want to see this…, ok, then this does not seem a bad idea,…., so now I will try to check that’. Structure your text as a sequence of logical steps and always explain where are we heading. Otherwise the text lacks structure, it looks too informal, it becomes messy and you lose the reader. In summary, do not try to write the mental process by which you got to the result. Instead, show the result and justify it directly, concisely and clearly. Do not write the document as if you were doing a transcript of an oral explanation or conversation. Naturally, in your report you will want to add all the failed attempts and paths tried. I suggest that you present the final results obtained immediately and that you present every path tried as a way to justify modeling choices or methodology. For example, you can say that in your model you consider an assumption X because if you consider the assumption Y as an alternative, then something fails; and then you can use your attempt to show why it fails.

5

• Explain always what you are going to do/explain/proof, specially at the beginning of each section. Do not keep the reader guessing.

• Be concise. Re-read your text several times; if you can erase words without changing the meaning of the sentence, erase them. If you can use one word instead of three, make that change. Save space and go to the point.

3 For non-English speakers

Here are some expressions that can be useful:

• To recast an equation into.

• This paper is devoted to

• The starting point of our mathematical analysis is

• Our main result is

• The goal of this paper is to investigate

• XXX is a very challenging and largely open problem (reference)

• The particular framework we are interested in was made popular by . (reference)

• These models have been widely studied since… (reference)

• Our focus will be on…

• This function/equation/model is introduced in (reference)

• Before going further, a discussion seems in order concerning…

• This is of course not surprising since…

• (A given statement) is still very much under debate.

• It is important to stress that

• XXX serves as our starting point of our rigorous study.

• (A given mathematical expression) leads to… Ex: the kinetic equation leads to a free transport equation.

• A complete review of this subject/discussion is beyond the scope of this paper, and we refer the interested reader to (references).

• There is also an important literature devoted to…

• The approach in (reference) is…

6

• Going back to the subject of the present paper…

• Our work is greatly indebted to… (reference)

• (A fact) indicates…

• This paper is organized as follows: in Section

• We will not attempt here to derive/proof/show…

• We recall the results from/ the following result…

• The properties of XXX will be further investigated in section XXX

• Recalling that (such and such property), we write/conclude/deduce…

• We drop a term (not ignore or neglect)

• The fact that (statement) will need to be addressed very carefully in the rigorous proof.

• XXX plays a significant role because…

• (Some methodology or proofs) is fairly classical.

• The main difficulty here is…

• More precisely… / To be more precise…

• (Such and such property) gives rise to (the following conclusions or equation).

• We note that… (some property or fact).

• To lack a property or feature (not to miss it).

• To prove that XXX, we need to…

• The claim follows from…

• By Proposition XX, we have that…

• We have thus showed that…

• We can thus improved (expression XXX) as follows:

• We deduce/ consequently / this last expression is consequence of…/ which implies / implying / (property XXX) follows / so XXX holds / Using the fact that XXX, we have YYY

• We refer to (References) for further details on (something in particular).

• We establish (some results)

7

• The main tool in deriving XXX is…

• Proceeding similarly we have…

• (Property XXX) relies on the following (lemma/proposition/bound)

• In order to establish (expression XXX), we…

• We need to show that…

8