How to write a good (maths) Ph.D. thesis
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1 How to write a good (maths) Ph.D. thesis Melina A Freitag Department of Mathematical Sciences University of Bath Postgraduate Away Day 3rd February of 30
2 The purpose of a thesis University regulations (the easy bit) Content and structure (the harder bit) Presentation and writing process Make your life easier - some helpful L A TEX The defense Summary 2 of 30
3 Outline The purpose of a thesis University regulations (the easy bit) Content and structure (the harder bit) Presentation and writing process Make your life easier - some helpful L A TEX The defense Summary 3 of 30
4 University requirements A Ph.D. shall be awarded to a candidate who shall have 1. pursued a programme of study as prescribed under Regulation 16.5(b) 2. presented a thesis on the candidate s advanced study and research which satisfies the Board of Examiners as: making an original and significant contribution to knowledge giving evidence of originality of mind and critical judgement in a particular subject containing material worthy of peer-reviewed publication being satisfactory in its literary and/or technical presentation and structure with a full bibliography and references demonstrating an understanding of the context of the research: this must include, as appropriate for the subject of the thesis, the scientific, engineering, commercial and social contexts 3. and passed a viva voce examination conducted by the examiners on the broader aspects of the field of research in addition to the subject of the thesis... 4 of 30
5 Outline The purpose of a thesis University regulations (the easy bit) Content and structure (the harder bit) Presentation and writing process Make your life easier - some helpful L A TEX The defense Summary 5 of 30
6 University regulations for submitting a Ph.D. thesis For details see 6 of 30
7 University regulations for submitting a Ph.D. thesis For details see Number of copies and submission procedure: about two months before submission - HD1 form. 3 soft bound copies to Graduate Office - HD2 form. hard bound copies and electronic submission to library only after the viva. 6 of 30
8 University regulations for submitting a Ph.D. thesis Paper and layout - double or single sided. 7 of 30
9 University regulations for submitting a Ph.D. thesis Paper and layout - double or single sided. Typeface and spacing - 11pt or 12pt, easy readable font. 7 of 30
10 University regulations for submitting a Ph.D. thesis Paper and layout - double or single sided. Typeface and spacing - 11pt or 12pt, easy readable font. Numbering of pages. 7 of 30
11 University regulations for submitting a Ph.D. thesis Paper and layout - double or single sided. Typeface and spacing - 11pt or 12pt, easy readable font. Numbering of pages. Title page and copyright declaration. 7 of 30
12 University regulations for submitting a Ph.D. thesis Paper and layout - double or single sided. Typeface and spacing - 11pt or 12pt, easy readable font. Numbering of pages. Title page and copyright declaration. Table of contents and abstract/summary. 7 of 30
13 University regulations for submitting a Ph.D. thesis Paper and layout - double or single sided. Typeface and spacing - 11pt or 12pt, easy readable font. Numbering of pages. Title page and copyright declaration. Table of contents and abstract/summary. Follow the University regulations for margin sizes/line spacing/fonts/binding etc. 7 of 30
14 Presentation and style Typical: 1. Title page (listing author, title, department, type of degree, year and month of submission). 2. Declaration that work has not been used in another degree. 3. A copyright statement. 4. A list of notation. 5. A brief statement of author s research career. 6. Acknowledgements and dedications. 7. Table of contents. 8. List of Figures. 9. List of Tables. 10. Abstract/Summary. 8 of 30
15 Presentation and style Typical: 1. Title page (listing author, title, department, type of degree, year and month of submission). 2. Declaration that work has not been used in another degree. 3. A copyright statement. 4. A list of notation. 5. A brief statement of author s research career. 6. Acknowledgements and dedications. 7. Table of contents. 8. List of Figures. 9. List of Tables. 10. Abstract/Summary. 11. THE ACTUAL WORK 8 of 30
16 Presentation and style Typical: 1. Title page (listing author, title, department, type of degree, year and month of submission). 2. Declaration that work has not been used in another degree. 3. A copyright statement. 4. A list of notation. 5. A brief statement of author s research career. 6. Acknowledgements and dedications. 7. Table of contents. 8. List of Figures. 9. List of Tables. 10. Abstract/Summary. 11. THE ACTUAL WORK Opening pages: indication which parts have been published. Optional: index. 8 of 30
17 Outline The purpose of a thesis University regulations (the easy bit) Content and structure (the harder bit) Presentation and writing process Make your life easier - some helpful L A TEX The defense Summary 9 of 30
18 Content Self-contained. 10 of 30
19 Content Self-contained. May include more than one topic. 10 of 30
20 Content Self-contained. May include more than one topic. Include more details than a paper. 10 of 30
21 Content Self-contained. May include more than one topic. Include more details than a paper. It is like a book. 10 of 30
22 Content Self-contained. May include more than one topic. Include more details than a paper. It is like a book. No unnecessary material. Most theses are too long. 10 of 30
23 Content Self-contained. May include more than one topic. Include more details than a paper. It is like a book. No unnecessary material. Most theses are too long. Organisation and structure is important. 10 of 30
24 Content Self-contained. May include more than one topic. Include more details than a paper. It is like a book. No unnecessary material. Most theses are too long. Organisation and structure is important. Who are you writing for? (your supervisor(s), internal and external examiner) 10 of 30
25 Plagiarism - DONT! If you copy text put it in quotation marks and cite the source. Do not copy proofs of theorems unless it is really necessary for the thesis. Your examiners will be particularly alert to plagiarism. 11 of 30
26 Grammar, Spelling, Punctuation - DO! Use spell checkers! Ask a friend/fellow student or family member to read through parts of your thesis. 12 of 30
27 Structure Clear communication of original ideas is most important! 13 of 30
28 Structure Clear communication of original ideas is most important! Do not waffle! 13 of 30
29 Structure Tell a story (Explain to someone (a mathematician) in 2-3 minutes what your thesis is about). 14 of 30
30 Structure Tell a story (Explain to someone (a mathematician) in 2-3 minutes what your thesis is about). Give talks to practice your communication skills! Great speakers are usually great writers, too! 14 of 30
31 Structure Tell a story (Explain to someone (a mathematician) in 2-3 minutes what your thesis is about). Give talks to practice your communication skills! Great speakers are usually great writers, too! Make an outline early on. 14 of 30
32 Structure Tell a story (Explain to someone (a mathematician) in 2-3 minutes what your thesis is about). Give talks to practice your communication skills! Great speakers are usually great writers, too! Make an outline early on. First chapter(s): describe the problem clearly; put it into context. 14 of 30
33 Structure Tell a story (Explain to someone (a mathematician) in 2-3 minutes what your thesis is about). Give talks to practice your communication skills! Great speakers are usually great writers, too! Make an outline early on. First chapter(s): describe the problem clearly; put it into context. Demonstrate a sound knowledge of existing work, give a critical survey (Literature review). 14 of 30
34 Structure Tell a story (Explain to someone (a mathematician) in 2-3 minutes what your thesis is about). Give talks to practice your communication skills! Great speakers are usually great writers, too! Make an outline early on. First chapter(s): describe the problem clearly; put it into context. Demonstrate a sound knowledge of existing work, give a critical survey (Literature review). What is new/original in your thesis? This should be the main part of your thesis (3-4 Chapters). 14 of 30
35 Structure Tell a story (Explain to someone (a mathematician) in 2-3 minutes what your thesis is about). Give talks to practice your communication skills! Great speakers are usually great writers, too! Make an outline early on. First chapter(s): describe the problem clearly; put it into context. Demonstrate a sound knowledge of existing work, give a critical survey (Literature review). What is new/original in your thesis? This should be the main part of your thesis (3-4 Chapters). For computational projects, normally a comparison with other methods is required. 14 of 30
36 Structure Tell a story (Explain to someone (a mathematician) in 2-3 minutes what your thesis is about). Give talks to practice your communication skills! Great speakers are usually great writers, too! Make an outline early on. First chapter(s): describe the problem clearly; put it into context. Demonstrate a sound knowledge of existing work, give a critical survey (Literature review). What is new/original in your thesis? This should be the main part of your thesis (3-4 Chapters). For computational projects, normally a comparison with other methods is required. Conclusions: What have you done? Identify future research directions/open problems. 14 of 30
37 Structure (more detailed) Introduction Define what your research is about; justify why it is important; explain your thesis structure. 15 of 30
38 Structure (more detailed) Introduction Define what your research is about; justify why it is important; explain your thesis structure. Background/Literature Review Put your research into context; give literature. 15 of 30
39 Structure (more detailed) Introduction Define what your research is about; justify why it is important; explain your thesis structure. Background/Literature Review Put your research into context; give literature. Methods Explain methods; theoretical approaches. Analysis/Results This will include your results. Experiments. Comparison to other methods. Proofs of theorems. 15 of 30
40 Structure (more detailed) Introduction Define what your research is about; justify why it is important; explain your thesis structure. Background/Literature Review Put your research into context; give literature. Methods Explain methods; theoretical approaches. Analysis/Results This will include your results. Experiments. Comparison to other methods. Proofs of theorems. Interpretation/Discussion Justify your interpretations. Put them into context. 15 of 30
41 Structure (more detailed) Introduction Define what your research is about; justify why it is important; explain your thesis structure. Background/Literature Review Put your research into context; give literature. Methods Explain methods; theoretical approaches. Analysis/Results This will include your results. Experiments. Comparison to other methods. Proofs of theorems. Interpretation/Discussion Justify your interpretations. Put them into context. Conclusions Short conclusion. Future research. 15 of 30
42 Outline The purpose of a thesis University regulations (the easy bit) Content and structure (the harder bit) Presentation and writing process Make your life easier - some helpful L A TEX The defense Summary 16 of 30
43 Presentation and style Make your thesis clear and enjoyable to read! You do not want the reader to get angry or bored or both. 17 of 30
44 Writing Process - The iterative process Start as early as possible. 18 of 30
45 Writing Process - The iterative process Start as early as possible. You can begin to draft the first chapters in your early months, when you start to become familiar with the problem - writing also helps to understand! 18 of 30
46 Writing Process - The iterative process Start as early as possible. You can begin to draft the first chapters in your early months, when you start to become familiar with the problem - writing also helps to understand! Publish papers during your time as a graduate student - so you just have to edit them and put them together. 18 of 30
47 Writing Process - The iterative process Start as early as possible. You can begin to draft the first chapters in your early months, when you start to become familiar with the problem - writing also helps to understand! Publish papers during your time as a graduate student - so you just have to edit them and put them together. Use early reports (6 month/12 month) - of course they will probably be rewritten, but it is better to start with something rather than an empty page. 18 of 30
48 Writing Process - The iterative process Start as early as possible. You can begin to draft the first chapters in your early months, when you start to become familiar with the problem - writing also helps to understand! Publish papers during your time as a graduate student - so you just have to edit them and put them together. Use early reports (6 month/12 month) - of course they will probably be rewritten, but it is better to start with something rather than an empty page. Write background and survey material at an early stage - it keeps you enthusiastic! 18 of 30
49 Writing Process - The iterative process Start as early as possible. You can begin to draft the first chapters in your early months, when you start to become familiar with the problem - writing also helps to understand! Publish papers during your time as a graduate student - so you just have to edit them and put them together. Use early reports (6 month/12 month) - of course they will probably be rewritten, but it is better to start with something rather than an empty page. Write background and survey material at an early stage - it keeps you enthusiastic! A sooner rather than later writing also helps you to become familiar with L A TEX. 18 of 30
50 Writing Process If you have not written up as you go along - plan at least 6 months for writing up. 19 of 30
51 Writing Process If you have not written up as you go along - plan at least 6 months for writing up. Make a timetable. 19 of 30
52 Writing Process If you have not written up as you go along - plan at least 6 months for writing up. Make a timetable. What have you done? What do you still need to do? 19 of 30
53 Writing Process If you have not written up as you go along - plan at least 6 months for writing up. Make a timetable. What have you done? What do you still need to do? Fill in the gaps. 19 of 30
54 Writing Process If you have not written up as you go along - plan at least 6 months for writing up. Make a timetable. What have you done? What do you still need to do? Fill in the gaps. Thoroughly read and check before submission - have as many people read it as possible. 19 of 30
55 Writing Process 20 of 30
56 Hints and tips for writing Try to analyse the work of writers/researchers you like. 21 of 30
57 Hints and tips for writing Try to analyse the work of writers/researchers you like. Read a lot of books, maths books, maths theses, maths papers. 21 of 30
58 Hints and tips for writing Try to analyse the work of writers/researchers you like. Read a lot of books, maths books, maths theses, maths papers. Keep a notebook of ideas. 21 of 30
59 Hints and tips for writing Try to analyse the work of writers/researchers you like. Read a lot of books, maths books, maths theses, maths papers. Keep a notebook of ideas. Be constructively critical (but positive) of your own work. 21 of 30
60 Hints and tips for writing Try to analyse the work of writers/researchers you like. Read a lot of books, maths books, maths theses, maths papers. Keep a notebook of ideas. Be constructively critical (but positive) of your own work. Set yourself short term targets. 21 of 30
61 Hints and tips for writing Try to analyse the work of writers/researchers you like. Read a lot of books, maths books, maths theses, maths papers. Keep a notebook of ideas. Be constructively critical (but positive) of your own work. Set yourself short term targets. Keep what you have written for a couple of weeks and then re-read it. 21 of 30
62 Outline The purpose of a thesis University regulations (the easy bit) Content and structure (the harder bit) Presentation and writing process Make your life easier - some helpful L A TEX The defense Summary 22 of 30
63 Packages L A TEX and text editors 23 of 30
64 Packages L A TEX and text editors baththesis.sty 23 of 30
65 Packages L A TEX and text editors baththesis.sty MakeIndex 23 of 30
66 Packages L A TEX and text editors baththesis.sty MakeIndex BibTEX 23 of 30
67 Templates A useful template for writing a thesis which follows the University of Bath regulations: Feel free to download the template and change it to use it for your own thesis. It follows all the necessary University of Bath requirements. 24 of 30
68 BibTEX collect your references for your bibliography at an early stage of your studies - it will be difficult to hunt them down later. 25 of 30
69 BibTEX collect your references for your bibliography at an early stage of your studies - it will be difficult to hunt them down later. BibTEX - a wonderful L A TEXprogram for collecting references in.bib files which then can be used in L A TEX. 25 of 30
70 BibTEX collect your references for your bibliography at an early stage of your studies - it will be difficult to hunt them down later. BibTEX - a wonderful L A TEXprogram for collecting references in.bib files which then can be used in L A TEX. MathSciNet, Google Scholar, CiteSeer, Mendeley and others. 25 of 30
71 Outline The purpose of a thesis University regulations (the easy bit) Content and structure (the harder bit) Presentation and writing process Make your life easier - some helpful L A TEX The defense Summary 26 of 30
72 The Viva In the UK: normally you are asked questions. Possibly: short talk. Read your thesis. Opportunity to tell interested people about your research. 27 of 30
73 Outline The purpose of a thesis University regulations (the easy bit) Content and structure (the harder bit) Presentation and writing process Make your life easier - some helpful L A TEX The defense Summary 28 of 30
74 Summary/Homework Your thesis should tell a story (try it!). Think about some good maths papers/books you have read, what were they doing well? Start as early as possible. Use baththesis.sty early on. Have a general structure (chapter titles/outline) in place early on. Make a timetable (set short term targets). (Re)-read your thesis as often as you can. Be positive. 29 of 30
75 Know your work cycle! 30 of 30
76 N. J. Higham, Handbook of writing for the mathematical sciences, Society for Industrial Mathematics, D. Knuth, T. Larrabee, and P. Roberts, Mathematical writing, no. 1193, Mathematical Assn of Amer, S. Krantz, A primer of mathematical writing: Being a disquisition on having your ideas recorded, typeset, published, read and appreciated, Amer Mathematical Society, Questions? 30 of 30
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