I taught a course in the US which was designated as "Writing in the Major". Once I got used to the idea, I found it invigorating: both to prepare and to teach.
I've managed to find a copy of the handout that I gave to the students. Unfortunately, I've lost the source file but I'll see what
ps2ascii can do (yes, it was in the days when PDF was too "cutting edge" to use).
I think that the key parts that made it work were the peer review and the detailed rubric.
Project on Fourier Series
The aim of this assignment is to give you practice writing mathematical prose that is both readable
The subject of the project is Fourier series. The central part of the project is to prove Fejer's
Theorem. This theorem deals with the question of uniform convergence of the Fourier series of
a function. The statement of the theorem can be found below, together with some details of the
There are several rounds of revision for this assignment. The first is to give a copy of your
assignment to another student in the class. Part of your grade will be the quality of feedback you
give to your partner in this phase. The papers will be then turned in a first time to me, at which
point comments and suggestions for improvement will be made. After the papers are returned, you
will be required to resubmit edited or rewritten versions. Editing is an integral part of the writing
- Tuesday 11th of May. First draft given to peer in class for review.
- Thursday 13th of May. Comments returned to peer.
- Tuesday 18th of May. Complete first draft due to me.
- Tuesday 25th of May. Assignments returned with comments.
- Tuesday 1st of June. Final rewritten versions due.
Note: When submitting the final version, you must also submit your first draft, your peer review,
your partner's review of your paper, and the tutor's comments on your first draft. Therefore, it is
vital that you keep copies of everything.
2 Parts of the paper
Your paper should consist of the following sections:
An Introduction: an ideal introduction gives a clear, concise, and accurate overview of the
paper, presenting enough information to interest a reader in the rest of the work and persuade
them of its importance without presenting so much that the reader is overwhelmed.
The Proof: an ideal section containing the proof of a major theorem proves the theorem in a
correct, logical way; it provides any information that the reader is unlikely to already know (or
should be reminded of); and is laid out in a manner such that the reader always knows which
step of the proof is being done, how it fits into the whole proof, and its relative importance
in the proof.
An Application: an ideal section about an application explains the application concisely including any context that may be useful for the reader to know; it demonstrates clearly the
relevance of the application to the main topic; and does all this with just enough detail to
convince the reader without so much that the reader is confused.
3 Guidelines for Writing
Your aim should be to make your paper understandable. You should imagine that another student
in the class has asked for your help on this topic.
Use full sentences. The only sentence fragments that are acceptable are headings such as "Theorem" and "Proof". You should not use symbols such as [symbols for therefore, implies, because, and so forth] nor should you use
abbreviations such as "s.t." or "iff". These detract from the clarity. It should be possible for someone with basic mathematical knowledge to read your paper aloud without hesitating over symbols
or poorly constructed sentences.
Different parts of the paper have different purposes and these lead to different styles. In the
first part, the primary aim is to interest a person in your paper, to give them an overview, but not
to burden them with minutiae. In the second part, the aim is to present the theorem and its proof.
In this part, accuracy is paramount but it is not possible to be accurate without being clear. In the
third part - the application - clarity is again foremost.
When proving the theorem, although the proof is in the book you should not regard this as a
copying exercise. The style adopted in the book is not the best style for this type of paper.
[Section 4 was some mathematical background on Fejer's theorem.]
The paper will be graded according to the scheme below. There are five categories: introduction,
proof, application, overall presentation, and review and revision. In each section, there are four
marks available, making a total of twenty. The specifics for each mark are laid out below. This
scale is incremental. That means that to get, say, two marks on the introduction you have to not
only satisfy the criteria laid out for two marks but also the criteria for one mark.
- Introduction is present.
- Aims of the paper are stated. Broad area of mathematics to which material belongs
- Aims of the paper are clearly stated. Concise background information is explained.
Relevance of subject matter is stated.
- A clear, concise, accurate introduction is present.
Proof of Theorem
- Methodological steps have been taken toward proving the result.
- Theorem is correctly proven.
- Relevant definitions are stated. Theorem is proved in a clear way with correct differentiation to the steps.
- A complete, precise, concise and detailed proof is given. Where relevant, especially
elegant or informative steps are highlighted.
- An application of the subject matter is given.
- The application is set in its proper context.
- The relevance of the subject matter to the application has been explained.
- The importance of this work to the application is evaluated.
- Paper is legible with adequate spelling, punctuation, and grammar.
- Paper is neatly and clearly presented with good spelling, punctuation, and grammar.
- Secondary sources are cited correctly.
- Segué between sections is smooth and logical.
Review and Revision
- First draft, peer review, partner's peer review, and tutor's review are present.
- First draft has all sections, peer review comments on all sections of partner's first
draft (even if said section is missing).
- Final version shows improvement in accordance with partner's review, where relevant.
Peer review is conducted according to this rubric. Tutor's recommendations have been
- Peer review gives practical guidelines for improvement in partner's paper.