Some writing hints
This is a summary of writing hints. To a certain extent
I have written this as a feedback from the exercises and reports from
previous years. It may help you both with the exercises and when you
write the final report. While I
think it contains many useful points, it obviously cannot be
considered as a
complete set of instructions for creating good explanations and for good
Creating good explanations
This is just as important whether you explain something to yourself, if
you write a short answer to a question, or if you write a long report.
DIFFERENT WAYS TO EXPLAIN
- Text only
- Figure/graph and explanatory
text (always explain a figure!)
- Formula and explanatory text
eg. where the meaning of the
expression is explained (always do this!)
- Explain a general idea with an example. This is also good to
illustrate a general statement.
- All of these can be used together if necessary. A combination of
text, figures, formulas and examples is often the best.
- Itemized lists can be a good tool to highlight several important
items. You can use a numbered list if the order is important.
For each part of your explanation, consider which way to explain is
the best. In particular, do not only use text but
remember to use figures and
formulas when appropriate
CLARITY AND COMPLETENESS
- A description of a concept or
algorithm should be such that
the description is complete, i.e. there should be no room for
alternatives or other interpretations.
- Especially in a mathematical
explanation, definitions, assumptions
and other concepts must be clearly and unambiguously defined
(what is known and
unknown, exactly what
do the variables mean, what exactly do the nodes and edges correpond
what are the reference directions, etc.) This clarity is the most
thing in mathematics, not formatting or mathematical notation.
- An argument in several steps
should be complete and without logical gaps. Every step should
be explained or at least motivated.
- Often it is good with a top-down approach, where principles and
ideas are explained first before the details. If you need, you can omit
details if there is no ambiguity in how these details can be
reconstructed, or if it is explained later.
- Concepts and notation should be defined before or immediately
after they are used.
- Do not introduce unnecessary notation that is not used.
- Hint for finding good explanations: what is the shortest
way I can explain this?
- It is worse to say that a false statement is true, than not
saying anything at all, or to to say that you believe something is
true. Note that this is
not a contradiction to the creative exploration that is necessary in
problem solving, where a lot of possibilites are tried out as
hypotheses (we try them, but do not consider them as true until we have
- Errors in mathematical text are expecially bad since the reader
can easily get lost.
STRUCTURE OF EXPLANATION
- Make sure that the most important parts, concepts etc, are
reflected in the overall structure of the explanation and not buried
in the text. Try to make
that the reader can easily distinguish these important parts. Important
and/or long equations should get their own line.
- It is important that the reader easily can distinguish facts,
and opinions. You may state beliefs and opinions, but then this must be
- Writing good mathematical explanations is not so easy, and
requires a lot of practice and attention to detail.
- You can learn how to explain mathematics from reading a well
written mathematical text. Study
something that is not too complicated that you liked and considered as
well written and easy to understand. However, remember that this
explanation will not tell you much about how it was originally found!
Writing a report
CHOOSING THE CONTENT
- How to do this depends a lot on the topic, the purpose of the
report and the expected reader(s). This is what ultimately determines
a suitable content.
- It is often good to consider a balance between breadth and depth.
- Make a selection based on what you find important.
- It can be good to find a balance between what you consider
important generally, and what
you find interesting yourself.
- The most important factor for readability is the structure all
the way down to the sentence level.
- Carefully structure the document in chapters, subchapters (only
documents), and paragraphs. Do not over-structure in too
short parts. Chapters and one subchapter level is sufficient for most
purposes. Names of chapters should reflect the content.
Try to create a modular structure so that the reader always knows
what the topic of the current chapter/paragraph/sentence is. Minimize
the number of theme changes along the sequential structure of the text,
paragraph by paragraph, sentence by sentence.
Meet the expectation of the reader so that the reader in every
step will read what she expects to read. This applies to all structure
The readability of a given text can often be improved
dramatically only by reshuffling its contents. The
chapter/paragraph/sentence structure and the names of chapters may
need to be changed along the way as the document develops.
Let the content determine the stucture and not vice-versa.
LANGUAGE AND CONVENTIONS
- Make sure that the language is good. About this you can probably
elsewhere. Carefully choose the style (formal/informal) so that it fits
with the topic and intended audience, and be consistent throughout the
- Make sure that the text looks good. Pay attention to details such
spelling, punctuation etc. Actively identify common spelling errors such
as "mattematisk", "jämnvikt", errors in writing words
together or separately, and other difficulties that you may know you have.
A good content can easily be hidden behind a bad or sloppy presentation!
- Use only one paragraph level, where paragraphs are preferably
by and empty line.
- Use "" only for citations.
- New concepts can be highlighed the first time they are used e.g
Links and references