Your
project report should be written as a document that stands on its own. While you may assume your reader has basic
mathematical knowledge, you should not assume that your reader has been
attending our class. Nor should
you assume that your reader knows more
mathematics than you do. A student who
is not in our class should be able to understand what you did (and why) by
reading your paper.
Your
report should consist of the following sections:
A title page, indicating the title of
your report, its author(s), the course name, and the date.
An
introduction,
consisting of a description of the questions to be answered (describe briefly
the problems in your own words, do not just repeat the assignment),
their context and importance, and the mathematical methods you used to answer
the questions. Depending on the
assignment, you may wish to include a summary of your findings in the
introduction.
A body, describing the problems in
mathematical terms and the solutions to those problems. In order to typeset math formulas use
special tools (the best tool is TeX but if you use MS Word you can use the
built-in Equation Editor by selecting Insert | Object | MS Equation).
A conclusion, summarizing the results
obtained from the solutions described in the body. Clearly state the relevance of the results to the original
questions as described in the introduction.
Comment on the significance of the results. Indicate if the problem needs further investigation, and, if so,
the direction future research should take.
Appendices (if
appropriate),
containing computer output (especially computer code) or long data lists that
the reader can skip on a first reading and still follow your exposition.
Your
report grade will be based on the following criteria:
·
Mathematical
computations are correct.
·
Mathematical
variables are clearly defined.
·
Mathematical
formulas and their relevance to the problem are clearly explained.
·
Assumptions
for models and formulas are explained; the models and formulas are used
correctly.
·
Methodology
is explained.
·
Graphs,
diagrams or tables are appropriate for the discussion of the problem at hand.
·
Mathematical
language is used correctly and appropriately.
The report should conform to the following
requirements:
·
The
report is written in the first person plural (e.g., "We observed
that...").
·
Passive
voice, slang, and acronyms should be avoided.
·
The
document is free of spelling, grammatical and punctuation errors.
·
The
body of the report is organized logically.
·
There
are smooth transitions between sections and paragraphs.
·
Mathematics
is embedded in sentences and paragraphs.
·
Graphs,
tables, etc. are included in the body of the report, as appropriate.
·
The
font is fairly standard (Times, Arial, etc.) and its size is at
least 10 pt.
·
Each
page (except the title page) is numbered on the lower right and contains the
authors' names on the lower left. All
pages are stapled (no need for fancy folders).
·
Acknowledgement
is given where it is due. In
particular, you should cite any book you consulted, any student you talk to
(whether in this class or not), any instructor you talk to, and any software
you used to analyze or solve the problem.
Plagiarism is a gross violation of the Honor Code and will not be
tolerated.
·
Conclusions
flow logically from the analysis.
·
The
report exhibits clarity and conciseness.
It avoids wordiness and extraneous details.
·
The
context and relevance of the problem and the solution are clearly explained.
·
The
presentation demonstrates clear understanding of the relationships between the
assumptions, the methodology, the results and the implications of the results.
·
Assumptions
(mathematical and non-mathematical) are explained and justified.
·
The
question(s) are considered with appropriate depth.
·
Subtleties
in the problem(s) or solution(s) are recognized, explored and discussed.
·
If
appropriate, future research directions (including possible generalizations of
the solution or methods) are discussed with demonstrated understanding of the
issues.
Students often wonder, "How much of the computations should I include?" There is no rule set in stone – writing in mathematics (just like most other types of writing) is about communicating ideas. Figuring out how much computational detail will help your reader get your ideas is part of the learning process. You may (and are encouraged to) omit some tedious and obvious computations from your report as long as a reader with basic understanding of mathematics (which, of course, depends on the level of the course) can follow your train of thought. In any case, you should set up the computation and state its results clearly. For instance, a Calculus 1 project may include something like this:
After setting t = 0 in the equation above and simplifying the result, we obtain the quadratic equation x2 – x – 6 = 0. It has two roots, x = – 2 and x = 3, but since x cannot be negative, the only possibility is x = 3.
There
was no need to include the formula for the roots of the quadratic, or to show
how the numbers plug into it – the writer safely assumed that the Calculus 1
reader knows the Precalculus material.
Note, however, that the example above does not apply to a Precalculus
project, where the way you solve the equation is central to your work and you
should include the appropriate (higher) level of detail in your project report.
E. Belogay,
S. Fitchett