MATH100: Introduction to Mathematics
Autumn 2020
Individual Research Report
Due Date: Friday the 8th of May before 5:00 pm (end of Week 8).
Further Notes
• This assignment will count for 6% of your final mark for MATH100.
• This assignment is to be submitted online, via Moodle. You must submit the assignment before the
due date and time.
• Your assignment submission must include your LaTeX code, pdf output, plus any files required for
the compilation of your code. If your code does not compile you will receive zero.
• You must also submit a pdf copy of your team rationale. If you’ve made any adjustments to the
team project or individual IRRs since the first submission, your team rationale should be updated
to reflect this.
Assignments involving your individual research report
• This assignment will be graded by two of your peers.
• In turn, you will grade two research reports from randomly selected students in the subject. The
quality of your grading of the other research reports is itself an assessment task, that will have its
own sheet, worth 4% + 4% due on the 4th of May (end of Week 9).
• Taking this assignment, your peer’s assessment, and tutor feedback, you are to produce a second
final version of your research report together with a reflection on all aspects of the process. This
task is worth 12% total, with 8% on the reflection and 4% on the content of the revised report.
• Overall, this means that your individual research report and assessments directly related to it are
worth
6% + 4% + 4% + 12% = 26%
of your overall grade. This does not include the rationale, the team poster, or the overall reflection
(which are worth another 36% together).
1 Individual Research Report
This assessment is your individual research report. The particular topic and content of your individual
research report is dictated by the Team Rationale assessment task.
2 Format and length
The research report is to be typeset using LaTeX on standard A4 paper. You are to use a 12pt font,
2cm margins, and single-spacing. The minimum length for your report is around 1,000 words or three
typed pages. This is a minimum and it is not expected that many will be this short. You may use
figures or images.
3 Referencing
You are expected to consult a wide variety of resources when researching your report. You are expected
to cite them using the numeric referencing system. You must use at least three respectable sources
in your report.
4 Layout
You are free to use any layout you wish. Below I give a recommended template for the anatomy of
your research report:
Title
Here you can give basic information such as your name and a table of contents.
Abstract
In the abstract you give an executive scientific summary of your report.
Introduction
In the introduction you set the scene for your report, giving context, motivation, and starting to
discuss the big picture themes and ideas.
Notation, Setting and Preliminaries
In this section you set up your conventions and basic mathematics to conduct your narrative. For
example, you might say that x represents a real number, n is a natural number, f : A → B is a
function from A ⊂ R to B ⊂ R and we always assume f to be continuous, and so on. Recall Lecture
2 for information about the types of things expected in this section.
The Body
This section is not called ‘The Body’ and is not just one section. In this part of your report you make
your detailed assertions, you dive into your topic and perform your analysis. This part of your report
is where the hard work is, and it is expected that this take up the majority of your report.
Conclusions and outlook
In this section you finish off your arguments and make conclusions based on what you have discussed.
This section and the report concludes with a perspective to the future.
5 Grading criteria
Every individual research report is different, in terms of topic, math content, and style. This is normal
and expected. To deal with this we give the following broad guidelines on how to grade the individual
research reports. These guidelines are used by your peers to grade your report, and you will use them
to grade the reports of others.
Each section below contains grading cutoffs that you are expected to award. For example, for
Team cohesion, you are expected to award one of 0, 3, 6, 8, or 10 points. However, what if you feel
as though there is more than significant but less than perfect correlation to the rationale? In other
words, you want to award 9 points? Then, you should award 9 points, and give clear justification for
why the given grading cutoffs don’t apply. This does not exclude the standard feedback and justifica-
tion you need to give as well. (See the ‘important’ note below.)
There are a total of 65 points to be awarded for the individual research report.
Important. One of the most crucial things that a good assessment of work contains is feedback
and suggestions on how the assignment could have been improved. When grading, you are expected
to write a short piece of text that gives feedback to the peer that you are grading.
Marking criteria for the peer assessment task. Your grading of two other reports is worth
8% (4% each). To obtain these marks you need to follow the instructions below to the letter and write
useful, constructive feedback for the people you grade.
5.1 Team cohesion
It is crucial that the individual research report align perfectly with the other reports in the team and
with the team topic itself. This is articulated in the team rationale, a copy of which you will be given
when asked to mark other students’ reports. Pin down what was said about this research report in
the rationale and check to see if it lines up.
Check the section of the rationale that discusses what a successful research report looks like and
what they wish to impart upon a reader. Did this hold true when you read the report?
This criteria is worth 10 points.
10 points There is perfect correlation to the rationale, and the rationale has all the required infor-
mation in it.
8 points There is significant correlation to the rationale, and the rationale has almost all the required
information in it.
6 points There is some correlation to the rationale, and the rationale contains a sufficient amount of
information to be able to tell it correlates.
3 points There is minimal correlation to the rationale, or the rationale is missing key information
making it impossible to determine anything more than minimal correlation.
0 points There is no correlation to the rationale.
Note that if the rationale submitted makes it impossible to assess this category (even worse than just
missing key information), you must award 0 points for this category.
5.2 Narrative
One of the most important aspects of a piece of writing is the journey that it takes the reader on.
From the introduction through to the body of the report and the conclusion, the reader is being taken
on a journey. The reader should be able to very clearly understand the point being made from the
beginning to the end, and also be able to understand the purpose of each section and why the sections
are organised the way they are. The report should flow naturally.
This criteria is worth 10 points. Since this section of the criteria is very much about how you feel
about the report as a reader, you need to make a judgement call about how well the author created
a compelling narrative.
10 points The report sets up proper context and contains a compelling narrative that expresses at
least one clear point.
7 points The report contains a narrative with some setting up of context, but is missing detail or
something else (say what it is) that hurts the effectiveness of the narrative.
3 points The report tries to build a narrative but doesn’t quite make it – essential parts of the
narrative are missing, such as a clear flow between sections, at least one clear point, or setting
up context.
0 points The report doesn’t even attempt to build a narrative.
5.3 Clarity of mathematical argumentation
This criteria is the technical part of the report. Here, you want to check that you can understand all
of the scientific/technical points that the report is trying to make. In this section, ’formal arguments’
refers specifically to mathematical proofs, calculations, and reasoning based in established mathemat-
ical principles.
This criteria is worth 15 points.
15 points The report presents all of its arguments perfectly, in a clear understandable manner.
All claims made in the report are properly justified, be it by specific citations or by giving a
mathematical/scientific proof.
12 points There are several formal arguments presented and you can follow their reasoning, as well
as agreeing that their reasoning is accurate.
9 points There are several formal arguments presented and you can follow some of their reasoning,
but some of the reasoning/justification is confusing.
6 points There are only a couple of formal arguments presented and they have minimal or very
confusing justification.
3 points The arguments are either too vague to understand or don’t really have much justification.
0 points There are no mathematical arguments presented.
5.4 Math Level
This criteria is related to how well the individual research report has kept to the following rule: All
students are expected to drill down mathematically into their topic until their maths can’t take them
any further, and then go just one tiny bit further. For reports on high-level maths this might mean
you can expect just some ideas and not full detail. For reports on high-school level or lower maths,
this means I expect full detail and all major ideas properly explained.
This criteria is worth 15 points.
15 points The exact right drilling-down into the maths, and also excellent treatment of that maths,
be it full detail if at high-school level or just a short but coherent introduction if at a higher
level. All relevant aspects of the mathematics are discussed in relation to the topic.
12 points The author drills down to the right level on the topic and makes some effort to engage in
an appropriate discussion about the maths in the report.
9 points The author drills down the right level on the topic but does not make a sufficient attempt
to engage in an appropriate discussion about the maths in the report.
6 points The author makes some attempt to drill down into the maths of the report but doesn’t get
there exactly in terms of getting to relevant maths for the topic or in terms of getting to the
edge of where high-school maths can take you.
3 points The maths in the topic hasn’t been properly discussed.
0 points The maths presented has no apparent link to the topic.
5.5 Compliance and expression
This criteria is to check two things. First, if the submitted assignment follows the formal requirements
of formatting, length, and kinds of files submitted. Second, as a very basic way to reward polished
submitted assignments.
This criteria is worth 10 points.
10 points The assignment meets all requirements, has no grammatical/spelling errors, and sounds
professional and academic.
9 points The assignment meets all requirements and has no grammatical/spelling errors, but lacks
an academic tone.
7 points The assignment meets all requirements, but there are several grammatical/spelling errors.
5 points The assignment meets all requirements and is readable but there is a significant amount of
grammatical/spelling errors.
3 points The assignment meets all requirements, but the amount of grammatical/spelling errors in
the report distract from the reading of it or make it difficult to discern the arguments presented.
0 points The assignment is in violation of any of the requirements (including minimum page/word
expectation, format, type of files submitted, and referencing requirements).
5.6 LaTeX
This criteria is about the LaTeX code and layout of the resultant report. To grade this you must open
the code and take a look. Is it easy to read? Is it easy to see what is going on? Does it look like there
are any errors in the code? Do a sanity check: see if the code would produce the submitted pdf. Are
there parts that could have been done better, for example, the omission of a table or bulleted list?
This criteria is worth 5 points.
5 points The assignment not only looks good with great code, but also includes all appropriate skills
at appropriate places – for example, used aligned display equations, bulleted lists, tables, figures,
packages, and so on, appropriately.
4 points The code and produced document is easy to read and follow.
2 points The code works, but has serious problems in terms of clarity and style (in both the code in
the .tex file and the report layout in the .pdf file).
0 points The code looks like it would not compile or would give errors (be mindful that some compilers
produce errors for too much white space while others ignore this), or it looks as though the code
wouldn’t produce the submitted report.