MATH100: Introduction to Mathematics

Autumn 2021

Individual Research Report

DueDate:Friday the 29^th of April before 11:55 pm (end of Week 8).

FurtherNotes

• This assignment will count for 8%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.
• This assignment is to be submitted online, via Moodle. You must submit the assignment before the due date and time. Your assignment submission must consist of the .pdf file produced by LaTeX (downloaded from Overleaf).

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 (the Research Report Peer Assessment) worth 8% = 4% + 4% due on the 6^th 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 critical reflection addressing aspects of the process. This task is worth 14% total, with 6% on the reflection and 8% on the content of the revised report. It is due on the 20^th of May (end of Week 11).
• Overall, this means that your individual research report and assessments directly related to it are worth

8% + 8% + 14% = 30%

of your overall grade. This does not include the rationale, the team poster, or the overall reflection (which are worth another 50% 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 TeamRationaleassessment 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, whichever is longer. 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 atleastthree respectable sources in your report, and these sources mustbecited.

Note that this is one difference with the MATLAB Report – in the MATLAB Report, we did not use any references.

4. Team cohesion

It is crucial that the individual research report aligns with the other reports in your research team and with the team topic itself. This is articulated in the team rationale. 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 successfulresearch report looks like and what they wish to impart upon a reader. Did this hold true when you read the report?

Team cohesion is notgradedfor the individual research report. It is a component of the grade for your teamprojectwhich is due in Week 13 and worth 20%.

In that task, this criteria is worth 10points. The grading for it is as follows:

10pointsThere is perfect correlation to the rationale, and the rationale has all the required infor- mation in it.

8pointsThere is significant correlation to the rationale, and the rationale has almost all the required information in it.

6pointsThere is some correlation to the rationale, and the rationale contains a sufficient amount of information to be able to tell it correlates.

3pointsThere is minimal correlation to the rationale, or the rationale is missing key information making it impossible to determine anything more than minimal correlation.

0pointsThere 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 0pointsfor this category.

5. Layout

You are free to use sectioning and headings that you prefer. Below we give a recommended template for the anatomy of your research report. The title, abstract, and introduction sections are compulsory. You may use your judgement on keeping the others and adding your own.

Note that there is a template that you can import as a .zip (don’t unzip it) directly into Overleaf here:

https://www.dropbox.com/s/83h9qgd7tt0706n/IRR%20Basic%20Template.zip?dl=0

Of course, you are free to use anything as a template, or just start from scratch. These additional resources are provided only to help you, you are not required to use them.

Title

Your report needs a title! You need to also include your name.

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 optional section you set up your conventions and basic mathematics to conduct your narrative. For example, you might say that xrepresents a real number, nis a natural number, f: A→ Bis a function from A⊂ R to B⊂ R and we always assume fto be continuous, and so on. This is not a compulsory section; you may choose to not include it and move straight from the Introduction to one of your body sections. However, note that all notation must be introduced so if you do not use this section (even if you do perhaps) then you might need to spend quite a bit of time on notation somewhere else in the report.

The Body

This section is not called ‘The Body’ and is not just one section. It should include multiple sections and possibly subsections (maybe even subsubsections…). 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 optional section you finish off your arguments and make conclusions based on what you have discussed. This section concludes with a perspective to the future. Note that even though the section is optional, the report must include both one or more conclusions and an outlook. You might find it more natural at the end of your introduction, which is fine; the important thing is that these elements are included.

5. IRR writing help and Glen’s IRR

The template above is bare-bones and far from a full, valid IRR. Later in the session when we discuss the peer grading task, there will be an example of an IRR to grade. However this example is also not great, since it makes a few deliberate errors, and is not really a true IRR.

Most helpful advice needs to be quite general, but it is also possible (since we have seen many similar mistakes repeated over the years) to get into specifics. We wrote an IRR Writing Help sheet that contains the best bits of this wisdom. Take a look at it here:

https://www.dropbox.com/s/6dypg6ka6n95xm9/IRRInfoSheet2022.pdf?dl=0

In 2021, a democratic process resulted in Glen putting in a restricted amount of time to produce a decent example. Take a look at the lecture recording from 2021 to see its beginning here:

https://www.dropbox.com/s/5jaliuieqmt2zay/GlenDoesAnIRR.mp4?dl=0

You can see me start the resultant IRR in that recording and demo the process of beginning an IRR. The full first draft of that IRR is here (as with other examples, this should be imported into Overleaf as a zip):

https://www.dropbox.com/s/3hp7qsg4lz0oprl/Glen%27s%20New%20Shiny%20IRR.zip?dl=0

The IRR was graded by M100 guru Thalia. Your IRR will be peer graded, and also graded by me. We will be using the same marking criteria. See if you can guess my score for each of the categories, or overall… The process and some other handy tips is documented in a book task on Moodle; jump straight there with this link:

https://moodle.uowplatform.edu.au/mod/book/view.php?id=2503657

If you just want to see Thalia’s anonymous grading report, use this one:

https://www.dropbox.com/s/ge7lbbsmemwhmo6/M100PeerAssessment%20-%20Glen%27s%20report.pdf?dl=0

This is not a typical example, and not representative either, but then again IRRs are intrinsically tied to the author so that is somewhat difficult. That’s why we have info sheets and guides instead of a lot of examples. Hopefully you can take the time to engage with these extra resources and they are helpful.

5. Grading criteria

Every individual research report is different, in terms of topic, math content, and style. This is normal and ex- pected. 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 gradingcutoffs. For example, for Narrative, you are expected to receive one of 0, 3, 7 or 10 points. However, it could be the case that you receive something in-between one of these. For instance, if there is a reasonable narrative, but it doesn’t quite succeed in setting up a proper context, you might receive 5 points. The reasoning behind your grade should be contained within your assignment feedback when you receive your grade. This grading report should give clear justification for your score, including (in this example) why the given grading cutoffs didn’t apply.

There are a total of 50pointsto be awarded for the individual research report.

5. 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 10points. 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.

10pointsThe report sets up proper context and contains a compelling narrative that expresses at least one clear point.

7pointsThe 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.

3pointsThe 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.

0pointsThe report doesn’t even attempt to build a narrative.

5. 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 mathematical principles.

This criteria is worth 15points.

15pointsThe 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 pointsThere are several formal arguments presented and you can follow their reasoning, as well as agreeing that their reasoning is accurate.

9pointsThere are several formal arguments presented and you can follow some of their reasoning, but some of the reasoning/justification is confusing.

6 pointsThere are only a couple of formal arguments presented and they have minimal or very confusing justification.

3pointsThe arguments are either too vague to understand or don’t really have much justification.

0pointsThere are no mathematical arguments presented.

5. 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 15points.

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 pointsThe 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.

9pointsThe 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.

6pointsThe 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.

3points The maths in the topic hasn’t been properly discussed.

0points The maths presented has no apparent link to the topic.

5. Compliance and expression

This criteria is to check two things. First, if the submitted assignment follows the formal requirements of format- ting, length, and kinds of files submitted. Second, as a very basic way to reward polished submitted assignments.

This criteria is worth 10points.

10pointsThe assignment meets all requirements, has no formatting/grammatical/spelling errors, and sounds professional and academic.

9pointsThe assignment meets all requirements and sounds professional and academic, but there are a few minor formatting/grammatical/spelling errors.

7pointsThe assignment meets all requirements but lacks an academic tone, and there are several minor formatting/grammatical/spelling errors.

5 points The assignment meets all requirements and is readable but there is a significant amount of format- ting/grammatical/spelling errors.

3pointsThe assignment meets all requirements, but the amount of formatting/grammatical/spelling errors in the report distract from the reading of it or make it difficult to discern the arguments presented.

0pointsThe assignment is in violation of any of the requirements (including minimum page/word expectation, format, type of files submitted, and referencing requirements).

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