I hope you are starting to think more about how you write mathematics than you have before. This should not only happen when doing homeworks for this module, but also homeworks for other modules. For example, you should have now received marked homework from some of those other modules. Did you get comments there relating to how you presented your ideas?
You may have received comments about the following:
Overall, presenting maths well does take effort but the effort will pay off (in better understanding and higher marks).
‘Academic misconduct’ refers to what is informally described as ‘cheating’. You must make sure you understand what is meant by academic misconduct as you can be penalised for academic misconduct even if you do it unintentionally. Ignorance is no defence. The onus is on you to ensure that you have not committed academic misconduct.
The university webpages says that acadmic misconduct means
“any act that compromises the integrity of the academic process, and/or has the potential to gain an unfair advantage for a student or group of students in a formal university assessment.”
The webpage mentions the following as examples of academic misconduct.
You must read the university webpages.
Academic misconduct in the mini-project
Each year students are penalised for academic misconduct during the projects. In particular, these include the following.
Plagiarism is, according to the Oxford English Dictionary,
“The practice of taking someone else’s work or ideas and passing them off as one’s own."
(Notice that I’ve referenced the source!)
Even if you don’t intend to mislead, including work that was originally written by someone else without explicitly saying so counts as plagiarism.
In order to avoid plagiarism (and subsequent penalties) you must do two things.
Avoid direct copying of words from elsewhere (unless you use quotaton marks).
Cite every source that you use.
An excerpt from the “Fermat’s Last Theorem” [Wikipedia]
“In number theory, Fermat’s Last Theorem (sometimes called Fermat’s conjecture, especially in older texts) states that no three positive integers , , and can satisfy the equation for any integer value of greater than two.[1em] “This theorem was first conjectured by Pierre de Fermat in 1637 in the margin of a copy of Arithmetica where he claimed he had a proof that was too large to fit in the margin. The first successful proof was released in 1994 by Andrew Wiles, and formally published in 1995, after 358 years of effort by mathematicians.”
Fermat’s Last Theorem (sometimes called Fermat’s conjecture) is a result of number theory which states that there are no positive integers , , and which satisfy the equation if is an integer greater than two.[1em]
Pierre de Fermat conjectured this result in 1637. He claimed he had a proof that was too large to fit in the margin of a copy of Arithmetica, where he had written the conjecture. After 358 years of effort by mathematicians, it was sealed by Andrew Wiles, who formally published a proof 1995.
This is plagiarism! The highlighted pieces are taken, almost word perfect, from the original. It doesn’t help that the ordering of the phrases has been changed, or that some sentences are slightly different. The overall tone and meaning is the same.
Fermat’s Last Theorem is a result of number theory. It states that, given a positive integer greater than two, there are no positive integers , , and which satisfy . In older books, it is sometimes referred to as Fermat’s conjecture.[1em]
Originally stated, but not proved, by Pierre de Fermat in 1637, Andrew Wiles formally published a proof 1995, some 358 years later. Interestingly, Fermat claimed he had a proof, but that it was too large to fit in the margin of the book where he had written his conjecture.
This still plagiarism!
The two paragraphs still contain exactly the same information as in the original case, and some of the same phrases are still there.
Almost always, the key idea is to use more than one source.
You need to become something of an expert on the subject first then write an account based on your knowledge.
You must avoid phrases that appear elsewhere, unless they appear in quotes or are standard constructions.
It is best if you write your account without the sources infront of you, but just your notes.
In 1637, Pierre de Fermat wrote in the margin of a book “It is impossible to separate a cube into two cubes, or a fourth power into two fourth powers, or in general, any power higher than the second, into two like powers. I have discovered a truly marvellous proof of this, which this margin is too narrow to contain” [1]. In other words, it is impossible to find integers , and satisfying whenever is an integer greater than 2. This statement has become known as Fermat’s Last Theorem.[1em]
Fermat’s ‘marvelous proof’ was never uncovered and, remarkably, the theorem remained unproved until Andrew Wiles, using techniques of modern number theory, published a rigourous 150-page proof in May 1995 [2].
This is now clearly different. It contains a selection of the facts from the original paragraph, along with information from elsewhere.
Notice, also, that facts are referenced with their sources.
A key part of avoiding unintentional plagiarism is proper referencing of sources.
This is not sufficient to avoid plagiarism, but is certainly necessary.
On a later lab sheet, there will be examples of how to cite sources in LaTeX.
There is much more advice on referencing, plagiarism, and good practice on the University of Wisconsin’s excellent Writer’s Handbook.
Academic intergrity according to the univeristy website is
“a positive commitment to approaching academic work in a way that is honest, fair, respectful and responsible”
Generative AI such as Google Gemini and ChatGPT are serious bullshitters and serious plagiarisers.
They do not have academic integrity built in to them.
In an academic context they need to be treated with a very cynical eye.
Whilst they can be useful tools, you need to learn about sources and citing and certainly never rely on them.
That is why we do not allow them in this Level 1 module.
Another place you must avoid plagiarism is in your Python code. The internet is helpful for learning to program. There are websites which help people when they are stuck.
It can often be easy for us to recognise Python code which has not been written by a student. We find such code every year.
You are doing a project about the Collatz conjecture.
You visit the Wikipedia page (which has lots of information) and base your work on a re-write of a selection of the material found there.
Acceptable?
No!
This project is based on a single source.
You must find more information to base your project on.
You want to write a function which carries out the Newton-Raphson procedure for finding a root.
You search the internet and find a script written in C++ which does the job.
You change the program line-by-line into Python commands and submit it as part of your project.
Acceptable?
No!
Your program is still based on someone else’s work, so counts a plagiarism.
The only way to stop this being an offense is to be completely explicit about where the code originated and what you had done.
You want to calculate the determinant of a matrix in your Python code.
Searching the internet, you find a page explaining that numpy.linalg.det() is the command you need.
You use the command in your script without comment.
Acceptable?
Yes!
This is good use of the internet to develop programming skills.
You want to calculate the determinant of a matrix in your Python code.
Searching the internet, you find a page explaining that numpy.linalg.det() is the command you need.
You can’t get it to work, so post on a forum for advice.
You are shown how to use it, and put the command in your script without comment.
Acceptable?
No, but almost!
You need to be careful here.
Please ask on the course discussion board instead.
Most likely you will know when you are breaking the rules.
Suspicion is unlikely to occur if you are doing things right!
If you have any doubts about what you can and can’t use, you should ask on the Discussion Forum.
In Computer Lab 3 we’ll look at using some of LaTeX’s auto-referencing features, looking at how to create numbered equations, propositions and theorems, and how to refer to them later.
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