Plagiarism is a serious academic offence and could result in suspension of your degree course. Plagiarism consists of submitting other people's work as being your own work. The most blatant form of plagiarism is simply copying from a book, a webpage or another student's coursework/project and passing this work off as your own. Less obvious forms of plagiarism consist of merely rewriting the work of other people or not giving credit for the help of others.
Sharing answers to assessed coursework
Within mathematics plagiarism arises most often by students sharing ideas and solutions to pieces of assessed coursework and then passing it off as their own independent work. Read the four cases below.
Student A borrowed the solutions to a piece of coursework from student B. Student A copied the answers out and submitted them as his/her own work.
Student A was sitting in the library with student B. They were both trying to do the same piece of coursework. The both got stuck on question 2. They discussed how to do the question and worked out an answer together. They then each wrote this answer down and submitted it as their own work.
Student A was sitting in the library with student B. Student B got stuck on some of the questions. They asked student A how to do it. Student A told student B how to do some parts so that some of the answers that B handed in were identical to those that were submitted by A.
Student A was sitting in the library with student B. They were both trying to do the same piece of coursework. They both got stuck on question 2. They looked at their lecture notes and related unassessed classwork. They discussed these, but did not discuss how to do the coursework. They independently attempted question 2.
Which of these would you regard as plagiarism and therefore cheating? In fact, cases 1, 2 and 3 are all unacceptable. While we encourage the discussion of the content of the lectures and unassessed exercise sheets with your fellow students, the coursework forms part of the assessment of your ability and knowledge in the subject. This should not be discussed with your fellow students: you know that it is not acceptable to discuss questions during exams and you should treat coursework in the same way. If you are stuck and need some guidance, the correct person to ask is the lecturer of the course. The safest way to avoid plagiarism of coursework is to avoid all discussion of assessed work with other students until after it has been marked.
Quotations and copying of text
Any material you choose to quote or refer to must be fully referenced and the referencing must be done immediately following the quote. For example, a direct quote should be indicated by quotation marks and a reference:
Devaney claimsWhat is a dynamical system? The answer is quite simple: take a scientific calculator and input any number whatever ...( page 2).
Quoting these sentences with proper referencing as above is not plagiarism. But if you wrote as the opening paragraph of your project:
What is a dynamical system? The answer is quite simple: take a scientific calculator and input any number whatever ... and only in the bibliography (or not at all) listed your source:
-  R Devaney, An Introduction to Chaotic Dynamical Systems, 2nd Edition, Addison-Wesley 1989
then this would be plagiarism. Sometimes it is appropriate to paraphrase a paragraph from a text in your own words. For example, consider the following paragraph on page 50 of :
To summarize, a chaotic map possesses three ingredients: unpredictability, indecomposability, and an element of regularity. A chaotic system is unpredictable because of the sensitive dependence on initial conditions. It cannot be broken down or decomposed into two subsystems (two invariant open subsets) which do not interact under f because of topological transitivity. And, in the midst of this random behaviour, we nevertheless have an element of regularity, namely the periodic points are dense.
Now take a look at the following two paragraphs:
- In summary we see that a chaotic map has three main ingredients: unpredictability, some degree of regularity and indecomposability. Sensitive dependence on initial conditions gives rise to unpredictable orbits. Since periodic points are dense, however, there is a degree of regularity in the system. Finally, the topological transitivity of a chaotic map means that it cannot be broken down into two subsystems which don't interact with each other
- Devaney (, page 50) considers that the three essential characteristics of a chaotic map are unpredictability, indecomposability and some degree of regularity. The time evolution of a chaotic system is unpredictable as the system displays sensitive dependence on initial conditions. Furthermore the topological transitivity of the system implies that it cannot be decomposed into two noninteracting open sets. On the other hand, mingling with this unpredicatable behaviour, there is a degree of regularity since periodic orbits are dense.
Even though paragraph (1) is rewritten to some extent, it will still be plagiarism to pass (1) off as your own work without referencing Devaney. Paragraph (2) is rewritten and refers correctly to the original source of the ideas in the paragraph.
There is often a fine line between what should be reference and what need not be referenced. For example, every time in a mathematical project that you use standard techniques like differentiation you do not need to provide a reference. Certain theorems are so well-known and commonly used that they do not need to be referenced, for example the fundamental theorem of calculus and the mean value theorem. If in doubt ask your project supervisor.
Acknowledgement of Joint Work
In the case of a group assignment it is important that all members of the group contribute approximately equally and if appropriate the different contributions of the group members should be listed on the submitted project. For example one student may have contributed more to the theoretical side of the project, while another concentrated more on numerics. If your individual project (for example, a project on the history of computing) benefitted from discussions with lecturers or fellow students then they should be acknowledged in the text. In this case it may be more appropriate to state at the beginning or end of the project something like,
I would like to thank Dr Devaney for very helpful discussions concerning Deep Thought and Tracey Cameron for help with maple programming.
All books and other sources must be referenced in a bibliography at the end of your project. A typical format for a reference would be
-  R Devaney, An Introduction to Chaotic Dynamical Systems, 2nd Edition, Addison-Wesley 1989.
Once again, any material that is quoted or rewritten from another source must be referenced at that place in your project — a mention in the bibliography is not enough.
The penalty for copying from other sources without proper referencing is that the project/coursework will be awarded zero marks. Repeat offences may result zero marks for the full module or even in termination of your degree programme. See Appendix G of the student handbook or the Academic Misconduct section of the University Calendar for more details.
There are many websites devoted to the subject of plagiarism. Here are some examples: