数学证明相关的task

SIT192 – Report
This assessment task is for students to demonstrate their ability to explain a mathematical concept or a mathematical proof. Select a topic from the list of concepts/mathematical proofs detailed below, and prepare your report on that topic.
The goal of this assignment is to put you in place of an expert explaining a technical subject to a general audience (managers, clients, students). Your report should be understandable for a general audience. You can assume reasonable (high-school level) general knowledge of mathematics and other topics, but no specific knowledge about the topic.
The report should be about 5 pages long (and no longer than 51 pages), typeset 2
in 12pt single-spaced font, including at least 1000 words. It may comprise illustra- tions, graphs, diagrams, code samples, or any other visual resource you feel aids understanding your arguments (please ensure that you have created these your- self). You also should include references (at least two) to any external material that you use.
Your report should be organised in a meaningful way and progress in a logical manner. It should contain an introduction where you explain to your audience what you will write about, and how the rest of the report is organised, and a conclusion where you summarise the main message of the report. You are strongly recommended to use headers to help structure your report.
As you are playing the role of the expert, mathematical mistakes are not ac- ceptable and will be penalised heavily.
Some things to check before submitting
• Report and does not exceed 5 pages (if the report exceeds 51 pages, only the 2
first 5 pages will be assessed).
• Report has an introduction that outlines the structure of your report. • Report has a conclusion that summarises the report.
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• Any specific background knowledge is explained (General high school knowl- edge need not be explained)
• Clear signposting is used throughout including section headings and labelled figures.
• Report contains no mathematical errors.
• Report contains reference section
• Check your Turnitin Report. Reports that have a Turnitin Score above 40% are automatically reported (lower scores will be checked and may also be reported)
Choose one topic from the list below for your report.
Question 1
Explain the relationship between congruences and the Euclidean algorithm for finding the greatest common divisor of m and n. Illustrate with an example. Ensure that you provide an explanation of congruences and their properties.
Question 2
Explain the relationship between the notion of induction in mathematics and the notion of recursion in computer science/programming. Illustrate with an example.
Question 3
Explain the different properties (reflexive, symmetric, antisymmetric, transitive) of relations using examples. Each example, should have a different set of properties. Explain why each of the properties may or may not be desirable.
Question 4
Identify and describe a real-world application of counting. Try to pick an ap- plication from your field of study. Make sure you include enough mathematical background to explain the connection.
Question 5
Identify and describe a real-world application of graph theory. Try to pick an application from your field of study. Make sure you include enough mathematical background to explain the connection.
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