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 in the next page, 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 lay 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 knowl- edge about the subject.
The report should be about 5 pages long, typeset in 12pts single spaced font, including at least 1000 words. It may comprise illustrations, graphs, diagrams, code samples, or any other visual resource you feel helps understanding your arguments. You also should include references (at least two) to external material that you used.
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 talk about, and how the rest of the report will progress, 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 acceptable and will be penalised heavily.
Choose one topic from the list below for your report.
Question 1
Prove the following result: if a = c mod m and b = d mod m then a+b = c+d mod m and ab = cd mod m.
Question 2
Explain the relationship between the notion of induction in mathematics and the notion of recursion in computer science/programming.
Question 3
Explain the different properties of relations by picking at least four (of which two mathematical and two non-mathematical) examples of relations. Each of them should be distinct, and have a different set of properties (reflexive, symmetric, antisymmetric, transitive) to each other. Use these examples to illustrate and discuss the different properties of relation- ships, and why these properties may or may not be desirable.
Question 4
Identify and describe a real-world application of counting. Try to pick an application from your field of study. Provide enough mathematical background.
Question 5
Identify and describe a real-world application of graph theory. Try to pick an application from your field of study. Provide enough mathematical background.