### Computer Mathematics

COMP 8781 Computer Mathematics, Semester 1, 2022
College of Science & Engineering, Flinders University
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Individual Research Project
Due date: Friday 5pm, June 17, 2022 Weighting: 10% (60 marks)
Do not leave this project to the last minute. There is a significant material that needs to be
researched in order to produce an adequate essay. Each student should select one topic from the
list below and get the topic coordinator approval by email not later than on
Friday 5pm, May
27, 2022
. Do not begin your research on a topic until you receive the approval.
1 Research topics
1. Discuss logical paradoxes, how they arise, including the paradox of Epimenides the Cretan,
Jourdain’s card paradox and the barber paradox, and how they are resolved.
2. Describe the principles and use of Fuzzy Logic in selected Artificial Intelligence/Engineering
applications.
3. ”Automated theorem proving” is the task of using computers to mechanically prove theorems. Discuss the goals and applications of automated theorem proving and the progress
made in developing automated theorem provers. Illustrate by using specific examples.
4. Explain the different ways in the
Encyclopedia of Integer Sequences has been useful. Also,
describe a few of the more unusual sequences in this encyclopedia and how they arise.
5. Describe the Rabin public key cryptosystem, explaining how to encrypt and how to decrypt
messages and why it is suitable for use as a public key cryptosystem.
6. Random? or Pseudo-random? When are the numbers of a sequence truly random numbers, and not pseudo-random? What shortcomings have been observed in simulations and
experiments in which pseudo-random numbers have been used? What are the properties
that pseudorandom numbers can have that truly random numbers should not have?
7. Describe the origins of mathematical induction (ordinary and strong). Who were the first
people to use it and to which problems did they apply it? Be specific.
8. Describe the use of mathematical techniques in software reliability models. Identify mathematical concepts and methods used to evaluate software reliability illustrated by selected
examples from concrete applications.
9. Explain how the theory of random graphs can be used in nonconstructive existence proofs
of graphs with certain properties.
10. Describe the history of the Four Color Problem. Was the problem solved?
11. Describe how Euler paths can be used to help determine DNA sequences.
12. Discuss some of the various methodologies used to establish the correctness of programs.
Explain how the ideas and concepts of program correctness can be extended to prove that
operating systems are secure.
13. Describe a variety of different applications of the Fibonacci numbers to the biological and
physical sciences.
14. Quantum computation – elaborate on current status, issues and prognosis. What are the
major difficulties faced by scientists developing quantum computers?
15. Look up the definition of a transcendental number. Explain how to show that such numbers
exist and how such numbers can be constructed. Which famous numbers can be shown to
be transcendental and for which famous numbers it is still unknown whether they are
transcendental?
COMP 8781 Computer Mathematics, Semester 1, 2022
College of Science & Engineering, Flinders University
p
q
rs
t

• •
·
Compu
ter Ma
thema
tics
·
M. Ba
jger
· F
linders
Uni
2 Specification
Your essay should be typed in Word using 11-point font (Times New Roman), single spaced
with 1-inch (2.5cm) margins. The length of the essay should be between 1800 – 2000 words, not
including words in references, diagrams, images, tables or figures. You should include images,
diagrams or tables in your essay to illustrate/emphasize the content whenever possible/relevant.
These will add value to your presentation and attract marks, if used properly. Clearly state the
actual number of words in your document at the end of your essay.
https://students.flinders.edu.au/study-support/slc/online-guides/
writing-resources
and familiarize yourself with the general rules of academic writing. In
particular, you may find useful sections on writing an essay, editing, proofreading, referencing,
paraphrasing and quoting.
2.1 Overall description
You are required to elaborate on one (and only one) of the above research topic using supportive
articles, statistics, respectful researchers opinions etc. The approved research topic becomes
stated in the title. You can assume that the report is intended for an audience with a reasonable
mathematics and computing background (first two years of uni). The intention is to present
and illustrate the key points rather than very technical details. Your project content should
be supported by at least 5 credible resources such as journal/conference articles, books, book
chapters, legitimate opinions accessible online (Wikipedia is NOT one of them but the articles it
refers to may be).
2.2 Citations
If you reference an outside source in your essay you should cite where you found that source (at
least 5 credible references are required in this essay). The appropriate style for citing sources
in this essay is ELSEVIER Reference Format outlined in
https://www.elsevier.com/__data/
promis_misc/apmrformat.pdf
. Make sure that ALL references are cited in the text at least once
(not cited items should not be listed in the ’References’ section). When citing sources adopt style
3 Plagiarism
The project is an individual work. Students who submit similar or surprisingly similar submissions will be suspected of academic dishonesty and subject to the applicable policy. This also
applies to assignments with significant amounts taken from outside sources or with significant
quotes and paraphrases with no source reference. Each student should carefully ensure that the
document is in their own words and any material directly sourced from the work of others, is
properly acknowledged. Paraphrasing does not remove the obligation to cite the source. Sources
of diagrams, tables, images etc. must also be given. The citing of sources gives the document
credibility and establishes that scholarly work has been carried out. Each submission will be
checked for originality by Turnitin software.
4 Assessment
Quality will be the deciding factor. The essay will be marked on content, conformance to the
requirements, and the look and style of the document (document presentation).
COMP 8781 Computer Mathematics, Semester 1, 2022
College of Science & Engineering, Flinders University
p
q
rs
t

• •
·
Compu
ter Ma
thema
tics
·
M. Ba
jger
· F
linders
Uni
1. Document presentation (15 marks) including style, formatting and proofreading.
2. Content (45 marks) including and roughly divided up as
(a) Title page including the author details (full name and FAN) and the date of completion
(b) Introduction (10 marks, up to 400 words)
(c) Body (30 marks, up to 1400 words)
(d) Conclusion (5 marks, about 200 words)
5 Handin
The Asignment Submission Box will open on FLO a week before the deadline. You should upload
your document in pdf format. Late submissions will attract 5% penalty for every day late and
will attract zero marks if late for more than 7 days.