MAST10005 Assignment 1
Semester 1 2023
This assignment consists of 3 pages
Due Date: Wednesday 22 March
Assignments are due in Gradescope at 11:59pm on the due date listed above. Late
assignments are not accepted. Please see the instructions on the page where you accessed
this file for details on submitting your assignment in Gradescope.
Students are encouraged to work together on understanding the problems and their solutions. However, submitted solutions must be prepared individually, in your own words,
and without the aid of others. For example, if you are asked to give an example as part
of your solution, your example should be meaningfully different from anyone you have
worked with on understanding the problems.
If you do not completely understand your submitted solutions, it is possible you are
committing academic misconduct. This is a serious offense.
Please do not upload this assignment paper or any of its questions/solutions to any online
“help” service (e.g., CourseHero, Chegg, etc...). By doing so, you are actively ruining the
learning experience for yourself and future students. In doing so you are more than likely
violating the University’s academic misconduct policy.
PART A
One of the goals of assessments in this course is to help you know how well you are
mastering the concepts presented in lecture and tutorials. The work that you hand in for
assessments is meant to reflect your level of understanding. And so it is important that
the work you hand in fully communicates your mastery of subject concepts.
Download the file called Writing Mathematics Well from the same place you accessed this
file. Read it and write a short typed response (⇡ 150 words) that considers the following
questions:
• Was there anything about the reading you found surprising?
• What other experiences, if any, do you have in mathematics classes where you
were expected to write in full sentences as part of your solutions? Do you find it
difficult to write in mathematics courses?
• How will your approach to crafting your submission for assignments this semester
change, if at all, as a result of having done this reading?
See over for PART B
PART B
Use the boxes below to write up your final draft of the work you are submitting to be
assessed. You will need to scan these pages in order to submit to Gradescope.
Let A = {n 2 N | there exists x 2 N such that n = x2 } and B = {n 2 N | n is odd }
(1) Prove A ✓ Q.
Hint – Your answer should take a similar form to the proof in question 1 on
Tutorial 2. Near the start of your proof you should say something like: Consider
a 2 A. Since a 2 A, then . . . Your proof should be about 5-7 sentences long.
(2) With a few sentences explain how you know the statement B ✓ A is false. In
your justification refer to a particular element of A and/or B, as needed.
(3) Give two examples of elements of the set A \ B. With a sentence or two, briefly
explain how you know your examples are elements of A \ B. In your explanation,
refer to the definition of \ as appropriate.
(4) Express the set A \ B using set-builder notation
Marking Scheme
Part A
• 3/3: Student has written approximately 150 words and shows evidence of having
authentically engaged with the reading.
• 1/3: Student has written very little (<50 words) and has not engaged with the
reading.
Part B
(1)
• +1 Proof is clearly laid out in full sentences
• +1 Logic of proof is fully correct
(2)
• +1 Proof has sufficient detail to convince a fellow student the statement is true
• 2/2: Solution clearly refers to a correct element and uses it to justify why the
statement is false in a few sentences.
• 1/2: Solution does not clearly refer to a correct element or refers to a correct
element but does not use the element to justify why the statement is false.
(3)
(4)
• 1/1: Examples are correct and are justified.
• 2/2: Answer is fully correct.
• 1/2: Idea is correct, but there are errors in notation use.
Calculus 1
After reading “writing mathematics well” I learnt a concise set of rules, that if followed would
allow me to effectively write and communicate my work. I have not had many instances in
which I was expected to write in full sentences as part of my solution. Initially this surprised
me and was challenging, but in time I am confident I will be able to correctly display my
solutions.
This reading helped me by ensuring I knew the correct format for submitting solutions. By
emphasising the target audience and particularly noting instances in which there can be too
much writing it has ensured I make a final solution that can be read clearly and has the
correct formatting. In addition to this, it will give me a chance to easily go back over my
working out and ensure my working out is accurate.