Aspect 5 of the marking criteria can be found in the assignment instructions.  This aspect covers correct mathematical typesetting.  All mathematical expressions and symbols should be typeset using an equation editor (in Microsoft Word) or math mode (in LaTeX). 

By ticking a box below, you are indicating that you acknowledge that you should be aiming for this.

You should write a clear and concise explanation for your assignments.

• You should always provide justification or working for any results that you obtain unless these results are trivial.
• When you apply a theorem, state the theorem and make sure you check and state if all conditions of the theorem are satisfied before using it.
• You should avoid giving unnecessary detail or irrelevant information.

Choose the best solution for the following question.

\begin{equation*}\mathbf{u}=\begin{pmatrix}2\\0\\1\end{pmatrix}\, \mbox{and}\, \mathbf{v}=\begin{pmatrix}-3\\1\\0\end{pmatrix}.\end{equation*}

One mistake students sometimes make is the so-called `proof by example'. The proof by example refers to the situation where the statement is validated for some examples or cases rather than validating for the general case. 

Choose the best solution for the question below.

Show that if is a square matrix, then is symmetric.

Before using a theorem or lemma, make sure you (carefully) check that all conditions of the theorem or lemma are actually satisfied.

Problem

Let .  Does there exist such that ? Justify your answer.

Solution

Since is continuous on and differentiable on , by the Mean Value Theorem we have

  for some .

This gives us as . Therefore, there exists such that .

Question: Is the above solution correct?

Consider the following question with different solutions. Choose the best solution from the list below.

"Prove that the product of two odd numbers is also an odd number."

One mistake students sometimes make is the so-called `proof by example'. The proof by example refers to the situation where the statement is validated for some examples or cases rather than validating for the general case.

For the question below, choose the correct solution.

Show that for all .

A common mistake students make when writing proofs is to start with the conclusion (the end) and end with the hypothesis (aka the beginning or the assumptions given in the question). While starting from the conclusion is a common technique to derive a proof in rough working, a formal proof should generally be written by starting with the assumptions and ending with the conclusion.

Consider the following problem and choose all the valid solutions from the options given below.

Prove that if and then for .

You should write a clear and concise explanation for your assignments.

• You should always provide justification or working for any results that you obtain unless these results are trivial.
• When you apply a theorem, state the theorem and make sure you check and state if all conditions of the theorem are satisfied before using it.
• You should avoid giving unnecessary detail or irrelevant information.

Choose the best solution for the following question.

u=(201)andv=(−310).\begin{equation*}\mathbf{u}=\begin{pmatrix}2\\0\\1\end{pmatrix}\, \mbox{and}\, \mathbf{v}=\begin{pmatrix}-3\\1\\0\end{pmatrix}.\end{equation*}

In mathematics, there are two modes of displaying expressions, namely an inline mode and a displayed mode.

• An inline equation refers to an equation that is within a line of text. An equation is placed inline if it is short and involves small symbols.

• A displayed equation refers to an equation which is displayed on its own lines.  Displayed equations are used when we need to label them or when they are hard to read if placed inline or when we want attention from the readers. A displayed equation should be centred, and any punctuation at the end should be inside the mathematical environment (that is, the punctuation should be next to the displayed expression, not on the next line).

• When you align several equations, it is advised that these equations should be centred and aligned along the relations and etc.

Choose the best options from the following choices.

Your arguments should be self-contained. For your written assignment, this means they should be understandable without access to the question.

Choose the best options to make your arguments self-contained.