How to Write a University Maths Assignment

At university, getting the right answer is only part of a maths assignment. Markers also want clear reasoning, correct notation and solutions that another student could follow without your help. This guide shows you how to plan, write and polish an assignment, with a model solution that demonstrates the standard markers expect.

Understand What Is Being Asked

Before writing anything, read the whole assignment carefully.

• Note the command words. "Show that" means prove a given result; "find" means calculate; "prove" requires a rigorous argument; "hence" means use the previous part.
• Check the marks for each part. A 2-mark part needs a short answer; a 10-mark part needs full working.
• Read the submission rules: deadline, format (handwritten scan, PDF, LaTeX), page limits and any collaboration policy.
• Note which lecture topics apply. Assignments usually test the methods from recent lectures.

Plan Before You Write

1. Attempt every question in rough first. Use scrap paper and do not worry about neatness yet.
2. Identify the hard questions early, so you have time to think, revisit lecture notes or ask for help in office hours.
3. Check each rough solution before writing the final version. Substitute answers back, test special cases, and make sure every step is justified.
4. Leave at least a day between your rough work and your final write-up. Fresh eyes catch errors.

A good rule: start on the day the assignment is released, even if you only read the questions. Your brain will keep working on them in the background.

Structure Each Solution Clearly

A strong solution has four parts:

1. Restate or label the question, e.g. "Question 2(b)".
2. State your approach: "We use the ratio test" or "We argue by contradiction."
3. Present the working in logical order, one step per line, with brief words connecting the steps.
4. State the conclusion clearly, and box or highlight the final answer.

Use words, not just symbols. Phrases such as "since", "therefore", "by Theorem 3.1" and "substituting into (1)" turn a list of equations into an argument.

Model Solution 1: A Calculation

Question. Find the eigenvalues of

$$ A = \begin{pmatrix} 4 & 1 \\ 2 & 3 \end{pmatrix}. $$

Solution. The eigenvalues are the roots of the characteristic equation \( \det(A - \lambda I) = 0 \).

We compute

$$ \det(A - \lambda I) = \begin{vmatrix} 4 - \lambda & 1 \\ 2 & 3 - \lambda \end{vmatrix} = (4 - \lambda)(3 - \lambda) - (1)(2). $$

Expanding,

$$ (4 - \lambda)(3 - \lambda) - 2 = 12 - 7\lambda + \lambda^2 - 2 = \lambda^2 - 7\lambda + 10. $$

Setting this equal to zero and factorising,

$$ \lambda^2 - 7\lambda + 10 = (\lambda - 2)(\lambda - 5) = 0. $$

Hence the eigenvalues are \( \lambda = 2 \) and \( \lambda = 5 \).

Check: The sum of the eigenvalues should equal the trace, \( 4 + 3 = 7 \), and their product should equal the determinant, \( 12 - 2 = 10 \). Indeed \( 2 + 5 = 7 \) and \( 2 \times 5 = 10 \).

Including a quick check like this shows the marker you understand the result, not just the procedure.

Model Solution 2: A Proof

Question. Prove that for every positive integer \( n \),

$$ 1 + 2 + \cdots + n = \frac{n(n + 1)}{2}. $$

Solution. We use mathematical induction on \( n \).

Base case. For \( n = 1 \), the left side is 1 and the right side is \( \frac{1 \cdot 2}{2} = 1 \). So the statement holds.

Inductive step. Assume the statement holds for some positive integer \( k \), that is,

$$ 1 + 2 + \cdots + k = \frac{k(k + 1)}{2}. \qquad (1) $$

Adding \( k + 1 \) to both sides of (1),

$$ 1 + 2 + \cdots + k + (k + 1) = \frac{k(k + 1)}{2} + (k + 1) = \frac{k(k + 1) + 2(k + 1)}{2} = \frac{(k + 1)(k + 2)}{2}. $$

This is exactly the statement for \( n = k + 1 \).

Conclusion. By the principle of mathematical induction, the formula holds for every positive integer \( n \). \( \blacksquare \)

Notice the labelled base case, the clearly stated hypothesis, the numbered equation and the explicit conclusion. These are what markers look for.

Presentation and Formatting

• Consider LaTeX. Many university departments prefer typed work, and LaTeX (for example via Overleaf) produces clean equations. Learn the basics early; it pays off throughout your degree.
• If handwriting, write neatly in dark ink, leave space between questions and scan pages in order at good resolution.
• Number your equations when you refer back to them.
• Define your notation: "Let \( f: \mathbb{R} \to \mathbb{R} \) be…".
• Draw diagrams for geometry, vector or graph questions, and label them.

Academic Integrity

Discussing ideas with classmates is often allowed, but the write-up should be your own. Check your university's policy, acknowledge any sources or collaborators where required, and never copy solutions directly. Assignments are practice for exams, so understanding the work matters more than submitting it perfectly.

Final Checklist Before Submitting

• Have I answered every part of every question?
• Is each step justified, with key theorems named?
• Did I check answers by substitution, special cases or alternative methods?
• Are final answers clearly highlighted, with units where relevant?
• Is my notation consistent and defined?
• Does the file follow the required format, name and deadline?

Key Takeaways

• Read the whole assignment, command words and marking scheme before starting.
• Solve in rough first, check thoroughly, then write a clean final version.
• Structure each solution: label, approach, step-by-step working, clear conclusion.
• Use words to connect steps and state which theorems you use.
• Present neatly, ideally in LaTeX, and follow your university's integrity rules.

If you are stuck on a university maths assignment, Amathify's subject experts and PhD scholars can provide clear, step-by-step solutions and guidance on presentation. Contact us on WhatsApp or use the "Ask a Question" form.