Writing maths and thinking maths are inseparable.
If you cannot write a proper solution, then you do not have a solution. A solution should be consistent and every step should be fully justified without logical gaps.
When one starts to write mathematics, it is common to write down false statements or even statements that make no sense. Students tend to write down statements that are clearly wrong. This is due to sloppiness and not paying attention. It is not due to lack of understanding.
Apply only definitions of objects and properties, not vague notions.
Have you used all the assumptions? Where?
Have you given a full answer?
Is it logically consistent? (Everything is well defined; every individual expression is correct; legit application of propositions).
Is the logical connection between lines clearly stated? (implication, equivalence,...).
Click here to download a document with the detailed quality control checklist.
Click here to download a list of common mathematical errors.
A good solution includes the following elements:
All notations are clearly defined.
The same notation is not used for different objects.
Assumptions made and theorems used are properly named.
The solution follows a sequence of logical steps, with each step justified based on the previous one, and these justifications are explicitly stated.
The solution is complete, with no logical gaps.
Anyone with the appropriate mathematical background should be able to understand the written solution.