Students need good role models for writing mathematics. This is a reason for the complete write-ups of solutions to many examples, since most additional situations do not provide students with any models for solutions to the standard problems. This is bad. Even worse, lacking full solutions written by a practiced hand, inferior and regressive solutions may propagate. I do not always insist that students give solutions in the style I wish, but it is very desirable to provide beginners with good examples. - Paul Garrett.
In the setting of the Open University this means that you should copy your TMA answers as much as you can from the 'Solutions to the exercises' section in the booklets. That's how the model solutions look like and that's what your tutor likes to see. - I have given perfect answers -not- in the style of a booklet which made the tutor rather nervous because it was not what she -expected-. Play along.
( Taking an advanced course like M336 requires -revision-. It is adviced to do this with the M208 materials, which is probably the best from the viewpoint of the M336 course. But if you are really interested in Algebra you should read the books as well. I suggest reading the following answers on Stack Exchange if you want advice on algebra books:
- Good abstract algebra books for self study
- Requesting abstract algebra book recommendations
Visit the course forums but there is much more:
- Social media for mathematicians )