# Mark scheme for fortnightly homeworks

## Learning outcomes

When you are writing your homeworks, I am looking for evidence that you can:

• construct coherent and mathematically rigorous arguments and proofs.

• communicate mathematical arguments clearly, effectively, and concisely, with no redundancy or ambiguity.

• construct counterexamples to false assertions.

• perform relevant calculations accurately and correctly interpret the results of those calculations.

• accompany your proofs or calculations by explanatory comments or remarks where appropriate.

• demonstrate good judgement about what level of detail to include.

Not all of these will apply to every single question you hand in. "Including a proof" might not really apply if the question is all about calculations. If I feel like I need to see more evidence of some particular learning outcome in a later coursework, I'll let you know.

Assessment in MATH426 will be based on letter grades (A+ to D- and various levels of F). If you're curious about what this means, an A+/A/A- corresponds to a first, a B+/B/B- to a 2:1, a C+/C/C- to a 2:2, a D+ or below to a third or fail (note that if you are a fourth-year taking this module then you need to get at least a C-, or aggregate score of 12, to pass). The precise details of how letter grades are handled can be found in the Part II handbook on p.26.

Questions will be divided into two categories ($\beta$ and $\alpha$ ) according to their approximate difficulty level. Roughly speaking, the more questions you do well, the better your letter grade will be, and to access the higher letter grades you will need to do more of the $\alpha$ questions.

You can submit as many questions as you want, and I'll take them all into account for marking. If you've achieved the required level for a particular grade and then write some extra nonsense for the remaining questions, that won't count against you, so feel free to submit half-baked attempts where you weren't sure what to do next and want feedback.

The reason I am marking this way is because I want you to focus on your mathematical writing and explanation skills, learning to write coherently and correctly, rather than worrying about "ticking boxes".

## Table

The following table is lightly adapted from the university's undergraduate assessment regulations. The take-home message is: the better you can demonstrate you have met the learning outcomes, the better your grade.

To attain a grade like A-, you would need to demonstrate the specified competence level in at least 5 questions, including at least 3 of the $\alpha$ questions. Similar requirements for each band are listed in the final column. The + or - decorations will allow me to make finer distinctions of quality, and reward extra work or quality above and beyond the specified "minimum".

Band Description Questions
A Exemplary range and depth of attainment of intended learning outcomes, secured by discriminating command of a comprehensive range of course material, and by deployment of considered judgement. 5 questions
(incl. at least 3 $\alpha$ )
B Conclusive attainment of virtually all intended learning outcomes, clearly grounded on a close familiarity with a wide range of course material, constructively utilised to reveal appreciable depth of understanding. 4 questions
(incl. at least 2 $\alpha$ )
C Clear attainment of most of the intended learning outcomes, some more securely grasped than others, resting on a circumscribed range of techniques and displaying a variable depth of understanding. 4 questions
D Acceptable attainment of intended learning outcomes, displaying a qualified familiarity with a minimally sufficient range of the course material, and a grasp of the analytical issues and concepts which is generally reasonable, albeit insecure. no minimum
F1 Attainment deficient in respect of specific intended learning outcomes, with mixed evidence as to the depth of knowledge and weak deployment of arguments or deficient manipulations. no minimum
F2 Attainment of intended learning outcomes appreciably deficient in critical respects, lacking secure basis in course material. no minimum
F3 Attainment of intended learning outcomes appreciably deficient in respect of nearly all intended learning outcomes, with irrelevant use of course materials and incomplete and flawed explanation. no minimum
F4 No convincing evidence of attainment of any intended learning outcomes, such treatment of the subject as is in evidence being directionless and fragmentary. no minimum