Number theory I.c - Combinatorial number theory

Each problem on a homework assignment is graded out of 8 points against two criteria: mathematical correctness (worth 5 points) and proof-writing quality (worth 3 points). These points will be given according to the following rubric:

Mathematical correctness (5 points)

Factors affecting this criterion include: assumptions made, accuracy, appropriate use of definitions and results, correctness of logical reasoning, and the degree to which the solution reaches the desired conclusion(s). Representative descriptions of solutions at the 5-, 3-, 1-, and 0- point levels are as follows:

• 5 points. Solution is correct and complete. Relevant definitions and results are applied accurately, irrelevant definitions and results are not invoked, logical reasoning is evident and valid, and the correct answer is reached.
• 3 points. Solution is only partially correct or partially complete. Relevant definitions and results are invoked, but may be incorrectly applied or inaccurately recalled. Logical reasoning is broadly valid, but may contain some gaps. Progress towards the correct answer is significant.
• 1 point. A serious attempt has been made but progress is limited. Relevant definitions or results may have been recalled, but there is not much success in their application. Logic used is questionable. Progress towards the correct answer is evident but not significant.
•  0 points. Reserved for answers where no progress towards the above mentioned criteria has been made.
  

Solutions may receive 4 or 2 points if they fit between two of these descriptions.

Proof-writing quality (3 points)

Factors affecting this criterion include: clarity of writing, neatness of presentation, accuracy of use of mathematical notation and terminology, level of detail provided, and logical flow. Representative descriptions of answers at the 3-, 2-, 1-, and 0-point levels are as follows.

• 3 points. Solution is neatly and logically structured and is easy to read. Notation and terminology are used accurately, and variables are appropriately quantified. Enough detail is provided that another student in the course would feel satisfied that the solution is correct without having to ask `why?' at any stage.
• 2 points. Solution is neatly presented and is easy to read overall, but contains instances where it would be difficult for another student in the course to understand, either because of a few inaccuracies in notation or terminology, or because insufficient explanation of logical reasoning is provided.
• 1 point. Solution is messy (but legible) or is difficult (but not impossible) to follow. Frequent errors are made with notation and terminology. Logical reasoning is rarely made explicit or is difficult to extract; another student in the course would struggle to understand the solution.
• 0 points. Reserved for answers where no progress towards the above mentioned criteria has been made.