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Subsection2.2Specifications for Assessing Proofs

In order to receive credit, your proof must meet all of the following criteria.

The first set of criteria relate to the overall logical and communicative structure of the proof. These help to ensure that the reader can understand exactly what is being proven, the approach being used to prove it, the symbols defined and used in that approach, and the source of authority for all logical claims.

These specifications will be referred to as A1, A2, ... , A6 in written feedback.

ObjectivesProof Structure
  1. Accurate statement of problem/claim/theorem is presented before the proof.
  2. Statement of problem/claim/theorem is worded positively (without commands such as "prove that").
  3. The chosen logical form (direct, indirect, induction, cases,...) and strategies of the proof are clearly evident from the writing.
  4. The burden of proof is explicitly stated ("we must show that...") both initially, and each time it is shifted.
  5. All new variables/notation are defined and quantified prior to their first use.
  6. "By-lines" and (where appropriate) citations are used to supply authority for any claim whose provenance would not be immediately obvious to the reader.

The second set of criteria relate to the adherence of the written proof to conventions of style and formatting appropriate in the discipline of mathematics. These are in place to maximize the readability and clarity of the writing, especially how mathematical expressions and equations are integrated into written prose.

These specifications will be referred to as B1, B2, ... , B6 in written feedback.

ObjectivesStyle and Formatting Conventions
  1. All mathematical notation is typeset using font styles and spacing conventional to mathematical writing (alphabetical names in italics; numbers, symbols, and operator names not in italics; operators separated by appropriate whitespace).
  2. Every part of a proof is written as a complete sentence according to the conventions of standard written English, even those that include uses of mathematical notation.
  3. Display-math (centered, alone on a single line) is used appropriately for longer and more significant mathematical expressions/equations.
  4. Boldfaced sectioning is used to mark the function of each main component of an argument (e.g., Theorem:, Proof:, Case 1:, Inductive Step:, etc.).
  5. Ends of proofs are marked with a boldfaced QED or a conclusion symbol such as \(\blacksquare\) (\blacksquare).
  6. Paragraph breaks are used frequently to separate individual components of an argument.