MCS  313:  Abstract Algebra
Fall 2006

 MCS-313 homepage Reading and class schedule Peer review guidelines Prof. Barbara Kaiser Proof checklist Feedback Homework guidelines

Guidelines for Peer Review of Practice Problems

•     When you read a solution to a problem, you need to be both respectful and skeptical.  Keep in mind that the author worked hard on the solution and she believes that it is a correct and well written proof.  Most problems in mathematics have more than one correct solution,  so remember that a solution which is different from the one you found may still be correct.  Since most problems in mathematics have even more incorrect solutions than correct ones, you also need to be very skeptical when you read solutions.  Ask yourself if you really know that each step of the proof is correct, that it follows from the previous ones.  Remember that even very famous mathematicians (Fermat, Minkowski,...) have published incorrect proofs and theorems that just plain aren't true.

• Checking for correctness

•     Check that the author solved the right problem and that he didn't transform it into a different problem that is not equivalent to the original.  Make sure that theorems, definitions, and algorithms are applied correctly.  Watch carefully for assumptions that aren't part of the original problem.  Check the logic.  Many students will assume the conclusion of a theorem in their proofs, they will use an implication backwards, and so on.

• Checking that the solution is well written

•    The problem should be clearly stated, and the order of the solution should be both logical and clear.  The individual steps should be roughly the same size and appropriate to the audience.  The format, handwriting (or fonts), grammar, spelling, sentence structure should enhance the readability of the solution, not obscure it.
Sometimes when   you read a proof,  you are left with a feeling that the proof is really cool and that  you now truly understand the problem.  Furthermore, you think that there couldn't possibly be a better way to proof the theorem.  This is one of the signs of a good proof.  On the other hand, a proof which  is  long, hard, and somewhat circuitous will often leave you with the feeling that there must be a better way to do the problem.  This may be the sign of a not-so-good proof.  (It may also signify that you don't have a good understanding of the underlying mathematics, or that this is just a hard subject...)  Determining when a proof is good is one of the hardest parts of reviewing someone's writing.