The extra credit problems (i.e., problems required for the graduate students) are usually more challenging than the regular problems. Therefore, I discourage undergraduate students from doing extra credit problems if they/you have difficulty completing the regular ones. In the latter case, you need to see the instructor for help. In other words, you may do extra credit problems if you are doing well on regular assignments (and possibly finding them too easy), but you should not try doing extra credit problems just to get a few extra points, and especially so if you are struggling with the regular assignments.

In order to have your extra credit problems graded, your regular part for this assignment must be more than 75% correct.

As with the regular homework, you are encouraged to seek help of the instructor with this additional homework. However, since this brings you extra credit, I will only give you a hint, but will not guide you through the entire solution, as I normally would do with a regular homework problem.

When doing an extra credit assignment, you may also work together with a classmate (but see a Clarification two paragraphs below this one). Keep in mind, however, that this will be beneficial to you only if you understand the solution and, most importantly, are able to repeat it on your own. I will check, at my discretion, whether you can do so, by asking you to repeat the solution. If you are unable to clearly explain to me the solution of the extra credit problem you had handed in, this will be considered academic cheating. As such, it will be reported to the UVM Center for Student Conduct. In addition, the first instance of it will result in an appropriate (at my sole discretion) reduction of your final course grade (by between 5% and 7% of the final course grade).  For the second instance, I will recommend to the Center for Student Conduct to give the student an XF for the course. No exceptions will be made from this policy. 

Given the accessibility of Generative AI, which can produce detailed, step-by-step solutions to, probably, any of the assigned problems, you should expect that, as a rule, I will be summonning everyone submitting an extra credit assignment for the first three--five submissions, i.e., until I know you well enough, to check whether you can explain the solution to me on your own. Of course, I can, at my sole discretion, continue doing so on any later submissions as well. Failure to explain the solution to my satisfaction will entail the consequences described in the previous paragraph.

Clarification on how I will handle collaborative work on extra credit problems
   (please note:  This is  different  from the (non-) collaboration policy on the regular problems!)
  You may work with your classmate(s) on a Bonus problem and figure out the entire solution together. (Again: Note that this is diffferent from the policy for regular problems!)
If you have worked as a group, you should just submit one solution and put all your names on it. (Each group member must still submit their regular homework, of course.) Then I will divide the extra credit points by the number of people in the group. This will still add bonus points to your final grade; just fewer of them than if you had done the work all by yourself. If you have collaborated only on a subset of extra credit problems, the above "division rule" will apply only to those Bonus problems on which you declare to have worked together.
Example: John and Mary did one extra credit problem (A) together and, in addition, John did one problem (B) by himself and Mary did two (B and C) by herself. Then:
 - They each submit their separate regular assignments. John also includes the bonus problem B with his, and Mary includes bonus problems B and C, with her regular assignment.
 - One of them (say, John) submits problem A and indicates that he and Mary have worked on it together. Mary should then not submit problem A.
 - Suppose each problem is worth 1 point. Then John gets 0.5+1=1.5, and Mary 0.5+2=2.5, bonus points.
- Note again that both John and Mary must be able to separately explain the solution of problem A to me; failure to do so will entail the consequences stated above in red to both John and Mary.

If several students submit essentially the same solutions that have merely cosmetic differences (at my discretion) and fail to acknowledge collaboration, then for the first time, I will subtract the whole weight of the problem in question (instead of adding part of it) to their scores. This will be done for each bonus problem that they have collaborated on but failed to acknowledge the collaboration.  Please note: Each person in the group is still responsible for being able to clearly explain to me the solution. Failure to do so by even one student in the collaborating group will entail - for everyone in the collaborating group - the consequences described three paragraphs above.
If a submission of merely cosmetically different works occurs for the second time, I will treat this as the 1st instance of academic cheating (see above) for each member of the collaborating group. (I.e., in this case I will not even go to the lengths of checking if any student understood the submitted solutions.) A repeated submission of merely cosmetically different works will be treated as a 2nd instance of academic cheating (see above).

If you are unsure about any of these rules, ask me before submitting your work.