Exams

See the syllabus for general information. In particular:

• You are allowed one sheet of notes; you may write on both sides. No other resources are allowed.
• Problems might resemble CC problems, FP problems, and problems we’ve discuss in class.
• If you are requesting disability-related accommodations, you must have OSD send an official letter well in advance of the exam. We might not be able to accommodate late requests!

Midterm 1 Information

Midterm 1 will cover chapters 0–3. Key ideas covered include: gcds, modular arithmetic, injective/surjective functions, equivalence relations, group axioms and properties, order, and subgroups. Make sure in particular that you understand the switch from multiplicative to additive notation, and that you’re comfortable working with a variety of groups (\(\mathbf{R}^*\), \(U(n)\), \(Z_n\), \(\mathrm{GL}(2, \mathbf{R})\), \(D_n\), …). I won’t ask you about centralizers.

There will be 10 problems (several of which are very short). You will have 50 minutes. This midterm will take place during class.

Midterm 2 Information

Midterm 2 will cover chapters 0–7, with an emphasis on chapters 4–7. Key ideas, in addition to those listed above, include: cyclic groups and their subgroups, permutation groups, isomorphisms, Cayley’s theorem, automorphisms, cosets, and Lagrange’s theorem.

There will be 10 problems (several of which are very short). You will have 50 minutes. This midterm will take place virtually. Details:

• You will be able to access the midterm through Gradescope starting Tuesday 11/15 at noon PT.
• You must submit your midterm through Gradescope within 1 hour and 20 minutes of when you access the exam, or by Wednesday 11/16 at 12:20pm PT, whichever comes first.
• You have 50 minutes to work on the midterm, and 30 minutes to take pictures and get them uploaded. If you’re uploading a single PDF instead of individual images, you must “assign pages” to your submission. Late submissions will not be accepted.
• There will be a “problem” 11 on the midterm, asking you to sign your name to affirm that you stopped working after 50 minutes and that did not use any unauthorized resources (friends, textbook, internet, calculator, …). This “problem” is worth 0 points, but you will receive a 0 on the midterm if this signature is missing! Please don’t miss doing this.
• If these logistics don’t work for you, please reach out to me right away to let me know what constraints you’re working around.

Midterm Corrections

After each midterm, you can do corrections to earn back some points that you missed. The maximum number of points you can earn back is capped at 10% of the total number of points on the midterm. You will earn back 0.5 points for each problem that you “correct,” where “correcting” a problem means writing up thorough responses to all of the following:

1. What specifically was incorrect about your solution?
2. What is the correct solution? (Write it out completely!)
3. What are the key concepts involved in this problem that you didn’t understand at the time of the midterm?
4. What resources did you use to help you get to the correct solution?

You can use any resources you like (textbook, classmates, office hours, …) as long as you acknowledge them (as indicated above), but your responses to all of the questions should ultimately be written up in your own words.

Corrections are due by 8am PT one week after the midterm. Submit your corrections through Gradescope. If you submit a single PDF, make sure to correctly “assign pages” to your submission.

Final Exam Information

The final will cover everything: chapters 0–10. Key ideas, beyond those mentioned in the lists above, include: normal subgroups, factor groups, external products, internal products, homomorphisms, kernels, images, and the first isomorphism theorem. You might find it helpful to review the midterms. You should also expect that roughly half of the exam might involve concepts that were not tested on either midterm.

There will be 18 problems. You will have 120 minutes. The exam will take place virtually. Details:

• You will be able to access the exam through Gradescope starting Monday 12/5 at noon PT.
• You must submit your exam through Gradescope within 165 minutes (2 hrs 45 mins) of when you access the exam, or by Tuesday 12/6 at 2:30pm PT, whichever comes first.
• You have 120 minutes (2 hrs) to work on the exam, and 45 minutes to take pictures and get them uploaded. If you’re uploading a single PDF instead of individual images, you must “assign pages” to your submission. Late submissions will not be accepted.
• The last (ie, 18th) problem on the exam will ask you to sign your name to affirm that you stopped working after 120 minutes and that did not use any unauthorized resources (friends, textbook, internet, calculator, …). This “problem” is worth 0 points, but you will receive a 0 on the exam if this signature is missing! Please don’t miss doing this.
• If these logistics don’t work for you, please reach out to me right away to let me know what constraints you’re working around.

Recall that there won’t be any “corrections” for the final exam.