Exam 1

Exam rules

The exam is modeled on https://mathinthetimeofcorona.wordpress.com/2020/06/11/june-11-day-95-finals-part-ii/.

You can use all available resources to prepare, including but not limited to: each other, books, notes, the internet. During the exam, however, please use only a single 8.5x11 sheet of notes. Your true/false questions for question 1 don’t count toward the sheet of notes (you can have a sheet of notes in addition to your true/false questions).

You will have 20 minutes to present two questions. The first question will be your choice and the second will be mine. You may reject my chosen question for a four point reduction, twice.

At the end of the exam I will ask you for a self-assessment of your performance.

During the exam we will talk in a conversational style. As part of this I will ask you to turn on your microphone and camera.

Please be prepared to present your work, including responding to questions. The following formats are suggested:

Writing on a tablet screen using a stylus
Writing on paper with a document camera
Writing on a chalkboard or whiteboard

Prepared slides may be part of your presentation, but they are not well suited for responding to questions where your response might involve writing. So even if you include slides, please be prepared to also use one of the above formats. If it will not be possible for you to use any of the above, please let me know in advance.

Questions

Write 5 true/false questions that illustrate a variety of ideas from this course that you might put on this exam if you were teaching the class. Explain the answers and explain why you chose these particular questions. Type your questions. Be prepared to share them onscreen and/or email a pdf to me.
Consider one mathematical idea from the course that you have found beautiful, and explain why it is beautiful to you. Your answer should explain the idea in a way that could be understood by a peer student who is familiar with rings but has not yet taken this class.
Discuss the parallels between algebra in Computational Algebra and algebra that you learned in secondary school (high school). In particular, what strategies work the same way and what do not? Illustrate your discussion with examples.
Choose one interesting proof problem from the text that was not turned in for homework. Describe why you find it interesting. Then either solve it, or find a solution online and work through it, using your own understanding to critique that solution and improve it (be sure to cite your sources).
Discuss how systems of polynomial equations arise in other areas of mathematics or science. Discuss how varieties arise. Explain what kinds of problems can lead to systems of polynomial equations or varieties, and what kinds of systems or varieties can result. Illustrate with examples.
Read section 8.2, about quotient ideals. (You may want to supplement with additional texts or online sources.) Digest, understand, and be able to explain the definition of, and basic facts about, quotient ideals, and what operation they correspond to on varieties.

Grading

Questions will be graded out of 50 points (each) following the rubric on the web page linked above. For convenience part of the rubric is repeated here:

A	50	Well-executed, well-communicated, essentially correct. Minor errors quickly corrected. No nontrivial errors.
B	43	Generally well-executed. Some minor errors not recognized or corrected. Nontrivial errors corrected when identified.
C	38	Adequately executed but numerous or repeated errors (minor and nontrivial) without satisfactory resolution.

Scheduling

You will schedule an online, one-on-one meeting with me for the exam. Meetings will be scheduled for half-hour blocks either from :00 to :30, or :30 to :00 (ie., aligned with hours). Exams are expected to take 20 minutes, not 30; the extra time is for safety, in case of delay or technical difficulties.

Available meeting times are:

Wednesday, October 14	2:00pm-4:00pm
Thursday, October 15	1:00pm-3:00pm
Monday, October 19	2:00pm-4:00pm
Tuesday, October 20	10:30am-11:30am

Please schedule your meeting with me at least 48 hours in advance. If other days or times are needed, please let me know. I will work with you to find a day and time that we can meet.