Assignments
On Wednesday (8/23) we'll start working on Worksheet 1. See also Supplement 1.
For Friday (8/25), please prove Propositions 4, 6 and 7 of Worksheet 1.
For Monday (8/28), please read through the additions to Supplement 1 and try to prove the Propositions from class (namely Proposition 6 and 8 from Supplement 1) and then prove Proposition 4 from the worksheet.
For Wednesday (8/30), please revisit your proofs of Propositions 4, 6, and 7 from Worksheet 1, and rewrite them if necessary.
For Friday (9/1), please prove or disprove Conjecture 5 and prove Proposition 8 from Worksheet 1. We'll discuss those and Propositions 6 and 7 on Friday, so revisit the latter is necessary.
For the week of 9/4, please read the new parts on the supplement about the ring R. For Monday (9/11), submit final versions of the proofs of Propositions 3-8 (including Conjecture 5) from Worksheet 1. This will be graded for correctness. As you write this up, pay careful attention to how your proofs also work for R (see Worksheet 1'). In class this week, try to figure out with your classmates how to prove Propositions 9,10 from Worksheet 1 and Conjecture 9' and Proposition 10' from Worksheet 1'---we'll discuss these next Monday.
For Monday (9/18), please prove (or disprove) Propositions/Conjectures 14-18 on Worksheet 2.
For Wednesday (9/27), please submit final drafts of W1:Prop 9,10 and W2:Prop/Conj 14-18.
For Monday (9/25), please prove W2:Prop 19-21.
For Friday (9/29), please prove/disprove W2:Prop/Conj 22-23.
Midterm on Monday Oct 2.
You will be asked to prove 3 or 4 of the statements among Prop/Conj 3-10 and 14-18 on Worksheets 1 and 2.
Solutions to all of these are in the above links.
You will be provided the axioms and the statements of all the propositions from Supplement 1. You may freely quote these, and you may also quote anything you've proven in a previous problem on the midterm (or a lemma you prove in your solution to a midterm problem). You may not quote lemmas proven in class or on the homework.
For Friday (10/6) please prove Lemma 25 and Prop. 26. on Worksheet 3. (Extended until Monday)
For Friday (10/13) please submit final drafts of W3: Prop/Conj 19-23.
For Wednesday (10/18) please submit first drafts of Lemma 30, Prop 31, and Thm 32.
Midterm 2 on Friday Nov. 10.
For Friday (10/27) please submit final drafts of Worksheet 3.
For Monday (10/23), please submit first drafts of Lemma 1 and Prop 2 parts (2),(4),(6) on Worksheet 4.
For Wednesday (10/25), please submit first drafts of Prop 3 on Worksheet 4 (see Supplement 2).
For Monday (10/30), please submit first drafts of Prop 8, Conjs 9(1),(3) and 10(1),(3) on Worksheet 4.
Solutions to Worksheet 3.
For Monday (11/6), please submit final drafts of the statements from Worksheet 4, up through Conj 10.
Solutions to Worksheet 4.
For Wednesday (11/15), please submit first drafts of Props 5,8,9 from Worksheet 5. Please also do Exercises 2,4,7, not to be turned in.
For Friday (11/17), please submit first drafts of Cor/Prop 10, 11 from Worksheet 5. Please also do Exercises 12, not to be turned in.
For Wednesday (11/22), please submit final drafts of Prop/Cor 5,8,9,10,11,15 from Worksheet 5.
Solutions to Worksheet 5.
For Friday (12/1), please submit final drafts of Prop/Lem 34,36,37 from Worksheet 6. You may submit final drafts of Prop 40, 42 as well for extra credit.
For Wednesday (11/29), please submit first drafts of Prop 36 and Lemma 37 from Worksheet 6.