Math 414 Problems, Comments
|
| week 1 : | ||
|
PP's: (Practice problems): Sec. 1.1: 1 a (last 4), b (1st one), 2a, 3a,b, 5
Sec. 1.2: 1, 2a, 3 b, c, 4
, 5, 6 d,f,g
|
||
| week 2: | ||
|
PP's: Sec. 1.3: 1 a,c, 2b, 5a 1.4: 1b,c, 2a,b, 3 b,c, 5 HW1 (Due FRIDAY, next week): 1.1 7c, 1.2 6d, 8 part b only, 1.3 5c, 1.4 1c, 3d (first part). Also complete addition table for field of order 3, explaining why each entry must be what it is. (Called Problem 1 in class).
Completion of proof of multiplication table for field of order 3: Our field has elements 0,1, A. The only entry left to work out was A*A. (I'll use A^{-1} to mean multiplicative inverse to A) First, A*A can not be A since then A^{-1}*(A*A) would be the same as A^{-1}*A. But associaating the left side gives 1*A=A, and the right side gives 1. Since 1 is not A we are done with this case.
Second, A*A can not be 0 since then, A^{-1}*(A*A)= A^{-1}*0 and the left side after associating parenthesis and using the A^{-1}*A=1 sinplifies to A, whereas the right hand side we know by theorem proved in class is 0. SInce 0 is not A we are done with this case. It follows that A*A must be 1.
|
||
| week 3: | ||
|
PP's: 1.5: 2,4,6;
1.7: 4a
|
||
| week 4 (Through 9-18): | ||
|
PP's: 1.7: 2 (find 1-1, onto function), 6a,b, 8 d,e,f, 14, 16 HW2: (Due mon 9-28): 1.4: 12(Assume B is a bounded subset of R), 13; 1.7: 12b, 13, 15; 2.1 8f, 13, 17
|
||
| week 5 (Through 9-25): | ||
|
PP's:2.1: 4,5,6abd, 7bd, 8d, 9e; 2.2: 6 bcd, 7bdf
Test 1 is friday next week.
|
||
| week 6 (Through 10-2 ): | ||
|
Test Friday. 5 questions. Topics up to and including section 2.2.
|
||
| weeks 7 (Through 10-9): | ||
|
PP's: 2.3: 3 c,e,4, 7a, 17a,c 2.4 : 2a,b, 3a,d,f, 7, 10 HW3: (Due friday the 16th) 2.3: 7f, 19; 2.4: 8, 9; 2.6 3
| ||
| week 8, 9 (Through 10-23): | ||
|
Here's a few PP's:
2.7: 1,2,3,6b, 8 3.1: 4,5,7,8, 11, 18 c,d,e, 19 b,c, 23
|
||
| week 10 (Through 10-30): | ||
|
HW (Turn in next monday): 2.6: 10; 2.7: 5; 3.1 8b, 9 b,c; 3.2: 1; Problems A and B below:
Problem A: Prove set F in R is closed if whenever {p_n} converges to p, with each p_n in F, p must also be in F. Problem B: Set S in R is sequentially compact if every sequence inXS S has a subsequence that converges to a point of S. Prove that a subset K of R is compact if and oly if it is sequentially compact. We have a test coming up probably a week from friday. PP's: 3.2: 3,6, 10
|
||
| week 11 (Through Nov. 6): | ||
|
PP's: 4.1: 1ce, 2e, 3acdf, 8cde, 17cegh
Test Monday. 2.3 through 4.1 (of sections we covered)
|
||
| week 12 (Through NOv 13): | ||
|
EXTRA CREDIT: DUE FRIDAY: Redo one test problem (besides number 4) that you did the worst on and turn it in friday with your exam. (I'll give up to half the points that you missed on that problem. e.g., if you got a 1 on problem 6 and you turn in a correct solution that would have been worth 6 on the test, I'll give 2.5 extra points on your test.) Here is the test .
PP's:4.2: 1ab, 2ab, 3, 5, 8a, 9b,15, 16,
17, 26 4.3: 1, 2c, 3bef, 6a
|