Difference between revisions of "MA 453 Spring 2009 Walther Homework" - Rhea

Latest revision as of 19:17, 29 April 2009

Week 2-Jan 22 (In[tro]duction, 0): Ch 0: 25, 24, 7, 14, 19, 21

Week 3-Jan 29 (Groups, 1+5): Ch 1: 6, 13. Ch 5: 6,8, 19, 43

Week 4-Feb 5 (Sub-, cyclic, solvable groups, 3+4+32): Ch3: 4,10,11,46,48. Ch4: 9,19,63

Week 5-Feb 12 (Cosets, 6+7): Ch6: 7,22,35(hint: R_90 in D_4). Ch7: 7,10. Question 1 from file

Week 6-Feb 19 (Morphisms, 9+10): Ch9: 7,11. Ch10: 7,24,31,32. Question 2 from file

Week 7-Feb 26 (Products, 8): Ch8: 2,8,28,34,37,52, Question 3 from file.

Week 9-March 12 (Rings, 12+13): Ch12: 2, 20. Ch. 13: 5,6,10,28

Week 10-March 26 (Ideals, 14+15): Ch13: 41,54. Ch14: 6,26. Ch15: 33,54

Week 11-April 2 (Division, 16): Ch16: 12,13,16,22,32,34,49

Week 12-April 9 (UFD's, 17+18): Ch17: 4,6,7,10,21. Question 4 from file

Week 13-April 16 (Fields, 20): Ch20: 1,29,31,5,19,21,25

Week 14-April 23 (Fields, 21): Ch21: 8,14,16,24,33,30

Week 15-Apr 30 (Finite fields, 22)Ch22: 1,2,4,10,30, Question 5 from file

Useful Homework Programs

@@ Line 2: / Line 2: @@
 [[Week 2]]-Jan 22 (In[tro]duction, 0): Ch 0: 25, 24, 7, 14, 19, 21
-Chapter 0: 24, 25, 7, 14, 19, 21
-Due Thursday, January 22
--- It's kind of funny that it starts at chapter 0.  Very CS of Joe!  [[User:eraymond|eraymond]] 13:56, 19 January 2009 (UTC)
+[[Week 3]]-Jan 29 (Groups, 1+5): Ch 1: 6, 13. Ch 5: 6,8, 19, 43
+[[Week 4]]-Feb 5  (Sub-, cyclic, solvable groups, 3+4+32): Ch3: 4,10,11,46,48. Ch4: 9,19,63
-[[Problem 24]]
+[[Week 5]]-Feb 12 (Cosets, 6+7): Ch6: 7,22,35(hint: R_90 in D_4). Ch7: 7,10. Question 1 from file
-*If p is prime and p divides a_1a_2...a_n, prove that p divides a_i for some i
-*In class we proved this for the case where <math>p|ab</math>. I was unable to extend that proof for <math>n</math> factors of <math>a</math>. Anyone figure this out?
-**I updated the page with a [[Problem 24|link]] to the solution. -Nick
-Problem 25
+[[Week 6]]-Feb 19 (Morphisms, 9+10): Ch9: 7,11. Ch10: 7,24,31,32. Question 2 from file
-*Use the Generalized Euclid's Lemma to establish the uniqueness portion of the Fundamental Theorem of Arithmetic
-Problem 7
+[[Week 7]]-Feb 26 (Products, 8): Ch8: 2,8,28,34,37,52, Question 3 from file.
-*Show that if a and b are positive integers, then ab = lcm(a, b) * gcd (a,b)
-*I completed this problem by writing a and b as prime factorizations, with the gcd and lcm having the min and max of their exponents respectively. --[[User:Podarcze|Podarcze]] 15:15, 20 January 2009 (UTC)
-Problem 14
+[[Week 9]]-March 12 (Rings, 12+13): Ch12: 2, 20. Ch. 13: 5,6,10,28
-*Show that 5n + 3  and 7n + 4 are relatively prime for all n
-*You can use Euclid's Algorithm to show that <math>gcd(5n+3,7n+4)=1</math>. Start with <math>(7n+4)=1*(5n+3)+(2n+1)</math> and iterate until the remainder is 0.
-Problem 19
+[[Week 10]]-March 26 (Ideals, 14+15): Ch13: 41,54. Ch14: 6,26. Ch15: 33,54
-*Prove that there are infinitely many primes. (hint: use ex. 18)
-[[Problem 21]]
+[[Week 11]]-April 2 (Division, 16): Ch16: 12,13,16,22,32,34,49
-*For every positive integer n, prove that a set with exactly n elements has exactly 2^n subsets (counting the empty set and the entire set)
+[[Week 12]]-April 9 (UFD's, 17+18): Ch17: 4,6,7,10,21. Question 4 from [http://www.math.purdue.edu/~walther/teach/453/hwq.txt file]
---[[User:Aifrank|Aifrank]] 13:56, 18 January 2009 (UTC)
+[[Week 13]]-April 16 (Fields, 20): Ch20: 1,29,31,5,19,21,25
+[[Week 14]]-April 23 (Fields, 21): Ch21: 8,14,16,24,33,30
+[[Week 15]]-Apr 30 (Finite fields, 22)Ch22: 1,2,4,10,30, Question 5 from file
+[[Useful Homework Programs]]

Difference between revisions of "MA 453 Spring 2009 Walther Homework" - Rhea

Latest revision as of 19:17, 29 April 2009

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