HOMEWORK - MATH 613, Section 600, Spring, 2008
The problems marked as circled will be graded and the others will only be
counted. However, in class I will be asking for solutions of ungraded problems.
Due Thursday, January 25: Read 1.1-1.8
p. 30 # 1, 2, 3, 4, 5, 6, 7 (# 2, 5 and 6 are circled)
Due Thursday, January 31:
pp. 30-31 # 9, 10, 11, 12, 13, 15, 16, 17 (# 11, 15 and 17 circled)
Due Thursday, February 7: Read 2.1-2.4
p. 31 # 19, 20, 22, 23, 24, 25 (# 20, 23, and 25 circled)
Due Thursday, February 14:
p. 31 # 26 (circled)
p. 51 # 1, 5, 6 (# 1 and 5 circled)
Due Thursday, February 21: Read 3.1-3.3
p. 52 # 10, 11, 12, 14, 15, 19 (# 10, 14, and 15 circled)
Due Thursday, March 6: Read 4.1-4.4, 4.6
p. 78 # 1, 2, 3, 4 (#1 and 2 circled)
Due Thursday, March 20: Read 5.1-5.3
pp. 78-79 # 5, 6, 7, 8, 9, 10, 16, 17 ,(# 6, 7, and 17 circled)
Due Thursday, March 27:
pp. 106-108 # 1, 3, 4, 5, 20, 23, 25 (# 4, 20, and 23 circled)
Due Thursday, April 3: Read 6.1, 6.3-6.4
pp. 133-135 # 2, 4, 5, 6, 9, 10, 14, 17, 18, 21 (# 9, 17, and 21
circled)
Due Thursday, April 17:
pp. 160-161 # 4, 5, 6 ,7, 8, 9, 10, 12 (# 5. 6. and 10 circled)
HOMEWORK - MATH 613, Section 600, Spring, 2007
Due Thursday, February 15: Read 2.1, 2.2, 2.4
p. 31 # 24, 25, 26 (# 25 and 26 circled)
p. 51 # 1 (circled)
Due Thursday, February 22:
pp. 51-52 # 5, 10, 14, 15, 19 (# 10, 14, 15 are circled)
Due Tuesday, February 27: Read 3.1, 3.2, 3.3, and 3.5
p. 52 #
Due Thursday, March 1:
Flow problems 1, 2, 3 (# 2 circled)
p. 78 # 1, 2, 3 (# 1 and 2 circled)
Due Tuesday, March 27: Read 4.1, 4.2, 4.4
pp. 78-79 # 4, 5, 6, 8, 16, 17 (# 8, 16, and 17 circled)
Due Thursday, March 29: Read 5.1, 5.2, 5.3
pp. 106-107 # 2, 3, 4, 5, 13, 15, 20 (# 4, 5, and 20 circled)
Due Thursday, April 5:
pp. 133-134 # 2, 4, 5, 8, 9, 10, 11, 14, 17, 18 (# 8, 10, and 17
circled)
Due Thursday, April 19: Read 6.1, 6.3, 6.4, 6.6, 10.1, 10.2, p. 281
p. 135 # 21 (circled)
p. 160 # 4, 6, 7, 8, 9, 10, 11 (# 6 and 10 circled)
Due Thursday, April 26: Read 10.1-10.3
pp. 289-290 # 1, 2, 3, 4, 5, 7, 11, 13 (# 3, 5, and 7 circled)
THE FOLLOWING ASSIGNMENTS ARE FROM Spring, 2006. These are probably not
the exact assignments to be made during the semester, but they are similar.
HOMEWORK - MATH 613, Section 600, Spring, 2006
Due Thursday, 26 January: Read Sec. 1.1 - 1.8
p. 30 # 1, 2, 3, 4, 5, 6, 7 (# 2 and 6 are circled)
Due Tuesday, 31 January:
pp. 30-31 # 9, 10, 11, 12, 13, 15 (# 11 and 15 circled)
Due Tuesday, 7 February: Read Sec. 2.1, 3.1
p. 31 # 16, 17, 19, 20, 22, 23 (# 20 and 23 circled)
Due Thursday, 9 February:
p. 31 # 24, 25, 26 (# 25 and 26 circled)
p. 51 # 1
Due Tuesday, 14 February: Read Sec. 3.3, 4.1, 4.2
p. 52 # 10 (circled)
p. 78 # 1, 2, 3, 5, 6 (# 2 circled)
Due Tuesday, 21 Bebruary:
pp. 79-80 # 7, 8, 10, 16, 17 (# 7 and 17 circled)
p. 106 # 2, 3
Due Thursday, 23 FEbruary: Read Sec. 4.4, 5.1
pp. 106-7 # 4, 5 (use hint), 15, 20 (# 4 and 20 circled)
Prove the theorem stated in class. See Prof. Hobbs for it if you did
not copy it.
Due Tuesday, 28 February: Read Sec. 5.2, 5.3
p. 107 # 18, 19 (both circled)
p. 133 # 1, 2, 5
Due Thursday, 2 March:
pp. 133-4 # 4, 6, 8, 9, 10, 11 (# 8 and 9 circled)
Due Thursday, 9 March: Read network flows handout.
p. 134 # 12, 14, 17, 18, 21 (# 14 and 17 circled)
Due Tuesday, 21 March: Read 7.1, 7.3, scan 7.2
Network flow problems on flows handout: 1, 2, 3 (# 1 and 3 circled)
p. 160 # 3
Due Tuesday, 28 March:
p. 189 # 1, 2, 3 (# 2 and 3 circled)
Due Tuesday, 4 April: Read 9.1, scan 9.2, 9.4
p. 189 # 4, 7, 8, 12 (# 7 and 12 circled)
Due Tuesday, 11 April: Read 10.1, 10.2
p. 237 # 2 (circled)
p. 277 # 2, 4, 12 (# 2 circled)
Due Thursday, 13 April: Read 11.1-11.3
pp. 289-90 # 1, 2, 3, 4, 5, 7, 11 (# 3 and 5 circled)
Due Tuesday, 25 April: Read 12.1, 12.2
p. 312 # 1, 2, 3, 4 (# 2 and 4 graded)
Due Thursday, 27 April:
p. 312 # 6, 7, 8, 10 (# 7 and 10 graded)
p. 350 # 1, 2
Due Monday, 25 April: Read Chap. 10
p. 165 # 2, 3, 4, 8 (all graded)
Due Wednesday, 27 April:
p. 226 # 1, 2 (both graded)
Due Tuesday, 3 May: Skim Chapter 12
pp. 226-7 # 5, 7, 8, 9 (# 5, 7, and 8 graded)
p. 277 # 1
The item on the study sheet calling for memorizing the theorem connecting flows with the 4 color theorem is actually two theorems:
1. Tait's Theorem: The 4 color theorem is equivalent to the statement that every plane cubic block is 3-edge-colorable.
2. Corollary: In order to prove the 4 color theorem, it suffices to prove that every plane cubic block has a 4-flow.
Recall that a matroid is a finite set S and a set \Cal I of subsets of S such that
(1) \emptyset is in \Cal I
(2) If A is in \Cal I and if B is a subset of A, then B is in \Cal I
(3) If A and B are both in \Cal I, and if |A| > |B|, then there is an x in A such that B union {x} is in \Cal I.
Recall also that a base is a maximal independent set in a matroid.
Prove the all bases in a matroid M = (S, \Cal I) have the same size.