Math 461
Homework #5
due Monday, November 5
1
Reading assignment: Read pages 95-96 of Section 5.2, and Section 9.1: skip Theorem 9.2 and
Corollary 9.3 for now, but make sure you read everything else i
Math 461
Solutions for Homework #5
November 5, 2012
1
1. (This is #35 on p. 107) Let an be the number of compositions of n into parts that are larger
than 1. Express an by an1 and an2 .
Solution 1: We
Math 461
Solutions for Homework #6
November 9, 2012
1
1. Which complete graphs Kn have Eulerian trails?
Solution: Observe that in Kn all vertices have degrees n 1. Observe also that n 1 is
even if and
Math 461A
Partial Solutions to review problems October 13
1
1. Show that in every graph with n 2 vertices, there are two vertices that have the
same degree.
Solution: Let G be a graph with n 2 vertice
Math 461
Homework #4
due Monday, October 27
1
Reading assignment:
After Fridays lecture, read carefully Lecture 11 notes and glance at p. 69 in the textbook.
After Mondays lecture, read carefully Le
Math 461
Homework #3
due Monday, October 13
1
Reading assignment:
After Mondays lecture, read carefully Lecture 6 notes and 3.2 in the Invitation to Discrete
Math book.
After Wednesdays and Fridays
Math 461
Homework #4
due Monday, October 29
1
Reading assignment: Read carefully Chapter 7 (you may skip Theorem 7.6) and glance through
pages 95-96 of Section 5.2.
Written assignments:
1. (this is #2
Math 461
Homework #6
due Friday, November 9
1
Reading assignment: Read Theorem 9.2 and Corollary 9.3 in Section 9.1; start reading Sections 9.2 and 9.4.
Written assignments:
1. Which complete graphs K
Math 461
Solutions for Homework #7
1
November 30, 2012
1. Let T be a tree on n vertices such that the degree of each vertex is either 1 or 3.
(a) Show that n is even.
Solution: Since the number of odd
Math 461
Homework #2
due Monday, October 6
1
Reading assignment:
After Mondays lecture, read carefully Lecture 3 notes. You may also want to take a look at 2.4
in the book by L. Lovsz, J. Pelikn, and
Math
October L5, 2074
First Midterm
467
Your Signature
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Student ID
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Problem
Points
Possible
1
6
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6
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6
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9
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Total
40
o No books allowed. You may use one 8| x
o Do not share
11 sheet
Math 461
Solutions for Homework #4
October 29, 2012
1
1. (this is #24 on p. 144) How many three digit positive integers are divisible by at least one of
six and seven?
Solution: Let
S = cfw_99 < x 999
Math 461
Solutions for Homework #1
October 1, 2012
1
1. Each box in a 3 3 arrangement of boxes is lled with one of the numbers 1, 0, 1. Prove
that of the eight possible sums along the rows, the column
Math 461
Solutions for Homework #3
October 14, 2014
1
1. How many four-digit positive integers are there in which all digits are dierent? (We do not allow the
rst digit to be zero.)
As we do not allow
Math 461
Homework #1
due Monday, September 29
1
Homework assignments in this class will be usually due on Monday. The importance of doing
all the homework cannot be overemphasized. Mathematics cannot
Math 461
Solutions for Homework #2
October 7, 2014
1
1. Let a0 = 0, a1 = 1, and let an+2 = 6an+1 9an for n 0. Prove that an = n 3n1 for all n 0.
The proof is by (strong) induction on n. If n = 0 or n
Math 461A
Course Information
September 24, 2014
1
Lecturer: Prof. Isabella Novik, e-mail [email protected]
Oce: Padelford C-416, (206)616-9373
Class web-page: http:/www.math.washington.edu/nov
Math 461
Homework #7
due Friday, November 30
1
Reading assignment: Read 10.1, the rst two paragraphs of 10.2, and the solution to Problem
#(5) on p. 234 (the solution itself is on pp. 239-240).
Writte
Math 461
Homework #3
Due October 22, 2012
1
Reading assignment: Read Sections 5.1 and 7.1.
Written assignments:
1. p. 81, #(50) If we expand the expression (x1 + x2 + x3 + x4 )6 , what will be the lar
Math 461
Homework #1
due Monday, October 1
1
Reading assignment: Read the rst two chapters of the book. I expect to cover Chapter 1 on
Mon-Wed, Sep 2426, and Chapter 2 on Fr-Mon, Sep 2628.
Written ass