Sample questions for the midterm:

1. How many bitstrings of length 10 have exaclty four zeros?
2. What is the coefficient of x^3*y^6*z^5 in (x+y+z)^14? Explain in
words why your answer is correct.
Extra Problem 1:
Suppose 2n people sit on a round table and are shaking hands in
pairs. Suppose that etiquette is observed and no 2 shakes cross. Let
S_n be the number of possible shaking hands arran
Math 373
Test 1
Fall 2012
September 27, 2012
1. Meng takes out a loan to buy a new motorcycle. The amount of the loan is 12,500. Meng will
repay the loan with 9 monthly payments of Q at a nominal inte
MATH 373
Test 3
Fall 2012
November 6, 2012
1. The preferred stock of Wang Corporation pays a quarterly dividend of 5.00. The next
dividend is paid in 1 month.
Yi buys the stock to yield an annual effe
Math 373
Test 3
Fall 2013
November 7, 2013
1. You are given the following spot interest rate curve:
Time t
Spot Rate rt
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
3.2%
3.5%
3.9%
4.4%
5.0%
5.7%
6.5%
7.5%
Calculat
Math 373
Test 2
Fall 2013
October 17, 2013
1. You are given the following table of interest rates:
2007
2008
2009
2010
2011
2012
2013
Year 1
0.060
0.055
0.053
0.050
0.047
0.045
0.043
Year 2
0.058
0.05
Math 373
Spring 2012
Test 2
March 8, 2012
1. A 20 year callable bond with semiannual coupons of 250 matures for 11,000. The bond can be
called at the end of 12, 14, 16, and 18 years. The following ca
@A’. A 20 year callable bond with semiannual coupons of 250 matures for 11,000. The bond can be
called at the end of 12, 14, 16, and 18 years.
End of Year
Call Value
The following call values a
Math 373
Test 3
Spring 2012
April 3, 2012
1. A stock pays quarterly dividends with the next dividend payable in one month. The first
dividend will be 4.00. The second dividend will be 4.50. The third
Math 373
Test 3
Spring 2012
April 3, 2012
1. A stock pays quarterly dividends with the next dividend payable in one month. The first
dividend will be 4.00 . The second dividend will be 4.50 . The thir
Math 373
Spring 2013
Test 1
February 12, 2013
1. Tracy is receiving an annuity immediate with quarterly payments of 250 for 10 years. Tracy
invests each payment in an account earning an annual effecti
MATH 373
Test 3
Spring 2013
April 2, 2013
1. The stock of Hillman Industries pays quarterly dividends. The next dividend will be D and
is payable in two months.
Future dividends are expected to increa
Math 373
Test 2
Spring 2013
March 5, 2013
1. Jana purchased a 20 year zero coupon bond for 20,000. The bond matures for 70,000.
Christian borrowed 50,000 to be repaid over 30 years with level monthly
Math 373
Fall 2012
Test 2
October 18, 2012
1. Jordan has the option to purchase either of the two bonds below. Both bonds will be purchased
to provide the same yield rate.
a. A 20year zero coupon bon
Sample questions for the 375 Final
* 11.1: 28,31,47  11.4: 1,9,33,39,44  11.5: 8.
* Give a recurrence and initial condition for the number of ternary
strings that contain 3 or more consecutive zero
Assignment 1
MA 375 Homework 1 Solutions
Section 5.1:
54: The claim is true if n=1 because if you pick 2 numbers from the
set cfw_1,2 then it is easy to see that there are 2 chosen
numbers that div
Section 4.2
29: By "strong" induction. If n=1, it's clear that n can be uniquely
written as a sum of distinct powers of 2, namely n=2^0.
For n>1, subtract from n the largest power of 2 not exceeding i
Solutions 3
7.1:
19: First find the number of hands with 5 different kinds: we choose 5
kinds out of the possible 13, and then each kind can be any of 4
suits. So there are (13 choose 5) * 4^5 such
Solutions Assignment 4:
7.2:
2: If 3 is twice as likely as all other numbers,
p(3)/2=p(1)=p(2)=p(4)=p(5)=p(6). Let x=p(1).
Since the sum of all p(i) is 1, x+x+2x+x+x+x+x=1, so x=1/7.
10: a) Note t
Assignment 5
Section 6.1:
6. Since the choice of routes from Boston to Detroit is independent of
the choice from Detroit to LA, the product rule says that we multiply
to get a total of 24 routes.
22.
Solutions 6
Section 6.3
20: a) To have 3 zeros means to have 7 ones. To count you just have
to decide where the 0's go, for which there are 10 choose 3 ways.
b) There are 6 or 7 or 8 or 9 or 10 0's.
Solutions 7
6.5:
10: For the purpose of this solution, bagels are croissants. (They have
fewer letters to write.)
a) Choosing 12 bagels from 6 types is like writing down 12 "b"'s and
then separati
Solutions 9.
9.1.
16: I can't really draw this on the computer. The graph has one vertex
for each person and then one edge for each acquaintance.
20: Team 4 beat 3, but was beaten by everyone else.
9
Solutions 10

9.3:
40: Not isomorphic. The left graph has 4 vertices of degree 3, the
right one only 2.
42: Not isomorphic. If you select all vertices that have degree 4 in
both given graphs, and
Solutions 11.
9.5:
22: Since b has odd degree, no Euler circuit (directed or not) can
exist. If there is a directed Euler path, it must go from c to
b. Fleury's algorithm gives (for example)
c,b,c,
Solutions 12 to 9.7

5: no, it's version of K(3,3).
6: yes. push the afedge up. and the cdedge down.
7: yes, but hard to explain.
8: no. there are no triangles, so the shortest circuit has length 4
Math 373
Test 1
Spring 2012
February 16, 2012
1. Yue borrows 10,000 to buy a car. She will repay the loan with monthly payments for 6 years.
The annual effective interest rate on the loan is 15%.
Calc