MAP 3170 Financial Mathematics for Actuarial Science
Homework 3
1. From Textbook: 3.14 Problems, Chapter 3
(3.2) (1), (4), (5)
(3.3) (1), (2), (4)
2. You wish to make a deposit now in an account ear
MAP 3170 Financial Mathematics for Actuarial Science
Homework 6
1. From Textbook:
(5.3) (1), (2), (3), (4), (5)
2. John borrows 1000 for 10 years at an annual effective interest rate of 10%. He can
r
MAP 3170 Financial Mathematics for Actuarial Science
Homework 5
1. From Textbook:
(3.6) (1), (2), (3), (4)
(5.2) (1), (2), (4), (5)
2. A loan is being amortized by means of level monthly payments at
1) Outline Pros and Cons and Winners and Losers of Trade Using information from
this Economist Article.
After Nafta trade with Mexico increased as did trade with China after they joined the WTO in 200
1) Outline Pros and Cons and Winners and Losers of Trade Using information from this
Economist Article. W
2) Below the first article is another one from the NYTimes (most of text is below but some
gra
MAP 4341
Exam 2, Take-Home
You are allowed any help from a non-human source. DO NOT discuss this exam with any
classmate, friend, or professor (other than me). Exam is due at 2:30 on December 10. You
MAP 4341
Exam 1, Take-Home
You are allowed any help from a non-human source. DO NOT discuss this exam with any
classmate, friend, or professor (other than me). Exam is due at the beginning of class on
Review: Exam 2
MAP 4341
In-Class Portion: The in-class portion of the exam will be during our regularly scheduled
exam time: Tuesday, December 7, 1:00-2:50. The exam will be closed book, closed note,
Review Sheet for Exam 1
MAP 4341
In-Class:
For the in-class portion of the exam, you may bring in a calculator (any type) and a
writing instrument. While I am allowing calculators of any type, I need
MAP 6385
Homework 4
September 18, 2009
1) By hand (yes, by hand), calculate z , where z = [1, 0, 3, 2].
2) I have said that z z is a linear transformation. This means we can represent it as a
matrix m
MAP 6385
Homework 3
September 9, 2009
WARNING: There are some big Mathematica problems on here. One of them is an openended question that requires experimentation. You probably shouldnt wait until the
MAP 6385 Homework 2
September 2, 2009
1) Graph the rst ve Legendre polynomials (P0 (x) through P4 (x) on the same graph. Then plot the rst ve Chebyshev polynomials (T0 (x) through T4 (x) on the same g
MAP 6385
Homework 1
August 27, 2009
1) The following table gives a list of data points. Find the least squares polynomials of
degrees 1, 2, and 3 for this data set. For each degree, calculate the erro
MAP 6385
Homework Rules
1) You are allowed to work together. HOWEVER, if you do work with someone else,
then when you submit your homework, I want to know with whom you worked. If
someone else solved
Huffman Compression
Steps for the Huffman Compression 1) Write down all of the letters appearing in the text in a list, most frequent to least frequent. For each letter, put the frequency as a subscri
MAP 6385 Exam 2
November 5, 2009
Same rules apply as from Exam 1. The exam is due on November 12 at 4:30 PM. Note that Problems 7 and 8 do not have explicit answers: they are more experimentation prob
MAP 6385 DWT, Part 3
Denition 18. Let M be an even number. Dene the down operator D : CM CM/2 by D(z )(k ) = z (2k 1) Furthermore, if M is any number, then dene the up operator U : CM C2M by k+1 z ( 2
MAP 6385 DWT, Part 2
Example 14. Let M be a number divisible by 4. The First Stage Shannon Wavelet Basis is the wavelet basis generated by the father and mother wavelets u and v satisfying: 2 if 1 n M
MAP 6385 DWT
Definition 1. A vector z CM is time localized if its entires with large magnitudes are clustered around a particular index. A vector z is frequency localized if the entries of z with ^ la
MAP 6385 DFT, Part 2
Denition: Let z and w be vectors in CM . The convolution of z and w, written as z w, is the vector dened by
M
z w(m) =
n=1
z (m n + 1)w(n)
Theorem: Let z , w, and y be vectors in
MAP 6385 DFT
Definition: Let CM be the vector m-dimensional complex vector space. We represent a typical element by z, written out as: z = [z(1), z(2), . . . , z(M )] The inner product on CM is define
MAP 6385 Convolution and Image Processing
1
Convlution
k = 1/2
Denition 1. Let z, w l2 (R), the set of sequences indexed on Z such that z (m)2
k=
<
The convolution z w of z and w is the sequence dened
96
Chap. 15 Limits to Computation
15.8 Represent a real number in a bin as an innite column of binary digits, similar to the representation of functions in Figure 15.4. Now we can use a simple
diagona
95
(b) It is possible to compute xn in log n time, and the rest of the formula
requires a constant number of multiplications. Thus, the number of
multiplications required is polynomial on the input si
15
Limits to Computation
15.1 This reduction provides an upper bound of O(n log n) for the problem of
maximum nding (that is the time for the entire process), and a lower bound
of constant time for SO
93
(b) Fill an array with 2n + 1 elements, which forces a nal growth to an
array of size 2n+1 . Now, do an arbitrarily long series of alternating
inserts and deletes. This will cause the array to repe
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Chap. 14 Analysis Techniques
B elements are repeatedly reinserted one fewer times, the next 2B elements
2 fewer times, etc. Thus, once we insert 2i B elements, we have done a total
number of insert
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n log n, so we will guess that
T(n) = ( n log n.
To complete the proof we must show that T(n) is in ( n log n), but this
turns out to be impossible.
On the other hand, the recurrence is clearly n.