Math 250 Homework Assignments
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HW A Write a short (at most one
page) introduction of yourself, including your
background in both mathematics and computer science,
why you are taking this course, and what you hope to
learn in this course. Write a few sentences indicating
which problems from Section 0.1: Some Problems seem most
interesting to you and why. Submit this via Kit.
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HW 1
The following are problems from the Cusack book that we have been reading:
- Problem 1.1 a, c
- Problem 1.2
- Problem 1.5
- Problem 1.6
- Problem 1.9
- Problem 1.10
- Problem 1.14
- Problem 1.15 a, b
- Problem 1.16 a, b, c, d
- Problem 1.17 a, b, c, d
- Problem 1.18 a, b, c
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HW 2
These exercises are all from the Cusack text, Section 2.10.
- Problem 2.1
- Problem 2.2 (no truth tables!)
- Problem 2.3
- Problem 2.4
- Problem 2.8 a, b
- Problem 2.9 a, b
- Problem 2.10
- Problem 2.23
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HW 3
All exercises except the last are from the Cusack text.
- Problem 3.3
- Problem 3.4
- Problem 3.5
- Problem 3.6
- Problem 3.8 (Give only 1 answer - the least positive
integer)
- Problem 3.9
- Problem 3.10
- Determine whether 3232 and 201 are relatively prime
by using Euclid's algorithm
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HW 4
These are all exercises from the text.
- Exercise 2.1.11
- Exercise 2.1.17
- Exercsie 2.2.1
- Exercise 2.2.7
- Exercise 2.2.10
- Exercise 2.2.12
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HW 5
- (1)
- Find a recurrence relation for the number of bit
strings of length n that do not have two
consecutive 0s.
- What are the initial conditions?
- How many such bit strings are there of length 5?
- What sequence is this similar to? Explain.
- (2) A computer system considers a string of decimal
digits a valid codeword it it contains an even number of
0 digits. For instance, 1230407869 is valid, whereas
120987046608 is not valid. Let an be the
number of valid n-digit codewords. Find a
recurrence relation for an and the initial
condition.
- (3) Solve the recurrence relation an =
3an-1 - 2an-2 for n ≥ 2, where
a0 = 4 and a1 = 1.
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HW 6
These are all exercises from the text. Your proofs should
be written using complete sentences mixed with mathematical
statements.
- Exercsise 2.5.7
- Exercise 2.5.10
- Exercise 2.5.16
- Exercise 2.5.17
- Exercise 2.5.29
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HW 7
These are all exercises from the text.
- Exercise 0.2.18
- Exercise 0.2.19
- Exercise 0.2.20
- Exercise 3.1.4
- Exercise 3.1.5
- Exercise 3.1.9
- Exercise 3.1.10
- Exercise 3.1.15
- Exercise 3.1.18