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Homeworks and ToDo's
- HW #1 (due 7th of October. Next Friday.) Solutions
1.1 Who is the mathematician who had lived in Kadıkoy?(In old times)
1.2 Define natural numbers
1.3 Define integers using natural numbers
1.4 Define rational numbers
- HW #2 (due October, 14 Friday.)
2.1 Given an exponential function such as 2^n
Is it possible to have a polynomial that is always larger than that exponential function
2.2 If b=a and c=a; how would you say b=c
2.3 1+1=2 why?
2.4 Which of these statements are true?
- Ø is an element of S
- Ø is a subset of S
- {Ø} is an element of S
- {Ø} is a subset of S
2.5. Text book page 55/44
Show that ∀xP(x) ∨ ∀xQ(x) and ∀x∀y(P(x) ∨Q(y)) are logically equivalent. (The new varible y is used to combine the quantifications correctly)
2.6. Text book page 75/25
Prove that the sum of an irrational number and a rational number is irrational using a proof by contradiction.
- HW #3 (due to October 21, Friday.) Solutions
Hw3.1. Text book 95/32
Hw3.2. Text book 109/32
Hw3.3. Text book 110/63
Hw3.4. Text book 111/70
Hw3.5. Given a one-to-one function f from A to B, such that |A| = n and |B| = m, prove that n<=m
- HW #4 (due to October 28, Friday.)
Hw4.1 What is the 'Fundamental Theorem of Algebra?
- HW #5 (due to November 23, Friday.)
Hw5.1. Write a matrix and then look your matrix in the mirror.How do you write the matrix in the mirror in terms of the first one?
Hw5.2. Prove that equivelence classes are disjoint.
- HW #6 (due to December 2, Friday.)
Hw6.1. Construct an algorithm to determine if there exists any cut point in an undirected simple graph or not.
Hw6.2. Text 576/22
Hw6.3. Text 577/38
Hw6.4. Text 590/26
Hw6.5. Text 577/43 (Think about it but do not turn in.)
Hw6.6. read the story of Euler in your book
- HW #7 (due to December 9, Friday.)
Hw7.1 Consider a nxn matrix having zeros(0) on main diagonal and on upper triangular part. and having ones(1) on lower
triangular part as shown below.
0 0 0 0 0
1 0 0 0 0
1 1 0 0 0
1 1 1 0 0
1 1 1 1 0 .....
.
.
.
What are the properties of a graph having that adjacency matrix?
Hw7.2. What is the algebraic structure of polinomials with respect to addition and multiplication? (group, semigroup or field)
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