INTEGERS AND INDUCTION
CSE 173 [AdF]
REVIEW OF SET THEORY
ANOTHER EXAMPLE
WRITE THIS PART ON THE LEFT!
NEW CHAPTER WOOHOO!
LETS DO SOME EXAMPLES
[TAKE HOME EXAMPLE PROBLEM]
H.W.
Read Chapter 4 Example 4.5, 4.6 AND WRITE IT DOWN (i.e. copy
it on a paper W
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DEFINITION
EXAMPLE
ANOTHER EXAMPLE
DEFINITION
EXAMPLE
EXAMPLE
FUNCTIONS
EXAMPLE
DEFINITION
INTERESTING FUNCTIONS IN C.S.
ONE-TO-ONE FUNCTION
EXAMPLE
EXAMPLE
DEFINITION OF IMAGE
EXAMPL
At a certain university the following sets are related for purposes of registration:
A1 7 the set of course numbers for courses offered in mathematics.
A; = the set of course titles offered in mathematics.
A3 : the set of mathematics faculty.
A4 m the set
CSE 173 (SECTION WHO
CARES?)
LECTURE 6
Adnan Firoze (AdF)
Important Sets
Example
Definition: Disjoint Sets
What does this look like?
Theorem
Proof: Homework (even if you simply copy
From the book)
Definition and Example of
Complement
Example to inspire th
Relations and Functions (Books Ch 5)
CSE 173 - AdF
5.1. Cartesian products and
relations
Definition 5.1. The Cartesian product of A
and B is denoted by AB and equals cfw_(a,
b)aA and bB. The elements of AB are
ordered pairs. The elements of A1A2
An are o
Number Theory: GCD and Euclidean
Algorithm
(CSE 173) Adnan Firoze (AdF)
1
ALGORITHMS
al-Khwrizm : Persian mathematician,
astronomer
ZERO (500 AD)
On the calculation with Hindu numerals; 825 AD
decimal positional number system
Natural numbers and integer
Solution: Quiz # 4
PHY 107
March 07, 2015
Write ONLY the CORRECT answer.
1. In Figure-1, if the box is stationary and the angle between the horizontal and force F is increased somewhat,
the frictional force fs
A. is increased.
B. is decreased.
C. remains
Solution: Quiz # 6
PHY 107. Sec # 01
March 28, 2015
Write ONLY the CORRECT answer.
1. Which of the following is equivalent to saying that the total linear momentum is conserved?
A.
Fext = 0.
B.
Pi = Pf .
C. J = 0.
D. All of these.
1. Answer is D
2. You dr
Solution: Quiz # 10
PHY 107
April 23, 2015
Write ONLY the CORRECT answer.
1. Here are three equations of three waves:
y(x, t) =
2 sin(4x 2t) ,
(1)
y(x, t) = sin(3x 4t) ,
and y(x, t) = 4 sin(3x t) .
(2)
(3)
In which equation, the wave speed is the lowest?
Quiz # 5 Solution
PHY 107 (Summer 2015)
Faculty: Abu M Khan
Choose only one answer
1. Two identical balls have been released from the top of a building simultaneously: one is dropped from rest and
the other has been thrown horizontally. Both reach the gro
Quiz # 4 Solution
PHY 107 (Summer 2015)
Abu M Khan
Choose only one answer
1. Which of the following diagrams in Figure-1 show the vector addition of forces F1 and F2 to yield the third vector,
which is meant to represent their net force Fnet ?
F2
F2
F1
F2
Solution: Quiz # 2
PHY 107
February 20, 2015
Write ONLY the CORRECT answer.
1. Figure-1 gives the acceleration of a cat chasing a mouse along the x-axis. In which time periods, the change in
velocity is zero?
A. b c.
B. d e.
C. f g.
D. Whole path.
1. Answ
Quiz # 3 Solution
PHY 107 (Summer 2015)
Abu M Khan
Write ONLY the CORRECT answer.
x
vi + vf
=
is valid?
t
2
C. Parabolic.
D. All of these.
1. For which of the following paths the relation
A. Straight line.
B. Circle.
1. Answer is A
2. Which of the followi
Solution: Quiz # 3
PHY 107
February 24, 2015
Write ONLY the CORRECT answer.
1. A projectile is detected 30 m above the ground with velocity v = (3i + 19.6j)m/s. How long will it take to reach
the maximum height from there?
A. 1 second.
B. 1.5 second.
C. 2
Solution: Quiz # 5
PHY 107
March 21, 2015
Write ONLY the CORRECT answer.
1. A crate is pulled by a force F on a horizontal rough surface with constant velocity as shown in Figure-1. The
crate has moved a distance d before the withdrawal of the pulling. Fo
Solution: Quiz # 9
PHY 107
April 19, 2015
Write ONLY the CORRECT answer.
1. Which of the following relationships between the force F and a particles position x implies simple harmonic
oscillation?
A. F = 5x.
B. F = 400x2 .
D. F = 3x2 .
C. F = 10x.
1. Answ
Solution: Quiz # 8
PHY 107
April 07, 2015
Write ONLY the CORRECT answer.
1. A torque on an object is given by = r F , and it can be zero when
A. the axis of rotation passes through the object.
C. the force and the position vector are parallel.
B. the appl
Quiz # 2 Solution
PHY 107
Abu M Khan
Write ONLY the CORRECT answer.
1. Which of the following are correct mathematical expression for any three vectors?
B
C.
B)
C.
A. A
B. (A
C. Both of these.
D. None of these.
1. Answer is C
2. Which of the following
Quiz # 6 Solution
PHY 107 (Summer 2015)
Faculty: Abu M Khan
Choose only one answer
1. The conservation law of the total linear momentum implies that
A.
Fext = 0.
B.
Pi = Pf .
C. J = 0.
D. All of these.
1. Answer is D
2. Which of the following statements a
Solution: Quiz # 7
PHY 107
March 31, 2015
Write ONLY the CORRECT answer.
1. In a uniform circular motion, the velocity of a particle is found to be v = (3 i 4 j)m/s. When the particle reaches
the diametrically opposite side of the circular path, its veloc
Quiz # 1 Solution
PHY 107
Faculty: Abu M Khan
Write ONLY the CORRECT answer.
1. Which edition of the textbook we will be using in this classes?
A. 7th .
B. 8th .
C. 9th .
D. 10th .
1. Answer is C
2. How many quizzes will be contributing towards your final
Solution: Quiz # 1
PHY 107
January 29, 2015
Write ONLY the CORRECT answer.
1. Which of the following is/are three significant numbers?
A. 2.57.
B. 0.00375.
C. 6.75 106 .
D. All of these.
1. Answer is D
2. The velocity as a function of time is given by
v(t
Chapter 5
Link Layer
A note on the use of these ppt slides:
Were making these slides freely available to all (faculty, students, readers).
Theyre in PowerPoint form so you see the animations; and can add, modify,
and delete slides (including this one) and
Chapter 5
Link Layer
A note on the use of these ppt slides:
Were making these slides freely available to all (faculty, students, readers).
Theyre in PowerPoint form so you see the animations; and can add, modify,
and delete slides (including this one) and
Chapter 5
Link Layer
A note on the use of these ppt slides:
Were making these slides freely available to all (faculty, students, readers).
Theyre in PowerPoint form so you see the animations; and can add, modify,
and delete slides (including this one) and
Eastern Mediterranean University
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Eastern Mediterranean University
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Eastern Mediterranean University
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Eastern Mediterranean University
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Eastern Mediterranean University
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Eastern Mediterranean University
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Eastern Mediterranean University
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Eastern Me
Computer Networks:
Transport Layer
Protocols
Rajesh Palit, Ph.D.
North South University, Dhaka
Transport Layer 3-1
Chapter 3: Transport Layer
our goals:
understand
principles behind
transport layer
services:
multiplexing,
demultiplexing
reliable data
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