COMP SCI 241 Discrete Mathematics I
Practice number system conversions
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x
2W , c How to use this recursive denition:
Denition ( a long one): Given a square matrix A, the elf O; d Jwpick any convenient row of A.
determinant of A, denoted |A|is the scalar whose value
i. >ary Counting Techniques.
Multiplication Principle: If an object can be constructed int
successive steps, where
step 1 can be performed in n1 different ways, and
step 2 can be done in n; different
)
Some denitions from Number Theory:
Aninteger a is divisible by an integer b, written bla if there
exists an integer e such that bc=a.'
If a is divisible by b, we say a is a multiple of b and b is a
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h L) a Computation W6 W111 need In a mathematical " ' , ' Heres an example from Discrete Mathematics-.11:
induction proof later in the course: '
102<k+1>1 =-102k+21=
Matrices
A matrix is a rectangular arrangement of objects
called element's (Or entries);
The entries are usually real numbers, and when they
are, the matrix is a real matrix. '
Sometimes the entries a
.L_ogi_c
The purpose of studying logic is to determine if our reasoning is
correct. It is not concerned with determining if a statement is
true or false.
There is a big difference betWeen mathematical
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) Positional Number Systems.
The concept of the "counting numbers or natural
numbers" is one of the oldest and most basic of
mathematical concepts.
As mathematics developed, the need for increasingly
Proofs Involving the Size of 3 Structure
Frequently in Computer Science, we need formulas and theorems to "scale up" to large
problems. For example, when we looked at matrix identities involving matri
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Elementary Counting Problems
1) In how many distinguishable ways can we arrange the letters, FRIEND?
6!
2) In how many distinguishable ways can we arrange the letters, FRIEND, if the I and
COMP SCI 241 Discrete Mathematics I
Practice Argument Validation
Spring 2010
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