Quantitative Methods: Appendix
3
Section 1
Basics of Mathematics
In this section, we will discuss:
•
Number Systems
•
Simultaneous Equations
•
Polynomials
•
Theory of Indices
•
Permutations and Combinations
•
Progressions
•
Functions
It is important to revise the decimal, binary and octal number systems before
proceeding on to study the quantitative methods. Also, it is important to understand
the concepts of Simultaneous Equations, Polynomials, and the Theories of Indices to
solve problems which are complex in nature.
Some of the other important concepts that have to be understood are Permutations and
Combinations and the three progressions – arithmetic, geometric, and harmonic.
NUMBER SYSTEMS
Apart
from
the
two
most
commonly
used
number
systems
–
decimal
(0,1,2,3,4,5,6,7,8,9) and Roman (I,II,III,IV,V,VI
....
), we have other systems such as
octal number system
represented by (0,1,2,3,4,5,6 and 7) and hexadecimal number
system based on the digits 0 to 9 and also the letters from A to F.
Decimal System
•
The decimal system has 10 digits (0 to 9).
•
Each digit is a number.
•
If there are two or more than two digits in a number, each digit has a value that is
ten times greater than the digit just to its right. For example, if 9628 is a number
that has four digits. We can say that 8 is in the units place, 2 is in the tens place, 6
is in the hundreds place and 9 is in the thousands place.
•
Each digit in a number has two values one is called the absolute value and the
other is called as the place value. If 9628 is taken, 9 has an absolute value which
is 9 itself and place value which is 9000, for 6, absolute value is 6 itself and place
value is 600, similarly for 2 and 8 the absolute values are 2 and 8 again and the
place values are 20 and 8 respectively.
•
A decimal system has number 10 as its base or radix.
•
A number in any number system can be represented as
0
1
1
2
2
3
n
1
n
r
d
r
d
r
d
.....
..........
r
d
N
+
+
+
×
=
+
Where, N = any number of any base system,
d
n
= digit in the n
th
position,
r
n
= the exponent for (n+1)
th
digit position.