Maths for Computing: A Comprehensive Guide to Essential Mathematical Concepts

Maths for Computing

Contents
LO1: Use applied number theory in practical computing scenarios..........................................2
Part 1 Number Theory............................................................................................................2
LO2: Analyses events using probability theory and probability distributions.........................10
Part 1 probability..................................................................................................................10
Part 2: Probability Distribution............................................................................................12
LO3: Determine solutions of graphical examples using geometry and vector methods..........13
Part 1: Geometr....................................................................................................................13
Part 2: Vectors......................................................................................................................16
LO4: Evaluate problems concerning differential and integral calculus...................................17
Part 1 Differential Calculus..................................................................................................17
Part 2 integral calculus.........................................................................................................19
References................................................................................................................................20
1

LO1: Use applied number theory in practical computing scenarios.
Part 1 Number Theory
[P1]
1.1 Convert the decimal 5613.9062510 into:
(a). Binary Number
5613
2 2806 1
2 1403 0
2 701 1
2 350 1
2 175 0
2 87 1
2 43 1
2 21 1
2 10 1
2 5 0
2 2 1
2 1 0
1
The integer number [5613] in decimal number is written as 1010111101101 in binary.
2
0.9062510*2 1 + 0.812502
0.812502*2 1 + 0.625004
0.625004*2 1 + 0.250008
0.250008*2 0.500016
0.500016*2 1 + 0.000032
0.000032*2 0.000064
0.000064*2 0.000128
0.000128*2 0.000256

The fractional part [0.9062510] in decimal number is written as 11101000.
In all, this conversion collectively will be written as 1010111101101.11101000
(b)Binary number via octal
8 5613
8 701 5
8 87 5
8 10 7
1 2
1
The integer number [5613] in octal number is written as 12755 in binary.
The fractional part [0.9062510] in octal number is written as 72000.
In all, this conversion collectively will be written as 12755.72000
3
0.9062510*8 7 + 0.250008
0.250008*8 2 + 0.000064
0.000064*8 0.000512
0.000512*8 0.004096
0.004096*8 0.032768