# Book

## An Introduction to Mathematics for Computing and IT Practitioners.

#### There are a number of topics within Mathematics which have a direct relevance to Computing and IT.
Some of these topics form the basis of how a computer processes data, some are used at a higher level
to enable a program to perform a required function, and others are algorithmic and can be easily
implemented within a computer program.

#### This books attempts to bring together many of these mathematical concepts and present them in a way
which is relevant to those studying ICT and Computing qualifications, and to those who would like to start
to explore this subject for themselves. This book not only demonstrates how to perform the relevant
calculations, but puts the topics into the context of computing.

#### Explanations include simple diagrams, tables of data, worked examples and questions with worked
answers to allow the reader to check their understanding of a topic. Some of the explanation include
the use of algorithms and flowcharts as well as coded examples. Additionally, throughout this book
there are examples to illustrate how the mathematical concepts are used within computing and IT.

#### This book is purely an introduction to the subject and many of the concepts are described in
their simplest form. The reader may then wish to go and explore a specific topic in more depth.

##### The following is a list of the topics which are covered by the book:

####
- Algorithms: Steps and Flowcharts.
- Matrices: Operations, Transformations, Simultaneous Equations, Maps and Graphs.
- Sequences and Series: Arithmetic, Geometric, Recursive Algorithms, Fibonacci Sequence, Golden Ratio.
- Searching and Sorting Algorithms: Bubble Sort, Quick sort and Binary Search.
- Probability: Tree Diagrams, Space Diagrams, Venn Diagrams and Simulation.
- Number Systems: Binary, Octal, Hexadecimal, Conversions between number systems, Operations on Binary.
- Boolean Algebra: Logical Operators, Venn Diagrams, Boolean Expressions and Logic Gates.
- Character Codes: ASCII, Unicode, UTF-8, Hamming Codes, MIME Base 64.
- IP Addresses: IPV4, Network and Host IDs, CIDR notations and Subnetting.