# High School Mathematics Extensions

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## Introduction[edit]

This online textbook is aimed at, but not limited to, 14 to 18 year olds who are interested in mathematics in general. Several interesting topics not covered in the standard high school curriculum of most countries are introduced in this text.

The materials presented here can be challenging. But at the same time we strive to make this book accessible to all with 9–10 years of formal education. We sincerely hope to interest, stimulate and challenge you with this book.

**From the authors**

It is our firm belief that math textbooks shouldn't just be a collection of mathematical facts carefully laid out, so the student can open it and cram in whatever formula they have to remember for tomorrow's exam. A math textbook, especially for the youthful, should be full of questions, not just exercises. Questions that require some thought to answer. After all, it's the questions that keep the students interested, not the answers.

*"In mathematics the art of proposing a question must be held of higher value than solving it."*- - Georg Cantor

## Topics[edit]

Table of Contents | |||||
---|---|---|---|---|---|

# | Chapter | Status | Pages | Difficulty | Solutions |

1 | Supplementary Chapters | 5 | - | ||

1 | Primes and Modular Arithmetic | 24 | ES - PS | ||

2 | Logic | 18 | ES - PS | ||

3 | Mathematical Proofs | 11 | ES - PS | ||

4 | Set Theory and Infinite Processes | 10 | ES - PS | ||

5 | Counting and Generating Functions | 14 | ES - PS | ||

6 | Discrete Probability | 12 | ES - PS | ||

7 | Matrices | 31 | ES - PS | ||

8 | Further Modular Arithmetic | 14 | ES - PS | ||

9 | Mathematical Programming | 4 | unrated | ES - PS |

## Authors & Contributors[edit]

A number of persons not listed below have also made important contributions to this book.

Name | Role | Affiliation | Quote |
---|---|---|---|

Zhuo Jia Dai | Author | Former Honours Student of University of Sydney | Welcomes any criticism or praise. |

R3m0t | Corrections | Student of JFS Secondary School | "To iterate is human; to recurse, divine." |

Martin Warmer | Corrections & Solutions | Student of HBL High School | Welcomes all corrections and other help. |

Tom Lam | Supplementaries & Solutions | Student of Sha Tin Methodist College | "Answer is merely the fuel for more questions." |