# High School Mathematics Extensions

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High School

Pure Maths Extensions

## Introduction

This online textbook is intended for, but not limited to, high school students without a rigorous understanding and knowledge of university-level mathematics. Therefore, the text's language reflects the expected mathematical maturity of the intended audience.

This book introduces several interesting topics not covered in the standard high school curriculum of most countries.

The materials presented can be challenging, but at the same time, we strive to make this book readable to all who are a few years from applying to higher education.

From the authors

It is our firm belief that math textbooks should not just be a collection of mathematical facts carefully laid out for rote memorization and cram sessions. A math textbook, especially for the youth, should be full of questions, not just exercises. These questions require some thought to answer and spark curiosity. After all, the questions keep the students engaged, not the answers.

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

We sincerely hope to interest, stimulate, and challenge all those who read this book.

## Topics

# Chapter Status Pages Solutions Commentary
0 Supplementary Chapters   5 ES - PS Basic counting. Polynomial division. Partial fractions. Summation. Complex numbers. Differentiation.
1 Primes and Modular Arithmetic   24 ES - PS

Fundamental Theorem of Arithmetic, Divisibility/Division, Primes

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 ES - PS
10 Markov Chains   1 ES - PS
11 Peano's Axioms   1 ES - PS

## Authors & Contributors

A number of persons not listed below have also made important contributions to this book. Contributors are encouraged to edit and include themselves in this list.

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."