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High School

Pure Maths Extensions

Introduction

This online textbook is intended for, but not limited to, high school students that do not have 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 may read this book.

Topics

Table of Contents
#	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."