High School Mathematics Extensions

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Introduction[edit]

This online textbook is intended for, but not limited to, 14 to 18 year old teenagers who have a general interest in mathematics. The text's language is aimed at high school students without a rigorous understanding and knowledge of university-level mathematics.

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 with 9–10 years of formal 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[edit]

Table of Contents
# Chapter Status Pages Difficulty Solutions
0 Supplementary Chapters Development stage: 50% 5 100 percents.svg100 percents.svg100 percents.svg ES - PS
1 Primes and Modular Arithmetic Development stage: 100% 24 100 percents.svg100 percents.svg100 percents.svg ES - PS
2 Logic Development stage: 70% 18 100 percents.svg100 percents.svg ES - PS
3 Mathematical Proofs Development stage: 80% 11 100 percents.svg100 percents.svg ES - PS
4 Set Theory and Infinite Processes Development stage: 50% 10 100 percents.svg100 percents.svg100 percents.svg ES - PS
5 Counting and Generating Functions Development stage: 70% 14 100 percents.svg100 percents.svg100 percents.svg100 percents.svg ES - PS
6 Discrete Probability Development stage: 30% 12 100 percents.svg100 percents.svg100 percents.svg ES - PS
7 Matrices Development stage: 90% 31 100 percents.svg100 percents.svg100 percents.svg100 percents.svg ES - PS
8 Further Modular Arithmetic Development stage: 60% 14 100 percents.svg100 percents.svg100 percents.svg100 percents.svg100 percents.svg ES - PS
9 Mathematical Programming Development stage: 10% 4 unrated ES - PS

Authors & Contributors[edit]

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."