High School Mathematics Extensions

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High School

Mathematics Extensions


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.


Table of Contents
# Chapter Status Pages Solutions Commentary
0 Supplementary Chapters Development stage: 50% 5 ES - PS Basic counting. Polynomial division. Partial fractions. Summation. Complex numbers. Differentiation.
1 Primes and Modular Arithmetic Development stage: 100% 24 ES - PS In in maximus leo. Cum sociis natoque penatibus et magnis.
2 Logic Development stage: 70% 18 ES - PS Integer sit amet viverra nisi, sed iaculis augue. Donec tincidunt.
3 Mathematical Proofs Development stage: 80% 11 ES - PS Quisque dui nunc, elementum sed ornare nec, egestas vel libero.
4 Set Theory and Infinite Processes Development stage: 50% 10 ES - PS Cras porttitor sem enim, eu consequat purus sodales sit amet.
5 Counting and Generating Functions Development stage: 70% 14 ES - PS Ut tincidunt enim tempor libero varius, id imperdiet ex aliquet.
6 Discrete Probability Development stage: 30% 12 ES - PS Etiam quis turpis mollis, mollis ipsum eu, feugiat lorem. Donec.
7 Matrices Development stage: 90% 31 ES - PS Aliquam erat volutpat. Donec dui nibh, finibus in pretium id.
8 Further Modular Arithmetic Development stage: 60% 14 ES - PS Cras id eros mi. Suspendisse non felis ut odio mollis.
9 Mathematical Programming Development stage: 10% 4 ES - PS Nunc malesuada et ligula aliquam luctus. Interdum et malesuada fames.

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."