High School Mathematics Extensions

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


  1. Basic Counting - ES
  2. Partial Fractions - ES
  3. Summation Sign - ES
  4. Complex Numbers - ES
  5. Differentiation - ES

Note: * Means that the chapter is currently under active development by the author.


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."

  • Also (as it seems fitting): Facts alone are as alike to math as bricks are to a house. However, when math is explained, toughed and thought about, shown in context, etc. — it resembles a house.

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."