High School Mathematics Extensions
High School
Pure Maths Extensions
 |
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Introduction
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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
[edit | edit source]| 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
[edit | edit source]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." |