Introduction {-}

Purpose of This Guide

This handbook aims to be a concise yet comprehensive reference for key mathematical first principles, covering topics essential for high school mathematics, university preparation, and STEM-related fields. It is designed for fast navigation, allowing readers to look up topics easily, find clear explanations, quickly learn new topics or revise specific ones.

How to Use This Handbook

Each chapter focuses on a single topic, beginning with definitions and essential formulas. Mathematical notation follows a standardised convention throughout. Where topics are built upon, cross-references to other sections are included for further exploration or for revisiting relevant material.

Notation and Conventions

• Definitions are shown in italics.
• Variables are italicised (e.g. $x, y, z$).
• Constants such as $e$ or $\pi$ retain their standard mathematical meaning.
• Essential formulas are highlighted in boxes (e.g. $\boxed{e^{i\pi}+1=0}$).
• All angles are expressed in radians unless stated otherwise.