This book is a website edition of the popular Malone Algebra mathematics series. It covers mathematics from high school algebra through linear algebra. It blends foundational skills with advanced concepts, moving quickly while keeping explanations clear. We begin with algebra, introduce calculus early, and bring in just enough geometry and trigonometry to cover all essential topics. The goal is to prepare you not only for university placement exams but also for advanced study—up to the equivalent of a master’s level foundation.

Because this is an ambitious undertaking, emphasis is placed on building strong foundations through precise definitions, vocabulary, and cross-linked concepts. Rather than isolating topics, I weave them together so that you see mathematics as one connected whole. Every operation is thoroughly explained with definitions, illustrations, and step-by-step processes. The more you understand how math works, the less you will have to memorize or struggle with later.

My goal is to compress time: four years of high school math in one year, four years of undergraduate math in another—while also introducing abstraction. Exposure to advanced concepts early gives you a sense of how mathematics progresses and encourages creativity in building your own formulas and methods.

Formal logic and proof-writing will be included, but early definitions are written plainly so even younger readers are not overwhelmed. Explanations are intentionally short at first to preserve flow, then gradually grow in rigor. The book is based on my own experience, research, and synthesis of countless resources. If you ever feel you need more practice, I encourage you to pick up a used algebra or calculus book as a supplement—but my intention is to give you a self-contained reference.

In truth, you do not need endless repetition of the same problem. What you need is a clear overview of the mathematics and their relationships to each other. This book will equip you to create equations for real-life situations and solve them with increasing sophistication. You will also gain confidence to explore mathematics beyond this volume, engage with others online, and even contribute your own ideas.

Mathematics has two sides: pure and applied. Pure math defines the rules and logical framework; applied math uses those rules to solve real-world problems. If math is not enriching your life or helping solve problems, it has failed its purpose. Here, concepts are presented in a nontraditional but practical way, always with an eye toward usefulness.

Here are some things to keep in mind:

1. Audience – I wrote this book for everyone, regardless of age or skill level. Only arithmetic (+, −, ×, ÷) is assumed. Younger readers will encounter terms earlier than usual, giving them a head start. Adults will find gaps in their knowledge filled. Even if some material feels advanced, the book remains a valuable reference that prepares you for college and beyond.

2. Format – This book is part formal textbook, part upperclassman’s notes, and part conversation with a peer. Skip what you already know, pause where you need more clarity, and treat it like a guided dialogue. I wrote this at significant personal cost of time and resources because I believe access to complete, clear math instruction should not require endless subscriptions or piecemeal internet searches.

3. Style of Explanation – Definitions begin casually, then grow in rigor. Examples are sometimes long—not to waste time, but to ensure every step is illuminated. I refuse to leave gaps that might cause confusion later, especially when moving from one course or resource to another.

4. Beyond Basics – Many books stop at fundamentals. I take advanced concepts and make them understandable, then show how they apply to real-world situations. Instead of a detached teacher-student tone, I write as someone eager to share insights and clear approaches.

5. Order – We start with simple algebra and quickly incorporate higher-level concepts like functions and Greek notation. The problems are intentionally easy, so that the focus is on understanding the machinery behind the math. This allows you to walk into any course and recognize what to do.

6. Progression – After algebra, we move into calculus and then linear algebra. Once terminology and foundations are in place, math is applied directly to nearly 200 real-world problems.

7. Language – Every math term and symbol is explained thoroughly. If you can read English, you can use this book. Along the way, your reading and writing skills will improve alongside your math.

8. Enrichment – History, anecdotes, and side concepts are sprinkled in to make learning engaging, even when they aren’t strictly necessary for solving problems.

9. Scope – The most advanced fields are beyond this single volume. This book focuses on building foundations so that you can later approach engineering, physics, programming, economics, finance, manufacturing, and other advanced sciences. A sequel will take on those challenges.

You’ll also find glossaries, reference tables, and data sets placed at the front and back of the book for convenience.