This book is your all-in-one guide to understanding mathematics clearly and efficiently. Each page tackles a single, central question with straightforward explanations on the left and practical examples on the right.

Ideal for anyone who

• wants (or needs) to truly understand math,
• prefers visual learning,
• likes finding the essentials at a glance,
• only wants to read what’s relevant right now.

What makes this book unique?

• Every page is self-contained and easy to follow.
• Concepts are explained in a conversational style.
• Examples are comprehensive, yet easy to follow.
• No prior knowledge required, we start from the very beginning.

From the basics to more advanced questions:

• How do you expand and reduce fractions?
• What does “if and only if” mean?
• ...
• How do you find the derivative of an inverse function?
• When does an improper integral of a function exist?

This book is a translation of the original German edition Mathe übersichtlich: Von den Basics bis zur Analysis, 3rd edition, by Adriane Gründers, published by Springer-Verlag GmbH, DE in 2025. The translation was done with the help of an artificial intelligence machine translation tool. A subsequent human revision was done in close cooperation with native speakers, but the book might still read stylistically differently from a conventional translation.

Adriane Gründers (pseudonym) holds a PhD in mathematical physics and works in a science-oriented company. Sharing mathematics with others is a matter close to her heart. She is firmly convinced that many more people could understand and enjoy mathematics than is currently the case. This book aims to contribute to that vision.