This personal project is a free and open-source mathematics textbook aimed mostly at people who haven't yet been exposed to formal mathematics. I like to say that it is the book I would have liked to read when I was in secondary school. Currently, these are the topics that it covers:
- Informal logic and set theory.
- Formal propositional and predicate logic.
- Zermelo–Fraenkel set theory.
This list will surely grow over time.
The book is conceived to have nearly zero prerequisites. The whole point of it is constructing mathematics from scratch: using some basic intuition as a starting point, then working on mathematical logic and, from then on, doing some mathematics. I have tried to write with a deep focus on formality and rigour while keeping in mind that I am "talking" to a fellow human being. This balance is difficult to strike, and I am fully aware that, most likely, I haven't fully achieved it.
You can choose to download the latest release, which is updated somewhat regularly, or a fixed edition. In addition, you can customise the format of the book. The book is available on the A4 and A5 paper sizes, and it can be optimised for double-sided printing or for on-screen reading.
Open access and open source
This work is open-source and is distributed under a very permissive Creative Commons license (CC BY 4.0). You can find all the information and the source code on the book's Git repository.
What's next?
Nothing is ever truly finished, and this book is no exception. My intention is to update it indefinitely, but I suppose only time can tell if I will. At the moment, I am in the process of thoroughly reviewing Edition 1.0. I plan to release Edition 1.1 once this review is over.
I also have plans for an Edition 2.0 with new material, but that will take quite some time to materialise. I am also working on other big projects, and I want to make this book fit with them. Hopefully (and this is just a hope) all of these aims will become a reality some day.