I self-published my first book Higher Mathematics from a Lower Point of View, Part 1 (in Croatian) exactly 20 years ago and I am still proud of it. As it is often the case, Part 2 was never written. When I paid taxes to the state, I ended up financially at a loss. This book was the basis for “serious” books for students, which were methodically better, but never reached the charm and fun of this first book. I believe that in the Understanding and Doing Math series I have managed to combine the charm and fun of this first book and the methodicalness of the later books. I also hope that after paying taxes, I will still have something left.
For the needs of teaching at the University of Applied Sciences Velika Gorica, where I teach mathematics, I wrote a series of five books with a very poetic common title Mathematics for Technical High Schools (in Croatian). In them, the topics highlighted in the subtitles are presented on an intuitive and picturesque level:
Part 1: Numbers, Language, Functions
Part 2: Elementary functions
Part 3: The mathematics of change, Mathematical structures
Part 4: The mathematics of change – additional topics
Part 5: Multidimensional mathematics of change
I later added two more books to that series, Elementary Numerical Mathematics with the Help of Microsoft Excel and Elementary Probability and Statistics with the Help of Microsoft Excel.
And finally, there is the book Introduction to Mathematical Logic and Foundations of Mathematics. As the title itself suggests, the book lays out the very basics of logical thinking and mathematics. The front cover of the book outlines some successes – the precise notion of proof, and the notion of a cumulative hierarchy of sets in which almost all mathematics can fit. The back cover outlines some “failures” – the existence of paradoxical multitudes and problems that cannot be programmed.
One day, two teachers, Gordana and Željko, asked me if I would write math textbooks for elementary school with them. I told them I didn’t feel capable of it – I’ve been working with students for decades and I have no sense of how to introduce math to children’s world. They asked me to try. They gave me two small plastic triangles and a compass and asked me to write a lesson. I started drawing angles, triangles, transversals of parallel lines, … And I liked that. So I became a co-author of books for elementary school with the common title Mathematical Challenges. I especially liked to write stories: what connects a drop of water and the Taj Mahal and what Pythagora and an electric guitar.