I’ve written a mathematics book. It’s called Fondamenti di matematica per studenti di informatica, it runs to 316 pages, fifteen chapters, ninety-eight exercises and fifty-eight figures, and the cover carries one line that sums the whole project up better than I can: written by a software developer, for computer scientists.
That wasn’t the plan. The plan was to pass three exams.
At nineteen, first-year engineering maths made me drop out of everything, and when I went back to university I found it waiting for me unchanged: Calculus, Algebra, Probability. The difference is that twenty-odd years later I had a method, which is the same thing I do at work when a system won’t fit in my head: I rewrite it. I started reorganising in writing every topic I studied, in LaTeX, because handwritten mathematics can’t be refactored.
At some point I noticed that what I was producing weren’t notes. They were chapters. So I went looking for the real book, the one written by someone who knows what they’re doing, so as not to waste time redoing something others had already done well.
I didn’t find it. I found excellent textbooks for mathematics students, which are rigorous and complete and assume you want to become a mathematician. I found popular books that tell you about mathematics without asking you to do any. What I did not find, in Italian, is an introductory book written for people who program: one that when it explains modular arithmetic also tells you this is the same thing sitting underneath a hash function and half of cryptography, that when it reaches graphs reminds you you’re looking at the most used data structure in your trade, that when it defines the asymptotic behaviour of a function points out you already use that notation daily without calling it by name.
The book is organised in three blocks. The first is language and tools: how to read mathematical writing, elementary algebra, analytic geometry, trigonometry, functions, sequences and induction. The second is logic, propositional and predicate, with proof techniques. The third is discrete mathematics: sets, cardinality, relations and functions, graphs, combinatorics, elementary number theory. Every chapter carries its link to computing, stated explicitly.
One clarification that matters to me. The book is not a course summary and does not recycle any university’s teaching material: it is written from sources, with a bibliography of a hundred and seventy-three titles that are the books I actually studied from. It was a rule I set myself at the start and never felt tempted to bend, because a textbook that copies another textbook is of no use to anyone.
What convinced me to see it through, though, was something else. The chapters I was writing started circulating among my coursemates, and they used them to prepare the same exams. Until that moment they were my way of studying. From that moment they were a book.
Previews and chapters are at matematica.lornova.it.
The handbook I wanted to find at nineteen didn’t exist. Now it does, and it was written by the person who needed it most.
Last modified on 2026-06-10