A Programmer's Introduction to Mathematics

I am a professional programmer but always struggled with math at school. I could repeat what was taught and pass the tests, but always wanted a deeper intuitive understanding of many numeric areas of mathematics the way I had with algorithms, graphs and computer science related math. This book has been a revelation, not only does it teach the topics well but it deals with the culture and underlying thought patterns a mathematician needs. Right from the introduction I knew the author's attitude towards learning aligned with my own. It has been a joy. Concepts that escaped me for years all of a sudden were clear, simple and intuitive. Concepts I found boring, difficult or unpleasant suddenly became engaging, simple and FUN. This book is all the missing pieces I wish I had been taught in school. This book has marked a new chapter in my life, one in which I enjoy mathematics for its own sake and not as a necessarily evil of the more academic parts of my programming profession.

First of all, this is not an absolute introduction to mathematics. The author expects that you will already have at least an excellent understanding of algebra, and some familiarity with mathematics as a whole. When I say some familiarity, I mean understanding of how proofs work and how to produce them. So no, this is not an introduction, it is a "programmer's" introduction, and as a result the author expects you to already have at least college level (high school level if you're reading from the States) mathematics education, and Bachelor's level mathematics for Computer Science education, similar to the author's own Mathematics/Comp Sci Bachelor's degree. Therefore, the book is aimed very specifically at people with this level and area of education, looking for a bridge to undergraduate Mathematics. So is the book useless for everyone else? No. The book is actually an excellent primer to 'culture' in Mathematics and mathematical notation. Even if you don't have the background necessary to get the most out of this book, it will equip you with at least the notation and proof reading skills you'll need to get some level of understanding from a proof. In that regard, this book is a great first step. The key is to not be intimidated by the sheer volume of theorems and proofs the author throws at you, at times the pacing of this book can be overwhelming, and it's common for the author to go through 20+ proofs in 40 pages with not a single line of accompanying code to help the reader digest what they're seeing. From that perspective, the book has really failed to make Mathematics digestible to your average programmer. I think that the root cause of this problem is the author's PhD in Mathematics. At times it seems he fails to translate from his level of understanding of the topics to a much less mature understanding that the reader is likely to have, but at other times he does this masterfully. Finally, I think that some chapters and all of the exercises in the book expect way too much from the reader in terms of prior knowledge. Perhaps this speaks more to my inexperience with mathematics, but all of the exercises I felt incredibly under-equipped for even after reading the chapters thoroughly, and I skipped most of them. Solutions aren't provided as a source of ground-truth if you get lost. Overall I got quite a lot out of this book, and I do feel like I am now better equipped to tackle the areas of mathematics introduced in the book, and maybe some new ones. It has served as a good introduction, a first baby step, but it is literally just that, and I don't feel like I have come away with anything more than a very high-level understanding of the topics covered. As mentioned by other reviews, this book served as a reminder that Maths is really hard, and I'll need to get my hands on many other resources and spend a lot more time learning before I can say I really understand what was covered in this book.

It doesn’t only teach mathematics, it teaches you how to comprehend and navigate in the mathematics way of writing things. For example in the first chapter it gives you his hand and goes with you all the way from a definition to a complete understanding of what is expected from you to do while reading a mathematical definition in any book. It explains what no other book explains about the process of learning new mathematics, what’s explicit, what’s implicit, what you have to figure out, although it also explains interesting mathematics. I really recommend this book, and I don’t have any affiliation with the author, only gratitude for his effort of writing such a profound different kind of mathematical book.

As someone who has been programming for years without much of a formal introduction, this book helped me to visualise the otherwise alien concepts that maths brings to computer science. Opened my eyes to how much of my work has been spent essentially writing my own expressions / proofs without understanding their true significance. Do consider however, that as a self-published work, this book contains multiple typos - which caused (later to be discovered as unnecessary) scrutiny as I read.

Fantastic book and has re-ignited by interest in mathematics I thought long dead and buried. The book is written by someone who knows just how difficult it is to a non-mathematician to try to digest the notation and using code snippets as a translation for these algorithms and equations just makes it even better. Don't worry if you find even the first few chapters uncomfortable to take in, the book is not meant to be speed read but will guide you through what you need to know well.

This book reminds the reader that Mathematics is difficult. I'm only about a third of the way through, and I've given up on trying to understand every concept that has been presented. It walks through proofs and the reading of proofs from the very beginning, which from a mathematics standpoint, is a very good thing. Unfortunately reminds me that despite being a programmer, I am no natural mathematician.

Can’t believe it took so long to find this book. Long realised that I needed to fill in the gaps as my ComSci course was overly practical. This was a great way to do it and a great intro to proper maths. Fantastic book not just for the knowledge it contains but for the amount of knowledge it has enabled me to go on and obtain beyond it.

Nice learning curve for the programmer with interests in maths.