I think it will be pretty rough to start out on that book. I'd start with The New Turing Omnibus -- it's very readable and accessible and also covers a wide range of topics.
I would also recommend How to Design Programs if you're looking to just write better software in general.
The New Turing Omnibus is updated, (but it's still a bit long in the tooth at this point).
Not particularly, but here are a couple recommendations (make good gifts):
The Turing Omnibus — it's a bit dated, but it's eighty-five topics, each given a ~5-page overview. It's good for the lay-person, but also great for a CS person to fill in inevitable gaps. (No matter how good your undergrad degree, there are several of those 85 topics that one should have a clue about, but didn't get mentioned in any class.)
I enjoyed Douglas Hofstaedter's Metamagical Themas — a collection of interesting essays, makes for good bedtime reading. Most of it isn't CS per se, but CS people would probably like it.
I see that both of these can be bought used on amazon for about $3. Not sure if that makes me happy, or sad.
In my experience people proficient in Applied Maths transition very well to software.
My personal advice is to look into open source or some personal projects. Working on a decently sized project is great experience that will give you good tools to pass interviews. You'll also need too practise problem solving for interviews, using Leetcode or hackerrank.
If you're having trouble deciding what type of software to work on, you could try reading for inspiration. I have some book recommendations:
The New Turing Omnibus - This is a super useful book. As somebody who originally self learned computer science, it gives you a good insight into a lot of different subdomains. You might find something you're particularly interested in.
Pragmatic Programmer. This is less of an "inspiration" book, but it lays out a lot about approaches to software development you might find useful.
Programming Pearls - This is more code oriented. It goes through some interesting problems and is a fun read if you'd like something with more practical example.
It's also fun to just look through O'Reilly books to find something you're interested in. I'm reading Designing Data-Intensive Applications at the moment; which is great.
I love this one. The book cover a lot of important topics in computer science and does it in such a way that is in the middle of divulgation and technical reading. Have fun!