Very first sentence of 2.1 is full of notation, symbols and terms that I, as a prospective student, might not understand.So many teachers seem incapable of stepping outside their sphere of knowledge and seeing what they know and others do not. And so much work went into this.

 Even as someone who did their undergrad in math, it's a bit tough to digest. I'd have to look up a lot of the terms again. It's been five years since I was in college. Shows how little I've used it all since I graduated.It definitely looks more like, "math basics" for x field. Kinda like "automotive basics" for Honda or Ford vehicles. Where it's presumed that you know a lot of automotive lingo to begin with and you just need to know what spark plugs go with what engine. And not, "what is a spark plug?"
 It sounds like you correctly identified a mismatch between audience and material, but I don’t think it’s appropriate to describe the teachers/authors as having made an error. Why would you assume that you are the intended audience of this text and thus that the authors have made some mistake?
 That's a valid question, but the title of the post begins with "Math Basics..." The title of the paper is totally different. Maybe my point should have been directed at OP rather than the authors.
 Indeed, I think the HN submission title is erroneous.The actual paper’s title:> Algebra, Topology, Differential Calculus, and Optimization Theory For Computer Science and Machine Learning
 As mentioned in the paragraph above it, the chapter is a review, i.e. it's trying to quickly refresh the reader's memory on things they're already supposed to know; it's not trying to teach something new. So the sentence (“The set R of real numbers has two operations +: R × R → R (addition) and ∗: R × R → R (multiplication) satisfying properties that make R into an abelian group under +, and R − {0} = R∗ into an abelian group under ∗”) seems fine for that purpose.If you look at any of the later chapters that are trying to teach something new, they are much more gentle and motivate the topic of that chapter: see e.g. “24.1 Affine Spaces” on page 759, or “26.1 Why Projective Spaces?” on page 823, etc.Other chapters that are meant as a review are similarly terse and quick to the point (like Chapter 2), e.g. Chapter 37 “Topology” on page 1287.I think it's good when books make conscious choices about what they're teaching versus assuming as a prerequisite (and communicate it to the reader, by using terms like “reviewed” — presumably the yet-to-be-written Introduction chapter will also mention this more explicitly).
 On the other hand, it's a perfect refresher for those of us who "know" this, but somehow forgot most of it.
 As someone in the same boat I've found this book to be very helpful.https://www.amazon.com/gp/product/1466230525 - Mathematical Notation: A Guide for Engineers and Scientists
 I purchased this. I've been trying to brush up on CS fundamentals (it's been a long time since college), but I get stuck just on trying to understand what I'm being asked to learn.Thank you