5 ms·

Previous discussion: https://news.ycombinator.com/item?id=20570025 https://news.ycombinator.com/item?id=20570025 Tl;dr: * This is dense * This is hard to und

Previous discussion: https://news.ycombinator.com/item?id=20570025 https://news.ycombinator.com/item?id=20570025 Tl;dr: * This is dense * This is hard to understand if you don't have an education in mathematics * This is not really meant to be an "introduction to X" book unless you have the background knowledge * Gallier (who imo is an awesome professor) really values rigor and not hiding anything behind hand-wavy statements. He is an incredibly serious mathematician + computer scientist (https://en.wikipedia.org/wiki/Jean_Gallier https://en.wikipedia.org/wiki/Jean_Gallier). Accordingly, this book (work in progress) tries to be incredibly detailed on the topics it chooses to cover (and may miss out on some areas of CS + ML solely bc it chooses detail over comprehensiveness).

chombier 7y ago
A few years back I read Gallier's notes on matrix Lie groups, this was definitely the most accessible (yet complete) introduction to the subject I found.
wenc 7y ago
The title is interesting because it purports to cover the areas of math relevant to CS and ML. So I took at a look at the topics covered, and my impression is that they were chosen by a generalist mathematician rather a specialist in each of the areas -- in optimization for instance, some of the topics would not be developed or weighted in quite in this fashion in a state-of-the-art course. Other subtopics serve purely theoretical interests -- either too theoretical or lack sufficient depth to be useful to the practitioner or the earnest researcher. I fear this may mislead some into thinking that the topics proposed are the primary ones in each area of study -- I would be wary of using this a trunk of a semantic tree to build knowledge on. There seems to a lack of mathematical unification in the work except perhaps these were a collection of topics that were of interest to the author(s). I want to say this could be a good handbook, but handbooks (e.g. engineering handbooks) are usually collections of pieces written by specialists in each subfield. I suspect that by attempting to cover such a large chunk of the mathematical landscape, some things may have been lost in the treatment (except in topics that the authors are specialists in). Still, it is a good effort and I congratulate the authors on the ambitious attempt but would advise readers to consult texts written by experts in each subfield to get a sense of what topics are important and what are not.
- graycat 7y ago
  > my impression is that they were chosen by a generalist mathematician rather a specialist in each of the areas -- in optimization for instance, some of the topics would not be developed or weighted in quite in this fashion in a state-of-the-art course. Yes. Compared with this book, the one semester course "Foundations of Optimization" I took was better balanced and usually deeper. > I want to say this could be a good handbook I see it as best as a handbook. So, e.g., if hear about some topic X, want to know more, and find a treatment in this book, then give the book a shot but don't take the book too seriously as the balanced view of an expert. > advise readers to consult texts written by experts in each subfield to get a sense of what topics are important and what are not. Yes. And not just for "a sense" but for the actual content. E.g., I would go to some of the books in my professional library for the numerical analysis, linear programming, non-linear programming, regression analysis, Hilbert space, exterior algebra, abstract algebra, Lagrangian techniques, etc. And in the table of contents I didn't see anything on network flows which, considering what else is in that book, is a curious omission. But, again, in summary, if want to know about topic X that is in the book, then likely give the book a shot, at least for a few minutes. One more point: For students who want careers in academic research, one reason, likely the most important reason, to study such advanced and specialized topics is as an introduction to some promising streams of research. Well, I'd try to avoid using this book much for that goal and, instead, look for better material from better sources.
graycat 7y ago
> This is hard to understand if you don't have an education in mathematics Right: Sure, some undergraduate math major who has been rushing ahead in math since, say, middle school, could study all of this book, but most of the book is mostly more advanced and/or specialized than undergraduate math majors will encounter. But, yes, it would be wise to regard an undergraduate math major as a nearly necessary prerequisite for the book. In that case, the 70+% of the academic computer science community will have a tough time having math background enough to make good use of this book.

chombier 7y ago

A few years back I read Gallier's notes on matrix Lie groups, this was definitely the most accessible (yet complete) introduction to the subject I found.

wenc 7y ago

The title is interesting because it purports to cover the areas of math relevant to CS and ML. So I took at a look at the topics covered, and my impression is that they were chosen by a generalist mathematician rather a specialist in each of the areas -- in optimization for instance, some of the topics would not be developed or weighted in quite in this fashion in a state-of-the-art course. Other subtopics serve purely theoretical interests -- either too theoretical or lack sufficient depth to be useful to the practitioner or the earnest researcher. I fear this may mislead some into thinking that the topics proposed are the primary ones in each area of study -- I would be wary of using this a trunk of a semantic tree to build knowledge on. There seems to a lack of mathematical unification in the work except perhaps these were a collection of topics that were of interest to the author(s). I want to say this could be a good handbook, but handbooks (e.g. engineering handbooks) are usually collections of pieces written by specialists in each subfield. I suspect that by attempting to cover such a large chunk of the mathematical landscape, some things may have been lost in the treatment (except in topics that the authors are specialists in). Still, it is a good effort and I congratulate the authors on the ambitious attempt but would advise readers to consult texts written by experts in each subfield to get a sense of what topics are important and what are not.

graycat 7y ago
> my impression is that they were chosen by a generalist mathematician rather a specialist in each of the areas -- in optimization for instance, some of the topics would not be developed or weighted in quite in this fashion in a state-of-the-art course. Yes. Compared with this book, the one semester course "Foundations of Optimization" I took was better balanced and usually deeper. > I want to say this could be a good handbook I see it as best as a handbook. So, e.g., if hear about some topic X, want to know more, and find a treatment in this book, then give the book a shot but don't take the book too seriously as the balanced view of an expert. > advise readers to consult texts written by experts in each subfield to get a sense of what topics are important and what are not. Yes. And not just for "a sense" but for the actual content. E.g., I would go to some of the books in my professional library for the numerical analysis, linear programming, non-linear programming, regression analysis, Hilbert space, exterior algebra, abstract algebra, Lagrangian techniques, etc. And in the table of contents I didn't see anything on network flows which, considering what else is in that book, is a curious omission. But, again, in summary, if want to know about topic X that is in the book, then likely give the book a shot, at least for a few minutes. One more point: For students who want careers in academic research, one reason, likely the most important reason, to study such advanced and specialized topics is as an introduction to some promising streams of research. Well, I'd try to avoid using this book much for that goal and, instead, look for better material from better sources.

graycat 7y ago

> This is hard to understand if you don't have an education in mathematics Right: Sure, some undergraduate math major who has been rushing ahead in math since, say, middle school, could study all of this book, but most of the book is mostly more advanced and/or specialized than undergraduate math majors will encounter. But, yes, it would be wise to regard an undergraduate math major as a nearly necessary prerequisite for the book. In that case, the 70+% of the academic computer science community will have a tough time having math background enough to make good use of this book.