I find this a bit funny. You are comparing books that are used by advanced undergraduates or graduate students to a book written essentially for the subset of programmers with almost no math background. There are beautiful mathematics books by Springer (Undergraduate Texts in Mathematics), Carus Mathematical Monographs and Dover that provide both intuition and rigor at an introductory level. The main problem for a beginner though is knowing where to start and getting a survey of the arena they are entering. They might think linear algebra is adding vectors together with a vector being just a list of numbers.
This book hopefully fills that gap. There are other introductory books like Mathematics: Its Content, Methods & Meaning by Aleksandrov and Kolmogorov but that requires a serious investment of time.
Lastly, I apologize but I am going to rant about this physicist phenomenon. I am a physicist myself (high-energy theory) that entered quantitative finance after my PhD (a heavily disliked field on HN). I found a lot of physicists outside academia who tend to be aggressive and condescending and often haven't actually gone through the rigors of a PhD program themselves. Maybe it makes one feel smarter to tell other people that they are reading easy books or can't jump straight to Landau or Bourbaki (those two couldn't be more different but you get the point) and there are no other physicists around to correct the notion that there are multiple ways to gain knowledge and build intuition.
It doesn't matter who says what about which book. Sample some books, find what you like as long as its not junk science/mathematics, do plenty of exercises, and try to derive things yourself and don't fool yourself that you understand something deeply by studying it for a year.
This book hopefully fills that gap. There are other introductory books like Mathematics: Its Content, Methods & Meaning by Aleksandrov and Kolmogorov but that requires a serious investment of time.
Lastly, I apologize but I am going to rant about this physicist phenomenon. I am a physicist myself (high-energy theory) that entered quantitative finance after my PhD (a heavily disliked field on HN). I found a lot of physicists outside academia who tend to be aggressive and condescending and often haven't actually gone through the rigors of a PhD program themselves. Maybe it makes one feel smarter to tell other people that they are reading easy books or can't jump straight to Landau or Bourbaki (those two couldn't be more different but you get the point) and there are no other physicists around to correct the notion that there are multiple ways to gain knowledge and build intuition.
It doesn't matter who says what about which book. Sample some books, find what you like as long as its not junk science/mathematics, do plenty of exercises, and try to derive things yourself and don't fool yourself that you understand something deeply by studying it for a year.