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I'm a big fan of Herstein's exposition. The text is plenty rigorous, without too getting bogged down in formalism, and he also manages to come across as persona

I'm a big fan of Herstein's exposition. The text is plenty rigorous, without too getting bogged down in formalism, and he also manages to come across as personable and funny in a way that doesn't feel condescending. The people who update/glue stuff onto the 23rd edition of those 1200-page doorstop undergrad calculus texts would do well to revisit books of that era and learn the difference between "engaging" and "patronizing." That's not a dig at the books not being Spivak or Apostol - there's absolutely a place for that kind of undergrad textbook (though maybe not 1200 pages of it, updated every three years) - but in terms of attempts at being 'relevant' that transparently read as 'Hi, fellow kids!' I also dig Herstein's problem sets, there's a good breadth of difficulty, and they really elucidate key ideas, or point to other topics not covered in the text. Some of the problems are absolutely wicked, but in a good way. (IIRC, doesn't the introduction say that some are meant more to be attempted than actually solved?)

newsoul 4y ago
I am searching for a good calculus book. Not those 1200 pages of boring stuff. Something reasonable that teaches in good depth and breadth.
- MikeBVaughn 4y ago
  There are lots of cool options, depending on what you want to do with it. If you're interested in rigorously proving how calculus works, starting from the structure of the real numbers, I hear nothing but fantastic things about Spivak. I've not worked much of it myself, but the exercises seem very well chosen from the sections I've read. It exists in an interesting space between a calculus textbook and an introduction to real analysis, and you'll see stuff like the intermediate value theorem proven rigorously. If you want to practice computational applications, you may have to supplement it with some other exercises and material, from what I've heard, though. Apostol also exists in the same space as Spivak, and was (possibly still is) the calculus textbook of choice at Caltech. For a more applied approach in line with the general content of the enormous undergrad omnitext, this seems cool: https://ocw.mit.edu/courses/res-18-001-calculus-online-textbook-spring-2005/pages/textbook/ https://ocw.mit.edu/courses/res-18-001-calculus-online-textb... Dover and Springer have some pretty neat slim volumes that occupy the 'less rigor/intended for applications' side, though the names and authors escape me right now. (Edit: Morris Kline was the Dover book I was thinking of, and I've heard good things about Serge Lang's introductory calculus book.) (Second Edit: Kline doesn't seem particularly slim at 900ish pages, but it is well-liked. Let's go with 'comparatively slim.' In my defense, most Dover books ARE comparatively concise.)
  - newsoul 4y ago
    Thanks! I think I am either going to go by Apostol or Spivak. I have had calculus years ago. I remember the mechanics faintly. I need a solid revision with the associated theory behind it. The only problem with Spivak is that it covers single variable while Apostol's two volumes cover much much more.
    - MikeBVaughn 4y ago
      Glad to help! Posting about this inspired me to review all the calculus that I've barely touched in a decade, so I checked out a library copy of Apostol for myself :)

newsoul 4y ago

I am searching for a good calculus book. Not those 1200 pages of boring stuff. Something reasonable that teaches in good depth and breadth.

MikeBVaughn 4y ago
There are lots of cool options, depending on what you want to do with it. If you're interested in rigorously proving how calculus works, starting from the structure of the real numbers, I hear nothing but fantastic things about Spivak. I've not worked much of it myself, but the exercises seem very well chosen from the sections I've read. It exists in an interesting space between a calculus textbook and an introduction to real analysis, and you'll see stuff like the intermediate value theorem proven rigorously. If you want to practice computational applications, you may have to supplement it with some other exercises and material, from what I've heard, though. Apostol also exists in the same space as Spivak, and was (possibly still is) the calculus textbook of choice at Caltech. For a more applied approach in line with the general content of the enormous undergrad omnitext, this seems cool: https://ocw.mit.edu/courses/res-18-001-calculus-online-textbook-spring-2005/pages/textbook/ https://ocw.mit.edu/courses/res-18-001-calculus-online-textb... Dover and Springer have some pretty neat slim volumes that occupy the 'less rigor/intended for applications' side, though the names and authors escape me right now. (Edit: Morris Kline was the Dover book I was thinking of, and I've heard good things about Serge Lang's introductory calculus book.) (Second Edit: Kline doesn't seem particularly slim at 900ish pages, but it is well-liked. Let's go with 'comparatively slim.' In my defense, most Dover books ARE comparatively concise.)
- newsoul 4y ago
  Thanks! I think I am either going to go by Apostol or Spivak. I have had calculus years ago. I remember the mechanics faintly. I need a solid revision with the associated theory behind it. The only problem with Spivak is that it covers single variable while Apostol's two volumes cover much much more.
  - MikeBVaughn 4y ago
    Glad to help! Posting about this inspired me to review all the calculus that I've barely touched in a decade, so I checked out a library copy of Apostol for myself :)