“[Talking of Spivak, Calculus] This is a book everyone should read. If you don’t know calculus and have the time, read it and do all the exercises. Parts 1 and 2 are where I finally learned what a limit was, after three years of bad-calculus-book “explanations”.”
Well, this doesn’t even seem like consistent advice - he apparently read Spivak after three years of other courses YET he recommends it for those who don’t know calculus.
Aside from getting an official MA, I’ve done a lot of reading and teaching myself math on my own, including teaching myself calculus in 10th grade. Spivak isn’t a book I’d recommend for learning on one’s own.
As I recall from my self-teaching Odyssey, Spivak was a book that top-level school liked to teach from (I remember either Caltech or MIT using him). But it seemed pretty terrible to read from. I recall long explanations that weren’t actually good explanations, a unique and unhelpful order of presentation of the material and unnecessarily tortuous epsilon-delta proofs - the author admits that Spivak is doing actual analysis using just epsilons and deltas, thereby creating proofs more complex than either an introductory calculus book or a mid-level upper division text.
Calculus is arguably the biggest leap in mathematical understanding that people had in the last two thousand years. It actually doesn’t make much sense to jump simultaneously into both a greater level of rigor and a more difficult area of study simultaneously.
While this being the text for classes featuring the best and the brightest kids in top universities might seem like a great recommendation, actually I’d suspect a good portion of those kids already know the standard calculus outline and are itching for whatever problem one might throw them. Moreover, they have each other and a likely top-teacher to fall back on - so a book that by itself offers few good explanation and many challenges can seem great.
I would recommend any standard “doorstop” calculus text as long as it’s rigorous enough to include some epsilon-delta proof.
Anyway, the rest of document comes closer to acknowledging that “canonical text on the subject” and “good book to read on your own” aren’t usually the same thing unless someone understands they’re diving into a subject the hard way. But I just thought I’d jump on the one quote I started with.
“[Talking of Spivak, Calculus] This is a book everyone should read. If you don’t know calculus and have the time, read it and do all the exercises. Parts 1 and 2 are where I finally learned what a limit was, after three years of bad-calculus-book “explanations”.”
Well, this doesn’t even seem like consistent advice - he apparently read Spivak after three years of other courses YET he recommends it for those who don’t know calculus.
Aside from getting an official MA, I’ve done a lot of reading and teaching myself math on my own, including teaching myself calculus in 10th grade. Spivak isn’t a book I’d recommend for learning on one’s own.
As I recall from my self-teaching Odyssey, Spivak was a book that top-level school liked to teach from (I remember either Caltech or MIT using him). But it seemed pretty terrible to read from. I recall long explanations that weren’t actually good explanations, a unique and unhelpful order of presentation of the material and unnecessarily tortuous epsilon-delta proofs - the author admits that Spivak is doing actual analysis using just epsilons and deltas, thereby creating proofs more complex than either an introductory calculus book or a mid-level upper division text.
Calculus is arguably the biggest leap in mathematical understanding that people had in the last two thousand years. It actually doesn’t make much sense to jump simultaneously into both a greater level of rigor and a more difficult area of study simultaneously.
While this being the text for classes featuring the best and the brightest kids in top universities might seem like a great recommendation, actually I’d suspect a good portion of those kids already know the standard calculus outline and are itching for whatever problem one might throw them. Moreover, they have each other and a likely top-teacher to fall back on - so a book that by itself offers few good explanation and many challenges can seem great.
I would recommend any standard “doorstop” calculus text as long as it’s rigorous enough to include some epsilon-delta proof.
Anyway, the rest of document comes closer to acknowledging that “canonical text on the subject” and “good book to read on your own” aren’t usually the same thing unless someone understands they’re diving into a subject the hard way. But I just thought I’d jump on the one quote I started with.