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I used Tao's books on Real Analysis during college and my feelings are mixed on his capabilities as an educator. On the one hand his books were really great as

I used Tao's books on Real Analysis during college and my feelings are mixed on his capabilities as an educator. On the one hand his books were really great as he gave a lot of proofs (although most proofs were still left to the reader, but I guess that you can't really learn Analysis without proving Rolle's Theorem or the First Theorem of Calculus on your own) and what I also really liked was that he made no assumptions about your knowledge and started from scratch (first set theory, then properties of natural, whole and rational numbers before constructing the real numbers using Cauchy sequences). On the other hand there were a lot of errors in his books and sometimes he is hard to follow, I guess the books contents are too easy for him and he wrote the book without ever reading back. Even though his books weren't perfect I learned so much about pure mathematics as a non-math major and I don't think I could have learned so much through Rudin's books.

mahyarm 11y ago
Sounds like he just needed a few math grad student editors. A real reason for a new edition!
gohrt 11y ago
> (first set theory, then properties of natural, whole and rational numbers before constructing the real numbers using Cauchy sequences) This is the standard presentation in every textbook I have read.
qmalxp 11y ago
It's probably worth pointing out that Good Educator != Good Author. I have heard from people who would know that your guess is not so far off, but having taken classes from him I can attest he is an excellent teacher in addition to being a world class mathematician. I also want to add that although he is extremely friendly and helpful, it'd be dishonest to say he isn't a bit weird. However, that is probably just an ingredient/consequence of greatness; I reckon most of the big name tech founders discussed on these forums are a bit weird.
- javert 11y ago
  How is he weird? Just curious.
  - overpaidgoogler 11y ago
    Not in any specific way, but he has a nerdy demeanor. There are many interviews of him online your can watch.
jacobolus 11y ago
For anyone looking for a Real Analysis textbook, I’ve heard several recommendations for Pugh as an alternative to Rudin.
- shriphani 11y ago
  I used Abbott in college. The best math textbook I've ever read.

mahyarm 11y ago

Sounds like he just needed a few math grad student editors. A real reason for a new edition!

gohrt 11y ago

> (first set theory, then properties of natural, whole and rational numbers before constructing the real numbers using Cauchy sequences) This is the standard presentation in every textbook I have read.

qmalxp 11y ago

It's probably worth pointing out that Good Educator != Good Author. I have heard from people who would know that your guess is not so far off, but having taken classes from him I can attest he is an excellent teacher in addition to being a world class mathematician. I also want to add that although he is extremely friendly and helpful, it'd be dishonest to say he isn't a bit weird. However, that is probably just an ingredient/consequence of greatness; I reckon most of the big name tech founders discussed on these forums are a bit weird.

javert 11y ago
How is he weird? Just curious.
- overpaidgoogler 11y ago
  Not in any specific way, but he has a nerdy demeanor. There are many interviews of him online your can watch.

jacobolus 11y ago

For anyone looking for a Real Analysis textbook, I’ve heard several recommendations for Pugh as an alternative to Rudin.

shriphani 11y ago
I used Abbott in college. The best math textbook I've ever read.