This Legendary Math Book Has The HARDEST Calculus Problems

This is an amazing book titled Calculus. It was written by Michael Spivak.
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[nicku]

This was my intro to calculus. I only did OK in the course but it changed me as a person, taught me to think, and gave me a respect for rigor I carried forward to this day.

[tod]

A perfect example of why we DON'T need to update our books every 5 years

[causalitymastered]

This means, this is the perfect book to build your skill. You always want to be at a higher level than the math course you are enrolled. That's how you get 100%

[HuggableJohn]

This is one of the greatest mathematics books ever written. I use it to teach to first-year students of mathematics and physics. It challenges them immensely, but by the end of the semester, the good, hard-working students learn to love it. It teaches you what true mathematics is all about. Easy? No. Beautiful? Yes.

[johnrobinson]

I have it. The introductory problems killed me. Didn't even get to the Calculus part.
And I did rather well in Calculus in college.
This Spivak is a deep thinker.

[alexandrine]

This was the book that i used to start learning calculus at 16. Ive always contemplated going back and actually doing these problems. Genuinely one of the greatest books of any kind i have ever read

[philj]

This book looks amazing! I'm currently in calculus 2 and would like to try all of the practice problems. By the way, thank you for addressing my email that I sent when doing calculus 1 (I'm the related rates guy). It made my day to see that you made a good video out of it. I loved it and your insights are always appreciated. I finished calculus 1 with an A despite that setback!

[ingiford]

This is good as your second time going though Calc. The way he builds things is non-standard, but works without needing things such as proving the limit in finding the derivative of sin(x)

[Jack_Callcott_AU]

I met this book in my undergraduate mathematics courses at the University of Queensland. It wasn't a set text for my course, but the lecturer praised it highly. You are right: it has many challenging problems, but so many of them are very interesting. I would so like to get a copy of it, but it is so expensive. It costs $177 on Amazon in Australia.
BTW; The YouTuber mathematician Michael Penn said it is his favourite calculus textbook.

[juaneliasmillasvera]

With that book I finally understood the basics of Calculus, totally recommended.

[bryanbain]

Wish he could have done more volumes of Physics for Mathematicians after Mechanics

[johngough]

I have fond memories of this book when I was an undergraduate at University, College Dublin. Tom Laffey was the professor in first year (1984) and he used Spivak as the recommended text. I remember well the "three hard theorems". First I remember that the were really hard! Second, I was worried about explaining to my dad that I spent the first year at university showing that if a continuous curve started off negative and ended up positive that somewhere in between it had to be zero - more exactly I was worried that he would think what he has wasting his money on sending me through third level! With retrospect, this was of extreme importance!

[gavinmonson]

I’d like to see a review of ‘Calculus and Analytic Geometry’ by George B. Thomas Jr. I used this book in high school calculus and it was much more challenging than the one used in college.

[deoradh]

I have 4e, and the exercises felt pretty proof-heavy at the start. I enjoyed the number theory but I’d probably have preferred that as just a separate course. Apostol felt more approachable, even if it starts with integration and measure theory.

[postyoda]

I have a friend who doesn't like any math books unless they're old Soviet ones; this is one of his rare exceptions 😂

[ShaneShelldriick]

That Bacon quote was wild. Math made you what you are, so now pay up and make math beautiful

[KevinFournier-xdub]

Spivak is a good author and is a joy to read. I really love his five-volume set "A Comprehensive Introduction to Differential Geometry". They are such a fun read! Thank you for another great video Math Sorcerer. While I am here, on the oft chance you read this, would you happen to have a book to give a review on something in Finsler Geometry?

[zoonpolitikon]

This is the textbook used at México's UNAM math and actuarial sciences Calculus courses. It's brutal and hardly anyone passes first try despite the grading curves...

[AR-csri]

So, if you skip to the 5:43 mark, page 313 #*5, it is a fairly easy graph to sketch. Why is it marked as a difficult problem?

An easy way to think of this is noting the points k(pi)/2; k an element of the Natural Numbers. The Domain is (0, infinity).

[rome]

You can feel it's one great book. It's definitely a must have for all mathematician and every mathematician should definitely have that experience.
I would love to go through that book right now, but i have other problems more on the applied mathematics side and Physics that needs my devoted attention.
It's definitely something that i could do for fun though.