If I'm heading into Calculus (self-study w/ Spivak-I think, not sure

[BloodyFrozen]

If I'm heading into Calculus (self-study w/ Spivak--I think, not sure

If I'm heading into Calculus (self-study w/ Spivak--I think, not sure on which edition), should I buy a proofs book?

I've decided on this one:

https://www.amazon.com/dp/0521675995/?tag=pfamazon01-20

Is this a good one or is there another better one? Please note that I'm only starting high school.

P.S. How important is it to know proofs in Calculus?

Thanks

 

[gb7nash]

Is this a good one or is there another better one? Please note that I'm only starting high school.

You're only starting high school and you're already wanting to do proofs? You must be in one of those gifted high schools. That's good though, I wasn't exposed to a proofs class until I was in the middle of my undergrad. The earlier you can start developing good techniques to write proofs, the better though. You'll be way ahead of the game when you get to college.

P.S. How important is it to know proofs in Calculus?
Thanks

For your first time around, not very. A lot of the retention from introductory calculus comes from the techniques learned, not the proofs. Very seldom do I see somebody using the difference quotient to derive the power rule for differentiation (which involves binomial expansion). One reason for this is that a lot of kids in college have calculus as a required class (outside major). Many kids don't care about the proofs and just want to apply the techniques. There are probably some calculus classes out there that do focus more on the proofs, but from where I came from. It was mostly tailored toward learning the techniques.

However, if you can prove results from differentation and integration, you'll be waaaay ahead of the pack.

 

[BloodyFrozen]

Thanks, but my school is not gifted. I'm just self studying

Do you have any recommendations for a proofs book?

 

[gb7nash]

My proofs class actually didn't have a book, so I don't sorry.

 

[BloodyFrozen]

My proofs class actually didn't have a book, so I don't sorry.

Ok, thanks anyways.

Anyone else got a suggestion?

 

[Mark44]

The Nuts and Bolts of Proofs (https://www.amazon.com/dp/0534103200/?tag=pfamazon01-20)
How to Read and Do Proofs (https://www.amazon.com/dp/0471406473/?tag=pfamazon01-20)

 

[BloodyFrozen]

The Nuts and Bolts of Proofs (https://www.amazon.com/dp/0534103200/?tag=pfamazon01-20)
How to Read and Do Proofs (https://www.amazon.com/dp/0471406473/?tag=pfamazon01-20)

Of which of these two do you prefer the most (as I need to cover this in a little less than a month)? and..
Is this apropriate leveled?

Thanks

 

[miglo]

heres a book on how to write proofs that you can download for free
http://www.people.vcu.edu/~rhammack/BookOfProof/index.html

 

[BloodyFrozen]

heres a book on how to write proofs that you can download for free
http://www.people.vcu.edu/~rhammack/BookOfProof/index.html

Thanks, this seems like a good proof book.

 

[Skins]

Well, If your interested in really understanding the theorems, why they work, and how they are proved I have found the Book "Calculus" by Tom Apostol Volumes 1 and 2) to be quite thorough and rigorous with respect to doing proofs. However, if you are at high school level it may seem like overkill and/or be a bit hard to follow. It depends to a large extent on your abilities. You can also find a lot of theorems and proofs online.

You might also hit your school, college library, or the web and look for reading material that deals with the underlying logic and reasoning behind mathematical proofs. For instance, sometimes it might be best to use an inductive argument. Other times a direct proof
Proposition A => Proposition B works best but sometimes it might be easier to prove the contrapositive "Not B => Not A". Or proof by contradiction. Or,as often arises in Calculus, is it best to use an Analytic proof, an Geometric proof, or both ? Getting to know which argument might work best in a given situation comes with time and experience.