Is Completing All Practice Problems Essential for Self-Learning Calculus?

[pooka12321]

Hi everyone,

I am teaching myself calculus from Spivak's book.
I am wondering if it is necessary to do all or 1/2 of the problems in the book to gain a good understanding of calculus.

Thanks.

 

[Char. Limit]

Do as many as you can. The more you do, the better you understand.

 

[pooka12321]

The thing is though, is that many of the problems require writing proofs, which I am absolutely terrible at. Can anyone point me towards any good threads? I've already read https://www.physicsforums.com/showthread.php?t=166996 but I am still very weak.

 

[sponsoredwalk]

Thanks for the above link, I hope it helps me.

I found this set of books which looks like it would help a lot.

If you go ahead and use it please post here & tell me how it's going for you.

I'm too busy right now to read this but I will in a while, it looks like it'd help me out with Spivak but I could be wrong.

From the description;

This book helps the student complete the transition from purely manipulative to rigorous mathematics. The clear exposition covers many topics that are assumed by later courses but are often not covered with any depth or organization:

Here is a quote from another book on this site, the author has condensed the book into an intro for his Real Analysis book;

For students who need a review of basic mathematical concepts before beginning "epsilon-delta"-style proofs, the text begins with material on set theory (sets, quantifiers, relations and mappings, countable sets), the real numbers (axioms, natural numbers, induction, consequences of the completeness axiom), and Euclidean and vector spaces; this material is condensed from the author's Basic Concepts of Mathematics, the complete version of which can be used as supplementary background material for the present text.

From - http://www.trillia.com/zakon-analysisI.html

Here is the link to the book he is talking about,

http://www.trillia.com/zakon1.html

 

[rezeew]

I believe that the best way to gain a good understanding of any subject is through practice and application. While it may not be necessary to do all or half of the problems in Spivak's book to understand calculus, I would highly recommend completing a significant number of practice problems to solidify your understanding and develop your skills. Additionally, working through a variety of problems will expose you to different concepts and applications, helping you to develop a more comprehensive understanding of calculus. So, while it may not be necessary, I believe that completing a substantial number of practice problems will greatly benefit your understanding of calculus.