Is Spivak's Calculus 4th Edition Too Dry for Beginners?

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    Calculus
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Discussion Overview

The discussion revolves around the perceived dryness of Spivak's Calculus 4th Edition, particularly in the context of self-study for beginners. Participants share their experiences and opinions on the book's rigor, clarity, and suitability for learning calculus concepts, including differentiation, integration, and series.

Discussion Character

  • Exploratory
  • Debate/contested
  • Homework-related

Main Points Raised

  • Some participants express that Spivak is an excellent book for learning calculus, emphasizing its rigor and the mathematical maturity it fosters.
  • Others suggest that the book may be perceived as dry, especially for those unfamiliar with the style of many mathematics texts.
  • There is a discussion about the book's lack of coverage on multivariable calculus, with some participants noting that additional resources may be needed for those topics.
  • Participants share their personal experiences with self-study and the importance of finding a book that aligns with their learning philosophy.
  • Some participants inquire about specific calculus topics covered in the book, such as power series and methods for finding surface area and volume.
  • There are suggestions for alternative geometry books, indicating a broader interest in foundational mathematics beyond calculus.

Areas of Agreement / Disagreement

Participants do not reach a consensus on whether Spivak's book is too dry for beginners, as opinions vary based on personal learning styles and experiences. Multiple competing views remain regarding the book's suitability for self-study.

Contextual Notes

Some participants mention the need for additional resources for multivariable calculus topics, indicating that Spivak's book may not cover all necessary material for a comprehensive understanding of calculus.

Who May Find This Useful

This discussion may be useful for individuals considering self-study in calculus, particularly those evaluating the appropriateness of Spivak's Calculus for their learning needs and preferences.

  • #31
micromass said:
Try a basic proof book, such as "How to prove it" from Velleman. But be warned, you can only learn proof in applications. Learning proofs just for learning proofs gets boring after a while.

Also, I wouldn't bother with two-column proofs, nobody uses them these days. They only seem to be used in american high schools, and I wouldn't know why. They only obfusciate the argument...

But if you want to learn them anyway, try any high school geometry book. (I can't recommend you any because I didn't study geometry from an english book)

Are you sure(not doubting your expertise:smile:) I should get this book?

I'm wondering because it doesn't seem like it has many proofs methods in a normal high school proofs class (all of this proofs, calc ,etc. is for preparing for school transfering placement)

Thanks:-p
 
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  • #32
It's good you're being critical! :smile: I like that in a person

What proof methods does one see in high school? Direct proofs, contradiction, contraposition, induction, that's it basically. It's all in that book (with much more.

This book is made for aspiring mathematicians and gives a lot of background information. A reason that this book would not be for you is because it might have too much information. I'm sure that anybody reading this book will be able to do their own proofs.

Don't take my word for it though, wait for other people to chim in and see if they give you other (probably better) recommendations! :smile: (the best would actually be to set up a new thread asking for a proof book)...
 
  • #33
BloodyFrozen said:
all of this proofs, calc ,etc. is for preparing for school transfering placement

Transferring to where? I mean, what do you want to do later in your new school? Because if you want to be an engineer (for example), then my suggestions of Spivak and Velleman are not so good.
If you want to be a mathematician, then my suggestions are a little better.

So it might help us to give some more information... :-p
 
  • #34
micromass said:
Transferring to where? I mean, what do you want to do later in your new school? Because if you want to be an engineer (for example), then my suggestions of Spivak and Velleman are not so good.
If you want to be a mathematician, then my suggestions are a little better.

So it might help us to give some more information... :-p

I'm transferring to a new shool. I don't not sure what I'd like to do (probably doctor and I know I only need up to around calc II so no rush), but I'm not 100% positive and would always like a backup (math). I'm asking all these questions so I can get the best understanding. I like to go above and beyond and my favorite subject is math (yay:smile:, don't see why people despise it:smile:). I think right now, I'd like a book with good with the standard word problems (finding acceleration, velocity etc with derivatives and the other concepts), but still with mathematical rigor.

Thanks for helping me so far:-p

EDIT: I started a thread in General Math for a good proofs book for more suggestions, but business is slow today.:rolleyes:

EDIT #2: Sorry for replying so late
 
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  • #35
I also have this "proof" book, but I'm not sure it covers the method you mentioned (Direct proofs, contradiction, contraposition, induction) -- You can look at the table of contents.:smile:

https://www.amazon.com/dp/0691080976/?tag=pfamazon01-20

Mine looks like the colorful one (if you check the pictures) --I don't know if this matters

I'm not really sure as I'm kinda confused by how the book is ordered. It seems that mostly it gives examples (not necessarily bad thing) rather than an explanation (although it does have it sometimes).

Would it be as good as Velleman?

:smile:Cheers
 
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  • #36
Hmm, first off, if you're going to be a doctor, then you really don't need to read Spivak or proof books. If you're interesting in mathematics, then great, you should read the books :smile: But if you just want to know the material to pass the test, then Spivak really isn't necessary.

Not that I don't want you to read Spivak or Velleman, but I don't want to give you false information!

Anyway, I have read Polya's book and the book is not a proof book. It doesn't explain proof methods like induction and stuff. The book is actually written for future teachers to give them methods how to make coherent explanations and how to teach students the art of problem solving.

It's a good read, but it's not the book you're looking for! :smile:
 
  • #37
micromass said:
Hmm, first off, if you're going to be a doctor, then you really don't need to read Spivak or proof books. If you're interesting in mathematics, then great, you should read the books :smile: But if you just want to know the material to pass the test, then Spivak really isn't necessary.

Not that I don't want you to read Spivak or Velleman, but I don't want to give you false information!

Anyway, I have read Polya's book and the book is not a proof book. It doesn't explain proof methods like induction and stuff. The book is actually written for future teachers to give them methods how to make coherent explanations and how to teach students the art of problem solving.

It's a good read, but it's not the book you're looking for! :smile:

I'm not just learning to pass the test, but also to have a solid foundation for the future.

Ok, so I'm probably getting Velleman.:smile:

MATH is the best!:smile:

@The teacher part-- I knew it! I was wondering why he kept talking about what the teacher could tell to the student to help him/her solve the problem. (I'll be able to use this if I ever tutor lower leveled classes)


One last question: Any concepts I should know really well before I attempt Spivak? I know about the standard algebra and trigonometry. Anything else?

Thanks for taking the time to help me!:wink:

EDIT:What about knowing deMorgan's Laws for proofs etc? I hear a lot of people talking about proofs mention this.
 
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  • #38
Nice!

For attempting Spivak, you'll need nothing more than basic algebra, ability to reason logically and some knowledge of proofs. It'll still be a hard book though, but hard books can be fun!

Good luck!
 
  • #39
micromass said:
Nice!

For attempting Spivak, you'll need nothing more than basic algebra, ability to reason logically and some knowledge of proofs. It'll still be a hard book though, but hard books can be fun!

Good luck!

Thanks to everyone (especially micromass:smile:).

I proclaim this thread to be done. (unless someone responds:zzz:)
 

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