Spivak's Calculus 4th Edition

[BloodyFrozen]

I'm sure many of you guys have read this book. I want to know how "dry" this book is.

Any comments/examples/etc.?

All appreciated.

Here is the link:

http://www.amazon.com/Calculus-4th-Michael-Spivak/dp/0914098918/ref=sr_1_1?ie=UTF8&qid=1306870677&sr=8-1

[micromass]

Hi BloodyFrozen! :smile:

You would help us a lot if you would tell us a bit about your situation. What do you want to study? What do you already know about calculus?

In my opinion, Spivak is an excellent book. It's the best calculus book out there. The exercises are not at all easy, but I think that's a good thing. If you know Spivak, then you know calculus very well!

[BloodyFrozen]

Hi BloodyFrozen! :smile:

You would help us a lot if you would tell us a bit about your situation. What do you want to study? What do you already know about calculus?

In my opinion, Spivak is an excellent book. It's the best calculus book out there. The exercises are not at all easy, but I think that's a good thing. If you know Spivak, then you know calculus very well!

Hey micromass (seen you a lot :smile:)

Well, my situation is self-study.


EDIT: Wow, I used v instead of c in calculus. Already failing..lol

Also, about series (converging, diverging, and a good explanation on limits--not too good at them)
I know this may seem very challenging, I am prepared to try it out.:bugeye:

I already know most about derivatives, definite integrals, integrals, etc.

I don't know the more advanced topics. [ie. power series (don't know if this is calc 2), etc.; integrating by parts- finding surface area and volume and mostly important how to derive these.]


Overall, a good calculus book to study from over the summer.:wink:

[micromass]

Ah, selfstudy :smile: The thing with selfstudy is that you need to find the book for you. A lot of people prefer different approaches, and if your philosophy doesn't match the book's, then the study becomes unpleasant.

I think Spivak is good for self-study because it's very clear. The book is quite rigourous, that means that all results are proven. So you will quickly gain a lot of mathematical maturity from this book, which is very good.

As for dryness. Well, perhaps you might call the book dry if you're not acquainted with the style in which many math books are written. But beware, books which are not dry are often dumbed down a lot, and I don't think you really want this.

I suggest taking a look at the book, and if you like it, then continue with it. It may very well be that the book isn't in the style you want, but take a look at it anyway.

Also, Spivak doesn't contain multivariable calculus. You'll need a seperate book for that...

[BloodyFrozen]

Ah, selfstudy :smile: The thing with selfstudy is that you need to find the book for you. A lot of people prefer different approaches, and if your philosophy doesn't match the book's, then the study becomes unpleasant.

I think Spivak is good for self-study because it's very clear. The book is quite rigourous, that means that all results are proven. So you will quickly gain a lot of mathematical maturity from this book, which is very good.

As for dryness. Well, perhaps you might call the book dry if you're not acquainted with the style in which many math books are written. But beware, books which are not dry are often dumbed down a lot, and I don't think you really want this.

I suggest taking a look at the book, and if you like it, then continue with it. It may very well be that the book isn't in the style you want, but take a look at it anyway.

Also, Spivak doesn't contain multivariable calculus. You'll need a seperate book for that...


What do you mean about multivariable Calculus?:bugeye:

Did I mention something about multivariable Calculus? (not sure:smile:)

EDIT: Comparison to a textbook in middle school math (with the diagrams, etc.), How dry is Spivak?

EDIT#2: Which edition do you suggest? Is 4th ok?

[micromass]

What do you mean about multivariable Calculus?:bugeye:

Did I mention something about multivariable Calculus? (not sure:smile:)

Ah, you mentioned finding surface area and volume. This involves multivariable calculus. It's not something you need to know right away, but I justed wanted to let you know that Spivak doesn't have that (which isn't that bad).

[BloodyFrozen]

Ah, you mentioned finding surface area and volume. This involves multivariable calculus. It's not something you need to know right away, but I justed wanted to let you know that Spivak doesn't have that (which isn't that bad).

Wow, really?

Like washer, cross section, dish and shell method is not covered?

Also, Is this 4th edition Calc 1, 2 or both?

By the way, any good High school geometry proofs book (you seem to be very knowledgeable:smile:) ?

[micromass]

Wow, really?

Like washer, cross section, dish and shell method is not covered?


Nope, you'll need another book for that. Apostol covers both single variable as multivariable calculus, and it's a very good book too. (Somehow, I like Spivak better, I'm not sure why...)


Also, Is this 4th edition Calc 1, 2 or both?


I'm not american, so I have no idea what Calc I and Calc II involves. The book contains differentiation, integration, sequences, series, power series. So I guess this would be both Calc I and Calc II.


By the way, any good High school geometry proofs book (you seem to be very knowledgeable:smile:) ?

Uuh, depends on what you want. I've always found high school geometry a bit useless. Only things like equations of lines and stuff is really handy.

A good geometry book is "Geometry" by Moise and Downs. It really challenges the students and should be perfect.

The book "Geometry" by Serge Lang is also good. It's a mathematics book, and not a high-school book though (I don't know which one you really prefer). Also, it contains a lot of interesting material such as vectors and dot products, which are sadly missing from a lot of geometry courses. A possible criticism is that the book doesn't contain all the material from a high school book and focuses very much on coordinate geometry. But I don't really mind, because most material from high school is useless and most geometry that happens nowadays is coordinate geometry.

A geometry book that I've really liked are "Introduction to Geometry" by Coxeter. However, this is not a book that they would use in a high school. The book presents geometry from a modern and mathematical point-of-view and the book is very intriguing. Coxeter is also one of the best mathematician of the last century. However, the book might be too advanced...

Anyway, here is a site with a lot of good high school math books: http://hbpms.blogspot.com/2008/05/stage-1-elementary-stuff.html
It also includes some geometry books.

Perhaps you should PM Tiny-Tim to join in in this thread. He likes classical geometry very much, so he probably knows better references than the ones I've just given you...

[BloodyFrozen]

Nope, you'll need another book for that. Apostol covers both single variable as multivariable calculus, and it's a very good book too. (Somehow, I like Spivak better, I'm not sure why...)



I'm not american, so I have no idea what Calc I and Calc II involves. The book contains differentiation, integration, sequences, series, power series. So I guess this would be both Calc I and Calc II.



Uuh, depends on what you want. I've always found high school geometry a bit useless. Only things like equations of lines and stuff is really handy.

A good geometry book is "Geometry" by Moise and Downs. It really challenges the students and should be perfect.

The book "Geometry" by Serge Lang is also good. It's a mathematics book, and not a high-school book though (I don't know which one you really prefer). Also, it contains a lot of interesting material such as vectors and dot products, which are sadly missing from a lot of geometry courses. A possible criticism is that the book doesn't contain all the material from a high school book and focuses very much on coordinate geometry. But I don't really mind, because most material from high school is useless and most geometry that happens nowadays is coordinate geometry.

A geometry book that I've really liked are "Introduction to Geometry" by Coxeter. However, this is not a book that they would use in a high school. The book presents geometry from a modern and mathematical point-of-view and the book is very intriguing. Coxeter is also one of the best mathematician of the last century. However, the book might be too advanced...

Anyway, here is a site with a lot of good high school math books: http://hbpms.blogspot.com/2008/05/stage-1-elementary-stuff.html
It also includes some geometry books.

Perhaps you should PM Tiny-Tim to join in in this thread. He likes classical geometry very much, so he probably knows better references than the ones I've just given you...

Ok, thanks for all your help. I will get Spivak 4th Edition.:smile:

[BloodyFrozen]

Anyone else who has other suggestions, feel free to post.:smile:

[jbunniii]

I have the 1st edition and I think it's a great book, not dry at all. Spivak's treatment is rigorous but also well-explained: he presents proofs for everything but also gives a good narrative explaining why the proofs are structured as they are, and why they work. I can't think of a better place to learn epsilon-delta arguments. The exercises are fantastic! Do as many of them as you can.

[I like Serena]

I don't know Spivak, but I have to ask.

Apparently there are a lot of proofs in it.
If I know anything about it, it's proofs that makes a math book dry!

It's about calculus. What do you want to do with calculus?
Do you want to know how to apply it in real life situations?
Or do you want to learn how to proof propositions?

The exercises you'll want to do are very different in both cases.

How is Spivak set up?

[BloodyFrozen]

Right now, I'm mostly looking for a pure math that includes the usual word problems such as acceleration, area, etc.

[jbunniii]

FYI, there is a preview of Spivak's 3rd edition at Google Books, so you can judge for yourself whether it is what you are looking for.


Apparently there are a lot of proofs in it.
If I know anything about it, it's proofs that makes a math book dry!


In my opinion, it's not a math book if it doesn't have proofs! It's more like... theology.

But seriously, a big part of Spivak's goal is to teach you how to prove things in calculus, and he does it very engagingly. It is probably the least dry math book I've ever read.

[I like Serena]

In my opinion, it's not a math book if it doesn't have proofs! It's more like... theology.

My point is, that if you want to know about derivatives, you don't really need to know how to proof for instance what the derivative of xn is.

Usually the only thing you want to know and exercise, is that it is nxn-1. :smile:

[micromass]

My point is, that if you want to know about derivatives, you don't really need to know how to proof for instance what the derivative of xn is.

Usually the only thing you want to know and exercise, is that it is nxn-1. :smile:

I agree that the only thing you really need to know is how to calculate derivatives. But I find such proofs to be essential, because with proofs of such statements, we can see what we're doing.

Here in Belgium (I guess the netherlands would be thesame), you can choose in high school how much hours of math you want. You essentially see the same things but in the classes with more hours you see the proofs of statements and you see some extra stuff. I've notices that people who've seen the proofs of things tend to understand and retain things better than people who didn't see the proofs.

It's an interesting discussion though. How soon should we give proofs to students, if ever? I'd say that we give them as soon as possible, but 'm sure a lot of people would disagree with me...

[jbunniii]

It's an interesting discussion though. How soon should we give proofs to students, if ever? I'd say that we give them as soon as possible, but 'm sure a lot of people would disagree with me...

My first proof-based course was geometry in 2nd year high school (age 15 or so). My high school calculus course was also proof-based, with rigorous delta-epsilon arguments. These were honors-level courses in the mid 1980s. I'm not sure if it is still done that way today.

I don't claim to have achieved full mastery of the material during high school, but I did feel comfortable with proofs once I started taking university math courses, so I think the earlier exposure was very valuable.

[I like Serena]

If you're going to study mathematics or physics at university level, I say yes, learn it! :smile:

In every other case, I find it's just too hard too explain, it's to dry, there's too much material to cover, and you don't really need it.

But as micromass already said, there's probably lots of people who would disagree with me too! :wink:

[jbunniii]

I think this Amazon review summarizes the Spivak book perfectly. If you agree with the reviewer's point of view, you will probably like Spivak's book:

"This book was used as the texbook for a first year introductory calculus course at the university I attend, and I made a point of reading any parts of it that weren't explicitly covered in the course itself. This book covers calculus unlike any other book I've seen to date. For the first time in my life, I've found a book that develops calculus from scratch, with nothing assumed (except of course, for a fundamental axiom or two!). Finally, I don't have to deal with "this proof is beyond the scope of this book" garbage. Up until I read this book, it was quite possible (to me) that all of calculus was a farce! Every book I've read previously always relied on other, unproven tools, and many of the definitions seemed totally unfounded and out of the blue - this is not the case with this book! Everything makes sense, because nothing is even defined until a reason has been developed to define it! A reader could pick a random theorem in this book, and trace it's underlying theorems all the way back to the fundamental axioms of calculus! It's incredible! I think every theoretical mathematics text book should be written in a format similar to the one used in this book."

[BloodyFrozen]

My point is, that if you want to know about derivatives, you don't really need to know how to proof for instance what the derivative of xn is.

Usually the only thing you want to know and exercise, is that it is nxn-1. :smile:

I like proofs, but I don't know how to do them myself:frown:

The power rule uses binomial expansion. :smile:

[micromass]

I like proofs, but I don't know how to do them myself:frown:


Wait, you've never done proofs? You're going to find Spivak quite a challenge then. Oh well, you've got to start some day :smile:

[BloodyFrozen]

Wait, you've never done proofs? You're going to find Spivak quite a challenge then. Oh well, you've got to start some day :smile:

Nope, that's why I asked for a book:smile:

[micromass]

Nope, that's why I asked for a book:smile:

Hmm, now I'm starting to doubt whether my recommendation of Spivak was good. It's a good book obviously, but maybe you're going to find it a bit over your head...

Try out the first chapter at google books, and see whether it's too hard or not.

[BloodyFrozen]

It doesn't look that hard.

Maybe just a brush-up on induction.

Any other kinds of proofs used in this book? (only skimmed it):smile:

[micromass]

Check out the exercises. :smile: They're the hard part about the book...

[Samuelb88]

I didn't learn about mathematical reasoning until my 3rd year at a university.

[BloodyFrozen]

Check out the exercises. :smile: They're the hard part about the book...

I think I can handle almost all of it. It's the discrete mathematics holding me back.

(ie.induction, proofs, and sequences:frown:)

[wisvuze]

yes I remember going through this book for the first time. I thought that I was super smart because the chapter readings were easy and intuitive enough.. but all was changed when I attempted some of the exercises aha.
To get a taste of the "harder proofs" in the book, they should start around the limits and supremum chapters ( then most of the other proofs in the book borrow the same ideas )
no discouragement here though! it's a fun book

[BloodyFrozen]

Ok, before I attempt this book is there a book to learn induction, two column proofs, etc?

[micromass]

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)

[BloodyFrozen]

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:tongue:

[micromass]

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)...

[micromass]

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... :tongue:

[BloodyFrozen]

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... :tongue:

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:tongue2:

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

EDIT #2: Sorry for replying so late

[BloodyFrozen]

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:

http://www.amazon.com/How-Solve-Aspect-Mathematical-Method/dp/0691080976/ref=sr_1_6?ie=UTF8&qid=1307050377&sr=8-6

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

[micromass]

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:

[BloodyFrozen]

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.

[micromass]

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!

[BloodyFrozen]

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:)