Quick question about Michael Spivak's Calculus

[singleton]

I'm about to buy Michael Spivak's Calculus book sight unseen (no bookstores here have it--will be ordering online) and was hoping someone could clarify it for me.

When people discuss the rigour of it, will it give proof of common theorems and features of Calculus? Or does it presuppose the reader has a decent (or at least introductory) knowledge of Calculus already and skip over many things like the chain rule, quotient rule, etc?

I have been introduced to Calculus and want to learn more, but also retrace my steps and learn the "how" not just "plug your numbers in" :)

Additionally, how strong should your Algebra be for this book?

Cheers,

 

[fourier jr]

I'm about to buy Michael Spivak's Calculus book sight unseen (no bookstores here have it--will be ordering online) and was hoping someone could clarify it for me.

When people discuss the rigour of it, will it give proof of common theorems and features of Calculus? Or does it presuppose the reader has a decent (or at least introductory) knowledge of Calculus already and skip over many things like the chain rule, quotient rule, etc?

I would say if you've seen calculus before you may be able to get through Spivak's book, but the problems will still be pretty hard. I thought they were really hard anyway, and I'm in 4th year. There aren't any real easy problems where you just plug numbers in just to get the hang of them; you can either do hard problems or no problems at all.

I have been introduced to Calculus and want to learn more, but also retrace my steps and learn the "how" not just "plug your numbers in" :)

Additionally, how strong should your Algebra be for this book?

Cheers,

Algebra beyond what you do in high school isn't necessary; there aren't any groups, etc in Spivak's book, if that's what you mean.

 

[JasonRox]

You prove the theorems yourself. That's how hard it is.

I got myself a copy and I can't get through half the questions. Some of them I have no clue what they are asking for!

 

[philosophking]

Is there a study guide or a website or anything for the book? You've got me interested.

Also, is it like an analysis-type book?

 

[JasonRox]

In the book, it says they should have called the book "An Introduction to Analysis".

I find it hard to answer all the problems. Especially Chapter 2.

I only read Chapters 1 to 3 for now. I haven't finished all the problems in Chapter 3 yet, I got like ten more to go. I'll try to finish them on the weekend. I'll be reading chapter 4 soon too. I must admit even questions in Chapter 1 are hard.

Any advice?

 

[JasonRox]

Also note, I am also reading James E. Stewart with the class and having no problems with that one. I just want a deeper understanding.

 

[singleton]

Also note, I am also reading James E. Stewart with the class and having no problems with that one. I just want a deeper understanding.

Yep that's what I heard about Michael Spivak's book. Picked up a copy over at the UofT bookstore last month. Unfortunately haven't had much time to work on it because of college work :/

I must say that after reading the first dozen pages of it vs Tom Apostol's it looks much more accessible to first-time students.

 

[JasonRox]

Reading through it is easy, but answering problems is hard. Sure you can answer the first five, but all 30.

 

[singleton]

Reading through it is easy, but answering problems is hard. Sure you can answer the first five, but all 30.

I never said it was easy--I said it was accessible Open Tom Apostol's book and you'll know what I mean... :tongue:

 

[JasonRox]

I see what your saying now.

I feel like an idiot not being able to solve some most of the questions. I'm at Chapter 3 and answered 15 out of the 16 I tried so far. Chapter 1 and 2 on the other hand...

 

[mathwonk]

when I was a kid, i was the math (algebra) champ of my (small southern) state. my school did not offer calc. i went to harvard on a full merit scholarship and fought to get into a beginning super honors calc course. just to get in, i had to prove the real numbers were uncountably infinite using cantors second diagonal method, based on reading i had done at the library.

the course was extremely hard, and most of the kids were valedictorians of their high schools. after spivak wrote his book, it beacme the etxtbook for that course.

eventually harvard dropped the course because so many kids have already had calc in high school.

so spivak is qwriten for very bright kids who,have never seen calc. in fact it is better in some ways if they have not.

does this help?

 

[JasonRox]

Um... After working with Spikvak's text for awhile, I think its fine now.

You truly have to understand what is going on.

I'm having trouble with the sequences and series, but I learned some new tricks and can now find the sum of any series (that can be written as a polynomial).

I got a test in one minute later.

 

[JasonRox]

Micheal Spivak's text is challenging for anyone. I've talked to other people who used it and they just dropped their jaw.

Put it this way. Most of the time you forget the name of the author of a text, but for this one it won't happen. You will be old and dying in your deathbed and at the same time repeating to yourself "Spivak is insane. Spivak is insane. Spivak..."

 

[mathwonk]

on the contrary. spivak has done a wonderful service to all the students hoping to achieve a mastery of calculus at a level that was impossible for most of us to reach before he wrote his book.

if it is not your cup of tea, lower your sights and pick another book.

 

[trancefishy]

after reading about this, i think I'm going ot order it online as well, work on it over christmas break. maybe i could even weasel out some independent study credit for it...

 

[JasonRox]

after reading about this, i think I'm going ot order it online as well, work on it over christmas break. maybe i could even weasel out some independent study credit for it...

You won't get very far within two weeks, not to mention by yourself.

 

[trancefishy]

i guess i didn't say what i meant very clearly. work on it over break, see what's up, and then work on it all of next semester, hopefully garnering some indedpendent study credit along the way.

oh yeah, i found it online only 2 places. amazon, new, for 70, but it won't ship for 3-4 weeks, and alibris, used, 134 bucks. did you spot it cheaper/faster?

EDIT: found one. it was hidden in amazon. really bizarre. 23 bucks.

 

[mathwonk]

the reason amazon takes 3-4 weeks to ship is that they are a reseller and have to first buy it from the publisher, who will also galdly sell it direcvtly to you.

that would be "publish or perish" publishers, located at

http://www.mathpop.com/mainhtms/bip.htm


In general, after looking on amazon or barnes and noble, try abebooks.com for used, or the publisher for new copies. often barnes and noble or amazon are reselling a copy to you, after marking it up for no good reason at all from your point of view.

in this case however, EDIT has found on amazon the cheapest available copy. of course you might want to invest in a new one.


From the preface of spivak's book:

Every aspect of this book was influenced by the desire to present calculus not merely as a prelude to but as the first real encounter with mathematics. Since the foundations of analysis provided the arena in which modern modes of mathematical thinking developed, calculus ought to be the place in which to expect, rather than avoid, the strengthening of insight with logic. In addition to developing the students' intuition about the beautiful concepts of analysis, it is surely equally important to persuade them that precision and rigor are neither deterrents to intuition, nor ends in themselves, but the natural medium in which to formulate and think about mathematical questions.

 

[JFo]

I would love to get a copy of Spivak's book!... What is the title??
Is there a specific edition that's better than the others?
An ISBN # would help too if you happen to have it.
Thanks much!

PS
Same info for Apostol and Courant would also be appreciated.

 

[JasonRox]

I would love to get a copy of Spivak's book!... What is the title??
Is there a specific edition that's better than the others?
An ISBN # would help too if you happen to have it.
Thanks much!

PS
Same info for Apostol and Courant would also be appreciated.

Calculus - Micheal Spivak

Note: Go to a second hand bookstore.

 

[JFo]

much obliged jason
is there a specific edition?

any info on apostol or courant?

 

[JasonRox]

much obliged jason
is there a specific edition?

any info on apostol or courant?

I got the Third Edition, but I'm sure any edition will do. If you have attended post-secondary school, you know what I'm talking when I say 7th Edition=2nd Edition.

I got it for $10CDN at a used book store.

If you weigh that against a new one, you will see that a small sacrifice saves a lot of $$$.

Note: My textbook is pretty much brand new. There is no wear on it and not even on the corners. It's like the owner opened it and got scared ****less and sold it off.

Note: I have no clue about the other text.

 

[mathwonk]

books like apostol, spivak, and courant do not change as much as other books through different editions, because they were written right the first time, and the authors are not tempted to dumb them down to sell more the second time around.

however in general the standard rule is that the earlier the edition the better the book. that is because the first edition is the authors own view of the best way to do things, before fashion and success have influenced him to water it down or change or add stupid stuff for people who do not know high school math.

for excample apostol gave into the current trend to include linear algebra in his calculus book and the second edition is very different from the first (a two volume set).

one cannot go wrong by buying all three of these outstanding books, spivak, courant, and apostol. indeed it is my opinion that spivak wrote his book to give a more modern spin to the material in courant's book. several of the proofs appear to have been adapted from courant to spivak.

spivak attended harvard as an undergraduate in the days when courant was the standard text, so he probably studied from courant. i studied also at harvard when courant was the text, then taught from spivak at brandeis and in washington, and then from apostol at georgia. they are all wonderful. I actually prefer apostol as the most scholarly.

young people seem to like spivak however, as more fun. i certainly enjoyed it as a grad student.

 

[JFo]

Well thank you kindly for your response... I do plan on getting all of those books at some point. I saw on some earlier thread (might even be this one) that you mentioned setting up a section that is dedicated to book recommendations for all classes. I think that's a great idea and would love to see it happen, although I am already thoroughly impressed with this sight as is!
take care!
JF

 

[JasonRox]

Well thank you kindly for your response... I do plan on getting all of those books at some point. I saw on some earlier thread (might even be this one) that you mentioned setting up a section that is dedicated to book recommendations for all classes. I think that's a great idea and would love to see it happen, although I am already thoroughly impressed with this sight as is!
take care!
JF

I personally think that it wouldn't be wise to get all three.

 

[tornpie]

I've been tutoring math to HS kids on the side while being a math graduate. I've been toying with the idea of trying to use Spivak or Courant to teach one of my tutees. One in particular is actually in 9th grade and seems enthusiastic about mathematics. The reason why I think it will work is that my kids seem to learn best when I'm not pulling my punches. As long as I do this in combination with being able to dismantle all of their problems to give them maximum clarity, I've been able to teach them some serious math. I've never read or used Spivak or Courant's Calculus, but I have read Calculus on Manifolds and I really liked it.

Anyone ever try this?

Also, if any of you ever find yourself losing the joy of math, I've found that tutoring is great way to restore it.

 

[plover]

Spivak's Calculus is wonderful, and I learned a great deal from it on my own. It was, however, not my first exposure to calculus—I was relearning it after having ignored math for several years.

A couple of caveats:

Spivak's pedagogical style makes for a book that is great for learning and as a source of problems but is a reasonably lousy reference work.

Also, for some reason Spivak's works are, as a rule, some of the most badly proofread math texts I've encountered. The third edition of Calculus isn't too bad, but the solution manual for it is truly dreadful in this respect.

As for editions, I suspect it depends a lot on the author whether later editions have useful amendations or not. However, in buying used math books my recommendation is to avoid first printings whenever possible—especially if you are using the book for self-teaching. (Take it from someone who compared a first printing copy of Spivak's Calculus On Manifolds—the one with purple illustrations —to a later printing to find all the typos and other corrections...)

 

[singleton]

I would love to get a copy of Spivak's book!... What is the title??
Is there a specific edition that's better than the others?
An ISBN # would help too if you happen to have it.
Thanks much!

PS
Same info for Apostol and Courant would also be appreciated.

Calculus
Michael Spivak
ISBN: 0914098896
Publisher: Publish or Perish; 3rd edition (September 1, 1994)