Prerequisites for Spivaks Calculus/Diff Geo, etc.

1. Jul 14, 2014

TheKracken

Hello, I just purchased Spivaks Calculus book ( 4 th edition) and as well as the answer book. Currently I am taking calculus 1 over the summer and I am curious exactly what are the pre req's for this sort of text? I also have the book "How to Prove it" that I can use to supplement proof technique. But anything else?

How about his text on Calculus on Manifold's? Is that the next step? Or how about about his 5 book series on Diffrential Geometry? Would that be next after that? I am hoping to work on some self study for a while and Diff Geo is my main goal at this point, but ofcourse I have a long way to go. Also any advice of how to go through Spivaks calc would be appreciated.

Thank you
Chris

2. Jul 14, 2014

micromass

Spivak actually has very little formal prerequisites. You just need to be acquainted with High School mathematics and proofs. However, the text is quite difficult and you need quite some mathematical maturity. That is sadly not something that can be found in a specific book, it needs to be built up in time.

Also, while it is not a formal prerequisite, I suggest to be familiar with calculus already before tackling Spivak. If you never calculated a limit, a derivative or an integral before, then Spivak is going to be nearly impossible for you.

Sure, Calculus --> Calculus on Manifolds --> Differential Geometry is a good path. There are better books out there than Spivak though.

Self-studying is very difficult. The book is quite dense. It would really help if you found a mentor who could explain you key concepts and who advised you on problems. Sure, a forum like this could be a substitute, but it's not the same thing. It's still better than going through it completely alone though.

Finally, not all exercises are worth doing. Some are too easy, some are too hard. A mentor who knows your competence in mathematics and who can advise a selection of exercises would be helpful.

I have mentored several people in math and the process for them is always a lot smoother and a lot faster. It's something you should really consider.

If you read Spivak then chances are incredibly big that you'll find it too difficult. Don't worry about that, don't think of yourself as a failure if that happens. It's perfectly normal. It just means you need to go through an easier text first.

3. Jul 14, 2014

TheKracken

Currently I am going through Calculus I and am half way through the course, so by the end we will have calculated a limit, derivative and integral. We will also go through the fundamental theorem of calculus. The Text we use is Calculus for Scientist and Engineers by Briggs. Would this be a sufficient start before tackling Spivaks?

Also you said there are better text's than Spivak's though? Which do you recommend? I heard Spivak has a interesting and conversational type approach to it's readers so that sounded very appealing to me.

As for a mentor, I have a professor who has his Phd in Algebra who is slightly willing to help me go through some topics and guide me, but I don't know realistically what I can expect from him in that regard since he has no obligation to help me.

4. Jul 14, 2014

micromass

It kind of depends on you. You'll only know if you try Spivak and succeed/fail. If you try Spivak, then you'll know what you're missing.

Spivak's calculus book is very good, so definitely go with that provided you can handle it. His calculus on manifolds is way too terse. His differential geometry is ok, but I'm not a fan.

Go with his calculus book now. Once you're done with that, you can still see if you like his style or not. That said, Apostol's calculus is a worthy alternative too.

Maybe you have the opportunity to do an independent study course with him? You could always ask him.

5. Jul 16, 2014

tridianprime

I have recommended this in another thread but I'll do it again. It is highly enjoyable and should anyone to an acceptable level to tackle Spivak - it will be a challenge though (thats the fun part :tongue:).

6. Jul 16, 2014

verty

Micromass said:

That said, it is possible to do almost all the questions, most of them can be solved. But, I don't advise it.

I tried that, I bought the book thinking "I am going to beat Spivak, I'm going to crush it". This was the first edition, I did get through the first 3 chapters answering almost all the questions. But then, I put the book down and haven't looked at it since. Why? Because I thought to myself, I've got all that these three chapters can give me. And what have I gained, some knowledge of some pretty elementary math. Value versus cost wasn't there, I just couldn't see what the author was trying to achieve except write a book more difficult than it needed to be.

I strongly advise not doing all the questions, do the easier questions only is my recommendation.

7. Jul 16, 2014

TitoSmooth

Ditch the solution manual. If you need a manual you do not understand Spivak.

His hitchhiker book is a good supplement however.

8. Jul 17, 2014

homeomorphic

I'm not familiar with Spivak's calculus on manifolds book, but I think the place to go next would be differential geometry of surfaces, not calculus on manifolds. So, I'd say O'Neill's Elementary Differential Geometry or a similar book.

9. Jul 17, 2014

TheKracken

What are the pre reqs for a text like that?
@ homeomorphic

10. Jul 17, 2014

homeomorphic

I think just Calculus 3.