Spivak's Physics for Mathematicians?

[Voivode]

Main Question or Discussion Point

I'm in AP Physics now, and I was in AP Calculus last year, and I was wondering whether I'd be able to understand this book.

 

[redrzewski]

AP as in high school? I haven't read Spivak's Mechanics, but I have read a couple volumes of his differential geometry series. (They are tremendous, and I highly recommend them.)

1 amazon review says that Spivak recommends you read vols 1 and 2 of his differential geometry series before reading Mechanics. So based on that, I'd say this book is too advanced for high school.

 

[yenchin]

I am reading the book right now... the first few chapters are pretty readable even without differential geometry background. There's actually an online draft [http://www.math.uga.edu/~shifrin/Spivak_physics.pdf] [Broken] that gives you a feel of how he treats the subject, but the book is *much* nicer.

 

[qspeechc]

Well, the title is "Physics for Mathematicians", which should tell you something (or not). There is no preview function on amazon.com, but the extract from the preface says:

The purpose of this book, or possibly series of books, is indicated precisely by the title Physics for Mathematicians. It is only necessary for me to explain what I mean by a mathematician, and what I mean by
physics.

By a mathematician I mean some one who has been trained in modern mathematics and been inculcated with its general outlook. ...

So I'm guessing you need at least a degree in mathematics to understand the book.

 

[yenchin]

Well, the title is "Physics for Mathematicians", which should tell you something (or not). There is no preview function on amazon.com, but the extract from the preface says:



So I'm guessing you need at least a degree in mathematics to understand the book.

It's really not like your typical mathematics text. There are a lot of discussions of concepts that I find useful. I realize my previous link does not work... So http://www.math.uga.edu/~shifrin/Spivak_physics.pdf" it is again.

 

[qspeechc]

I'm not going to argue with the author of the book. Spivak himself says the book is for "someone trained in modern mathematics".

The first reviewer says:
"The premises of the book are great: to analyse, besides the advanced mathematical tools avaiable to theoretical Physics (tangent and cotangent bundles, sympletic geometry, etc),...
As for the subject, it covers essentially the whole subject of Classical Mechanics, from elementary portions to Lagrange's and Hamilton's equations...
The book should interest not only mathematicians, contrary to Spivak's opinion, but theoretical physicists as well..."

From the second review:
"this book is a wonderful introduction to mechanics for mathematicians..."

If you want to recommend an advanced book to a beginner, go ahead.

Voivode, if you want to spend $90 on a book you won't understand for at least another 5 or so years, then go ahead.

 

[yenchin]

Well, I wasn't recommending it. I merely posted the link, so that the OP can decide whether or not he want to get a copy of the book for himself. :-)

 

[qspeechc]

The 2nd reviewer on amazon.com says the notes and the book are very different. Since we can't preview the book on amazon, we'll just have to take his word for it.

 

[yenchin]

I think the first half of the book can be a great *supplemental* reading even for beginners [I especially like how he spends lots of effort to discuss the three laws of motions].

I would say that the book is a blend of physicist's way of doing mechanics with lots of caveats spelled out, and once in a while some rigorous mathematics. At least for me the book is worth getting just for all the discussions [for example, there are many places where Spivak discussed "why easy physics is so hard (for mathematicians)" and spells out the underlying concepts that physicists tend to assume, and why some of these really are misleading] and historical remarks.

The exercises tend towards mathematical details, so one probably can't learn much physics problem solving from the exercise. Flipping ahead, I do think that the second half of the book is rather technical and is not suitable for most beginners.