Need some suggestions with regards to books for practice

[mathnewbie]

Hello.

I am planning to appear for the subject GRE exam for Mathematics this year. I needed some suggestions for books. I know there is Cracking The GRE by Princeton Review. But I guess the book is for a review . I was looking for books other than it for problem solving practice. I intend to try to solve as many problems as possible from recommended texts. But there are a few subjects about which I am unsure where to study from.

For instance I am studying Calculus from Apostol , and somewhat from Spivak. I guess, problems given in these books are good. What do you reckon ?

Similarly I plan to study Linear Algebra from Friedberg ,Algebra from Pinter , (and if time permits from Artin).


But I am confused with respect to Calculus -2 , i.e Multivariable Calculus , I found Apostol Volume 2 a lot more tough for the purpose of learning Multivariable Calculus. Which book should I use for the same ?

Similarly I am a bit clueless about Complex Analysis , and Probability ? Can you suggest books for these topics.

By the way , how is Munkres for Topology ? Is it too tough for problem solving ?


Basically I am looking for books that cover theory well enough but not overkill like Calculus -2 by Apostol. And the books should have exercises as well.


Thanks. Great Forum. Unique in it's own right.
Cheers. (New to the forum so bear with my basic queries )

[IIes]

Hello.

I am planning to appear for the subject GRE exam for Mathematics this year. I needed some suggestions for books. I know there is Cracking The GRE by Princeton Review. But I guess the book is for a review . I was looking for books other than it for problem solving practice. I intend to try to solve as many problems as possible from recommended texts. But there are a few subjects about which I am unsure where to study from.

For instance I am studying Calculus from Apostol , and somewhat from Spivak. I guess, problems given in these books are good. What do you reckon ?

Similarly I plan to study Linear Algebra from Friedberg ,Algebra from Pinter , (and if time permits from Artin).


But I am confused with respect to Calculus -2 , i.e Multivariable Calculus , I found Apostol Volume 2 a lot more tough for the purpose of learning Multivariable Calculus. Which book should I use for the same ?

Similarly I am a bit clueless about Complex Analysis , and Probability ? Can you suggest books for these topics.

By the way , how is Munkres for Topology ? Is it too tough for problem solving ?


Basically I am looking for books that cover theory well enough but not overkill like Calculus -2 by Apostol. And the books should have exercises as well.


Thanks. Great Forum. Unique in it's own right.
Cheers. (New to the forum so bear with my basic queries )

How about looking around the Internet for suggestions such as here: http://math.stackexchange.com/search?q= ... bject+Test

and in particular here: http://math.stackexchange.com/questions ... bject-test

Hope this helps.

[is2718]

The Mathematics Subject GRE does not really test for understanding of the material. Certainly, having a good understanding is useful if you wish to prepare for the exam, but it does not suffice, and may not even be entirely necessary. If you are asking for general textbook recommendations, I'd be happy to suggest some, but I can't really say that it will make a difference modulo the subject exam. What might be better is to read through the "Cracking the Math GRE" book by Princeton, and take the practice exams, and then afterwards get a sense for what areas you are weak in. I would say that books by the "Schaum's Outline" series, while not adequate for general study, are precisely the sort of text you want when studying for the GRE; that is, lots of basic examples.

To give an example, the MGRE often has "theory" problems like "how many abelian groups are there of order N?" or "let f be a continuous function differentiable on some given interval and satisfying this property. What can we conclude...?" You won't have stuff on group actions, Sylow theorems, Arzela-Ascoli, etc. A proper textbook, even one with many exercises, will focus on the latter rather than on the former.

[mathnewbie]

The Mathematics Subject GRE does not really test for understanding of the material. Certainly, having a good understanding is useful if you wish to prepare for the exam, but it does not suffice, and may not even be entirely necessary. If you are asking for general textbook recommendations, I'd be happy to suggest some, but I can't really say that it will make a difference modulo the subject exam. What might be better is to read through the "Cracking the Math GRE" book by Princeton, and take the practice exams, and then afterwards get a sense for what areas you are weak in. I would say that books by the "Schaum's Outline" series, while not adequate for general study, are precisely the sort of text you want when studying for the GRE; that is, lots of basic examples.

To give an example, the MGRE often has "theory" problems like "how many abelian groups are there of order N?" or "let f be a continuous function differentiable on some given interval and satisfying this property. What can we conclude...?" You won't have stuff on group actions, Sylow theorems, Arzela-Ascoli, etc. A proper textbook, even one with many exercises, will focus on the latter rather than on the former.

Ya. The math stack exchange page suggests reading Dummit and Foote , while it is no doubt an excellent book , I guess something like the book by Charles Pinter may suffice for Abstract Algebra. Mainly because one doesn't need to write down proofs in MGRE.

I wanted practice books mostly. Are Schaum's outlines good ? I wanted one for Multivariable Calculus.

And yeah , I needed some help with general text books as well. Mainly for subjects like Probability , Complex Variable Functions. Just to get my basics right. These are topics I need to brush up my theory on. For others, I guess problem solving is what I need.

[IIes]

Some what on topic (GRE advice & strategy): http://www.mathematicsgre.com/viewtopic.php?f=1&t=217