I recently bought the analysis book by Rosenlich, it's at a very good price for a book that appears to be really good, which is hard to find in a math or physics book these days.
However, it's quite compact at only pages. Is this really all the real analysis I'd need to take on higher texts in topology and differential geometry?
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Does this include group theory as well? Also, what about any advanced linear algebra more advanced and rigorous than physics' majors usually cover such as in Axler's book?
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Or is basic linear algebra good enough? Yes, it's really everything you need, although it might be helpful to read up a bit on metric spaces, I don't think Rosenlicht covers that. It doesn't do group theory, but there's not really much group theory you need anyway. The thing is that many group theory books start of explaining finite groups, while the groups in differential geometry are usually infinite. So group theory texts aren't really all that useful. If you know things like Axler, then you're all set.
You don't need more than that. You certainly do need to be acquainted with vector spaces and linear transformations though. Will a grad-level GR class cover the necessary math or will I need to study topology first? TomServo said:.
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You will not have to go to all this trouble. Tensor calculus and tensor algebra are done very differently in most GR texts so most of what you learn from the aforementioned texts won't even be of much help to you in the end as far as solving GR problems goes. Go ahead and learn topology and differential geometry from the aforementioned math texts, open up a GR text like Wald, and see how much of what you learned actually has any relevance in solving the end of chapter problems.
I can tell you from experience that not even the first 4 chapters of Lee's text on topological manifolds which I went through thoroughly had much if any relevance except for some basics that showed up in chapter 8 of Wald's text global causal structure. I don't think you realize how different the math in a math textbook is from what is presented in a physics textbook. You have to take a look yourself to see. As a side note, I like to learn pure math for the sake of pure math. Thinking that learning pure math will somehow help you understand a physics text better than someone who doesn't have a background in pure math is absolutely ridiculous.
EDIT: In fact what going through various pure math texts has really done for me is make it really hard to go through physics textbooks without being nitpicky about every single detail that the physics textbooks get wrong from a mathematical standpoint. Go through a functional analysis text like Conway and try to read a standard QM text like Sakurai or Shankar and take note of how impossible it is not to burn the text because of how badly it butchers the math. Last edited: Nov 21, I hope that one day, I too will annoy mathematicians.
Wannabenewton: I hope you're not arguing that learning the proper mathematics is useless because it isn't necessary in the end-of-chapter problems in your textbooks! When the time comes to actually do some research, I'm sure you'll be glad you studied it. Depends on the research. There is enough research in physics where pure mathematics is useless. How so? Mathematical physics is different from theoretical physics and the term "theoretical" is not even connoted properly in informal discussions. Can you give examples of theoretical GR research wherein a thorough study of e.
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I will introduce the flow, provide a brief survey of the general theory and describe some recent progress. The generic member of each family has so-called asymptotically locally conical ALC geometry. At a special parameter value, the nature of the asymptotic geometry changes, and we obtain a unique member of each family with asymptotically conical AC geometry. On approach to a second special parameter value, the family of metrics collapses to an AC Calabi-Yau 3-fold. In all of the known examples, this local homeomorphism is a global homeomorphism onto R 4.
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