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So I'm thinking of doing the following course progression:

Baby Rudin

Finite dimensional vector spaces Halmos

Abstract Algebra Herstein

Big Rudin (Real and complex analysis).

Is this a good course progression, assuming I already have calculus through multivariable, a decent understanding of differential equations, and a basic understanding of real analysis to begin with? Any suggestions with going through these books or time estimates for thoroughly working with the texts (preferably in hours, not days or weeks or anything like that)?

Thanks

EDIT: I am willing to commit 2-3 hours a day, occasionally more.

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Does this mean you plan to do Baby Rudin, then Halmos, then Herstein, etc or are some of them at the same time? In all honesty, I'd do Halmos, then Herstein and Rudin concurrently. Linear algebra will come up in Rudin, and later on abstract algebra will come up. Algebra will probably take longer to digest since you have some intuition for analysis from calculus and some analysis, so I'd start that as early as possible. –  Matt Aug 30 '11 at 16:19
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@analysisjb: Herstein is a good "first book", but you should keep in mind that old-fashioned-ness and perhaps supplement it with some more modern treatments later. You won't find anything that covers as much ground as succinctly, though Dummit-Foote is a good option if you are willing to pay for it and don't mind the extra material. –  Arturo Magidin Aug 30 '11 at 17:14
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Honestly? No, I don't. 2-3 hours a day is what I would expect to spend on my own working on a graduate course/good undergraduate course for each of these topics, on top of a good lecture, in about 16 weeks or so. Herstein would be a two semester undergraduate course, a 1 semester very heavy course (certainly requiring more than 2-3 hours a day); Halmos might be at least one a half semesters. So I certainly would not think myself capable of learning that much at that rate. –  Arturo Magidin Aug 30 '11 at 17:20
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I don't mean to discourage you; I can only say that, with the benfit of hindsight, I would have found covering just chapters 2, 3, and 5 of Herstein (not doing anything with vector spaces except 4.1 and 4.2 to get the notion of dimension; skipping all of chapter 6 on linear transformations, and all of chapter 7 on finite fields, quaternions, Wedderburn's theorem, and Frobenius's theorem) by myself, 2-3 hours a day with an occasional longer day, very challenging at 40 weeks. I cannot even wrap my head around attempting to tackle Rudin in less than 16 with a lecturer on hand. –  Arturo Magidin Aug 30 '11 at 18:56
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In that case, I would suggest nothing but linear algebra; when you are done with that, go to either Herstein or Baby Rudin, but not both together if you only have 2 hours a day. When you are done with one, go on to the other. I would expect basic linear algebra to take you about 30-36 weeks, Herstein (skipping Chapter 4 and 6 since you will have covered it in Linear Algebra) about 35-40 weeks, and about the same for baby Rudin, assuming you are doing them by themselves. –  Arturo Magidin Aug 31 '11 at 0:16
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Those are nice choices. If you haven't studied linear algebra before you may want to replace Halmos with a slightly more elementary book. I like Lang's linear algebra but just about any "Intro to Linear Algebra" book should do. No one can argue with you choosing both Rudins. Herstein is a fine book as well but the book by Dummit and Foote is only slightly more advanced and much more comprehensive (as well as readable). As far as the time you'll spend it's really hard to say. If you spent 2 hours a day in intensive seclusion studying these books I guess you could be done in a year. So 700-800 hours? Hope this helps.

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Thank you. 700-800 for all courses? or just algebra? –  analysisj Aug 30 '11 at 16:06
    
see above comment –  analysisj Aug 30 '11 at 16:18
    
I agree with Dummit and Foote. –  Matt Aug 30 '11 at 16:20
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Are we all thinking about the same Big Rudin here? The graduate text? Even if you are gifted and decide to focus solely on Analysis, starting from basic real analysis, through all of Baby Rudin, then through Big Rudin, in 1 year is quite unfeasible. There's a reason those Analysis topics are spread over from the first year of an undergraduate course, to the graduate level. I know you are eager to learn lots, but you don't want to set impractical goals. –  Ragib Zaman Aug 30 '11 at 16:22
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@analysisjb you say you start at "basic understanding of real analysis". To get to the point where you can even commence that book will take you at absolute minimum 1 year of work. Not that I would even recommend you do cram it all into 1 year like that. –  Ragib Zaman Aug 30 '11 at 16:37
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