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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.2011-08-30
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    @Matt so you are suggesting baby rudin, halmos, then herstein and big rudin concurrently? Do you have a time estimate?2011-08-30
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    I have converted the question to [community wiki](http://meta.stackexchange.com/questions/11740/what-are-community-wiki-posts/11741#11741), as it's asking for advice, and there is no single right answer.2011-08-30
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    By "Abstract Algebra Herstein" do you mean "Topics in Algebra"? Although I have a very soft spot for Herstein and I think it's a good book, it is also somewhat old fashioned. In particular, I think that the group theory section suffers from having almost nothing (if not absolutely nothing) on group actions.2011-08-30
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    @ArturoMagidin what book would you recommend? Also, how long do you think this course sequence would take, preferably in hours?2011-08-30
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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.2011-08-30
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    @ArturoMagidin thank you very much. Do you think that it would be feasible to complete these 4 books well in 36 weeks given the amount of time I spend on it? If not, what would you recommend as a course of study?2011-08-30
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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.2011-08-30
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    @ArturoMagidin thank you very much! How about baby Rudin 9 weeks, herstein 18 weeks, and big rudin 18 weeks, or even a different sequence?2011-08-30
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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.2011-08-30
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    @analysisjb No. I was suggesting Halmos first on its own. Linear algebra is pretty foundational to everything. Then doing the Herstein and baby Rudin second at the same time because they are introductory and don't really use eachother. Then Big Rudin last since it requires a bit of abstract algebra here and there. I'd say get some basics of linear algebra for probably 2 months, then spend a year on baby Rudin and algebra. I might throw in Munkres topology book after that and before big Rudin if you really want to understand the topology of what is going on.2011-08-30
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    @ArturoMagidin Thank you. If then I had 36 weeks, assuming 2 hours a day, what course(s) would you recommend?2011-08-30
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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.2011-08-31

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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?2011-08-30
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    see above comment2011-08-30
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    I agree with Dummit and Foote.2011-08-30
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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.2011-08-30
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    @RagibZaman Big Rudin=Real and Complex Analysis. How long do you think it would take?2011-08-30
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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.2011-08-30
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    @RagibZaman baby rudin or big rudin?2011-08-30
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    I have started Baby Rudin and am understanding it pretty well.2011-08-30
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    I was talking about Big Rudin in my previous comment. You can commence Baby Rudin now.2011-08-30
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    @RagibZaman Oh okay thank you. What prerequiites are there then for Big Rudin? Again, I am willing to spend 2-3 hours a day if not occasionally more.2011-08-30
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    Undergraduate Analysis. People most usually spread that over 3 years. Please read my answer below.2011-08-30
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    700-800 hours was a bit of a wild guess. I think most would agree with me that after that much time you're not going to reach "Fahrenheit 451" status with any of these books. Assuming each hour is undistracted quality time it's possible you could have mostly vanquished the first three and started to make headway on big Rudin.2011-08-31