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I have basically completed a good deal of Single Variable Calculus from Spivak's Calculus and since I leave school in May next year,I intend to put in some effort to pick up college mathematics.I am a bit confused as to what to study next.I did buy Herstein's Topics in Algebra.

Question: So can anyone please tell me what I should study and in what order or what constitutes a coherent course of study .I am open to various suggestions!

Thanks in advance.

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That probably depends on what would you like to learn. You might want to learn some (very) basic set theory and topology, it does pay off later. – tomasz Jun 22 '12 at 13:01
@tomasz Can you please elaborate.As I said I wish to learn them all(I cannot do that though due to time constraints). – user31029 Jun 22 '12 at 13:02
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It seems to me that Rudin's book should be the easiest for you since you already know a fair amount of calculus from a fairly abstract treatment. You ought to make the fastest progress with Rudin's book. Linear Algebra interacts with analysis really well. In quite a few fields which have use of applied mathematics, a strong foundation in linear algebra and analysis constitute the bulk of mathematics people know and use regularly. So, this should set you up to be able to read quite a bit of physics, engineering, machine learning etc should you so choose.

Algebra is an entirely different direction. At least, in my experience, it's likely to feel that way. Quite a few people, who have a head for analysis, flounder in algebra; and vice versa. This might not be you, but it's something to keep in mind.

So, my best guess as to order of ease: Analysis, Linear Algebra, Algebra. My best guess as to what will be most useful to you if you are an applied person: Linear Algebra (since you already know a lot of analysis), Analysis, Algebra. In order of what might be least like the background you've mentioned: Algebra, Linear Algebra, Analysis.

I don't know enough to tell you what to do directly, but hopefully my answer has provided enough guidance for you to make the decision for yourself.

(Have you considered a more concrete Linear Algebra book like Strang's "Linear Algebra and Its Applications"? It seems like you are starting at few levels up of abstraction. I find it's good to get a sense of how the calculations work at a lower level first.)

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I have already had some introduction to linear algebra as we did cover elementary theory of determinants, matrices, transpose , invertible matrices etc at school.I do not wish to do anything of computational character. :) – user31029 Jun 23 '12 at 2:32

Hoffman and Kunze is a great book. If you understand the abstractions in Spivak's book, you should be able to handle it. The problems are great. I have worked many of them.

Go there next.

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