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I want to plan the next few subjects I learn (by self-study) in mathematics. I have made it through the equivalent of maybe half a Calculus I class so far, but I would like to start a bit on linear algebra and/or differential equations (which I will not do until maybe I work on my calculus some more). Is it a good idea to take this path?

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  • $\begingroup$ It is a good idea to download 30 courses/books of different level on different subject and try to understand them, yes. So try it, and you'll see very soon what you need to work on / study before. $\endgroup$ – reuns Jun 4 '16 at 23:13
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    $\begingroup$ The first part seems sarcastic, the second part seems sincere, I mostly agree with the second part, the first... hm... maybe. $\endgroup$ – asher drummond Jun 4 '16 at 23:14
  • $\begingroup$ Also, where could I get some courses/books? $\endgroup$ – asher drummond Jun 4 '16 at 23:15
  • $\begingroup$ It is if you can do it and it's what you're interested in. You don't need calculus as a prerequisite to linear algebra. (Some of the exercises in linear algebra might mention calculus; e.g. the linear nature of the differentiation operator. But it is possible to learn linear algebra without that.) $\qquad$ $\endgroup$ – Michael Hardy Jun 4 '16 at 23:15
  • $\begingroup$ you have to search books one by one, or try to find some lists such as google.fr/… and nothing sarcastic here, it's how I made all my studies $\endgroup$ – reuns Jun 4 '16 at 23:17
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It's probably better to learn linear algebra independently of differential equations at first, and then see how vector spaces and eigenvalue problems appear in systems of ODEs. Of course, you want to make sure you get a decent book for self-study. Gilbert Strang's book on linear algebra is great if you want something that is focused on applications (but still contains some theory). A more theoretical approach would be Axler's "Linear Algebra Done Right."

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  • $\begingroup$ I think that's Sheldon Axler, not Peter Lax. $\qquad$ $\endgroup$ – Michael Hardy Jun 4 '16 at 23:16
  • $\begingroup$ @MichaelHardy Ahh, you're right. Got confused for a sec. $\endgroup$ – Mnifldz Jun 4 '16 at 23:16
  • $\begingroup$ I don't have a strong opinion, but there are a lot of people who think learning linear algebra at the same time as ODEs (in one coherent course) is a good idea because ODEs provides a lot of motivation for linear algebra. For example, Gilbert Strang recently wrote a book called Differential Equations and Linear Algebra which combines the two subjects. There's also this book by Hirsch and Smale. $\endgroup$ – littleO Jun 4 '16 at 23:34
  • $\begingroup$ @littleO I think that's fair. This is a question with no one right answer. My experience in learning ODEs first (with linear algebra merely as supplementary material) was really frustrating, especially since the concepts of linearity, eigenvalues and eigenvectors got muddled and weren't explained all that coherently. I definitely advocate one to learn them as separate subjects and then see how lin alg is used for solution sets and systems of ODEs. $\endgroup$ – Mnifldz Jun 4 '16 at 23:48
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I had begun Linear Algebra when I was doing Calculus, and didn't encounter any issues, but you will definitely need aspects of Linear Algebra and Calculus in differential equations, so I wouldn't start that yet.

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