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I've just finished my first analysis course, unfortunately I will not be able to continue studying as my family needs me to work for income. I was wondering if there is any meaningful research I can do until I can continue my education, if so any sources?

I have taken: 1 analysis course, book = Calculus by Michael Spivak 1 Linear algebra course , book = Linear algebra done right by Sheldon Axler

thank you.

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First of all, I hope your family's financial situation improve soon. Why don't you give some background information about yourself? What else did you take? Any Algebra, for example? – HbCwiRoJDp Jan 13 '12 at 13:39
Review the material you have already covered in greater depth; work through parts of your texts that weren't covered in class; pick a few random calculus problems to work each day so you don't forget fundamental techniques such as integration by parts, the chain rule, multiple integrals, etc. Doing all of this thoroughly will keep you busy for awhile and give you a much better understanding of the material and keep it fresh in your mind until you are able to go back to school – ItsNotObvious Jan 13 '12 at 13:39
Research is just doing something no-one else has done before. So, how do you know if someone has done something before? Well, you do some reading in the area... Reading is better than asking such a broad question here, primarily because you will most likely learn lots of wonderful new things! – user1729 Jan 13 '12 at 14:14

(1) Talk to your professors, who will have a better sense of what is appropriate for you at this point. They will be better able to give you specific suggestions.

(2) You're going to need a lot more tools in your toolbox to do research eventually, so while your enthusiasm for research is great and I certainly encourage you to dabble in any questions that come up along your way, you are going to need to take lots of coursework in the future as well. At this point in your development, doing coursework on your own -- going through the additional material in the textbooks you have as 3Sphere mentioned, as well as reading one or two appropriately chosen, more advanced textbooks (here, specific advice from your profs can be useful to select texts that match your current knowledge base) -- is likely going to be the best way forward.

(3) Given your background, you might be ready for an introductory undergraduate text on Fourier analysis. You could also read a text in a new area, such as algebra, topology, or combinatorics.

(4) If you are interested in combinatorics, Kenneth Bogart made freely available a self-learning textbook that he was working on when he sadly passed away. It is available here.

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thank you for your comments, this is truly a beautiful site. I will use your advice. – fifthprime Jan 13 '12 at 15:20

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