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I'm far from the level of mathematical knowledge every user on this website posseses, however I am very much determined to get there as my love for mathematics increases. These are the topics:

Thanks, Im not from US so I don't know what grade level this stuff is. However it is a further maths course here are resources for these topics are either scarce or of poor quality. I would like to improve my knowledge of mathematics, and not just learn to pass an exam.

Simarly, is there a solid text I can use to self teach statistics? I have to cover basic topics like deviation/variance all the way to harder probability.

Thank you very much!

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Wow now we are getting government issued math-checklists on math.stackexchange? What's next? – Peter Sheldrick Nov 26 '12 at 18:48
up vote 6 down vote accepted

Try looking first at Khan Academy for help with stats and linear algebra (matrices), as well as to review on the fundamentals, which you'll need to fully grasp in order to successfully master more advanced topics. Another helpful resource for learning linear algebra and differential equations, and for reviewing the "basics" is Paul's Online Math Notes and tutorials.

Then perhaps you'd like to explore MIT's Open Courseware - Mathematics for access to classes and topics of interest and where you'll also learn which texts are used for the available classes. Often, course notes, videos of lectures, and exams are available to assist learners, all free of charge.

For learning how to read and write proofs, including proof by induction, a wonderful text t0 read and work through is How to Prove It: A Structured Approach by Daniel Velleman.

Note: It would help to post the topics in which you are interested directly in your question. Many of us are wary of downloading/opening files on our computer.

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All great references, so I'll just add something on this answer. Schaum's collection is a really good way to learn too, and it covers from basic topics to advanced ones in a lot of areas of math. – Ivan Lerner Nov 26 '12 at 18:44

William Chen offers brilliant lecture notes for undergraduates (= students trying to achieve a bachelor's degree), covering nearly every first-year topic and also a little more.

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