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I self studied A Level Maths (UK equivalent to high school) and am now embarking on self study of undergrad material. I am working through "How to prove it?" By Velleman to learn about proof writing and logic but I am also working through Spivak for calculus as I believe it will give me a thorough understanding. Following this, I intend to study linear algebra, which I have looked a little at, and ODE's simultaneously. I will most likely use Shilov and Halmos for linear algebra and then I'm not sure for ODE or, following that, for PDE. I would appreciate recommendations for this.

I have also picked up a good undergrad classical mechanics book which will be delivered soon so I can work through that for fun.

I would like to receive any feedback such as recommendations in maths, or physics, or just any ideas you may have in terms of material to learn or even books.

Thank you, Sam.