Hi, I'm a maths student in Brazil myself :) I'll answer in english, though, since I'm not sure about the HN policy on comments in foreign languages. Can I ask

Hi, I'm a maths student in Brazil myself :) I'll answer in english, though, since I'm not sure about the HN policy on comments in foreign languages. Can I ask you which university you're from? I'm not aware of many universities besides UFRJ which offer an "Applied Maths" degree. About real analysis, I took the summer course in IMPA, an I used only Elon's books. I really like them (for the books themselves, not just because they're in portuguese). There are two: the thick one: "Curso de Análise", and the thin, silver one: "Análise Real" (I like to call them Elão and Elinho :)). Elão is very detailed and has lots of examples, but mentions topics which may be too specific and not covered in your course. Elinho is much more terse, and great if you need a quick summary. I would also consider reading David Bressod's "A Radical Approach to Real Analysis". It's an awesome book, which mentions historical motivations for everything, and has a really different approach to teaching analysis (it will certainly help you learn analysis, but might not help too much in your course, since it's quite non-traditional). If you're not used to proof techniques, I highly recommend Keith Devlin's "Introduction to Mathematical Thinking". About strategies to studying analysis: examples. I think it's really important to work out lots of examples by hand all the time. Every time you read a definition in your textbook, whatever it is, close the book and try to think of some examples of mathematical objects which satisfy the definition. When you're done, try to think of other examples which differ significantly from the ones you came up with before. When you open your book again, if the author presents examples, read them with attention. TLDR: as the other comments have made it very clear, you shouldn't be reading an analysis book without a pencil on your hand; you should feel active, not passive, while studying analysis. Finally, I don't know about any youtube channels that could help you with an analysis course, but you should be aware of Mathematics.StackExchange. It's a great Q&A website/community; I've asked a lot of questions there while studying for my undergrad courses. Wish you the best in your course and you maths career :)