I'm a 17 year old junior looking to further develop my mathematical skills in order to better prepare myself for university level pure mathematics. I'm looking for books/courses in Analysis, Linear Algebra, Discrete Maths, Combinatorics, Statistics or anything that could be helpful. I've already applied to different universities for summer courses but would also like to get more information by people who have studied maths themselves.
Thanks in advance!
On
For introductory book on analysis, I would recommend Stephen Abbott's Understanding Analysis. It's written both very cleanly and concisely, giving it the advantage of being extremely readable, all without missing the formalities of analysis that are the focus at this level, especially if you are self studying. After this book, you may proceed with baby Rudin or Bartle's Elements of Real Analysis
For linear algebra, Sheldon Axler's Linear Algebra Done right and Gilbert Strang's Linear Algebra and Its Applications are the books to go with.
For abstract algebra, Fraleigh's A First Course in Abstract Algebra, 7th Edition is a good book for self study. It is easy and good for the beginners, and it has a complete solution manual written by the author.
You might enjoy Combinatorics Through Guided Discovery.