Just finishing highschool, even though I am doing "well" (in the context of the math course itself), I have significant holes in my actual math knowledge.
As I think many people who explore math outside the typical walls of highschool will realize, the math in high school is often very selective, taught with shallow depth. Most questions are looking for simple cookie cutter solutions, explained in easy to understand language.
In my spare time, I have been attempting to patch holes in my math knowledge by looking through various text's attempting problems and reading the material. I find however, often in word problems from alternate sources other than school curriculum, that I struggle on questions usually due to wording and abstraction. I do realize completely though that this is all part of math and being able to read abstraction is the name of the game.
What is the best way to prepare myself for the transition of H.S. Math to undergraduate math? I have often heard horror stories of people being shocked by the difference between H.S. and University and stating that "H.S. never prepared them for that".
However, as I enjoy math and intend to do something math intensive in the future, possibly CS, Engineering or Math, I would really like to be as well prepared as possible.
I am mainly looking to understand wording, proofs, terminology and being able to apply my algebra knowledge to word problems.
Currently started "Serge Lang - Basic Mathematics". Has lot's of content and questions but I struggle with wording frequently, this is one of the first "real" math textbooks I have read and though the math itself isn't difficult I get caught understanding the wording.
Also interested in other book suggestions.