I know that several similar questions to this one have already been posted, but I can't find an answer that really suits me and my needs and after some research and reading I'm starting to feel quite desperate and lost, to the point that I don't really know which way to take or what to do.
This is my situation. I finished high school education eight years ago and I'm planning to go to University next September to study, if everything goes well, Physics. I'm preparing a couple of exams I need to pass (physics and chemistry) with my old textbooks and even if it's not everything I'd like to study, it's everything I need to focus on for the moment. But when it comes to mathematics I have a big issue. I know I'm going to need them for my degree, but I'm not quite worried about this particular thing because I'll deal with that during the course. The problem is that even though I've made some maths during these years just to spend some time I had, I feel (and know) that I'm quite rusted with the maths I once knew and that I have a lot of gaps in my knowledge of preuniversity mathematics. The point is that I'd like to prepare myself, to level up my maths, as well as fill as many gaps as I could have in my knowledge. In addition, since I feel also quite interested in maths themselves, I'd like to get a grip of general maths.
But I don't know what to do. I know some places, like Khan Academy, but I'm more the (text)book-oriented person.
I've been looking around and found several books, but I can't make up my mind about which ones to choose and start learning. I know that, I shouldn't be this picky or worry too much with such a basic knowledge I have and that almost everything should be good enough for me to start, but my time is limited, and so are my resources and means.
I know some trigonometry, algebra, analytic geometry and calculus (differentiation and integration).
Maybe a good way to start could be a book with lot of exercises to practice and review the things I used to know and to assess the things I don't know and so start working on them.
It's a triple problem: I don't know which things to study, since I ignore them, so I need some sort of way of figuring out what I ignore and need to study. I need to be prepared to deal with the maths I'm going to find during my degree. And I'd like to expand my knowledge of general maths.
So far, this is what I've found when it comes to books:
- Geometry: A High School Course, by Serge Lang.
- Schaum's Outline of Geometry
- Trigonometry, Corral
- Trigonometry, Gelfand
Precalculus in general:
- Precalculus Mathematics in a Nutshell, by Simmons
Algebra and general preuniversity mathematics:
- Schaum's Outline of College Mathematics
- Schaum's Outline of College Algebra
- Fundamentals of University Mathematics, McGregor
- A Concise Introduction to Pure Mathematics, Liebeck
- What is Mathematics?, Courant and Robbins
I'd like to read and know about everything, but it's not about knowing, reading or collecting books, but about learning and going straight to the point. This is why I think I should try to avoid repeated subjects (even if repetition is basic for learning).
And when it comes to fields or topics, I think I'd need to work on the following:
- Probability, combinatorics and statistics.
- Some calculus and linear algebra.
- Proof, sets, concepts of mathematics.
I also know some places on the Internet:
- Paul's Notes (I've already gone through the College Algebra, but it's too elementary and easy).
- Khan Academy (I learnt a lot in the past, but I see it more like a complement to the actual learning through books, exercises and readings).
- Math is fun
But I don't think it's a good idea to go jumping from one page to the following, skimming through their content just to learn an isolated bit of information.
I've wasted too much time all these years, and I know I may never be able to make up for lost time, but at least I'd like to be as prepared as I could, without unnecessary stress and overworking.
For my degree I would add some books on mathematical methods for Physics, but I need not worry for that right now, as I said above.
What do you think about Schaum's Outlines?
What do you think I should do? To try to go straight to the point and to focus on the main and most basic concepts?
Any advice will be helpful.