How should I go up stages in mathematics?

[superduck]

I'm a student of a university in Japan. I'm enrolled in correspondance course. I'm a philosophy of science major.
I need to study mathematics and physics basically.I think I need to study maths and physics or other subjects in English. I can barely understand them in Japanese because Japanese textbooks use too many difficult "kanji" to translate academic words and they don't have so clear description.
When I checked some words with English dictionary for learners, I found that it is very clear and simple description. So, I thought ,perhaps, it is a good way to study these subjects in English.
How do you think about my idea?
Next question is a more concrete.
I found a old book written in English about mathematics in a local library in a university. It deals with pre-algebra. Is it a correct type of mathematics to start to learn mathematics? Or if not, would you recommend some books for beginners? And would you advise me how I should go up stages of matrhematics step by step?
I don't know how pupils and students from other country study mathematics or other subjects. So, I don't know which types of mathematics they begin to learn maths.
Once I've got a good information from this site which recommend some books, but I found that I had enough money to buy it.
At present,my purpose is to achieve A level in Cambridge International Examinations.
I'm looking forward to hearing from you.

 

[SteamKing]

It depends on when your mathematics instruction stopped in secondary school in Japan. For example, if you only received instruction in arithmetic, it might be a good idea to start with a refresher in arithmetic (especially if it has been some time since your last class) before going on to study more advanced topics.

It is also a little unclear when you say you need to study 'mathematics'. In English, mathematics includes many topics, from arithmetic to algebra, trigonometry, calculus, etc. Most of the math curricula in the US proceed from arithmetic to algebra to geometry to trigonometry to advanced algebra to calculus at the secondary level. In college, depending on the subject major, some of these topics can be repeated before studying more advanced topics in calculus or other branches of mathematics.

 

[superduck]

Thank you for replying : it's very helpful

Thank you for replying. Your advice is accurate. To tell the truth, I don't know how mathematics branches are expand. So, I don't know each name of categories in mathematics well. In Japan, it is not taught well, I think. For example, one textbook contains several types of mathematics in Japanese high school. It doesn't systematic. If you could, would you recommend some books for self-learning arithmatic and algebra? I also want to know the meaning of pre-algrebra. In the textbook I mentioned before, several kind of mathematics are contained. I hope that I could find best way to learn basic mathematics. I'm looking forward to hearing from you. Thank you.