- #1
Seydlitz
- 263
- 4
Hello all,
I know that perhaps this question has cropped frequently in a lot of places, but I would like to be quite specific in my case. I've just finished High School with UK A level syllabus. The syllabus inside Math A level is mostly straight solving equation type of questions, such as for example integrating or finding root to complex polynomial. I know how take a derivative a function, to find its maxima or minima but I don't know how to do so with the so to say rigorous theorem and so on. I have to say that my Math skills in such type of question are normal, in a sense that I have to do questions carefully and cannot just simply solve one in some prodigious manners but I can grasp concepts quickly.
Now the question is where to start with proof-based Math, the one where you need to apply definition and etc to do proof? What kind of books and what books do you recommend if you were in my position and background? I am also hoping that there's at least informal introduction or just helpful website on this matter, since most of the time I can only find sites that discusses straight questions. My target is to go and take Physics major when I enter university later on next year, and I am hoping to get as prepared as possible, especially with the maths.
Also from looking at some examples I also want to know how do you recognize if a proof is correct? When given something to proof I often think as it's simply true, like 1+1 = 2. How else can you proof such thing, to what extent we need to prove? Previously I just need to plug in number to see if I'm solving equation correctly. In Physics you can usually do experiment or thought-experiment to see if equations or what you are doing are true, here I'm quite lost.
Here's the syllabus for A Level Math if you are interested:
http://www.cie.org.uk/docs/dynamic/43807.pdf
Thank You
I know that perhaps this question has cropped frequently in a lot of places, but I would like to be quite specific in my case. I've just finished High School with UK A level syllabus. The syllabus inside Math A level is mostly straight solving equation type of questions, such as for example integrating or finding root to complex polynomial. I know how take a derivative a function, to find its maxima or minima but I don't know how to do so with the so to say rigorous theorem and so on. I have to say that my Math skills in such type of question are normal, in a sense that I have to do questions carefully and cannot just simply solve one in some prodigious manners but I can grasp concepts quickly.
Now the question is where to start with proof-based Math, the one where you need to apply definition and etc to do proof? What kind of books and what books do you recommend if you were in my position and background? I am also hoping that there's at least informal introduction or just helpful website on this matter, since most of the time I can only find sites that discusses straight questions. My target is to go and take Physics major when I enter university later on next year, and I am hoping to get as prepared as possible, especially with the maths.
Also from looking at some examples I also want to know how do you recognize if a proof is correct? When given something to proof I often think as it's simply true, like 1+1 = 2. How else can you proof such thing, to what extent we need to prove? Previously I just need to plug in number to see if I'm solving equation correctly. In Physics you can usually do experiment or thought-experiment to see if equations or what you are doing are true, here I'm quite lost.
Here's the syllabus for A Level Math if you are interested:
http://www.cie.org.uk/docs/dynamic/43807.pdf
Thank You
Last edited by a moderator: