My experience in learning mathematics...opinions?

[Kilo Vectors]

Hello

I have noticed that there are hundreds of ways of teaching one theorem/concept in maths, often very complicated with pure math terminology the likes of which I find an absolute nightmare! to very basic and just using similies. It always "blows my mind" that there are so many different ways the mathematics is taught and presented across the vast material for learning that I use. It does not help that I come from a school where we were taught to be robots and not mathematicians. We were never taught what a derivative actually is (how it is presented in the textbooks) but just taught how to do it. We were drilled into solving thousands of functions of trigonometry but never touched upon what their origins or meaning were.anyway.its just unbelievable how many ways of teaching one concept exist.

Has anyone else noticed this? I wish there was one book which I could stick to, but there really won't ever be. I am pretty shallow in my knowledge and don't practice it enough, but I feel like I am learning.

Re: the significance of my school experience, well I really feel lost sometimes as I know I truly don't understand what I am doing. This troubles me, as I don't trust anything which I don't completely understand. This is what motivates me to learn math inside out..I know how to derivate functions and trigonometric identikits but the real reasons and why is missing? We were never taught that..Guess it really is upto the student.

 

[fresh_42]

Mathematics has been closely related to philosophy for centuries. And in a way it is still. The fact that physics and engineering uses mathematics as their language kind of conceals this fact. Mathematics in its core is a language about abstractly defined objects. There are no circles in the real world, smooth motions or real numbers. The real world is highly discreet stuff: atoms. Nevertheless mathematical concepts prove very suitable to handle the world around us. I've read several times here on PF that physics is the art of finding models for physical phenomena that allow us to make descriptions about what we know and even more important predictions about what we don't know yet. These models have to be formulated in some language and mathematics turned out to be more precise than words. The more you go back in time the more words you will find in texts about physics or mathematics. The common usage of logical expressions and formulas is a quite new way to present knowledge.
So a main part about these fields is about learning a language and developing a feeling for what is meant by those special words used. It can still lead you into traps for sometimes terms are used as well in common English language as well as in science, usually not meaning the same thing.

There is one question that can guide you through all obstacles ahead: Why?

The different concepts of presenting mathematical results are probably attempts to narrow the gap between those abstract models and everyday experiences. Once you've seen how often, e.g. $π$ or $e$ naturally occur in complete different contexts it won't matter how they have been introduced or defined in the first place. They are abstract bricks that apply to many (colloquial language!) buildings.

 

[Student100]

What's stopping you from reading the textbook? Lectures are no replacement to reading the assigned/supplementary texts.

 

[Andreol263]

Because when you are in the beggining of the course you probably couldn't understand what is the real definition of the thing, thia is why a E.M course is taught with different levels of deepness, for a freshman in college the E.M is nothing compared to a graduate E.M, the last is much more deep, is so for mathematics, if you want to know what a derivative really is and even more, go to real analysis, if you want to know more about the propertries of objects in space, go for topology, and so on..

 

[Kilo Vectors]

Mathematics has been closely related to philosophy for centuries. And in a way it is still. The fact that physics and engineering uses mathematics as their language kind of conceals this fact. Mathematics in its core is a language about abstractly defined objects. There are no circles in the real world, smooth motions or real numbers.
The different concepts of presenting mathematical results are probably attempts to narrow the gap between those abstract models and everyday experiences. Once you've seen how often, e.g. $π$ or $e$ naturally occur in complete different contexts it won't matter how they have been introduced or defined in the first place. They are abstract bricks that apply to many (colloquial language!) buildings.

What's stopping you from reading the textbook? Lectures are no replacement to reading the assigned/supplementary texts.

Because when you are in the beggining of the course you probably couldn't understand what is the real definition of the thing, thia is why a E.M course is taught with different levels of deepness, for a freshman in college the E.M is nothing compared to a graduate E.M, the last is much more deep, is so for mathematics, if you want to know what a derivative really is and even more, go to real analysis, if you want to know more about the propertries of objects in space, go for topology, and so on..

Yes, I hope to one day completely understand them. I do read the book but I have just really started 1 month ago. I use the schaums outlines for basic knowledge, but I find it a hurried introduction. So I use other books. I had got accepted into a Bsc physics program back home but because of my poor mathematics I had to abandon it. Any books you would be able to recommend? I just got comfortable with the basic theory of numbers and properties of number sets. Not once during school were we taught that numbers are such an abstract concept. I don't think I am intelligent enough naturally to pick up this stuff fast.

Basically I have a collection of books but going through each slowly, is not a good strategy..I find it difficult to know what is the ideal time to really learn concepts like this?