Making the Transition from Basic to Advanced Math

[someperson05]

Making the "Transition"

Hello. I am currently a freshman in college, finishing up my second semester. I am looking at basically majoring in mathematics. (My actual major title will be Applied Mathematics and Computational Science, I am creating a major plan to better suit my needs.) Regardless of that though, I will always be a mathematician at heart.

Let me get to the point. I have been trying my hardest beyond class to study as much mathematics as possible. I've been doing a mini project, taking an extra problem solving seminar class, reading extra books, etc. etc. No matter what I do however, no matter how much I feel like my mathematics skills progress, I can't seem to make the leap into "advanced mathematics." I feel somewhat like Zeno's Paradox, getting ever closer to a higher level of mathematical ability but never actually getting there.

I am acing my multi-variable calculus class, and I will continue to ace all of my classes, I am confident of that. They are easy, just doing the problems seems so simple. I always do well when there is a teacher to explain the concepts. Its when I attempt to learn things on my own, like set theory, proofs, that I can only ever pull out fragments from the text and then feel stuck, left to find another book or ask a teacher. I feel like a true mathematician must eventually be able to deduce things on their own, lest they be left to do little original research.

So my question is, can anyone make any recommendations on how to achieve this transition beyond simply reading more? I will continue to read and try, but if there is anything that someone has found that has helped them to make this "transition", I would love to know. I am willing to devote any hours of effort and work, which is what it probably amounts to anyway. Is there a textbook or just a book in general that helped you to see mathematics in a different light that you think would be useful to me? Or a book that helped open up this elusive world of mathematics, this world of deeper and higher levels of truth? I don't care if its from an applied or pure perspective, I just love mathematics.

Thank you for any help that you can give me.

 

[Petter]

You are a freshman. You shouldn't expect to become an expert in a year. You seem to be doing fine.

 

[Studiot]

It's not more work, it's more time you need.

Time to allow it to stew in your subconcious. You acquire a vast amount of facts, ideas and techniques but it takes time for your mind to draw the connections. It will suddenly happen. Just keep doing the exercises. and good luck.