Math Fundamentals: My 2nd Wind in Middle School

[Codester09]

Up until middle school.. math was my thing. I wouldn't say I "enjoyed" it, but it definitely came naturally. My teacher even forced me to do math counts in 7th and 8th grade. We had a grad student as our coach and he always tried to get me into math, and, for whatever reason, I just really didn't care about it. Since then, I went through high school absolutely loathing math. I remember sitting in algebra II (as far as I got in high school) and literally wanting to die, wondering why the evil state made this class a requirement.. until now.

I'm in college now and half-way through algebra II (I chose the easiest possible class over xmas break) and, surprisingly, am loving it. I talk about math with my prof after every class. I've aced all the tests, read the entire book, done all the homework, and am ready for the next course to start. I enrolled in pre-calc for the summer I semester and calc for summer II. If that goes well, I think I'm going to take a stab at calc II and phys I this fall. I don't know how steep the learning curve gets in the upper-level courses, and I don't really see myself having any problems, but just to make sure, I thought I'd read a introductory calculus book or something like that if it exists. I just mainly want to learn more.. I've been looking up integrals & derivatives on wikipedia for christ sake.. my roommate thinks I'm off the deep-end.

I'm thinking about physics as a degree choice, I know it probably sounds halfway ridiculous for a algebra II pupil to say something like that, but I'm pretty confident in my ability and really just can't see any other route for myself. I don't know where this obsession came from, but does anyone (preferably physics/math majors) have any books/tips/learning resources that helped them out in college?

 

[VeeEight]

Hi Codester09,
I am not familiar with 'algebra II' or the specific things you like in math but I will try to give you some small advice. Stewart's Calculus is pretty standard for a high school student - you should try going through each section and then completing the exercises as it's the best way to learn the techniques.

I preferred analysis as an undergrad - analysis can be thought of as an extension of calculus. The book "Understanding Analysis" by Abbott is a good introduction to the subject. Even though it is very small, it is packed with information and every little detail in the book should be understood. Have you gone through the proof for the square root of two being irrational (cannot be expressed as the fractions of two integers)?

So I would suggest looking into that and posting any questions you have. There are many fields of math (as you can see by going thorough the math forums) and education in math is all about learning and understanding the language of each field so you have the tools to solve problems and understand the big ideas.

 

[davesface]

...I don't know how steep the learning curve gets in the upper-level courses...

In my experience, the material became conceptually easier after the initial difficulties with epsilon/delta definitions in Calc I. Once you get the basic ideas down, the rest of most calculus sequences is just generalization (one variable to n variables, 3 dimensions to n dimensions, etc.).

That's not to say that the later classes are a cake walk, though, because they do become more computationally intensive.