Questions of Self-studies in Maths

[Shing]

Presently,
I am following three paths of studies in Maths at the same time.

1. elementary Set theory. (College year 1 level) ( I just started.)

2. Calculus (High school level) ( I am almost finished 2/3)

3. 3-D vectors ,Matrices and linear algebra, complex number. (high school level) ( I just started)

May I have your suggestions, please?
Thanks.

 

[daniel_i_l]

You should take a look at this site:
http://tutorial.math.lamar.edu/
for the calculus and linear algebra.

 

[teleport]

Yes that's a great site, especially for the calculus part. About a year ago I used it a lot while in High School, trying to study by myself out of interest for the subject. It did pay off when I got into university and didn't have to study calculus and differential equations for an entire year. What really surprised me was my Math prof puting the same link on his website.

 

[Shing]

Thanks!
That is so good!
I found out how to download it!

 

[Werg22]

You should take a look at this site:
http://tutorial.math.lamar.edu/
for the calculus and linear algebra.

Seems more application based than true exploration of mathematical theory, as I see no proofs being presented.

 

[teleport]

I think the link was meant as auxiliary tool, as in integration techniques, but Werg is right depending on what is your interest focused on: pure or applied. You should definitely concentrate on books. I'm sure mathematicians here will give you great advice regarding this.

 

[Shing]

I am interested in pure more,
but I think applied is also important.

So I will focus on pure more than applied, But I still will study some applied.

 

[Werg22]

One is inclusive of the other: if you learn pure, you'll have no problem with applied. Take a look at the book recommendation board on this forum, you'll find a great deal of suggestions. But I noticed: why focus on three branches, especially when you're at a different level in each? I suggest you focus on calculus first, as it's the best way to sharpen your understanding of mathematics. I personally learned calculus through Courant, whom I recommend, but there are many other books for you to chose.

 

[daniel_i_l]

One is inclusive of the other: if you learn pure, you'll have no problem with applied. Take a look at the book recommendation board on this forum, you'll find a great deal of suggestions. But I noticed: why focus on three branches, especially when you're at a different level in each? I suggest you focus on calculus first, as it's the best way to sharpen your understanding of mathematics. I personally learned calculus through Courant, whom I recommend, but there are many other books for you to chose.

While it's true that if you understand the pure you'll have no trouble with the applied, I also have noticed that if you first parcatice the practical part ie: knowing how to solve problems, then when you start reading up on the pure part you can understand it much faster as you're already familier with the material.
And about what to learn first. I can see why you recommend calculus, but there're also reasons to start with LA. For one, it's easier that cal, but it's logic is very intutitive and it let's you get familier with mathamatical proofs.

 

[Shing]

May I know what LA is?
So is that you mean I should learn LA and logic , set theory first and then calculus then 3-D vectors ,Matrices and linear algebra, complex number?
But I think deeper calculus required knowledge in complex number, Matrices... right?

 

[WolfOfTheSteps]

LA=Linear Algebra

Linear algebra is much better for learning how to write proofs, so it should suit your pure math interests. You might have proofs in a calc course, but not as many (unless it's actually an analysis course, which would probably be too advanced at your stage).

 

[Ks. Jan Jenkins]

Some good videos

For Calculus, I found these videos are very well done:

http://www.math.armstrong.edu/faculty/hollis/calcvideos/

JJ+