What Are the Best Resources for a 16-Year-Old to Study Higher Math?

[EnergyDust]

Hello everyone. I have alredy introduced myself(https://www.physicsforums.com/threads/lets-get-started.901297/#post-5674898).

As I mentioned, now in school we are studying log's, but in my self-studying I have already read about Complexs number and how to work with them(simple math calculations), matrix and determinant. I read everythink from my current school math textbook, but this is not enough for me.

I want to start with something challenging, I know that higher math will be tough.But I know i can do it, so if someone want to help I will be pleased

 

[fresh_42]

If you start to read a book on calculus / analysis you can't do anything wrong, because it will probably be needed in any of your fields of interest.
Perhaps you can find out, what students of mathematics use in their first year. Also a book on linear algebra is likely a good idea to read. Maybe you will have some initial difficulties to get used to the way mathematics is done at university or in textbooks, because it's different from the way it's taught at school, but you could always find help here on PF. These two subjects are usually the ones in the first year at universities for they are basic to all what comes next: physics, engineering, information theory, mathematics. Depending on your interest, you could add some topology to the calculus and group theory to linear algebra. Just make sure to get introductory books, which are normally available as affordable paperbacks.

 

[PeroK]

Hello everyone. I have alredy introduced myself(https://www.physicsforums.com/threads/lets-get-started.901297/#post-5674898).

As I mentioned, now in school we are studying log's, but in my self-studying I have already read about Complexs number and how to work with them(simple math calculations), matrix and determinant. I read everythink from my current school math textbook, but this is not enough for me.

I want to start with something challenging, I know that higher math will be tough.But I know i can do it, so if someone want to help I will be pleased

You could take a look here (it's free) and see what you make of it:

http://tutorial.math.lamar.edu/

 

[fresh_42]

Another hint: If you try to find out, what's used at universities in the first year, ask in the university's book store, not the professors! This way you will know what normally is used and bought and reduce the risk to run into a professor who might try to impose his personal preferences on you.

 

[EnergyDust]

I live in a small town, where universities don't exist and we have only bookstorts for books(captain Obvious). I am not scared about how math textbooks are written, but I have some thoughts that I won't find the right books to start and everything will be complete mess. Yes i really want to start with something basic to make good solid basis and then i will be able to go deeper.

 

[fresh_42]

You could find out the name of the book store in София for books in natural sciences, e.g. by an email to the university or so, then look for their homepage and send them an email and ask. This way you will get recommendations in your own language rather than those in English which you will likely get here. There are probably many online sources, too, like the Khan academy, but it's difficult to distinguish the good ones from the bad ones. @PeroK's link is a good starting point. I find books better than online texts, because it's easier to go back and repeat stuff or to look up concepts again.

 

[EnergyDust]

I really don't have problem with reading English textbooks, it will be even a good idea to do it, because there will be more opportunity later on. This weekend I am going to travel to Sofia, so I think to visit some big bookstores and see what is all about. Nevertheless I will be glad if I get some names about good basic English books.I will try to find some Bulgarin and then to read English one just for practicing. I am old school, I like to have book in front me insted of reading on screen, because I can easy manage studying techniques such as underlining, adding sticky notes and just writting on the book. Thanks a lot fresh_42, as I said i will take your advice, but I am here for some ideas about English books

 

[Mark44]

You could find out the name of the book store in София

Showoff!

For all of you who can't read Cyrillic, that's Sophia, the capitol of Bulgaria.

 

[fresh_42]

Showoff!

For all of you who can't read Cyrillic, that's Sophia, the capitol of Bulgaria.

Actually I couldn't decide whether to write it Sofia or Sophia, and Wiki was so kind to offer me a cut and paste solution. That was a click less than to switch to the English page ...

But as you mention it, this is another tip for the OP:

You often can use Wikipedia for the translation of technical terms: look it up in one language and then switch language on the left. Doesn't always work, and normally the content isn't 1:1, but this gives you a translation and sometimes two perspectives on the same thing.

 

[EnergyDust]

Showoff!

For all of you who can't read Cyrillic, that's Sophia, the capitol of Bulgaria.

Stop the cringe, It's Sofia

 

[Dr. Courtney]

https://www.physicsforums.com/insights/resources-high-school-math-home/

 

[hilbert2]

Hello everyone. I have alredy introduced myself(https://www.physicsforums.com/threads/lets-get-started.901297/#post-5674898).

As I mentioned, now in school we are studying log's, but in my self-studying I have already read about Complexs number and how to work with them(simple math calculations), matrix and determinant. I read everythink from my current school math textbook, but this is not enough for me.

I want to start with something challenging, I know that higher math will be tough.But I know i can do it, so if someone want to help I will be pleased

Also, check out the problems they've had in the recent International Mathematical Olympiads: https://www.imo-official.org/problems.aspx . If you're good enough and start studying those subjects early, you might get to represent your country in that competition.

 

[EnergyDust]

This is what I found, It's Bulgarian ones, but I think you can get the point.

http://stancho.roncho.net/HighMath/Ini/Ini.html

http://justmathbg.info/

http://umis.tugab.bg/prep/disc_view1.php?discs=0065&stepen=0