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**Applied mathematics vs. "pure" mathematics in high school?**

I've just started working through "Basic Mathematics" by Serge Lang. It immediately struck me, when I skimmed through the pages, that there is a large emphasize on proving things and manipulating expressions, and very little exercises that is applying the mathematical theory to the physical world.

In my country, it's quite the opposite. In high school, about 80% of the exercises are basically applied math. For example, when we learn functions, most of the exercises are of the type:

"The resistance of a metal wire with a definite length is inversely proportional to the square of the wire's diameter. If one reduces the diameter by 25%, with how many percent will the resistance increase" (My own loose, unauthorized translation)

In Basic Mathematics, most of the exercises are of the type:

"Show that any function defined for all numbers can be written as a sum of an even function and an odd function."

The subject of this thread is: What do you think is the most advantegous way of learning mathematics? Would you even make a distinction between these two approaches like I've done, and if so, how would you describe the distinction? Is the latter approach (the "Serge Lang-approach") more popular in America?

(I'm sorry for any eventual language errors, my english proficiency isn't exactly perfect...)