# Applied mathematics vs. pure mathematics in high school?

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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...)

Gold Member

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The subject of this thread is: What do you think is the most advantegous way of learning mathematics?
This depends on what you're planning to do. If you want a degree in mathematics, you'll need to be comfortable with both approaches. If your plans are for something else, then you won't be as concerned with proving things.
Would you even make a distinction between these two approaches like I've done, and if so, how would you describe the distinction?
While the training for each distinction will have some overlap, the goals are often different. Pure/theoretical mathematicians are not usually concerned with the physical implications of whatever they're working on.
Is the latter approach (the "Serge Lang-approach") more popular in America?
I don't know what you mean by "more popular," so I can't really answer the question. More popular with whom: school systems, teachers, students, research?

Simon Bridge
Homework Helper

In NZ - at secondary level - "applied math" means probability and statistics, while "pure math" means functions and calculus. The rest of math is shared between the courses.

The most advantageous way of learning mathematics is any that you find easy which also gets you the grades... i.e. the topic is too broad.

Is the latter approach (the "Serge Lang-approach") more popular in America?

I would be surprised to find Lang's book used for any High-School in the world. I would love to be surprised, though.

It's definitely about which way you think you want to study. Pure math and applied math aren't clearly separate disciplines, but a different approach and emphasis.

I personally think that pure mathematics is the "purest" way to study mathematics. Applied math is what it says it is, applying math, but the subject of mathematics is really pure mathematics.

I don't know what you mean by "more popular," so I can't really answer the question. More popular with whom: school systems, teachers, students, research?
I meant in high school (in general). It would be interesting to know what the high school curriculums in other countries generally put their emphasize on.

Simon Bridge