Higher/additional/further/advanced level .... math

Question

Hi,Could somebody please explain the main differences among these "types" of math?(1) Which of the terms are equally common (and mean the same thing) in AmEng and BrEng? [ The only difference I am aware of is this: "math" - US, "maths"-GB,etc.    ](2) Where is the "boundary" between  a typical secondary school's math and higher math? Differential/integral calculus is part of higher math? (3) What does "pure math" mean to you?Thank you in advance!vlivef

Anonymous · Accepted Answer

In the US, freshmen in high school (students from 14 to 15 years of age) generally take algebra I. Sophomores (15-16 year olds) take geometry. Juniors (16-17 year olds) take algebra II. And seniors (17-18 year olds) take trigonometry. Then, such students take pre-calculus in their freshman yr. in college, calculus I (differential and integral calculus) in their sophomore year (if they're in a technical major like physics, chemistry, geology, engineering, math, computer science, etc. - non-technical majors would usually stop at pre-calculus). Technical majors would continue with multi-variate calculus in the first semester of their junior year. Then, in the second semester of their junior yr. the next course taken is typically differential equations. And in the senior yr. all math courses would be elective, that is, not required but chosen according to the students' interests, of example: advanced calculus, linear algebra, partial differential equations, abstract algebra, probability, etc.

But the above is for "average" high school students. The "better" students would start with algebra I in the 7th grade (age 12-13) and end with calculus I in the senior yr. of high school. Then in the first yr. of college they'd take multivariate calculus in the first semester, and so forth.

"Pure mathematics" would be the courses taken by a math major. Technical majors stop their math education at differential equations, but math majors continue on with "less practical" math courses like linear algebra, advanced calculus, and abstract algebra.

Higher/additional/further/advanced level .... math

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