How to say maths terms in English?

On Maths Presentation Workshop at Carnegie Mellon University, Professor Brandon was trying to to help us understand the undergrad in United States and improve our teaching skills. This was my first time knowing how to say maths terms in English. And I want to share with you some of the tips. Before I start, I would like to abbreviate some of the points that Prof. Brandon mentioned concerning teaching.

  • Lousy background. American students have a lousy background in mathematics, but it doesn’t mean they are not smart. You will see students writing \frac{1}{a}+\frac{1}{b}=\frac{1}{a+b} or \sqrt{a}+\sqrt{b}=\sqrt{a+b}, but it’s not their fault. Even their high school teachers would say ‘Well, it’s just a different way to do those calculations.’
  • Cheat on homework. A student who is copied by others is considered cheating as much as the student who copied him or her.
  • Handholding. Some students do not know how to learn things. They need someone to guide them, for instance, how to use textbooks, how to prepare exams, etc.
  • 2 tips on teaching skills. Keep eye contact. Reword things and write it down.

Finally, here is the list that gives you some examples of spoken Maths.

Maths Terms How to say it?
\frac{1}{x^n} 1 over x to the power of n
\sqrt[3]{x}, \sqrt[4]{x} cube root of x, fourth root of x
\sin^{n}x sine to the power of n of x
f\circ g f composed with g
\lim_{x\rightarrow a}f(g(x)) limit as x approaches a of f of g of x
x\rightarrow \pi^{-} x approaches pi from the left
\frac{d}{dx}f(x) the derivative of f of x (with respect to x) or d over dx of f of x
\frac{\partial x}{\partial y} del y over del x
\nabla, \Delta gradient, Laplacian
\log_a(xy) log (with respect to) base a of x times y
\ln x natural log of x or ln of x
f(x)g(x)]_a^b f of x times g of x evaluated from a to b
f(x,y), (a,b) f of x comma y, a comma b
f'(x), f^{\prime\prime}(x), f^{\prime\prime\prime}(x) f prime of x, f double prime of x, f triple prime of x
S_n, \cdots, f_x s sub n, dot dot dot or etc, f sub x

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