Math 12 - 1 (Advice)

Email hints:

Here are some ideas that should help:

• Use "^" to represent superscripts, as in "x^2" for "x squared", and "x^(1/2)" for "the square root of x". Use parentheses to avoid confusion about what belongs in the power. E.g., "x^(2n)+1" rather than "x^2n + 1" since this could be read incorrectly as either "(x^2)n + 1" or "x^(2n+1)".

• Use "_" to represent subscripts, as in "x_i" for "x sub i". Use parentheses as above to make more complicated subscripts clear.

• Use spaces around low-precedence operators like addition, subtraction and equals, but not around multiplication and division, as in "2x^2 + 3 = -1" rather than "2x^2+3=-1"

• Use parentheses to make the numerator and denominator clear when you write fractions using "/", as in "(x+1)/(2x-3)", not "x+1/2x-3" since this could be read as "x + (1/2)x - 3" or a number of other ways.

• For long equations, set them off from the rest of the mail by blank lines and indentation. For example:

     I can't figure out how to factor the equation
  
          x^3 - 2x^2 + 1 = 0
     
     Can you give me any advice?    
  

• Use spaces, not tabs, of you are forming a multi-line equation (like a large fraction or a series of equalities). E.g.

                  1
       f(x) =  -------
                1 - x
                
                 -1
   so f'(x) =  -------
               (1-x)^2
  

• We need a notation for integrals. One suggestion is to use a dollar sign "$" for the integral sign, and use superscript and subscript symbols to give the limits. E.g., "$_0^1 x dx" for "the integral from 0 to 1 of x (with respect to x)". This isn't great, but it works.

  Another possibility would be to use "I" or "Int" instead. For example: Int_0^Infinity (1/x^2) dx for "the integral from 0 to infinity of 1 over x squared dx".

  There is no standard for this, so we will try it out and see what we like best.

• We need a notation for limits. I suggest the following: lim_(x -> infinity) e^x for "the limit as x goes to infinity of e to the x".

• In general, use spaces and parentheses liberally to make your meaning as clear as possible.

Math 12 - 1 (Winter 2000) web pages Created: 25 Mar 1998 Last modified: 03 Jan 2000 22:23:10 Comments to: dpvc@union.edu

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