When doing algebra in Math 323, keep in mind the following three guidelines:

1. When dividing, you should always make sure that what you are dividing by is not zero. Dividing by zero is not defined; it is meaningless. In order to make sure that you are not dividing by zero, perhaps unconsciously, state explicitly, whenever dividing by a “variable” quantity, that it is not zero and state why. (In later courses you might not be asked to justify your divisions in all cases, but making sure one is not dividing by zero is a good habit to get into.)
   
   
2. When taking a square root (or any even root) in Math 323, you should always make sure that what you are taking the square root of is not negative. Although we deal with many different kinds of things in Math 323, the only NUMBERS we deal with are real numbers, so taking the square root of a negative number is meaningless. In order to make sure that you are not taking the square root of a negative number, perhaps unconsciously, state explicitly, whenever taking the square root of a “variable” quantity, that it is not negative and state why. (It is good practice for later courses to make sure that the operations you are performing are justified in the mathematical structures you are using.)
   
   
3. When doing “routine algebra” of the introductory algebra variety, use the “Common Errors” which you discussed in Project I as a guide to what needs to be explained. The only steps you should worry about writing out an explicit justification for are those which are related to the “common errors”. The biggest problem here, in connection with Math 323, usually occurs when dealing with inequalities. For example, it is not always true that if  a² < b²,  then  a < b,  and it is not always true that if  a < b,  then  a² < b².

Last modified Aug 21, 2007

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