Algebra tricks / points to remember

Forum for the GRE subject test in mathematics.
fullofquestions
Posts: 18
Joined: Sun Oct 07, 2007 1:49 pm

Algebra tricks / points to remember

Does anyone know of a list of pointers/"common blunders" for the algebra in the Math GRE? For now I have found the following link that has a basic list: http://tutorial.math.lamar.edu/pdf/Alge ... _Sheet.pdf

While studying for the test I've found many subtleties that lead to errors which are actual answers. Also, there are some tricks that really speed up the solution of a problem... For instance, below is a list of some of the mistakes I've made

v^w = e^(w log v) if w is not a constant

e^(2ln x) = e^(ln x^2) = x^2 NOT (e^(2ln x) = 2x)
e^(-ln x) = e^(ln x^-1) = x^-1 NOT (e^(-ln x) = -x)

b^(lob(base b) x) = x

log(cos x) = - log ((cos x)^-1)

infinity * 0 = 0 and such (I know that for many series questions when you are faced with an indeterminate form you have to use L'Hopital's rule).

the zero vector is not counted in the dimension of a vector space even though "every vector space must contain the zero vector"

etc