I think that students could explore what happens to our current number system when one or more of the essential properties are eliminated. The study of different systems as they compare to the real number system gives students a feel for the structure. This is also a good place for students to be involved in more complex deductive thought processes. With the proofs involved, students can gain experience proving abstract ideas. This topic lends itself to developing thinking skills, and reasoning abilities.
Calculators make trig and log tables obsolete.
This topic has no usefulness other than to obtain an approximation that a calculator can give. Solving systems of equations has traditionally be taught by manipulating the equations around to obtain an answer. Students should spend most of their time graphing to find solutions than manipulating the equations. I think that they should still use algebraic methods, but they should not be tunneled into using methods that are cumbersome, or that they are not comfortable using. For example, one student might be more comfortable using substitution, and one might like to use linear combination, most will not enjoy determinants.