| Abstract: | In a first proof-oriented mathematics course, students will often ask questions – for example, What is this problem asking me to do? or What would a proof of this even look like? – that have more to do with logic than mathematics. The logical structure of a proof is a dance involving those basic logical forms – such as p or q, if p then q, for every x in A we have p(x), there exists x in A such that p(x) – that appear in the theorem being proved, and at various stages of this dance these basic logical forms are either being proved or used. How does one prove a statement of the form There exists x in A such that p(x)? How does one use a statement of the form For every x in A we have p(x)? We introduce particular “proving and using words” that encourage the fledgling mathematics major to pay attention to these sorts of questions and to the logical structure of proofs in general. |
