Logicians don't really use logic; they study it. Because of this, logic is usually taught only as an object of study. For example, few discrete math texts use logic and its notation outside of the chapter on logic, and logic is usually taught in a week or two at the most. And NO one, including logicians, does proofs in mathematics in the way proposed by logicians. 

We believe that  ``logic is the glue that binds together methods of reasoning, in all domains'', and we teach it that way. But we don't use logic as typically taught, we use a "calculational logic", which formalizes nicely the way mathematicians and other scientists actually use math. Teaching a calculational logic and then USING it in discussing other topics (e.g. a theory of integers, set theory) imparts an appreciation for logic and rigorous proof, gives the student a skill in formal manipulation, and lessens the fear students have for mathematics and and mathematical notation.

In fact, we are so excited with the results of this approach that we believe ALL students in science  --mathematicians, physicists, etc.-- would benefit greatly from taking such a course. We'll try to convince you of this in this talk, which should be accessible to all college students in science majors.

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