Mathematics is a language for expressing ideas precisely. But novices to the language can be easily baffled by the maze of twisty formalisms and informalisms one finds in mathematical texts, and high school often leaves students thoroughly unprepared to study what mathematicians consider mathematics. This course will cover the basics of logic, sets, relations, functions, and the bizarrely elusive idea of numbers; the concept of infinity, infinite sets, and why you'll never hit a rational number on a dart board of real numbers; and all those funny words like lemma, theorem, corollary, proposition, and proof.

Often calculus is taught as a collection of symbolic methods for calculating derivatives and integrals. But the whys and wherefores of these methods are left as hand-waving `infinitesimals', and there is a rich array of mathematical ideas that we shall explore as we build the calculus not from infinitesimals but from basic mathematical objects such as sets and functions. This course is not about specific techniques to answer AP questions; instead, it will emphasize the meaning and physical intuition of ideas in calculus, and how to think about solving problems.

You've taken a class titled `Calculus' in high school, and you have probably been inundated with d's and elongated S's that you had to juggle until you got the right answer. Perhaps you took the AP exam, or plan to, and memorized tables of integrals to get a five on it. But calculus isn't just about pushing symbols! In this class we shall discuss not how to whack at symbols until an answer falls out, but what it all really means -- or at least, the meaning of what we can fit in two hours!

Mathematics is a language for expressing ideas precisely. But novices to the language can be easily baffled by the maze of twisty formalisms and informalisms one finds in mathematical texts, and high school often leaves students thoroughly unprepared to study what mathematicians consider mathematics. This course will cover the basics of logic, sets, relations, functions, and the bizarrely elusive idea of numbers; the concept of infinity, infinite sets, and why you'll never hit a rational number on a dart board of real numbers; and all those funny words like lemma, theorem, corollary, proposition, and proof.

Often calculus is taught as a collection of symbolic methods for calculating derivatives and integrals. But the whys and wherefores of these methods are left as hand-waving `infinitesimals', and there is a rich array of mathematical ideas that we shall explore as we build the calculus not from infinitesimals but from basic mathematical objects such as sets and functions. This course is not about specific techniques to answer AP questions; instead, it will emphasize the meaning and physical intuition of ideas in calculus, and how to think about solving problems.

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