About MATH 2001 A
Project-based course. Historical development of mathematical sciences emphasizing interrelations among them. Individual assignments correspond to background and interests of students. Prerequisite: Nine hours of college mathematics.
Notes
Prereqs: Nine hours of college mathematics; Open to Degree and PACE students
Section Description
The course will focus on the development of calculus. It will look at the work of the ancient Greeks, Hindus, Muslims, and the medieval Europeans mainly as background and introduction to problems and paradoxes associated with concepts of continuity, infinity, and the limit (e.g., the Pythagorean discovery of irrationals, Zeno’s paradoxes), and their attempted solutions (Eudoxus’ method of exhaustion and theory of proportion, Archimedes’ and Democritus’ implicit use of infinitesimals, the medieval ‘latitude of forms’, etc.). This preparatory section, which I expect to take up the first third of the semester, will also look at the origins of trigonometry in mathematical astronomy. Then the course will turn to the relatively short (but rich) period from roughly 1600 to around 1900, when calculus as we know it came into shape: early approaches to tangent and area problems, the controversies over infinitesimals, the rigorous definitions of limit and continuity (‘epsilon-delta’), and the discovery of the ‘completeness’ of the real numbers and its consequences, such as Cantor’s discovery of ‘orders of infinity’. If time permits we will look at some of the discoveries and innovations of Baire and Lebesgue. Required texts for the class are The History of Calculus and its Conceptual Development, by Carl Boyer, and The Calculus Gallery, by William Dunham. Both are paperbacks and will be on reserve in the library. I recommend buying them online.
Section Expectation
The course will emphasize PROOFS and the development of mathematical ideas rather than biography and political history (though these will receive mention). The grade will be based on 3 in-class exams (each worth 10% of the grade), and 2 papers, each fifteen hundred to twenty-five hundred words long, and each worth 35% of the grade.
Evaluation
The grade will be based on 3 in-class exams (each worth 10% of the grade), and 2 papers, each fifteen hundred to twenty-five hundred words long, and each worth 35% of the grade.
Important Dates
Note: These dates may change before registration begins.
Note: These dates may not be accurate for select courses during the Summer Session.
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Interest Form
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