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Fall 1997 MAA 4226/5306 MWF 10:10-11:00 107 Love Bldg |
Advanced Calculus |
Spring 1998 MAA 4227/5307 MWF 10:10-11:00 200 Love Bldg |
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instructor |
Philip L. Bowers 113 Love Building bowers@math.fsu.edu http://www.math.fsu.edu/~bowers/ 644-2889 (office) 644-2202 (front desk) |
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office hours |
M 9:00-10:00 W 9:00-10:00 R 11:00-11:45 F 1:00-3:00 and by appointment |
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eligibility |
Undergraduates must have completed successfully MAC 2313/3313, Calculus III, and MAS 3105, Applied Linear Algebra I. There are two introductory advanced calculus courses on the books available for undergraduates, MAA 4224 and MAA 4226. MAA 4224 is a gentler introduction to the topics of advanced calculus designed with MGF 3301, Introduction to Advanced Mathematics, as a formal prerequisite, and open only to undergraduates. MAA 4226/5306 is open to both undergraduate and graduate students, and assumes a higher level of mathematical maturity than MAA 4224. The student is expected to become comfortable with proofs quickly, if not already so, and to have significant time in their schedule for thinking about and ``doing'' mathematics. The second semester continues the material of the first. |
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text |
Principles of Mathematical Analysis, Third Edition, by
Walter Rudin. |
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content |
Chapters 1-4 for Fall and 5-8 for Spring. |
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homework
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Assignments, updated periodically, are listed here. |
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objectives |
This course develops the calculus of real and complex valued functions
in depth. The emphasis throughout is on careful argument and proof.
After clearly stating the properties of real numbers that we accept as
given, we develop in detail the basic topics of mathematical
analysis, proving all claimed results precisely. These topics include:
euclidean space topology, numerical sequences and series, continuity
of functions, differentiation of functions, integration theory,
uniform convergence, and special functions. This Advanced Calculus
sequence together with the one year sequence in Abstract Algebra
serve as the two pillars of pure mathematics at the undergraduate
level, preparing one for advanced course work at the graduate level.
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attendance |
I strongly advise you to attend class regularly. A student absent from
class bears the full responsibility for all subject matter and
procedural information discussed in class. |
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courtesy |
Generally, I expect you to get to class on time and not to leave class
until I have dismissed it. If you must leave class early, please let
me know before class begins. |
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grading |
Your grade in the course will be based on your performance on written homework assignments, a mid-term, and a written comprehensive final, with equal weight given to these three items. |
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