MATH
6101: Foundations of Real Analysis
Tentative
Outline of Topics
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Aug. 27 |
Day 1 a) What is the
Mathematics that we teach? b) History and
prehistory of numbers |
|
Sept 3 |
Day 2 Aristotle
and the Parabolic Segment(Method of Exhaustion) |
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Sept 10 |
Day 3 Fermat and his approach to tangents |
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Sept 17 |
Day 4 Newton and
Calculus – Episode I |
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Sept 24 |
Day 5 Newton and
Calculus – Episode II |
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Oct 1 |
Day 6 Euler and
Trigonometric Functions |
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Oct 8 |
Day 7 The Real
Numbers |
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Oct 15 |
Day 8 The Cauchy Property of real numbers |
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Oct 22 |
Day 9 Series and Convergence |
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Oct 29 |
Day 10 Power
Series |
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Nov 5 |
Day 11 Continuity |
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Nov 12 |
Day 12 Differentiability |
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Nov 19 |
Day 13 Uniform Convergence |
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Nov 26 |
Day 14 Thanksgiving Break |
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Dec 3 |
Day 15 Putting it all together |
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Dec 10 |
Reading Day |
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Dec 17 |
Final Exam
(1830 – 2130) |