Text: R. B. Bartle and D. R. Sherbert, Introduction to Real Analysis, 3rd Edition, John Wiley & Sons, 2000.
| Chapter | |
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| 1. | Preliminaries (Notation from logic,set theory, and cardinality of countable and finite sets) |
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| 2. | The Real Numbers (How to go from the natural numbers to the real numbers, groups, fields, order fields, max/min/sup/inf, completeness axiom, Sqrt{2}, Archimedian property, nested intervals) |
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| 3. | Sequences (Examples, basic properties of limits, the n(epsilon) game, mononte subsequences, Bolzano Weierstrass,) |
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| 4. | Toplogy in R open, closed and compact sets. |
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| 5. | Continuous Functions (Definition, the K(eps) game, basic properties, continuous function on compact intervals, applications) |
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| 6. | Differentiation (Basic definition, the mean value theorem) |
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| 7. | The Riemann Integral (Definition and approximation, the fundamtal thereoms) |
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| 8. |
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This course is an introduction to e
- d analysis on the real line for students
who do
not plan graduate study in mathematics. (Those students should take
Math 347.) The students do not have much experience in writing proofs,
and they will need practice in doing so. They should leave the course
not only with a basic understanding of the fundamental concepts of real
analysis, but also an improved ability at reading and writing
mathematical arguments. Regular homework is an important aspect of the
course.
For many students this is unique chance to see mathematics tick
very
improtant to bridge between school and universty mathematics. The
emphasis lies on doing proofs-not comsuming proofs.
Grading: Exams: Practice quizes, two midterm (20% each). final exam (30%) 8:00-11:00 AM, Saturday, May 3 in class, Homework (30%) (submission in pairs-to practice team work-every Wednesday)
Course hotline
(email to students
and instructor): Share
your questions on homework, course material, homework problems
will only be discussed after explicit request.
Next Midterm: Wednesday April 9