| WEEK # | TOPICS | READINGS |
|---|---|---|
| 1 | Sets and Fields, The Real Numbers | pp. 1-17. |
| 2 | Countability, Metric Spaces | pp. 24-35. |
| 3 | Closed Sets, Compact Spaces | pp. 34-38. |
| 4 | Compact Subsets of Euclidean Space | pp. 38-40. |
| 5 | Completeness, Sequences and Series | pp. 42-43, 47-69, and 71-75. |
| 6 | Continuity | pp. 83-86. |
| 7 | Continuity and Compactness | pp. 85-93. |
| 8 | Differentiability, Mean Value Theorem | pp. 103-110. |
| 9 | Taylor Series, Riemann-Stieltjes Integral | pp. 120-127. |
| 10 | Integrability, Fundamental Theorem of Calculus | pp. 128-136. |
| 11 | Sequences of Functions | pp. 143-151. |
| 12 | Uniform Convergence | pp. 150-154. |
| 13 | Uniform Convergence, Equicontinuity | pp. 150-161. |
| 14 | Power Series, Fundamental Theorem of Algebra | pp. 83-86 and 180-185. |
Table of Contents
Study Materials
Readings
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All readings are from Rudin, W. Principles of Mathematical Analysis. 3rd ed. McGraw-Hill Science/Engineering/Math, New York, NY: McGraw-Hill, 1976. ISBN: 007054235X.