Readings

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All readings are from Amazon logo Rudin, W. Principles of Mathematical Analysis. 3rd ed. McGraw-Hill Science/Engineering/Math, New York, NY: McGraw-Hill, 1976. ISBN: 007054235X.


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.