Readings

The text for this course is:

Rudin, Walter. Principles of Mathematical Analysis. 3rd ed. New York, NY: McGraw-Hill, Inc., 1976. ISBN: 007054235X.

All page numbers refer to this book.

Course readings.
ses #	TOPICS	READINGS
L1	Real Numbers	pp. 1-12
L2	Complex Numbers Euclidean Spaces	pp. 12-17
L3	Countable, Uncountable Sets	pp. 24-30
L4	Metric Spaces	pp. 30-36
L5	Compact Sets	pp. 36-39
L6	Heine-Borel Theorem Connected Sets	pp. 40-43
L7	Convergent Sequences	pp. 47-52 and 58
L8	Cauchy Sequences, Completeness	pp. 52-57
L9	Series	pp. 59-72
L10	Limits of Functions, Continuity	pp. 83-88
L11	Continuity, Compactness, Connectedness	pp. 89-93
L12	Discontinuities, Monotonic Functions	pp. 94-97
L13	Differentiation Mean Values Theorem	pp. 103-107
L14	l'Hopital Taylor's Theorem	pp. 108-112
L15	Riemann-Stieltjes Integral	pp. 120-124
L16	Riemann-Stieltjes Integral (cont.)	pp. 124-127
L17	Properties of the Integral	pp. 128-133
L18	The Fundamental Theorem of Calculus	pp. 133-136
L19	Sequences of Functions Uniform Convergence	pp. 143-151
L20	Uniform Convergence, Equicontinuity	pp. 151-158
L21	Stone-Weierstrass Theorem	pp. 159-165
L22	Analytic Functions Algebraic Completeness	pp. 173-185
L23	Fourier Series	pp. 185-192
L24	Review