Paul L. Bailey, Ph.D.
Real Analysis with Topology 2018-2019
Texts:
Ross: Elementary Analysis
Thomas' Calculus 11th edition
Documents:
Topic I - Sets and Functions
Topic II - Natural Numbers
Topic III - Integers
Topic VI - Metric Spaces
Topic VII - Cardinality
Topic VIII - Topological Spaces (Updated 01/08/2019)
Topic IX - Relations
Topic X - [0,1] is Connected
Topic XI - The Heine-Borel Theorem
Topic XII - The Bolzano-Weierstrauss Theorem
Topic 31 - Calculus Review
Topic 32 - The Darboux Integral
Topic 33 - The Baire Category Theorem
Topic 33a - Continued Fractions
Topic 34 - Algebras of Sets
Topic 35 - Measure
Topic 36 - Integration
Course Syllabus
Links to Topology Lecture Notes:
Colorado State
Harvard
Clemson
Ho Chi Minh
Without Tears