My notes for when I took this course in Fall 2025, taught by Kendric Schefers through Baby Rudin.

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Please submit any errors you might find in the errata, thank you!

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Phoenix Wilson

Course by Week

Week Topics
1 Motivation, Ordered Sets
2 Fields, The Real Numbers
3 Cardinality
4 Metric Spaces
5 Closure, Open Covers, Compactness
6 Connectedness, Sequences
7 Subsequences, lim-inf and lim-sup
8 Cauchy Sequences
10 Series
11 Limits of Functions, Continuity, Uniform Continuity
13 One-Sided Limits, Discontinuity, Monotonicity, Limits at Infinity
14 Differentiation
15 Integration

Motivation, Ordered Sets

Fields, The Real Numbers

Cardinality

Metric Spaces

Closure, Open Covers, Compactness

Connectedness, Sequences

Subsequences, lim-inf and lim-sup

Cauchy Sequences

Series

Limits of Functions, Continuity, Uniform Continuity

One-Sided Limits, Discontinuity, Monotonicity, Limits at Infinity

Differentiation

Integration