Real Analysis I
The rigorous treatment of calculus: epsilon-delta proofs, convergence of sequences and series, continuity, differentiability, and the Riemann integral. Where intuition meets proof.
Course Overview
Textbook |
Rudin, Principles of Mathematical Analysis ("Baby Rudin") |
Chapters |
TBD |
Sections |
TBD |
Prerequisites |
|
Target |
Foundation for Complex Analysis, Topology, Real Analysis II, Functional Analysis |
Status |
Planned |
Chapters will be scaffolded when this course becomes active.
Why This Course
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Proof maturity — this is where you learn to think like a mathematician
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Foundations — everything in advanced math assumes you can write proofs about limits and continuity
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Topology gateway — metric spaces introduced here lead directly to general topology
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Numerical methods — convergence guarantees matter when computation approximates reality
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Functional analysis — understanding function spaces starts with understanding \(\mathbb{R}\)