Here are my notes for real analysis based on Chapters 1 to 7 of Rudin’s Principles of Mathematical Analysis. In addition to the standard definitions, theorems, and proofs, I have provided my own commentary to motivate the ideas of real analysis. I have also included interesting exercises to train the reader’s intuition and proof technique, and to expand on the main text.

Prerequisites: first-year calculus, linear algebra, and an “introduction to proof” course.

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