Reading list(draft)

Analysis

• Terence Tao, Analysis (Vol. I, Vol. II.)
• Terence Tao, An Introduction to Measure Theory
• Terence Tao, An Epsilon of Room
• Gerald B. Folland, Real Analysis, Modern Techniques and Applications(2nd edition)

Algebra and number theory

• Stephen H. Friedberg, Linear Algebra
• David M. Burton, Elementary Number Theory

Others

• Loring W. Tu, An Introduction to Manifolds
• Theodore W. Gamelin and Robert Everist Greene, Introduction to Topology(2nd edition)
• Gerald B. Folland, Introduction to Partial Differential Equations

A nice picture

A type diagram for function spaces from Terence Tao:

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