一.內容：
1. Set theory and real numbers.
2. Measure theory (Carath谷odory approach), Lebesque integration, convergence theorems, the Riesz representation theorem, product measure and Fubini`s theorem.
3. Lp-spaces and the dual spaces, Hilbert space, weak and strong topologies, integral operators.
4. Differentiation and integration, Radon-Nikodym theorem.
5. Some Applications in PDE, Introduction to Fourier Analysis.
　註：下學期可能延續課程有富氏分析或泛函分析。
二.教科書(參考書)：
H. L. Royden: Real Analysis
三.成績評量方式：
　含平時作業、期中考、期末考（可能Take-home採形式）