This course starts from the basic linearized theory of wave phenomena: examples are chosen from electromagnetics, acoustics, elastics and other subjects, and explores the recent developments in wave propagation. The topics include: basic concepts in wave propagation; waves in layered media; two and three dimensional cases; scattering, transmission and reflection; waves in random media; effective medium properties; resolution analysis; applications in wave functional materials and imaging; and numerical techniques in solving wave equations in heterogeneous media. Prerequisite: AMCS 201, or equivalent knowledge on Fourier transform, eigenvalue problem, Special functions (Bessel/Hankel/Spherical Harmonics). This course starts from the basic linearized theory of wave phenomena: examples are chosen from electromagnetics, acoustics, elastics and other subjects, and explores the recent developments in wave propagation. The topics include: basic concepts in wave propagation; waves in layered media; scattering, transmission and reflection; waves in random media; effective medium properties, resolution analysis; applications in wave functional materials and imaging; and numerical techniques in solving wave equations in heterogeneous media. Basic knowledge on eigenvalue problem, Fourier transform, linear algebra, vector analysis is desired.