(Same as Physics and Biology and Medicine M209.) Lecture, four hours; laboratory, four hours. Preparation: basic calculus or linear algebra and undergraduate probability. Mathematics and statistical fundamentals prevalent in biomedical physics studies. Notion and basic descriptions of linear shift-invariance and point spread functions in continuous and discrete time. Sampling theory and Fourier analysis. Signal representation of vector spaces, projection theorem, and least-squares approximations. Discussion of signal subspace methods, correlation and independence, principal component analysis, and independent component analysis. Basic ideas in inverse problems and optimization. Application in medical and signal processing. Development of geometric and informatics intuitions behind mathematics and statistics. Light derivations and MATLAB programming. S/U or letter grading.