# Gil Strang: Linear Algebra and Deep Learning

### On decades of teaching linear algebra, mathematical perspectives on deep learning, and the future of ML and mathematics pedagogy.

In episode 86 of The Gradient Podcast, Daniel Bashir speaks to Professor Gil Strang.

Professor Strang is one of the world’s foremost mathematics educators and a mathematician with contributions to finite element theory, the calculus of variations, wavelet analysis, and linear algebra. He has spent six decades teaching mathematics at MIT, where he was the MathWorks Professor of Mathematics. He was among the first MIT faculty members to publish a course on MIT’s OpenCourseware and has since championed both linear algebra education and open courseware.

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**Outline**:

(00:00) Intro

(02:00) Professor Strang’s background and journey into teaching linear algebra

(04:55) Undergrad interests

(07:10) Writing textbooks

(10:20) Prof. Strang’s interests in deep learning

(11:00) How Professor Strang thought about teaching early on

(16:20) MIT OpenCourseWare and education accessibility

(19:50) Prof Strang’s applied/example-based approach to teaching linear algebra and closing the theory-practice gap

(22:00) Examples!

(27:20) Orthogonality

(29:15) Singular values

(34:40) Professor Strang’s favorite topics in linear algebra

(37:55) Pedagogical approaches to deep learning, mathematical ingredients of deep learning’s complexity

(42:04) Generalization and double descent in deep learning, powers and limitations

(46:20) Did deep learning have to evolve as it did?

(48:30) Teaching deep learning to younger students

(50:50) How Prof. Strang’s approach to teaching linear algebra has evolved over time

(53:00) The Four Fundamental Subspaces

(56:15) Reflections on a career in teaching

(59:49) Outro

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