Great courses (DVD)

"Course No. 1056."

Linear algebra may be the most accessible of all routes into higher mathematics. It requires little more than a foundation in algebra and geometry, yet it supplies powerful tools for solving problems in subjects as diverse as computer science and chemistry, business and biology, engineering and education, and physics and psychology, to name just a few. It is also the gateway to almost any advanced math course, such as calculus, abstract algebra, and number theory. Mastering Linear Algebra: An Introduction with Applications is the ideal starting point, surveying the traditional topics of a first-semester college course in linear algebra in 24 half-hour lectures taught by award-winning Professor Francis Su of Harvey Mudd College. Focusing on a wide range of interesting applications, Professor Su works through problems step by step, covering vectors and vector spaces, dot products and cross products, matrix operations, linear transformations, systems of linear equations, bases, determinants, eigenvectors, and much more. He illustrates how problems can be envisioned in both geometric and algebraic terms, with the geometric picture feeding intuition and the algebraic tools showing the way to a solution. Applications covered include computer graphics, image compression, speech recognition, recommender systems, error detection, satellite navigation, and even quantum mechanics. A background in algebra and analytic geometry is recommended. Previous exposure to calculus is useful, but not required

Closed captioned for the hearing impaired

Contains 24 lectures; each lecture is approximately 30 minutes

Lecturer: Professor Francis Su, Harvey Mudd College

Disc 1.

Linear algebra: powerful transformations -- Vectors: describing space and motion -- Linear geometry: dots and crosses -- Matrix operations -- Linear transformations -- Systems of linear equations --

Disc 2.

Reduced row echelon form -- Span and linear dependence -- Subspaces: special subsets to look for -- Bases: basic building blocks -- Invertible matrices: undoing what you did -- Invertible matrix theorem --

Disc 3.

Determinants: numbers that say a lot -- Eigenstuff: revealing hidden structure -- Eigenvectors and eigenvalues: geometry -- Diagonalizability -- Population dynamics: foxes and rabbits -- Differential equations: new applications --

Disc 4.

Orthogonality: squaring things up -- Markov chains: hopping around -- Multivariable calculus: derivative matrix -- Multilinear regression: least squares -- Singular value decomposition: so cool -- General vector spaces: more to explore