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Linear Algebra – Foundations to Frontiers

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“Linear Algebra Foundations to Frontiers (LAFF) is packed full of challenging, rewarding material that is essential for mathematicians, engineers, scientists, and anyone working with large datasets. Students appreciate our unique approach to teaching linear algebra because:

  • It’s visual.
  • It connects hand calculations, mathematical abstractions, and computer programming.
  • It illustrates the development of mathematical theory.
  • It’s applicable.

In this course, you will learn all the standard topics that are taught in typical undergraduate linear algebra courses all over the world, but using our unique method, you’ll also get more! LAFF was developed following the syllabus of an introductory linear algebra course at The University of Texas at Austin taught by Professor Robert van de Geijn, an expert on high performance linear algebra libraries. Through short videos, exercises, visualizations, and programming assignments, you will study Vector and Matrix Operations, Linear Transformations, Solving Systems of Equations, Vector Spaces, Linear Least-Squares, and Eigenvalues and Eigenvectors. In addition, you will get a glimpse of cutting edge research on the development of linear algebra libraries, which are used throughout computational science.

MATLAB licenses will be made available to the participants free of charge for the duration of the course.

This summer version of the course will be released at an accelerated pace. Each of the three releases will consist of four ”Weeks” plus an exam . There will be suggested due dates, but only the end of the course is a true deadline.

What you’ll learn

  • The connection between linear transformations, matrices, and systems of linear equations
  • Partitioning methods and special characteristics of triangular, symmetric, diagonal, and invertible matrices
  • A variety of algorithms for matrix and vector operations and for solving systems of equations
  • Vector spaces, subspaces, and various characterizations of linear independence
  • Orthogonality, linear least-squares, projections, bases, and low rank approximations
  • Eigenvalues and eigenvectors
  • How to create a small library of basic linear algebra functions

Recommended Prerequisites: High School Algebra, Geometry, and Pre-Calculus.

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