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Linear Algebra - Foundations to Frontiers (LAFF) - University of Texas at Austin



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Learn the mathematics behind linear algebra and link it to matrix software development.
With an apprenticeship you earn while you learn, you gain recognized qualifications, job specific skills and knowledge and this helps you stand out in the job market.With this course you earn while you learn, you gain recognized qualifications, job specific skills and knowledge and this helps you stand out in the job market.

Important information

Requirements: High School Algebra, Geometry, and Pre-Calculus.


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What you'll learn on the course

Linear Algebra
Foundations to Frontiers

Course programme

EdX keeps courses open for enrollment after they end to allow learners to explore content and continue learning. All features and materials may not be all available. Check back often to see when new course start dates are announced.

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.

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

Additional information

Maggie Myers Dr. Maggie Myers is a lecturer for the Department of Computer Science and Division of Statistics and Scientific Computing. She currently teaches undergraduate and graduate courses in Bayesian Statistics. Her research activities range from informal learning opportunities in mathematics education to formal derivation of linear algebra algorithms. Earlier in her career she was a senior research scientist with the Charles A. Dana Center and consultant to the Southwest Educational Development Lab (SEDL). Her partnerships (in marriage and research) with Prof. van de Geijn have lasted for decades and seem to be surviving the development of this MOOC.