Linear Algebra:Foundations to Frontiers - Notes to LAFF With
(with IPython Notebooks - Spring 2014 Edition)
Looking for the 2015 materials that use MATLAB? Click HERE .An e-book (PDF) that integrates the materials for the 2014 offering of LAFF, including 270+ short videos, answers to exercises, browser-based activities, and programming exercises in Python. This artifact encompasses a full undergraduate introductory course on linear algebra and is used at the primary resource for such a course at UT-Austin.
Who should LAFF?
Here are some people who may want to consider Linear Algebra: Foundations to Frontiers - Notes to LAFF With:
The Independent Beginner. There were MOOC participants for whom LAFF was their first introduction to linear algebra beyond the matrix manipulation that is taught in high school. These were individuals who possess a rare talent for self-learning that is unusual at an early stage in one's schooling. For them, LAFF was a wonderful playground. Others like them may similarly benefit from these materials.
The Guide. What we also hope to deliver with LAFF is a resource for someone who is an effective facilitator of learning (what some would call an instructor) to be used, for example, in a classroom setting. While this individual may or may not have our level of expertise in the domain of linear algebra, what is important is that she/he can use the LAFF materials to guide, inspire, and teach.
The Refresher. At some point, a student or practitioner of mathematics (in engineering, the physical sciences, the social sciences, business, and many other subjects) realizes that linear algebra is as fundamental as is calculus. This often happens after the individual has already completed the introductory course on the subject and now he/she realizes it is time for a refresher. From our experience with the MOOC, LAFF seems to delight this category of learner. We sequence the material differently from how a typical course on "matrix computations" presents the subject. We focus on fundamental topics that have practical importance and on raising the participant's ability to think more abstractly. We link the material to how one should translate theory into algorithms and implementations. This seemed to appeal even to MOOC participants who had already taken multiple linear algebra courses and/or already had advanced degrees.
The Graduate Student. This is a subcategory of The Refresher. The material that is incorporated in LAFF are meant in part to provide the foundation for a more advanced study of linear algebra. The feedback from those MOOC participants who had already taken linear algebra suggests that LAFF is a good choice for those who want to prepare for a more advanced course. Robert will expect the students who take his graduate course in Numerical Linear Algebra to have the material covered by LAFF as a background, but not more.
Ready to LAFF?
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