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WildLinAlg1: Introduction to Linear Algebra (N J Wildberger)

This is the full first lecture of a course on Linear Algebra. Given by N J Wildberger of the School of Mathematics and Statistics at UNSW, the course gives a more geometric and natural approach to this important subject, with lots of interesting applications. Our orientation is that Linear Algebra is really ``Linear Algebraic Geometry'': so teaching the algebra without the geometry is depriving the student of the heart of the subject.The first lecture discusses the affine grid plane and introduces vectors, along with the number one problem of linear algebra: how to invert a linear change of coordinates!Intended audience: first year college or undergraduate students, motivated high school students, high school teachers, general public interested in mathematics. Enjoy!CONTENT SUMMARY: pg 1:? @00:10 N. J. Wildberger Webpages: pg 2: @02:10 Linear Algebra to Linear Algebraic Geometry; example; applicationspg 3: @04:52 2-dim affine geometry (no notion of perpendicularity); affine grid plane; the core problem of linear algebrapg 4: @09:27 no distance measurement, no special point (origin), no angle measurement; relative positions can be described; affine grid plane; vector; connection between algebra and geometrypg 5:? @13:52 refinement of the affine grid plane; rational numberpg 6: @17:34 Multiples of a vector; adding vectors; basis vectors e1 and e2pg 7: @22:34 Two? affine grids and 2 sets of basis vectorspg 8: @27:13 change of basis vectors examplepg 9: @30:47 change of basis example continued; Main Problem of Linear Algebra (MPLA)pg 10: @34:03 summary of previous example; (MPLA) General case in 1dim; (MPLA) General case in 2dimpg 11: @40:32 questions; Exercise 1.1pg 12: @41:42 Exercises 1.2-4. (THANKS to EmptySpaceEnterprise)
Length: 43:31


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