Videos and presentations from lectures LA 1

1. Introduction
   Course overview (1:16, 100M) smaller version (3M)
   Applications in practice (13:00, 218M) - slides only, smaller version (15M)
2. Systems of linear equations
   Systems of linear equations, elementary transformations (20:54, 233M) - slides only, smaller version (22M)
   Gaussian elimination (10:01, 132M) - slides only, smaller version (11M)
   Describing all solutions (20:33, 261M) - slides only, smaller version (22M)
   Comments to the correctness test
3. Matrices
   Matrix operations, regular matrix, inverse matrix (31:33, 340M) - slides only, smaller version (33M)
4. Groups
   Groups, abelian, additive, multiplicative (14:28, 227M) - slides only, smaller version (17M)
   Permutations, inversion, transposition, sign (16:03, 137M) - slides only, smaller version (17M)
   Optional topic: Subgroups, cosets, quotient groups (22:02, 181M) - slides only, smaller version (23M)
5. Fields
   Fields, properties, characteristic, Fermat's little theorem (28:27, 229M) - slides only, smaller version (29M)
6. Vector spaces
   Vector spaces, properties, subspaces, linear hull, matrix spaces (28:18, 226M) - slides only, smaller version (29M)
   Linear independence, bases, exchange theorem, dimension (34:02, 411M) - slides only smaller version (37M)
   Row and column space of a matrix and their dimension (11:14, 176M) - slides only, smaller version (13M)
7. Linear maps
   Linear maps, affine subspaces (21:51, 250M) - slides only, smaller version (23M)
   Matrices of linear maps, basis change (19:44, 177M) - slides only, smaller version (21M)
8. Applications
   Number of even subgraphs (6:05, 86M) - slides only, smaller version (7M)
   Constrained set systems (5:45, 109M) - slides only, smaller version (6M)
   Partition of a rectangle (5:42, 78M) - slides only, smaller version (6M)

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