Watch Current Video List All Videos ✓ Sets and Vectors Discussion Forum ✓ Introduction to this Tutorial ✓ Introduction (4:32) Download Video Subtitles & Transcripts ✓ Sets and Set Notation ✓ Common Sets of Numbers, Part 1 (6:43) Download Video Subtitles & Transcripts ✓ Common Sets of Numbers, Part 2 (8:31) Download Video Subtitles & Transcripts ✓ Common Sets of Numbers, Part 3 (3:13) Download Video Subtitles & Transcripts ✓ Proof of the Infinitude of Primes ✓ Proof of the Infinitude of Primes (7:30) Download Video Subtitles & Transcripts ✓ Boolean Set Operations ✓ Union and Intersection (4:40) Download Video Subtitles & Transcripts ✓ Quiz #1 ✓ Quiz #1 Solution ✓ Empty Set and Set Complement (6:50) Download Video Subtitles & Transcripts ✓ Quiz #2 ✓ Quiz #2 Solution ✓ De Morgan's Law and Cartesian Products (8:08) Download Video Subtitles & Transcripts ✓ Quiz #3 ✓ Quiz #3 Solution ✓ Vectors and Vector Operations ✓ Introduction to Vectors (5:11) Download Video Subtitles & Transcripts ✓ Scalar Multiplication (6:41) Download Video Subtitles & Transcripts ✓ Vector Addition (4:32) Download Video Subtitles & Transcripts ✓ Quiz #4 ✓ Quiz #4 Solution ✓ The Dot Product (6:00) Download Video Subtitles & Transcripts ✓ Quiz #5 ✓ Quiz #5 Solution ✓ Geometric Interpretation of the Dot Product (6:39) Download Video Subtitles & Transcripts ✓ The Dot Product and Projections (8:26) Download Video Subtitles & Transcripts ✓ Quiz #6 ✓ Quiz #6 Solution ✓ The Cross Product, Part I (8:06) Download Video Subtitles & Transcripts ✓ The Cross Product, Part 2 (4:05) Download Video Subtitles & Transcripts ✓ Quiz #7 ✓ Quiz #7 Solution ✓ Matrices and Vector Spaces ✓ Matrices ✓ Introduction to Matrices, Part 1 (4:16) Download Video Subtitles & Transcripts ✓ Introduction to Matrices, Part 2 (4:39) Download Video Subtitles & Transcripts ✓ Matrix Operations ✓ Scalar Multiplication and Matrix Addition (4:04) Download Video Subtitles & Transcripts ✓ Quiz #8 ✓ Quiz #8 Solution ✓ Matrix Multiplication, Part 1 (4:36) Download Video Subtitles & Transcripts ✓ Matrix Multiplication, Part 2 (5:16) Download Video Subtitles & Transcripts ✓ Quiz #9 ✓ Quiz #9 Solution ✓ Transpose of a Matrix (4:02) Download Video Subtitles & Transcripts ✓ Quiz #10 ✓ Quiz #10 Solution ✓ Essential Types of Matrices ✓ Identity and Inverse Matrices (6:42) Download Video Subtitles & Transcripts ✓ Symmetric and Diagonal Matrices (3:50) Download Video Subtitles & Transcripts ✓ Orthogonal Matrices (3:48) Download Video Subtitles & Transcripts ✓ Quiz #11 ✓ Quiz #11 Solution ✓ Skew-Symmetric, Idempotent, and Nilpotent Matrices (6:53) Download Video Subtitles & Transcripts ✓ Vector Spaces ✓ Introduction to Vector Spaces (3:30) Download Video Subtitles & Transcripts ✓ Vector Space Axioms (4:11) Download Video Subtitles & Transcripts ✓ Abstract Vector Spaces (5:39) Download Video Subtitles & Transcripts ✓ Quiz #12 ✓ Quiz #12 Solution ✓ Determinants ✓ Introduction to Determinants (2:38) Download Video Subtitles & Transcripts ✓ A 3x3 Matrix Example (3:38) Download Video Subtitles & Transcripts ✓ Quiz #13 ✓ Quiz #13 Solution ✓ Properties of Determinants (4:31) Download Video Subtitles & Transcripts ✓ Quiz #14 ✓ Quiz #14 Solution ✓ Eigenvalues and Eigenvectors ✓ Introduction to Eigenvalues and Eigenvectors (4:05) Download Video Subtitles & Transcripts ✓ Computing Eigenvalues and Eigenvectors (7:53) Download Video Subtitles & Transcripts ✓ Computing Eigenvalues and Eigenvectors, Continued (3:47) Download Video Subtitles & Transcripts ✓ Quiz #15 ✓ Quiz #15 Solution ✓ Matrix Applications ✓ Diagonalization and Powers ✓ Diagonalizing a Matrix (8:52) Download Video Subtitles & Transcripts ✓ Quiz #16 ✓ Quiz #16 Solution ✓ Computing Powers of a Matrix (3:17) Download Video Subtitles & Transcripts ✓ Computing Powers of a Matrix: An Example (2:59) Download Video Subtitles & Transcripts ✓ Diagonalization, Recursion, and the Fibonacci Sequence (12:09) Download Video Subtitles & Transcripts ✓ Quiz #17 ✓ Quiz #17 Solution ✓ Geometric Transformations ✓ Rotations (7:28) Download Video Subtitles & Transcripts ✓ Quiz #18 ✓ Quiz #18 Solution ✓ Reflections; Sequences of Transformations (6:58) Download Video Subtitles & Transcripts ✓ Quiz #19 ✓ Quiz #19 Solution ✓ Differentiation as a Matrix Operation ✓ Differentiation as a Matrix Operation (9:08) Download Video Subtitles & Transcripts ✓ Quiz #20 ✓ Quiz #20 Solution ✓ Markov Chains ✓ Introduction to Markov Chains (3:31) Download Video Subtitles & Transcripts ✓ An Economic Example (9:56) Download Video Subtitles & Transcripts ✓ Steady-State of a Markov Chain (5:09) Download Video Subtitles & Transcripts ✓ Mouse in a Maze” Example (7:40) Download Video Subtitles & Transcripts ✓ Quiz #21 ✓ Quiz #21 Solution ✓ Tutorial Evaluation - Please Complete! ✓ 1.5 Vectors and Vector Operations » The Cross Product, Part I (8:06) Download Video Subtitles & Transcripts