1. What is linear algebra? -- Overview of linear algebra -- 2. The fundamentals -- Number systems -- Implication and equivalence -- Propositions -- Set theory -- Sets -- Set symbols -- Subsets -- Functions -- Images -- Domain and range -- Onto and one-to-one functions -- Inverse functions -- Linear transformations -- Combinations and permutations -- Not all "rules for ordering" are functions -- 3. Intro to matrices -- What is a matrix? -- Matrix calculations -- Addition -- Subtraction -- Scalar multiplication --Matrix multiplication -- Special matrices -- Zero matrices -- Transpose matrices -- Symmetric matrices -- Upper triangular and lower triangular matrices -- Diagonal matrices -- Identity matrices -- 4. More matrices -- Inverse matrices -- Calculating inverse matrices -- Determinants -- Calculating determinants -- Calculating inverse matrices using cofactors -- Using determinants -- Solving linear systems with Cramer's Rule -- 5. Introduction to vectors -- What are vectors? -- Vector calculations -- Geometric interpretations -- 6. More vectors -- Linear independence -- Bases -- Dimension -- subspaces -- Basis and dimension -- Coordinates -- 7. Linear transformations -- what is a linear transformation? -- Why we study linear transformations -- Special transformations -- Scaling -- Rotation -- Translation -- 3-D projection -- Kernel, image, and the dimension theorem for linear transformations -- Rank -- Calculating the rank of a matrix -- The relationship between linear transformations and matrices -- 8. Eigenvalues and eigenvectors -- What are eigenvalues and eigenvectors? -- Calculating eigenvalues and eigenvectors -- Calculating the pth power of an nxn matrix -- Multiplicity and diagonalization.