SWILA SCHEDULE OF TOPICS The numbers refer to the chapters and sections in my notes for the workshop (found in the Google drive folder). (1) Monday, June 6th: 1. Vector spaces: C’mon, it’s just algebra (except not quite); 1.1. Fields; 1.2. Vector spaces; 1.3. Linear independence; 1.4. Bases and coordinates; 2. Linear transformations: More than meets the I; 2.1. Linear transformations; 2.2. Linear transformations T : Fm → Fl as matrices. (2) Thursday, June 9th: 2.3. The matrix representation of a linear transformation; 2.4. Change of coordinate matrices; 2.5. The trace; 2.6. Dimension and isomorphism. (3) Monday, June 13th: 2.7. Row reduction and the general linear group; 3. Vector spaces: But wait, there’s more!; 3.1. Subspaces; 3.2. Direct sums; 3.3. Linear maps and subspaces. (4) Thursday, June 16th: 3.4. Quotient spaces; 4. A minor determinant of your success; 4.1. Determinant of a matrix; 4.2. Computing the determinant of small matrices; 4.3. Geometric interpretation and the special linear group; 5. Eigenstuff: of maximum importance; 5.1. Facts about polynomials. (5) Monday, June 20th: 5.2. Eigenvalues; 5.3. The minimal polynomial; 5.4. Diagonalizability. (6) Thursday, June 23rd: 5.5. Cyclic subspaces. (7) Monday, June 27th: 5.6. Rational canonical form. (8) Thursday, June 30th: 5.7. The Jordan canonical form; 5.8. Computing the Jordan canonical form. (9) Monday, July 11th: 6. Inner product spaces? ... More like winner product spaces!; 6.1. Inner products; 6.2. Angles and orthogonality in inner product spaces; 6.3. Orthonormal bases for finite-dimensional vector spaces. (10) Thursday, July 14th: 6.4. Orthogonal complements and projections; 6.5. The adjoint of a linear transformation. (11) Monday, July 18th: 7. Linear operators on inner product spaces; 7.1. Self-adjoint maps; 7.2. Isometries; 7.3. The orthogonal and unitary groups. (12) Thursday, July 21st: 7.4. The spectral theorem for self-adjoint operators. (13) Monday, July 25th: 7.5. Normal operators and the spectral theorem for normal operators; 7.6. Schur’s theorem (optional); 7.7. Singular value decomposition. (14) Thursday, July 28th: 8. Multilinear algebra; 8.1. Dual spaces; 8.2. Tensor products. 1