This is a full first course on proof-based linear algebra. Sessions are 1h30m daily except for Sunday, so the course is at an accelerated pace. Prerequisites: -Algebra 2 with trig (with Calculus preferred but not required) Syllabus: (UNIT I) Basic Vector Operations 1. Vector geometry in R^n 2. Planes in R^3 3. Span, subspaces, and dimension 4. Basis and orthogonality 5. Cross Products (UNIT II) Basic Vector Space Properties 2. Vector Spaces and Subspaces 3. Linear independence and Gram-Schmidt 4. Projections and Orthogonal Vector Decomposition (Unit III) Linear Transformations and Motivating Matrices 5. Linear Transformations, Properties, and Kernel 6. Matrix operations, special matrices, and matrix properties (Unit IV) Linear Systems 7. Determinants, Linear Systems, and Inverse Matrices 8. LU decomposition 9. Row, Column, and Null Space, Rank and Nullity (Unit V) Representing Linear Transformations as Matrices 10. Change of Basis and Matrix Multiplication 11. Eigenvectors and Diagonalizability (Unit VI) Special Topics in Applied Linear Algebra: -Euclidean Inner Spaces -Least squares regression -Markov chains -Raising numbers to matrices -Solving differential equations using matrices I will provide all reading and practice material. Note: Required reading of 25 pages a week + Weekly homework (with feedback) + 1 test per unit (with review in-class and the tests graded with feedback).

This series is all about fractional Calculus. Fractional calculus is a very narrow branch within analysis that deals with the order of differentiations. For example: d^(1/2) / dx^(1/2) or d^i/dx^i. Hop into the session and let's have some fun together!