Applied Linear Algebra

MATH5112/6012, Fall semester, 2021

Instructor: Yizao Wang
Email: yizao.wang@uc.edu
Office: 4302 French Hall.
Class Meeting: MWF, 1:25-2:20pm, 60 W Charlton, Room 140.
Office Hours: by appointment.

Textbook

Course Description

We shall cover the following topics from core basic linear algebra (chapter numbers from the textbook),
  1. Matrices, vectors, Gaussian Elimination, matrix factorizations, Forward and Back Substitution, inverses, determinants: 1.1–1.6, 1.8–1.9.
  2. Vector spaces, subspaces, linear independence, bases, dimension: 2.1–2.5.
  3. Inner products and their associated norms: 3.1–3.3.
  4. Orthogonal vectors, bases, matrices, and projections: 4.1–4.4.
  5. Positive definite matrices and minimization of quadratic functions: 3.4–3.5, 5.2
  6. Eigenvalues and eigenvectors: 8.2–8.3.
  7. Linear iterative systems: 9.1–9.2.
and the following applications,
  1. Cholesky factorization for simulations of Gaussian processes.
  2. Minimization, least squares, data fitting and interpolation: 4.5, 5.3-5.5.
  3. Signal processing: 3.6, 5.6.
  4. Probabilistic and statistical applications: 8.7–8.8.

Homework/Exams/Grades

There will be 4 homework sets, 3 projects (including optional ones for extra bonus credit), 1 midterm exam and a final exam. The projects require some minimal programming skills (at your choice of programming languages: Python, R, MATLAB). The total points a student could obtain is 115 = 100 + 15 (bonus) as explained below. The letter grades will be A (90+), A- (85+), B+ (80+), B (75+), etc.

Tentative Schedule

All homework (HW) due the Monday of the next week. Projects (P) due time see Canvas. All submissions via Canvas.