MATH 307 – Applied Linear Algebra

Definitely one of the harder courses. However, I came out with good MATLAB knowledge, which I used in other courses I was taking at the same time. The course felt like a combination of many of my past MATH courses but more in-depth and difficult.It always feels rewarding when you get to apply mathematical concepts to real world  problems like chemical systems, circuits, and Markov Chain probabilities.

Topics Covered:

  • Solving linear equations
  • Interpolation
  • Finite difference approximations
  • Subspaces, basis and dimension
  • The four fundamental subspaces for a matrix
  • Graphs and networks
  • Projections
  • Complex vector spaces and inner product
  • Orthonormal bases, orthogonal matrices and unitary matrices
  • Fourier series
  • Discrete Fourier transform
  • Eigenvalues and Eigenvectors
  • Hermitian matrices and real symmetric matrices
  • Power method
  • Recursion relations
  • Markov chains
  • Singular value decomposition
  • Principle component analyis (PCA)
  • Applications of linear algebra to problems in science and engineering
  • Use of computer algebra systems for solving problems in linear algebras

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