Welcome to the Semester 2, 2017 MATH7502 course, taught at the University of Queensland. The course coordinator and lecturer is Yoni Nazarathy.
Q:Why learn Linear Algebra and Multivariable Calculus for Data Science?
A:The theory taught in this course plays a part in the following types of applications:
- Understanding how basic clustering algorithms work.
- Solving linear systems of equations.
- Using the Jacobians for solving smooth non-linear systems of equations by iteration.
- Formulating optimality conditions for unconstrained and constrained optimization of smooth multi-variable functions.
- Using and understanding least squares approximations and generalizations.
- Modelling evolution of linear systems over time and understanding the role of eigenvalues in such evolution.
- Understanding linear transformations of multi-variate normal distributions.
- Understanding the operations of Principal Component Analysis (PCA).
- Understanding the use of singular value decomposition as used for lossy data compression.
- Understanding the math of gradient-descent, Gauss-Newton and the Levenberg-Marquardt, non-linear optimization methods.
Key Links:
Basic Resources:
Study units and related links
- Unit 1 - Introduction and application examples.
- Unit 2 - Vectors, norms, inner products and clustering
- Unit 3 - Matrix operations, linear transformations and systems of equations
- Unit 4 - Vector spaces, linear independence and basis
- Unit 5 - Projection and least squares
- Unit 6 - Determinants, Jacobian and affine approximations
- Unit 7 - Eigenvalues and similarity
- Unit 8 - Linear dynamical systems
- Unit 9 - Convexity, quadratic Forms, Hessian and optimization
- Unit 10 - Singular value decomposition and applications