MATH7502: Mathematics for Data Science 2 (Linear Algebra and Topics in Multivariable Calculus)
MATH7502: Mathematics for Data Science 2 (Linear Algebra and Topics in Multivariable Calculus).
Click Here for the Semester 2, 2020 version of the course.
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.
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