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.

- Detailed course schedule (to be updated). (includes schedule and assessment summary).
- Official UQ course profile.
- UQ Blackboard site with messages (requires login)

- Recommended book: To be updated.
- Course Notes (to be updated).

- 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*