This is a new and fundamental course designed for the freshmen in the school of data science (SDS). Different from traditional linear algebra courses, we introduce a modern syllabus and try to make the fundamental concepts in linear algebra more understandable while also provide students with rigorous math training. Instead of starting the first lecture by introducing methods to solve a system of linear equations, we think it is not only important to tell the students how, but also why to solve the problems. Lots of data science problems are provided to motivate the need of mathematical treatment and concepts, and demonstrate the usefulness of linear algebra.
This course introduces advanced theory, algorithms, and applications of machine learning. Topics include: advanced ensemble learning methods; advanced learning theory; advanced applications such as recommendation systems; nonlinear dimension reduction, denoising, spectral clustering; generative models such as VAE and GAN; semi-supervised learning and GNN; causal inference, causal discovery, graphical and structural models, DAGs; attributes in trustworthy machine learning, interpretability and explainability, biases, fairness and safety, fair causal reasoning, adversarial machine learning, NN robustness and applications. This course requires students to have intermediate mathematical and programming backgrounds in machine learning and deep learning.