Department of Mathematics Syllabus
This syllabus is advisory only. For details on a particular instructor's syllabus (including books), consult the instructor's course page. For a list of what courses are being taught each quarter, refer to the Courses page.
MAT 270: Mathematics of Data Science
Approved: 2019-04-01, Jesus A. De Loera, Thomas Strohmer
Suggested Textbook: (actual textbook varies by instructor; check your
instructor)
Bandeira, Singer, Strohmer: Mathematics of Data Science (draft)
Prerequisites:
127A, 167, 135A or equivalent preparation
Suggested Schedule:
| Lectures | Topics |
|---|---|
| 1 | Introduction: Basic goals of data science, machine learning, and AI, unsupervised/supervised learning |
| 2 | Probability: Curse and blessings of dimensionality, concentration inequalities, strange phenomena in high dimensions |
| 2 | Singular Value Decomposition and Principal Component Analysis |
| 2 | Clustering: k-means, spectral clustering, graph cuts, community detection |
| 1 | Diffusion maps, intrinsic geometry of data |
| 1 | Linear dimension reduction, (Fast) Johnson-Lindenstrauss projection |
| 2 | Randomized linear algebra: sketching, randomized SVD |
| 2 | Optimization: convex vs non-convex problems, Lagrange Duality and KKT optimality conditions, gradient descent algorithms |
| 1 | Logistic regression and LASSO |
| 2 | Classification/Deep learning: universal approximation theorem, convolutional deep networks, back-propagation, over/underfitting |
| 2 | Sparsity and compressive sensing |
| 1 | Low-rank matrix models, matrix completion |
Additional Notes:
The indicated number of lectures refers to 80-minute lectures. The syllabus accounts for 19 lectures of one quarter.