# 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.