FS22 MTH 496 Section 1: Machine Learning
Instructor: Guowei Wei
Machine learning (ML), including deep learning (DL), has had tremendous success in science, technology, industry, social media, etc. in the past decade. It is regarded as one of the most transformative technologies in human history. ML is the core technology in data science and is of fundamental importance for data-driven discovery. In this course, we will not only discuss the theoretical framework of ML algorithms and architectures but also put an emphasis on programming skills so that each student is able to implement ML algorithms for real-world problems. The course will start with linear regression (LR), logistic regression (LR), gradient descent, regularization, k-nearest neighbors (KNN), k-means, dimensionality reduction (i.e., principal component analysis (PCA) and uniform manifold approximation and reduction (UMAP)), support vector machine (SVM), kernel learning (KL), and decision trees (DT), including random forest (RF) and gradient boosting trees (GBT). If time permits, we will discuss some basic DL materials, such as artificial neural networks (ANN) and convolutional neural networks (CNN).
Prerequisites: (MTH 309 or MTH 314) & (CSE 231 or CMSE 202)
Text: There is no required textbook for this course A full set of lecture notes and tutorial materials will be provided.
FS22 MTH 496 Section 2: Intro. to Functional Analysis
Instructor: Brent Nelson
We will begin by studying the so-called lp spaces, which consist of sequences whose pth powers yield absolutely convergent series. For p>=1, it turns out that these are examples of Banach spaces, which are a fundamental objects in functional analysis. We will conduct a thorough study of Banach spaces and the continuous functions on them (called bounded operators), including proving the open mapping theorem, the inverse mapping theorem, the closed graph theorem, the principle of uniform boundedness, and the Hahn–Banach theorem. As a special case, we will also consider Hilbert spaces (which corresponds to p=2 for the lp spaces) and applications to Fourier analysis.
Prerequisites: (MTH 309 or MTH 317H) and (MTH 320 or MTH 327H). Some exposure to metric spaces in the form of MTH 421 or MTH 461 is recommended, but not necessary.