Special Topics Courses

Fall 2020

MA 591-003  Mathematical Foundations of Quantum Computation, Moody Chu T Th 4:30-5:45pm, SAS 2225

Quantum computing and quantum information science are emerging disciplines in which the principles of quantum physics are employed to store and process information. Quantum technologies are pushing forward the frontiers of the future. At the time when quantum computation is fully developed, many salient applications will stand to benefit from this fast, concurrent, and secure information processing ability — we will be able to handle some of the most pressing problems the world faces as well as leap to discoveries not yet known. As such, students should be curious and find it beneficial and of vital importance that they are exposed to this subject as early as possible. A solid grasp and holistic treatment of this subject will require disciplines across multiple academic fields, which is hard to come by. This course intends to serve as the first step by introducing this subject from the mathematical perspective. Mathematical and computational foundations useful for deciphering the rich structure within a quantum system and the quantum computation will be discussed.

Prerequisites: A familiarity with linear algebra, e.g., inner product spaces, unitary transformations, is sufficient. Some familiarity with basic logic gates for Boolean functions, e.g., AND, XOR, and truth table, will be useful.

MA 591-005: Teaching in the Math Department Elisabeth Brown W 1:55-2:45PM, Poe 312
This course focuses on methods pertaining to effective teaching in undergraduate mathematics courses. Other topics include technical aspects of teaching, assessment/grading, observations, classroom management, and content development.
Prerequisite: Graduate standing in mathematics, applied mathematics, biomathematics, or a related mathematical field. 

MA/FIM 591 Fixed Income: Markets, Analytics and Strategy, Richard Ellson M W 8:30-9:45AM, SAS 1108

This course is designed to provide a broad-based understanding of fixed income products including the Treasury market, corporate bonds, mortgage-backed securities, and asset-backed securities. Some fixed income derivative products such as interest rate swaps and credit default swaps will also be included. Significant focus will be on how fixed income products are analyzed in the context of trading, portfolio management, and risk management. Dr. Ellson worked on Wall Street for 25 years and has extensive experience in analytics, loan and bond trading, and portfolio management. Therefore, much of the course will evaluate how fixed income markets “actually work.”

Prerequisites: Basic calculus—Some background in economics/financial markets

MA 793-001 Data-driven Modeling and Analysis of Dynamical Systems, Mohammad Farazmand M W 10:15-11:30am SAS 1108

Data-driven methods are rapidly revolutionizing how science is being performed. This course introduces students to essential tools for analyzing observation data generated by dynamical systems. The main objectives are (i) reduced-order modeling of the data, (ii) using data to make predictions, (iii) discovering governing equations from data. To this end, we focus on a variety of tools such as: Embedding of data; Proper orthogonal decomposition (POD); Dynamic Mode Decomposition (DMD); Koopman operator; Clustering and classification; SINDy algorithm; Reservoir computing; Neural networks and deep learning.
The utility of the methods is demonstrated on various examples from physics and engineering; e.g., classical mechanics and fluid dynamics. 
Prerequisites: Differential Equations (MA 341), Linear Algebra (MA 305)

MA797 Convex Optimization Methods in Data Science, P. L. Combettes T Th 10:15-11:30 AM

This course is intended to provide an account of convex optimization methods and their applications in various areas of data science (signal and image processing, inverse problems, statistical data analysis, machine learning, classification, etc.). The basic theory will be provided and a strong emphasis will be placed on algorithm design and concrete applications.

Prerequisite: Basic calculus and linear algebra

MA797/BMA790 Mathematical theory and applications of machine learning, Kevin Flores T/H 11:45-1PM DAB 330

This course introduces students to machine learning concepts, including supervised and unsupervised approaches, with applications to biology. A wide range of machine learning techniques are covered including neural networks, SVMs, decision trees, random forests, and k-means clustering, as well dimensionality reduction techniques, including linear (PCA) and non-linear (auto-encoders, diffusion maps) methods. We discuss the theory and practical application of specific neural network architectures to data types relevant to biology, i.e., imaging (convolutional neural networks for segmentation and classification) and sequential data (recurrent neural networks for natural language processing or time series forecasting).