* AMTH 1600b / MATH 1600b / S&DS 1600b, The Structure of Networks  Gilles Mordant

Network structures and network dynamics described through examples and applications ranging from marketing to epidemics and the world climate. Study of social and biological networks as well as networks in the humanities. Mathematical graphs provide a simple common language to describe the variety of networks and their properties.  QR
MW 9am-10:15am

AMTH 2220a or b / MATH 2220a or b, Linear Algebra with Applications  Staff

Matrix representation of linear equations. Gauss elimination. Vector spaces. Linear independence, basis, and dimension. Orthogonality, projection, least squares approximation; orthogonalization and orthogonal bases. Extension to function spaces. Determinants. Eigenvalues and eigenvectors. Diagonalization. Difference equations and matrix differential equations. Symmetric and Hermitian matrices. Orthogonal and unitary transformations; similarity transformations. Students who plan to continue with upper level math courses should instead consider MATH 2250 or 2260. After MATH 1150 or equivalent. May not be taken after MATH 2250 or 2260. May not be counted toward the Math, CPSC + Math, or Econ + Math major.   QR
HTBA

AMTH 2320b / MATH 2320b, Advanced Linear Algebra with Applications  Ian Adelstein

This course is a natural continuation of MATH 2220. The core content includes eigenvectors and the Spectral Theorem for real symmetric matrices; singular value decomposition (SVD) and principle component analysis (PCA); quadratic forms, Rayleigh quotients and generalized eigenvalues. We also consider a number of applications: optimization and stochastic gradient descent (SGD); eigen-decomposition and dimensionality reduction; graph Laplacians and data diffusion; neural networks and machine learning. A main theme of the course is using linear algebra to learn from data. Students complete (computational) projects on topics of their choosing. Prerequisites: MATH 1200 and MATH 2220, 2250, or 2260. This is not a proof-based course. May not be taken after MATH 3400.  QR
MW 11:35am-12:50pm

AMTH 2440a or b / MATH 2440a or b, Discrete Mathematics  Staff

Basic concepts and results in discrete mathematics: graphs, trees, connectivity, Ramsey theorem, enumeration, binomial coefficients, Stirling numbers. Properties of finite set systems. Prerequisite: MATH 1150 or equivalent. Some prior exposure to proofs is recommended (ex. MATH 2250).  QR
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AMTH 2470b / MATH 2470b, Intro to Partial Differential Equations  Ruoyu Wang

Introduction to partial differential equations, wave equation, Laplace's equation, heat equation, method of characteristics, calculus of variations, series and transform methods, and numerical methods. Prerequisites: MATH 2220 or 2250 or 2260, MATH 2460 or ENAS 1940.  QR
MWF 10:30am-11:20am

AMTH 3220a / CPSC 4844a, Geometric and Topological Methods in Machine Learning  Smita Krishnaswamy

This course provides an introduction to geometric and topological methods in data science. Our starting point is the manifold hypothesis: that high dimensional data live on or near a much lower dimensional smooth manifold. We introduce tools to study the geometric and topological properties of this manifold in order to reveal relevant features and organization of the data. Topics include: metric space structures, curvature, geodesics, diffusion maps, eigenmaps, geometric model spaces, gradient descent, data embeddings and projections, and topological data analysis (TDA) in the form of persistence homology and their associated “barcodes.” We see applications of these methods in a variety of data types.  Prerequisites: MATH 2250 or 2260; MATH 2550 or 2560; MATH 3020; and CPSC 1001 or equivalent programming experience.   QR, SC
TTh 11:35am-12:50pm

AMTH 3610b / S&DS 3610b, Data Analysis  Brian Macdonald

Selected topics in statistics explored through analysis of data sets using the R statistical computing language. Topics include linear and nonlinear models, maximum likelihood, resampling methods, curve estimation, model selection, classification, and clustering. Extensive use of the R programming language.  Experience with R programming (from e.g. S&DS 1060, S&DS 2200, S&DS 230, S&DS 2420), probability and statistics (e.g. S&DS 1060, S&DS 2200, S&DS 2380, S&DS 2410, or concurrently with S&DS 2420), linear algebra (e.g. MATH 2220, MATH 2250, MATH 1180), and calculus is required. This course is a prerequisite for S&DS 4250 and may not be taken after S&DS 4250.  QR
TTh 2:35pm-3:50pm

* AMTH 3620b / CPSC 3620b / ECE 4351b, Decisions and Computations across Networks  A Stephen Morse

For a long time there has been interest in distributed computation and decision making problems of all types. Among these are consensus and flocking problems, the multi-agent rendezvous problem, distributed averaging, gossiping, localization of sensors in a multi-sensor network, distributed algorithms for solving linear equations, distributed management of multi-agent formations, opinion dynamics, and distributed state estimation. The aim of this course is to explain what these problems are and to discuss their solutions. Related concepts from spectral graph theory, rigid graph theory, non-homogeneous Markov chain theory, stability theory, and linear system theory are covered. Although most of the mathematics need is covered in the lectures, students taking this course should have a working understanding of basic linear algebra. The course is open to all students.  Prerequisite: Linear algebra or instructor permission.  SC
MW 2:35pm-3:50pm

AMTH 3640b / ECE 4541b / S&DS 3640b, Information Theory  Yihong Wu

Foundations of information theory in communications, statistical inference, statistical mechanics, probability, and algorithmic complexity. Quantities of information and their properties: entropy, conditional entropy, divergence, redundancy, mutual information, channel capacity. Basic theorems of data compression, data summarization, and channel coding. Applications in statistics and finance. After STAT 241.  QR
TTh 11:35am-12:50pm

AMTH 4200a / MATH 4210a, The Mathematics of Data Science  Gilles Mordant

This course aims to be an introduction to the mathematical background that underlies modern data science. The emphasis is on the mathematics but occasional applications are discussed (in particular, no programming skills are required). Covered material may include (but is not limited to) a rigorous treatment of tail bounds in probability, concentration inequalities, the Johnson-Lindenstrauss Lemma as well as fundamentals of random matrices, and spectral graph theory.  Prerequisite: MATH 3050.   QR, SC
MW 11:35am-12:50pm

AMTH 4441a / APHY 4410a / MENG 4441a / PHYS 4441a, Nonlinear Dynamics  Bauyrzhan Primkulov

This course introduces nonlinear dynamics and chaos in dissipative systems, tailored broadly for undergraduate students in science and engineering. It focuses on simple dynamical models, the mathematical principles underlying their behaviors, their connection to natural phenomena, and techniques for data analysis and interpretation. Key topics include forced and parametric oscillators, phase space analysis, periodic, quasiperiodic, and aperiodic flows, sensitivity to initial conditions, and strange attractors such as the Lorenz attractor. The course also explores phenomena like period doubling, intermittency, and quasiperiodicity, emphasizing nonlinear processes describable by a limited number of time-evolving variables. ENAS 1510 (Multivariable Calculus or equivalent), ENAS 1940 (Differential Equations or equivalent)  SC
TTh 11:35am-12:50pm

AMTH 4470a / MATH 4470a, Partial Differential Equations  Wilhelm Schlag

Introduction to partial differential equations, wave equation, Laplace's equation, heat equation, method of characteristics, calculus of variations, series and transform methods, and numerical methods. Prerequisites: MATH 3050
TTh 11:35am-12:50pm

* AMTH 4820a, Research Project  John Wettlaufer

Individual research. Requires a faculty supervisor and the permission of the director of undergraduate studies. The student must submit a written report about the results of the project. May be taken more than once for credit.
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* AMTH 4910a, Senior Project  John Wettlaufer

Individual research that fulfills the senior requirement. Requires a faculty supervisor and the permission of the director of undergraduate studies. The student must submit a written report about the results of the project.
HTBA