AMTH 2220a / MATH 2220a, 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 2440a / MATH 2440a, Discrete Mathematics  Catherine Wolfram

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 3220a / CPSC 4844a / MATH 3220a, 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 106, S&DS 220, S&DS 230, S&DS 242), probability and statistics (e.g. S&DS 106, S&DS 220, S&DS 238, S&DS 241, or concurrently with S&DS 242), linear algebra (e.g. MATH 222, MATH 225, MATH 118), and calculus is required. This course is a prerequisite for S&DS 425 and may not be taken after S&DS 425.  QR
TTh 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
HTBA