# Applied Mathematics (AMTH)

AMTH 222a or b / MATH 222a or b, Linear Algebra with ApplicationsStaff

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 225 or 226. After MATH 115 or equivalent. May not be taken after MATH 225 or 226.   QR
HTBA

This course is a natural continuation of MATH 222. 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 120 and MATH 222, 225, or 226. This is not a proof-based course. May not be taken after MATH 340 (previously MATH 240.   QR
TTh 11:35am-12:50pm

AMTH 244a or b / MATH 244a or b, Discrete MathematicsStaff

Basic concepts and results in discrete mathematics: graphs, trees, connectivity, Ramsey theorem, enumeration, binomial coefficients, Stirling numbers. Properties of finite set systems. Prerequisite: MATH 115 or equivalent. Some prior exposure to proofs is recommended (ex. MATH 225).  QR
HTBA

AMTH 247b / MATH 247b, Intro to Partial Differential EquationsErik Hiltunen

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 222 or 225 or 226, MATH 246 or ENAS 194 or equivalents.  QR
MWF 10:30am-11:20am

AMTH 260b / MATH 260b, Basic Analysis in Function SpacesRonald Coifman

Diagonalization of linear operators, with applications in physics and engineering; calculus of variations; data analysis. MATH 260 is a natural continuation of PHYS 301. Prerequisites: MATH 120, and 222 or 225 or 226.  QR
TTh 2:30pm-3:45pm

* AMTH 342a / EENG 432a, Linear SystemsA Stephen Morse

Introduction to finite-dimensional, continuous, and discrete-time linear dynamical systems. Exploration of the basic properties and mathematical structure of the linear systems used for modeling dynamical processes in robotics, signal and image processing, economics, statistics, environmental and biomedical engineering, and control theory. Prerequisite: MATH 222 or permission of instructor.  QR
MW 1pm-2:15pm

* AMTH 366b / CPSC 366b / ECON 366b, Intensive AlgorithmsAnna Gilbert

Mathematically sophisticated treatment of the design and analysis of algorithms and the theory of NP completeness. Algorithmic paradigms including greedy algorithms, divide and conquer, dynamic programming, network flow, approximation algorithms, and randomized algorithms. Problems drawn from the social sciences, Data Science, Computer Science, and engineering. For students with a flair for proofs and problem solving. Only one of CPSC 365, CPSC 366, or CPSC 368 may be taken for credit. Prerequisites: MATH 244 and CPSC 223.  QR
HTBA

AMTH 420a / MATH 421a, The Mathematics of Data ScienceKevin O'Neill

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 305.   QR, SC
MW 1pm-2:15pm

AMTH 431a / ECON 431a / S&DS 431a, Optimization and ComputationYang Zhuoran

This course is designed for students in Statistics & Data Science who need to know about optimization and the essentials of numerical algorithm design and analysis. It is an introduction to more advanced courses in optimization. The overarching goal of the course is teach students how to design algorithms for Machine Learning and Data Analysis (in their own research). This course is not open to students who have taken S&DS 430.  Prerequisites: Knowledge of linear algebra, multivariate calculus, and probability. Linear Algebra, by MATH 222, 223 or 230 or 231; Graph Theory, by MATH 244 or CPSC 365 or 366; and comfort with proof-based exposition and problem sets, such as is gained from MATH 230 and 231, or CPSC 366.
TTh 1pm-2:15pm

* AMTH 482a, Research ProjectJohn 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.
HTBA

* AMTH 491a, Senior ProjectJohn 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