Fall 2025
APC 524/MAE 506/AST 506/CSE 524: Software Engineering for Scientific Computing
- Romain Teyssier and Henry Schreiner
Tuesday/Thursday, 2:55-4:15pm, Location: TBA
The goal of this course is to teach basic tools and principles of writing good code, in the context of scientific computing. Specific topics include an overview of relevant compiled and interpreted languages, build tools and source managers, design patterns, design of interfaces, debugging and testing, profiling and improving performance, portability, and an introduction to parallel computing in both shared memory and distributed memory environments. The focus is on writing code that is easy to maintain and share with others. Students develop these skills through a series of programming assignments and a group project.(course details)
APC 588/AST 588/ GEO 588/ PHY 588: A Geometrical Introduction to Tensor Calculus
- Jeroen Tromp
Monday/Wednesday, 9:30am-11:00am, Location: TBA
Tensor calculus is a language used to describe physical phenomena in fluid dynamics, continuum mechanics, electromagnetism, and general relativity. The course explores the mathematical background for geometrical descriptions of tensors and their calculus. Students need to be familiar with multivariate calculus and partial differential equations. (course details)
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AOS 576/APC 576: Topics in Atmosphere/Ocean Sciences: Large-Scale Structure/Atmosphere
- Isaac Held
Tuesday/Thursday, 10:00am-11:30am, Location: TBA
Dynamical concepts needed to develop a qualitative understanding of the large-scale structure of the atmospheric circulation. The control of the angular momentum budget by Rossby wave fluxes. Theories for the Hadley circulation in the tropics and the "macro-turbulence" of midlatitudes. Linear theories for deviations from zonal symmetry of the mean flow. (course details)
AST 557/APC 503: Analytical Techniques in Differential Equations
Steven Cowley and Ilya Dodin
Monday/Wednesday, 1:00pm-2:20pm, Location: TBA
Asymptotic methods, Dominant balance, ODEs: initial and Boundary value problems, Wronskian, Green's functions, Complex Variables: Cauchy's theorem, Taylor and Laurent expansions, Approximate Solution of Differential Equations, singularity type, Series expansions. Asymptotic Expansions. Stationary Phase, Saddle Points, Stokes phenomena. WKB Theory: Stokes constants, Airy function, Derivation of Heading's rules, bound states, barrier transmission. Asymptotic evaluation of integrals, Laplace's method, Stirling approximation, Integral representations, Gamma function, Riemann zeta function. Boundary Layer problems, Multiple Scale Analysis. (course details)
MAE 501 /APC 501 /CBE 509: Mathematical Methods of Engineering Analysis
Dimitrios Fraggedakis
Tuesday/Thursday, 9:00am-10:20am, Location: TBA
Methods of mathematical analysis for the solution of problems in physics and engineering. Topics include an introduction to linear algebra, matrices and their application, eigenvalue problems, ordinary differential equations, Sturm-Liouville theory and eigenvalue problems, Green's functions, partial differential equation, finite Fourier Transform, method of characteristics, self-similar solution. (course details)
MAT 321 /APC 321: Numerical Analysis and Scientific Computing
Marc Gilles
Tuesday/Thursday, 1:20pm-2:40pm, Location: TBA
Introduction to numerical methods with emphasis on algorithms, applications and numerical analysis. Topics covered include solution of nonlinear equations; numerical differentiation, integration, and interpolation; direct and iterative methods for solving linear systems; computation of eigenvectors and eigenvalues; and approximation theory. Lectures include mathematical proofs where they provide insight and are supplemented with numerical demos using MATLAB or Python. (course details)
MAT 377 /APC 377: Combinatorial Mathematics
Instructor: TBA
Tuesday/Thursday, 10:40am-12pm, Location: TBA
The course covers the basic combinatorial techniques as well as introduction to more advanced ones. The topics discussed include elementary counting, the pigeonhole principle, counting spanning trees, Inclusion-Exclusion, generating functions, Ramsey Theory, Extremal Combinatorics, Linear Algebra in Combinatorics, introduction to the probabilistic method, spectral graph theory, topological methods in combinatorics. (course details)
MAT 522 /APC 522: Introduction to PDE
Instructor: TBA
Monday/Wednesday, 1:20pm-2:40pm, Location: TBA
The course is an introduction to partial differential equations, problems associated to them and methods of their analysis. Topics may include: basic properties of elliptic equations, wave equation, heat equation, Schr\"{o}dinger equation, hyperbolic conservation laws, Fokker-Planck equation, basic function spaces and inequalities, regularity theory for linear PDE, De Giorgi method, basic harmonic analysis methods, existence results and long time behavior for classes of nonlinear PDE including the Navier-Stokes equations. (course details)