Spring 2026
APC 199/MAT 199: Math Alive
- Jaydeep Singh
Tuesday/Thursday, 10:40am-12:00pm
Mathematics has profoundly changed our world, from the way we communicate with each other and listen to music, to banking and computers. This course is designed for those without college mathematics who want to understand the mathematical concepts behind important modern applications. The course consists of individual modules, each focusing on a particular application (e.g. compression, animation and using statistics to explain, or hide, facts). The emphasis is on ideas, not on sophisticated mathematical techniques, but there will be substantial problem-set requirements. Students will learn by doing simple examples. (course details)
APC 350/MAT 322: Introduction to Differential Equations
- Lili He
Monday/Wednesday, 1:20pm-2:40pm
This course will introduce the basic theory, models and techniques for ordinary and partial differential equations. Emphasis will be placed on the connection with other disciplines of science and engineering. We will try to strike a balance between the theoretical (e.g. existence and uniqueness issues, qualitative properties) and the more practical issues such as analytical and numerical approximations. (course details)
APC 523/AST 523/MAE 507/CSE 523: Numerical Algorithms for Scientific Computing
- Romain Teyssier
Monday/Wednesday, 1:20pm-2:40pm
This course gives a broad introduction to numerical algorithms used in scientific computing. It covers classical methods to solve Ordinary and Partial Differential Equations such as spectral, finite difference and finite volume methods. A brief introduction to finite element methods is given. Explicit and implicit time integration using various high-order methods are discussed. We review basic methods to solve linear and non-linear systems of equations. Issues related to the implementation of efficient algorithms on modern high-performance computing systems are discussed. Hyperbolic systems of conservations laws are covered in detail. (course details)
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MAE 541/APC 571: Applied Dynamical Systems
- Clarence Rowley
Tuesday/Thursday, 9:00am-10:20am
Phase-plane methods and single-degree-of-freedom nonlinear oscillators; invariant manifolds, local and global analysis, structural stability and bifurcation, center manifolds, and normal forms; averaging and perturbation methods, forced oscillations, homoclinic orbits, and chaos; Melnikov's method, the Smale horseshoe, symbolic dynamics, and strange attractors; introduction to ergodic theory and the ergodic theorems. (course details)
MAT 586/APC 511/MOL 511/QCB 513: Computational Methods in Cryo-Electron Microscopy
Amit Singer
Monday/Wednesday, 1:20pm-2:40pm
This course focuses on computational methods in cryo-EM with special emphasis on methods that play a significant role in many other inverse problems and data science applications and to their mathematical foundation. These comprise of key elements of statistical inference, image processing, optimization, and dimension reduction. Methods include rotation estimation and three-dimensional ab-initio modelling, structure refinement, resolving structural variability of heterogeneous populations, derivation of the image formation model, model validation, and resolution determination. (course details)
MSE 515/APC 515/CHM 559: Random Heterogeneous Materials
Salvatore Torquato
Tuesday/Thursday, 10:40am-12:00pm
Composites, porous media, foams, colloids, geological media, and biological media are all examples of heterogeneous materials. The relationship between the macroscopic (transport, mechanical, electromagnetic, and chemical) properties and material microstructure is formulated. Topics include statistical characterization of the microstructure; percolation theory; fractals; sphere packings; Monte Carlo techniques; image analysis; homogenization theory; cluster and perturbation expansions; variational bounding techniques; topology optimization methods; and cross-property relations. Biological and cosmological applications are discussed. (course details)