Ph.D. Applied and Computational Mathematics
Bachelor's degree
In Princeton (USA)
Description
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Type
Bachelor's degree
-
Location
Princeton (USA)
The Program in Applied and Computational Mathematics offers a select group of highly qualified students the opportunity to obtain a thorough knowledge of branches of mathematics indispensable to science and engineering applications, including numerical analysis and other computational methods.
Facilities
Location
Start date
Start date
Reviews
Subjects
- GCSE Mathematics
- Computational
- Media
- Engineering
- Systems
- Green
- Project
- Mathematics
- Computing
Course programme
AOS 576 Current Topics in Dynamic Meteorology (also
APC 576
APC 503 Analytical Techniques in Differential Equations (also
AST 557
APC 523 Numerical Algorithms for Scientific Computing (also
AST 523
MAE 507
) A broad introduction to scientific computation using examples drawn from astrophysics. From computer science, practical topics including processor architecture, parallel systems, structured programming, and scientific visualization will be presented in tutorial style. Basic principles of numerical analysis, including sources of error, stability, and convergence of algorithms. The theory and implementation of techniques for linear and nonlinear systems of equations, ordinary and partial differential equations will be demonstrated with problems in stellar structure and evolution, stellar and galactic dynamics, and cosmology.
APC 524 Software Engineering for Scientific Computing (also
MAE 506
AST 506
) 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 will develop these skills through a series of programming assignments and a group project.
APC 599 Summer Extramural Research Project A summer research project, designed in conjunction with the student's advisor, APC, and an industrial, NGO, or government sponsor, that will provide practical experience relevant to the student's research area. Start date no earlier than June 1; end date no later than Labor Day. A final paper and sponsor evaluation is required.
AST 559 Turbulence and Nonlinear Processes in Fluids and Plasmas (also
APC 539
CBE 502 Mathematical Methods of Engineering Analysis II (also
APC 502
CBE 554 Topics in Computational Nonlinear Dynamics (also
APC 544
MAE 501 Mathematical Methods of Engineering Analysis I (also
APC 501
CBE 509
) Methods of mathematical analysis for the solution of problems in physics and engineering. Topics include an introduction to functional analysis, Sturm-Liouville theory, Green's functions for the solution of ordinary differential equations and Poisson's equation, and the calculus of variations.
MAE 502 Mathematical Methods of Engineering Analysis II (also
APC 506
MAE 541 Applied Dynamical Systems (also
APC 571
MAT 522 Introduction to PDE (also
APC 522
MAT 572 Topics in Combinatorial Optimization (also
APC 572
MAT 585 Mathematical Analysis of Massive Data Sets (also
APC 520
MAT 586 Computational Methods in Cryo-Electron Microscopy (also
APC 511
MOL 511
/
QCB 513
) This course focuses on computational methods in cryo-EM, including three-dimensional ab-initio modelling, structure refinement, resolving structural variability of heterogeneous populations, particle picking, model validation, and resolution determination. Special emphasis is given to methods that play a significant role in many other data science applications. These comprise of key elements of statistical inference, image processing, and linear and non-linear dimensionality reduction. The software packages RELION and ASPIRE are routinely used for class demonstration on both simulated and publicly available experimental datasets.
MSE 515 Random Heterogeneous Materials (also
APC 515
CHM 559
) Foams, composites, porous media, and biological media are all examples of random heterogeneous materials. The relationship between the macroscopic (transport, mechanical, electromagnetic and chemical) properties and microstructure of random media is formulated. Topics include correlation functions; percolation theory; fractal concepts; sphere packings; Monte Carlo techniques; and image analysis; homogenization theory; effective-medium theories; cluster and perturbation expansions; variational bounding techniques; topology optimization methods; and cross-property relations. Biological and cosmological applications will be discussed.
ORF 550 Topics in Probability (also
APC 550
Ph.D. Applied and Computational Mathematics