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APM 525: High-Performance Computing
3.00 Credits
Arizona State University
Supercomputer architectures, parallel programming environments, languages, libraries, and algorithms for high-performance numerical simulations. Instructor/Department approval is required for this course.
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APM 525 - High-Performance Computing
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APM 526: Advanced Numerical Methods for Partial Differential Equations
3.00 Credits
Arizona State University
Partial content will vary from semester to semester, but may include hyperbolic conservation laws, finite element methods, multigrid methods, and parallel algorithms for partial differential equations. Applications to scientific, biomedical, and industrial problems. Students should have basic knowledge of PDE's and a programming language.
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APM 526 - Advanced Numerical Methods for Partial Differential Equations
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APM 530: Mathematical Cell Physiology.
3.00 Credits
Arizona State University
Mathematical modeling of dynamical aspects of cell physiology. Diffusion, membrane transport, intracellular calcium channel kinetics, calcium oscillations and waves.
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APM 530 - Mathematical Cell Physiology.
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APM 531: Mathematical Neuroscience I
3.00 Credits
Arizona State University
Mathematical modeling of electrochemical processes in nerve cells. Dendritic modeling, dendritic spines and synaptic plasticity, bifurcation analysis of excitable membrane models, deterministic and stochastic methods for threshold dynamics and bursting, relaxation oscillations. Students should have had a previous graduate-level PDE course.
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APM 531 - Mathematical Neuroscience I
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APM 532: Mathematical Neuroscience II
3.00 Credits
Arizona State University
Mathematical modeling of systems neuroscience. Network dynamics, coupled phase oscillators, central pattern generators, neural coding, learning and memory. Students should have taken ordinary differential equations or mathematical cell physiology or mathematical neuroscience prior to enrolling in this course.
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APM 532 - Mathematical Neuroscience II
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APM 533: Mathematical Population Biology I
3.00 Credits
Arizona State University
Selectively covers population biology models in the forms of systems of difference equations or ordinary differential equations. Focuses on mathematical analysis of population models as well as model formulation and simulation. Students should have a previous graduate-level course in ODE.
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APM 533 - Mathematical Population Biology I
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APM 534: Mathematical Population Biology II
3.00 Credits
Arizona State University
Selectively covers population biology models in the form of partial differential equations and systems. Focuses on mathematical analysis of population models as well as model formulation and simulation. Students should have a previous basic graduate-level course in ODE and PDE.
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APM 534 - Mathematical Population Biology II
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APM 535: Mathematical Models in Medicine
3.00 Credits
Arizona State University
Mathematical models for the etiology, epidemiology, pathogenesis, morphology and treatment of disease. Covers dynamical models of cancer and viral infections.
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APM 535 - Mathematical Models in Medicine
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APM 541: Stochastic Modeling in Biology
3.00 Credits
Arizona State University
Markov processes, random walks, martingales, branching processes, logistic growth model, Wright-Fisher model, Kingman's coalescent, bound and site percolations, contact processes, voter models. Students should have previously taken course work in probability and/or stochastic processes (or have a recommendation from their advisor). Recommendation from advisor is typically for students in biology or physics that have not taken statistics courses but have a good background in mathematics.
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APM 541 - Stochastic Modeling in Biology
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APM 553: Dynamical Systems
3.00 Credits
Arizona State University
Center manifolds, structural stability, normal forms, averaging, chaos, control and synchronization. Students should have a previous graduate course in ODE or applied analysis.
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APM 553 - Dynamical Systems
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