Applied Mathematics Courses and Certifications

Introduction to Dynamical Systems and Chaos

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In this course you'll gain an introduction to the modern study of dynamical systems, the interdisciplinary field of applied mathematics that studies systems that change over time.

• Complexity Explorer
• 10 weeks, 3-6 hours a week
• On-Demand
• Free Online Course

• Best of All Time

Why There Are No Three-Headed Monsters

Explore developmental constraints, brain tumors, and marriage dynamics through mathematical biology, offering insights into morphogenesis, medical interventions, and relationship predictions.

• YouTube
• 1 hour 19 minutes
• On-Demand
• Free Online Course

Institute for Pure & Applied Mathematics (IPAM)

Slow Time-Scale Behavior of Fast Microscopic Dynamics - IPAM at UCLA

Explores computational methods for understanding slow time-scale behavior of rapid microscopic dynamics, with applications in materials modeling and plasticity. Presents theory and examples for coarse-graining complex systems.

• YouTube
• 56 minutes
• On-Demand
• Free Online Course

Applied Algebraic Topology Network

Applied Topology for Discrete Structures

Explore topological concepts applied to discrete structures modeling real data, bridging network science and applied topology for innovative analysis of complex systems.

• YouTube
• 59 minutes
• On-Demand
• Free Online Course

Society for Industrial and Applied Mathematics

Matrix Equations and Model Reduction - Lecture 4

Explore matrix equations and model reduction techniques, focusing on SR method, high multiplicity, and theoretical background with renowned expert Peter Benner.

• YouTube
• 1 hour 38 minutes
• On-Demand
• Free Online Course

Society for Industrial and Applied Mathematics

Matrix Equations and Model Reduction - Lecture 3

Explore matrix equations and model reduction techniques with Peter Benner, covering enrichment, polar residual form, transfer functions, and moment matching for efficient system analysis.

• YouTube
• 1 hour 42 minutes
• On-Demand
• Free Online Course

Society for Industrial and Applied Mathematics

Spectral Problems in Inverse Scattering Theory - 21st IMAGINE OneWorld SIAM-IS Seminar

Explore scattering theory's spectral problems, focusing on poles, non-scattering frequencies, and transmission eigenvalues. Learn how these relate to scattering operators and material properties in inhomogeneous media.

• YouTube
• 1 hour 9 minutes
• On-Demand
• Free Online Course

Society for Industrial and Applied Mathematics

Certificates of Nonnegativity and Their Applications in Theoretical Computer Science

Explore nonnegativity certificates in real algebraic geometry, focusing on sums of squares and sums of nonnegative circuit polynomials, with applications to polynomial optimization and theoretical computer science.

• YouTube
• 58 minutes
• On-Demand
• Free Online Course

Society for Industrial and Applied Mathematics

Families of Polynomials in Biochemical Reaction Networks

Exploring polynomial systems in biochemical reaction networks, focusing on computational techniques for analyzing families of polynomials with combinatorial structures derived from reaction digraphs.

• YouTube
• 51 minutes
• On-Demand
• Free Online Course

Society for Industrial and Applied Mathematics

Applications of Homotopy Continuation in Science and Engineering

Explore homotopy continuation in numerical algebraic geometry and its applications in chemistry, mechanical engineering, and biological modeling. Learn about tracking solutions to parameterized nonlinear equations.

• YouTube
• 47 minutes
• On-Demand
• Free Online Course

Society for Industrial and Applied Mathematics

Wave Enhancement Through Spectral Optimization - 33rd IMAGINE Seminar

Explore efficient optimization of wave transmission in cavities through boundary condition adjustments, using spectral analysis and layer potential methods for accurate eigenvalue calculations.

• YouTube
• 57 minutes
• On-Demand
• Free Online Course

Steve Brunton

A Compressed Overview of Sparsity

Explore compressed sensing in engineering mathematics, covering sparsity, compression techniques, and L1 minimization. Learn key principles and applications beyond image processing.

• YouTube
• 35 minutes
• On-Demand
• Free Online Course

Society for Industrial and Applied Mathematics

Entropic Optimal Transport - Eighteenth SIAM Activity Group on FME Virtual Talk

Explore entropic regularization in optimal transport with Marcel Nutz. Learn about convergence, local behavior, and applications in high-dimensional data problems.

• YouTube
• 1 hour 5 minutes
• On-Demand
• Free Online Course

Society for Industrial and Applied Mathematics

Nonlinear Spectral Decompositions in Imaging and Inverse Problems

Explore nonlinear spectral decompositions in imaging and inverse problems, focusing on variational theory and applications in data science, with computational methods discussed.

• YouTube
• 1 hour 3 minutes
• On-Demand
• Free Online Course

Society for Industrial and Applied Mathematics

The Half-space Matching Method for Solving Scattering in Complex Media

Explore innovative wave scattering solutions in complex media using the Half-space Matching Method, offering efficient alternatives to traditional computational techniques.

• YouTube
• 1 hour 1 minute
• On-Demand
• Free Online Course