Applied Mathematics Courses and Certifications

The Mathematics of Wound Healing

Explore how mathematics, physics, and biology combine to understand the complex dynamics of wound healing in this insightful lecture by Professor Tanniemola Liverpool.

• YouTube
• 52 minutes
• On-Demand
• Free Video

Going for Gold - The Mathematics of Sporting Glory

Discover the mathematical secrets behind athletic performance, from optimal running strategies to swimming techniques and cycling stability principles.

• YouTube
• 45 minutes
• On-Demand
• Free Video

Steve Brunton

Monte Carlo Sampling and Bootstrapping in Bayesian Inference

Explore Monte Carlo sampling techniques and bootstrapping methods for Bayesian inference through practical algorithms and coin flip demonstrations.

• YouTube
• 18 minutes
• On-Demand
• Free Video

Ross Dynamics Lab

Normal Forms for Vector Fields

Introduction to normal forms for vector fields, focusing on simplifying nonlinear terms and determining topological equivalence. Covers theory, examples, and applications in dynamical systems analysis.

• YouTube
• 1 hour 20 minutes
• On-Demand
• Free Video

Ross Dynamics Lab

Center Manifold Theory - Computing Center Manifolds

Explore center manifold theory for dynamical systems, focusing on computing and approximating center manifolds. Learn to analyze stability and dynamics near equilibrium points using Taylor series expansions and tangency conditions.

• YouTube
• 1 hour 16 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Asymmetry in Dynamics

Explore symmetries in dynamical systems and progress on Smale's conjecture about generic smooth systems having only trivial symmetries. Delve into complex analytic, Hamiltonian, and smooth dynamics.

• YouTube
• 45 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

A Mathematical Adventure in Immunology by Carmen Molina-Paris

Explore the immune system's complexity through mathematical modeling, examining cell interactions, disease prevention, and quantifying pathogen infectivity.

• YouTube
• 1 hour 43 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

The Discrete Charm of Geometry by Alexander Bobenko

Explore the fascinating world of discrete geometry and its applications in architecture, computer graphics, and physics. Discover structure-preserving discretizations through simple examples and stunning visuals.

• YouTube
• 1 hour 36 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Introduction to Dynamical Systems - Lecture 1

Explore dynamical systems, from linear ODEs to nonlinear chaos. Learn about equilibrium points, eigenvalues, attractors, and bifurcations. Gain insights into Lorenz systems, Poincaré maps, and iterative methods.

• YouTube
• 1 hour 14 minutes
• On-Demand
• Free Video

ICTP Mathematics

Rotations of the Circle and Renormalization

Explore circle rotations, renormalization, and dynamical systems with Corinna Ulcigrai. Learn key concepts, proofs, and applications in this advanced mathematics lecture.

• YouTube
• 58 minutes
• On-Demand
• Free Video

Institute for Advanced Study

On the Spatial Restricted Three-Body Problem - Agustin Moreno

Explore the spatial restricted three-body problem, global hypersurfaces, and Hamiltonian return maps. Learn about a higher-dimensional Poincaré-Birkhoff theorem and its applications to orbital dynamics.

• YouTube
• 1 hour 17 minutes
• On-Demand
• Free Video

Institute for Advanced Study

Towards a Mathematical Model of the Brain - Lai-Sang Young

Explore mathematical approaches to modeling brain dynamics, from local neural populations to complex cognitive functions, with insights on synchronization, memory, and visual processing.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video

Institute for Advanced Study

Observable Events and Typical Trajectories in Dynamical Systems - Lai-Sang Young

Explore observable events and typical trajectories in dynamical systems with Lai-Sang Young, covering SRB measures, attractors, and infinite dimensional center manifolds.

• YouTube
• 56 minutes
• On-Demand
• Free Video

Institute for Advanced Study

Mathematical Models of Human Memory - Michail Tsodyks

Explore mathematical models of human memory, covering simplification, recall capacity, experiments, and recognition tests, with insights on memory dynamics and cognitive processes.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video

ICTP Mathematics

Symbolic Dynamics for Nonuniformly Hyperbolic Systems - Lecture 1 of 5

Explore symbolic dynamics for nonuniformly hyperbolic systems, focusing on Markov Partitions and Young Towers. Learn advanced techniques to analyze complex dynamical systems and their statistical properties.

• YouTube
• 2 hours 6 minutes
• On-Demand
• Free Video