### Imperial College London

#### PDEs in Action: Introduction to modelling in applied mathematics, MATH50008

Spring 2021

This module provides a hands-on introduction to partial differential equations and the concept of modelling in applied mathematics. We focus on the practical applications of partial differential equations. Along the way, students are introduced to classical partial differential equations and as well as more advanced examples. Throughout the course, the students learn basic techniques of resolutions of PDEs. Students are also introduced to basic numerical methods to solve partial differential equations.

#### Theory of Complex Systems, MATH96004

Spring 2020

Complex systems are systems composed of many components or agents which interact with one another. One finds examples of complex systems at all scales; these include systems as varied as biological organisms (from the single cell to the whole organism), financial markets, ecosystems, transportation/communication systems or the human brain. The theory of complex systems tries to establish an understanding of the intimate link between the emergent systemic collective behavior and the dynamics of its individual components. In this module, we introduce the theoretical and computational concepts needed to describe the spatial and temporal behaviour of complex systems. We start by introducing the necessary tools from statistical mechanics and the study of phase transitions. We then introduce a variety of examples including models of percolation, self-organized criticality (sandpile and forest fire models), out-of-equilibrium dynamics (Langevin and Fokker-Planck formulations), models of interacting agents on lattices and networks (e.g. Schelling model, Kuramoto model). Finally, we look beyond conserved interacting agents and discuss reaction-diffusion processes and evolutionary dynamics.

#### Introduction to University Mathematics, MATH40001

Fall 2019, Fall 2020

This module provides a transition towards the way ones thinks about, and does, Mathematics at university. It stresses the importance of precise definitions and rigorous proofs, but also discuss their relationship to more informal styles of reasoning which are often encountered in applications of Mathematics. Topics covered include an introduction to elementary set theory, common proof strategies as well as common functions, and elementary vector operations and geometry.

### Yale University

#### Musical Acoustics and Instrument Design, ENAS344&MUSI371

Fall 2014, Spring 2016

Exploration of the acoustic principles of musical instruments using a highly interactive hands-on approach. Understanding of the physics of musical instruments and how they are designed. Concepts such as standing waves, harmonics, musical scales, forced oscillations, radiation, interference, electronic interfaces, and spectral analysis.

#### Introduction to Engineering, Innovation and Design, ENAS118

Spring 2013

Hands-on introduction to engineering, MATLAB, Mechanical Engineering (CAD with SolidWorks, 3D printing), Electrical Engineering (Arduino, servos, LEDs and sensors), Chemical Engineering (Clean water technologies), Biomedical Engineering (Cell culture, nanotechnology, drug delivery, tissue engineering)

#### Mechanical Engineering III: Dynamics, MENG383

Fall 2012, Fall 2013, Fall 2015

Kinematics and dynamics of rigid bodies, energy and momentum methods, vibration

### Outreach

#### Musical Acoustics and Instrument Design, Yale Pathways to Science SCHOLARS program

Summer 2016

Hands on introduction to the principles of physical acoustics and musical instruments design as well as scientific reasoning to selected high school students.

#### Introduction to Material Science, Yale Pathways to Science SCHOLARS program

Summer 2016

Hands-on introduction to Metals, Ceramics, Polymers, Semi-conductors as well as Scientific Reasoning to selected high school students.