# HL with James Tanton (New Topics)

### An Inter-Connected Understanding of the new HL topics: Matrices, Eigenvalues and Eigenvectors, Markov Processes, Coupled Linear DEs, and more!

Dr. James Tanton, creator of the renowned Exploding Dots mathematics experience, a phenomenon that has enthralled over 6.5 million students and their teachers across the planet (see the opening video here), presents a suite of videos and training opportunities on the newest HL syllabus items on matrices and their applications. These videos are aimed at teachers new to the topics--and all students too! - in the Applications and Interpretations course. He makes clear the concepts, the motivations, and the connections that weave through the story of the arithmetic of matrices and their applications in geometry, to understanding long-term probabilistic behaviour, and to developing the tools to naturally analyse dynamical systems given by coupled linear differential equations and the geometry of their phase diagrams.

### Matrix Theory for Analysing Coupled Linear Differential Equations in DP Maths AI - REGISTER NOWOct 26-27, 16:00 CEST

James is running two training, seminar, 'Think-ins' on the below on the dates above. If you can, we strongly recommend signing up, James's depth of knowledge, thought and engaging style make for an exceptional training experience.

## Deep, Conceptual and Inter-Connected Understanding:

Click on the titles below to see the videos under that topic.

#### Motivating Matrices and their Arithmetic: Adjacency Matrices, Determinants, Solving Simultaneous Equations

What are 'Matrices' and anyone want to use them?

Why is their arithmetic so strange? Why do we multiply matrices the way we do (?

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#### Geometric Transformations and Matrices

Understanding the geometry associated with matrices and making real sense of the meaning of a matrix's determinant. .

#### The Problem of Large Powers: Diagonalisation and More

The definition of a mathematician could very well be "Someone who works very hard to avoid hard work." Is there a way to radically simplify some truly horrid matrix arithmetic?

#### Transition Matrices and Markov Processes

Many human interactions, natural world and biological processes, and quantum phenomena from physics, can be modeled by probabilistic systems. A lovely application of matrix work is the ability to model and analyse such systems.

#### Coupled Differential Linear Equations and their Phase Portraits

We know from a first calculus class how to solve some basic linear differential equations. Can we mimic that work and solve systems of linear equations too? Eigenvalues and eigenvectors provide the key!

#### Second Order Linear Differential Equations: A Brief Metnion

A sneaky way to turn a new problem into a previously solved problem!

### Visit James Tanton's Global Math Project:

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