Introduction to Computational Thinking

Overview

This class uses revolutionary programmable interactivity to combine material from three fields creating an engaging, efficient learning solution to prepare students to be sophisticated and intuitive thinkers, programmers, and solution providers for the modern interconnected online world.

Upon completion, students are well trained to be scientific “trilinguals”, seeing and experimenting with mathematics interactively as math is meant to be seen, and ready to participate and contribute to open source development of large projects and ecosystems.

Syllabus

Module 1: Images, Transformations, Abstractions
- 1.1 - Images as Data and Arrays
- 1.2 - Abstraction
- 1.3 - Automatic Differentiation
- 1.4 - Transformations with Images
- 1.5 - Transformations II: Composability, Linearity and Nonlinearity
- 1.6 - The Newton Method
- 1.7 - Dynamic Programming
- 1.8 - Seam Carving
- 1.9 - Taking Advantage of Structure
Module 2: Social Science & Data Science
- 2.1 - Principal Component Analysis
- 2.2 - Sampling and Random Variables
- 2.3 - Modeling with Stochastic Simulation
- 2.4 - Random Variables as Types
- 2.5 - Random Walks
- 2.6 - Random Walks II
- 2.7 - Discrete and Continuous
- 2.8 - Linear Model, Data Science, & Simulations
- 2.9 - Optimization
Module 3: Climate Science
- 3.1 - Time stepping
- 3.2 - ODEs and parameterized types
- 3.3 - Why we can't predict the weather
- 3.4 - Our first climate model
- 3.5 - GitHub & Open Source Software
- 3.6 - Snowball Earth and hysteresis
- 3.7 - Advection and diffusion in 1D
- 3.8 - Resistors, stencils and climate models
- 3.9 - Advection and diffusion in 2D
- 3.10 - Climate Economics
- 3.11 - Solving inverse problems