This course focuses on computational thinking, specifically the creation of models to represent the physical world—a skill essential for engineers. Through the study of algorithmic processes, rather than symbolic mathematics, students will be able to address problems in areas often associated with algebra and calculus. The aim is to equip learners with a strategic approach to solve complex problems more efficiently.

The course emphasizes on the following main themes:

• Representation: Encoding information and its impact on problem-solving.
• Decomposition: Breaking down complex problems into manageable parts.
• Discretization: Dividing space and time into small segments to improve accuracy and computation speed.
• Verification: Ensuring the reliability of model results.

• Institution: MITx
• Subject: Computer Science
• Level: Intermediate
• Prerequisites: Algebra, Calculus
• Language: English
• Video Transcript: English
• Associated skills: Discretization, Forecasting, Algebra, Calculus, Computational Thinking

By the end of this course, students will acquire skills to:

• Implement interpolation and numerical methods understanding their effects on model convergence.
• Employ simple methods for numerical integration.
• Apply numerical differentiation techniques.
• Develop programs to solve linear and non-linear equation systems.

• Week 1: Introduction to Computational Thinking - Concepts of representation, discretization, error, decomposition, verification.
• Week 2: Interpolation - Building surrogate models for complex functions.
• Week 3: Integration - Techniques in numerical quadrature.
• Week 4: Randomness - Using pseudorandom variables in models.
• Week 5: Differentiation - Approaches to numerical derivatives.
• Week 6: Solving Equations - Gaussian elimination for linear systems, Newton-Raphson for nonlinear systems.