Math for programmers. Module 1: Linear Algebra

Essential math for modern software developers

What you’ll learn
✓ Understand the core concepts of linear algebra, including vectors, matrices, rank, span, and subspaces.
✓ Apply linear algebra operations in code using Python, JavaScript, or C#.
✓ Solve problems with decomposition techniques (LU, QR, Cholesky, SVD) for efficient and stable computation.
✓ Connect linear algebra to real-world applications in AI, data science, and computer graphics.

Requirements
● No prior knowledge of linear algebra is required. A basic understanding of programming (in Python, JavaScript, or C#) will be helpful, but all mathematical concepts are explained step by step.

Description
Linear Algebra is one of the most important mathematical tools in modern software development. Whether you’re working in graphics, AI, simulations, data science, or game development, you’re using linear algebra, even if you don’t realize it.

Why is this relevant for developers?

Because vectors and matrices are everywhere

• In graphics: rotating and moving objects on screen

• In AI: powering neural networks and data representations

• In physics engines: motion, force, collisions

• In games: camera control, lighting, animation

• In data science: analyzing datasets, dimensionality reduction, regression, clustering

What you’ll learn in this module

You’ll start from the very basics, understanding vectors and matrices both conceptually and in code, and gradually build up to more advanced tools. Step by step you’ll see how simple operations like addition, scaling, and the dot product form the foundation for transformations in graphics, physics, AI, and data science.

In the later lessons you’ll go deeper into decomposition techniques such as LU and QR factorization, eigen decomposition, and singular value decomposition (SVD), powerful methods that make it possible to analyze and work with massive datasets efficiently.

You don’t need a math degree. You just need curiosity and code.

Lesson Format

• Learning objectives: clear goals at the start

• Theory with examples

• Applications in software development

• Code examples in Python, C#, and JavaScript

• Tasks and hands-on exercises

• Video lesson with guided explanation

• Multiple-choice quiz to test understanding

Who this course is for
■ This course is designed for programmers and software developers who want to strengthen their mathematical foundation in linear algebra. It is especially valuable for learners pursuing fields such as AI, data science, computer graphics, and simulations, who feel limited by their current knowledge of mathematics.

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