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Learn Through Visuals

Visual guides for complex technical topics — DSA, system design, security, cloud, AI, and beyond. Learn through interactive animations and flowcharts.

Latest Guides

Click any card to explore an interactive guide.

Understand how Bloom Filters use hash functions and bit arrays to answer membership queries with zero false negatives, perfect for space-constrained systems.

Client-Server Architecture

Client-Server Architecture is the foundational model of modern networked applications — clients send requests, servers process and respond. Understanding this model is the first step to mastering distributed systems, APIs, and scalable web applications.

A comprehensive guide to Forward Proxy and Reverse Proxy, their differences, use cases, and how they protect clients and servers.

Microservices Architecture

Breaking down monolithic applications into small, independent, loosely-coupled services.

Monolithic Architecture

A single-unit software architecture where all components are tightly coupled.

Serverless Architecture

Serverless architecture allows building and running applications without managing infrastructure.

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Latest Articles

In-depth reads on AI, systems, and engineering concepts.

Abstract Vector Spaces

Chapter 16, the finale. We started by calling vectors arrows. Now we zoom out: a vector is anything you can add and scale by the usual rules. That includes functions. Everything you learned applies far beyond arrows on a grid.

A Quick Trick for Computing Eigenvalues

Chapter 15. A short, practical chapter. With two easy numbers from any 2 by 2 matrix, the mean and the product of its eigenvalues, you can find both eigenvalues in your head. Great for interviews and quick checks.

Eigenvectors and Eigenvalues

Chapter 14. When a transformation warps space, most vectors get knocked off their original line. A few special ones do not: they only get stretched. Those are eigenvectors, and the stretch factor is the eigenvalue. This is one of the most useful ideas in all of applied math.

Change of Basis

Chapter 13. The same arrow gets different coordinates depending on which basis you use. This chapter shows how to translate vectors and even whole transformations between two coordinate systems. It is the formal version of an idea from Chapter 2.

Cramer's Rule, Explained Geometrically

Chapter 12. Cramer's rule solves a linear system using ratios of determinants. It looks like a magic formula in textbooks, but with the area picture from earlier chapters, it becomes something you can actually see.

Cross Products in the Light of Linear Transformations

Chapter 11. A bonus deep dive. Why does the cross product formula work, and why does a determinant show up in it? The answer uses duality from Chapter 9 and is one of the most elegant moments in the series.

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