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Explore our collection of mathematics and computer science articles.

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🔮Vibe Coding

Screenshot-to-Code vs. Specs-Driven Development: The 2026 Design Handoff Evolution

A real-world experiment reveals the profound gap between AI visual approximation and production-ready code. Learn why context pipelines are the future of design-to-code workflows.

January 9, 20268 min read
#vibe coding#AI development#design systems
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🔮Vibe Coding

Vibe Coding: Master AI-Assisted Programming with LLM Probability

Learn what vibe coding is, how LLM probability powers AI-assisted programming, and master the skills for the future of coding. Practical examples included.

January 6, 20266 min read
#vibe coding#AI programming#LLM
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🔮Vibe Coding

Why LLMs Can't Revise Tokens: The Feed-Forward Constraint Every Developer Must Understand

Learn why LLMs hallucinate and can't self-correct. Understand feed-forward token generation and master vibe coding strategies for better AI-assisted development.

January 6, 20269 min read
#LLM#token generation#feed-forward
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🔮Vibe Coding

The Generative Core: Understanding Hallucination in Large Language Models

Hallucination isn't a bug in LLMs—it's the generative process itself. Understanding this changes how we should think about working with these tools.

January 6, 202610 min read
#LLM hallucination#AI generation#confabulation
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🔮Vibe Coding

Why LLMs Fail at Complex Tasks: The Math Behind Compounding Error in AI Code Generation

Learn why LLMs fail on long reasoning chains due to compounding error. Includes mathematical proofs, real-world AI coding failures, and actionable engineering strategies to mitigate AI hallucinations in software development.

January 6, 202611 min read
#LLM limitations#compounding error#AI hallucinations
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🔮Vibe Coding

Attention Mechanisms in LLMs: The Complete Guide to How Transformers Really Work

Learn how attention mechanisms power large language models (LLMs) like GPT-4 and Claude. This in-depth guide explains Query-Key-Value math, multi-head attention, and long-context processing with real code examples.

January 6, 202612 min read
#attention mechanisms#transformers#LLM
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🎯Discrete Math

Graph Theory Basics: Nodes, Edges, and Paths

An introduction to graph theory covering fundamental concepts like vertices, edges, paths, and common graph algorithms.

January 4, 202611 min read
#graph-theory#discrete-math#algorithms
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∫Calculus

Unleashing the Power of Complex Numbers in Calculus

Discover how Euler's formula and complex exponentials can transform difficult trigonometric integrals into simple algebra.

January 3, 202610 min read
#calculus#complex-numbers#integration
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🔣Number Theory

The Beauty of Prime Numbers

Explore the fascinating world of prime numbers, from ancient discoveries to modern applications in cryptography.

January 3, 202612 min read
#number-theory#primes#mathematics
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🔢Algebra

Introduction to Linear Algebra: Vectors and Matrices

A comprehensive guide to understanding vectors, matrices, and their operations - the building blocks of linear algebra.

January 3, 20268 min read
#linear-algebra#vectors#matrices
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⚡Algorithms

Understanding Big O Notation

Learn how to analyze algorithm efficiency using Big O notation, with practical examples and common complexity classes.

January 1, 202610 min read
#algorithms#complexity#big-o
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∫Calculus

The Fundamental Theorem of Calculus

Explore the beautiful connection between differentiation and integration through the Fundamental Theorem of Calculus.

December 27, 202512 min read
#calculus#integration#differentiation
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