Tag: #math

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• The Math You Need for Robotics, in Order: And What You Can Safely Put Off ♪ Listenable

  An answer to how far you actually need to take your math to build a robot arm. Organized into six branches in order: linear algebra, trigonometry and rotation representations, calculus and multivariable methods, differen

  2026-08-02 · 25 min read #robotics#math#electronics#linear-algebra#control

• What a Robot Arm Is Made Of: Links, Joints, and What Actually Drives Them ♪ Listenable

  Buy six servos to build a robot arm and it almost always collapses under its own weight. This post starts from the precise definitions of link, joint, and end effector, explains what degrees of freedom actually count and

  2026-08-02 · 29 min read #robotics#hardware#electronics#arduino#math

• Forward Kinematics: From Joint Angles to End-Effector Position with Homogeneous Transforms and DH Parameters ♪ Listenable

  Forward kinematics is calculating where the end effector is when you know the joint angles. This post shows, with real numbers, how the 4x4 homogeneous transformation matrix resolves the mismatch between rotation (matrix

  2026-08-02 · 23 min read #robotics#math#electronics#raspberry-pi#hardware

• The Robot Arm Control Loop: From Trajectory Generation to PID and Gravity Compensation ♪ Listenable

  Everything past the point where inverse kinematics hands you joint angles belongs to control. This post explains, through discontinuous acceleration, why writing the target angle straight into the servo makes the arm jer

  2026-08-02 · 24 min read #robotics#electronics#arduino#hardware#math

• Inverse Kinematics: Working Backward from Where You Want to Be to the Joint Angles ♪ Listenable

  Forward kinematics is a single calculation — feed in angles, get a position. Inverse kinematics can have no solution, several solutions, or infinitely many. This post derives the analytic solution for a 2-link planar arm

  2026-08-02 · 22 min read #robotics#math#electronics#hardware#raspberry-pi

• The Birthday Paradox and Hash Collisions — Why 23 People Means a 50% Match

  Just 23 people in a room, and the odds that two share a birthday cross 50%. At the root of this counterintuitive result is a √N approximation, and the same math runs through UUID and hash collision probability, why 128 b

  2026-06-27 · 11 min read #math#hashing#fundamentals

• Math and Scientific Computing Tools in 2026 — Mathematica / MATLAB / Maple / SageMath / Julia 1.11 / R + Posit / JAX / GeoGebra / Desmos / GAP / Macaulay2 Deep Dive ♪ Listenable

  The math and scientific computing landscape in 2026 is no longer dominated by one or two tools. Wolfram Mathematica still owns premium symbolic computation. MATLAB and Simulink remain the engineering industry standard. M

  2026-05-16 · 29 min read #math#scientific-computing#wolfram-mathematica#matlab#simulink

• AI Agent & LLM Benchmarks 2026 — SWE-bench Verified / ARC-AGI 2 / GAIA / MMLU-Pro / GPQA / LiveCodeBench / Chatbot Arena Deep Dive ♪ Listenable

  A single-page map of the 30+ AI benchmarks that matter in 2026. From SWE-bench / SWE-bench Verified / SWE-bench Multimodal to AgentBench, WebArena and GAIA, ARC-AGI 2 (Chollet $1M prize), RE-Bench (METR), Frontier Math (

  2026-05-16 · 19 min read #ai-benchmark#llm-evaluation#swe-bench#swe-bench-verified#agentbench

• Linear Algebra Complete Guide: Zero to Hero from Vectors to SVD ♪ Listenable

  A comprehensive guide to linear algebra from first principles to advanced topics. Covers vectors, matrices, determinants, vector spaces, eigenvalues, and SVD with Python code examples throughout.

  2026-03-17 · 23 min read #linear-algebra#math#engineering-math#vectors#matrices

• Math + LaTeX/KaTeX Complete Guide for Reading AI/ML Papers ♪ Listenable

  A comprehensive summary of essential math concepts (linear algebra, calculus, probability/statistics, optimization) and LaTeX/KaTeX formula syntax for reading AI/ML papers with practical examples, symbol cheat sheets, an

  2026-03-08 · 20 min read #ai-papers#math#latex#katex#linear-algebra