My Notes

Robotics fascinates me because of its multidisciplinary nature, combining neuroscience, AI, mechanics, and electronics to create systems that can sense, process, and act in the real world...

The field draws inspiration from biological systems, particularly neuroscience, which provides insights into how natural intelligence functions. This connection between nature and technology creates...

Graph theory offers powerful abstractions for solving complex computational problems. In this note, I explore various algorithms like breadth-first search (BFS), depth-first search (DFS), and Dijkstra's algorithm...

The elegant mathematical foundation of graphs allows us to model relationships between entities in a way that facilitates efficient problem-solving...

The relationship between quantum mechanics and general relativity remains one of the most profound puzzles in modern physics. This note explores some of the conceptual challenges in reconciling these two foundational theories...

Drawing from Sean Carroll's work on spacetime geometry, I reflect on how our understanding of reality is shaped by these seemingly incompatible descriptions of nature...

Bach's Goldberg Variations represent one of the most remarkable achievements in keyboard literature. This analysis explores the structural symmetry, harmonic innovation, and contrapuntal mastery displayed throughout the work...

As both a pianist and music theorist, I find particular interest in how Bach develops the initial aria through a series of increasingly complex variations while maintaining...

Proper force and stress analysis is fundamental to creating robust mechanical systems. This note documents my approach to analyzing the forestry winch design project, including the calculation of static and dynamic loads...

I explore how different material choices affect the design constraints and safety factors, with particular attention to the balance between weight, strength, and cost...

Drawing from Brian Ward's "How Linux Works," this note explores the internal architecture of the Linux operating system, with a focus on kernel operations, memory management, and process scheduling...

Understanding these core concepts has greatly enhanced my ability to write efficient code and troubleshoot system-level issues in my projects...

Thermodynamics provides a powerful framework for understanding energy transformations. This note delves into the mathematical structures underlying thermodynamic principles, including differential forms, vector fields, and partial derivatives...

I explore how concepts from multivariable calculus illuminate the relationships between heat, work, entropy, and the fundamental laws of thermodynamics...

How does the brain process music? This note explores the neural mechanisms involved in music perception, drawing connections between my piano practice and the latest neuroscience research...

From pitch processing in the auditory cortex to emotional responses mediated by the limbic system, music engages a remarkably distributed network of brain regions...