ABOUT ME / ABOUT LAYERCHECKLIST

Nitish John Rawat

Learning mathematics, exploring nature, building intelligent systems.

Why this site exists

Layerchecklist is a growing learning notebook for understanding patterns, the physical world, living systems and the machines we build to study them. The aim is to make the connections visible: an equation should explain an observation, and an interactive model should give you something to test.

Start with something familiar. Give it a precise explanation. Try an example, change an assumption, and use what you learn to build the next layer.

Take in every experience. Give weight to what helps you grow. Learn from what causes loss. Adjust, try again, and move forward.
You don't need to begin with the right weights. You just need to keep learning.
— the perceptron, read as advice, from the front page

That learning metaphor still fits the expanded site. You can return to a foundation, follow a connection into another subject, and improve your understanding through a concrete experiment.

Math → Physics → Biology

Math supplies the language of patterns and uncertainty. Physics uses it to describe matter, energy and motion. Biology follows those mechanisms into cells, organisms and ecosystems, adding heredity, evolution and history.

Then use Python and its libraries to explore data and models, move through AI, machine learning and deep learning, and try the ideas in simulations and robotics. The order is a suggested path; every subject stays open to explore.

What is here

13 places to learn, from interactive subject atlases to courses, tool checklists and experiments.

MathThe first foundation: mathematical ideas, worked examples and an interactive atlas.PhysicsThe second foundation: physical laws, scales, mechanisms and their connections.BiologyThe third foundation: living systems, heredity, evolution and ecology, with interactive models.Python FundamentalsTurn an idea into a program with functions, data structures and small experiments.AI FoundationsWhat the field is, how a system works, and how to judge a result.Python LibrariesA practical checklist of the tools used to work with data, numerical models and visualizations.Machine LearningA week-by-week series, from data and evaluation to learning algorithms.Deep LearningA learning path through architectures, training and model behavior.SQLOrganize, query and combine the data behind an experiment or application.ROSConnect sensing, communication and control in a robotics workflow.CUDAExplore parallel computation and the hardware behind numerical workloads.Simulation EnvironmentsExplore the tools and environments used to model physical systems and train agents.Live Simulation LabEight interactive experiments in motion, collective behavior, robotics, control and sensing.

265mathematical ideas mapped

151physics ideas mapped

112biology ideas mapped

8 + 3simulation labs + biology models

Learn by changing something

A map helps you find a topic. An experiment helps you question it. Start with a prediction, move one control, and explain the result before moving another.

PHYSICS IN MOTIONKeep an orbit on course →Compare numerical integration methods and watch their energy error.PHYSICS INTO BIOLOGYFollow a concentration gradient →Change permeability and time in a two-compartment diffusion model.MATH INTO BIOLOGYExplore inherited variation →Connect allele frequencies to expected genotype proportions.

How it is built

The site is built with Next.js and React, with SVG and canvas for its visual explanations. The atlases connect related ideas; the labs let you explore simplified models. These four principles guide the work.

01Build one layer at a time
Begin with an observation, give it a precise language, then build a model. Definitions, assumptions and worked examples belong beside the result.
02Make the model explorable
Change a parameter and watch a prediction change. The labs calculate in your browser: some step equations through time, while others evaluate a mathematical solution directly.
03Check the limits
Use units, conservation laws and boundary cases to question a calculation. A model is useful only within its assumptions; a smooth animation does not establish that it matches the world.
04Keep questions open
Separate established results, useful approximations and unresolved questions. Follow sources, test an explanation, and revise it when the evidence changes.