First Principles Tutoring
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Math & Physics · One-on-one, online

Hard subjects, taught from first principles.

Math & Physics Tutor, Olympiad Medalist & Coach, who cofounded and led Science & AI at $QUBT — with years of teaching in schools and colleges. I tutor calculus, mechanics, quantum and statistics the way they were discovered — by deriving them, not memorizing them.

Calculus d/dx Mechanics F = ma Quantum iħ∂ψ/∂t Statistics σ² Linear algebra Av = λv Fourier Σ sin(nθ)/n Trigonometry sin²θ + cos²θ = 1 Electricity E = kq/r² Thermodynamics ΔS ≥ 0 ODEs · more
Competition
Olympiad medalist
Coaching
Olympiad coach
Classroom
Schools & colleges
Industry
Science & AI Lead @ $QUBT

The subjects — running live on this page

Every board below is real math, computed in your browser.

This is how lessons feel: nothing stays abstract for long. We draw it, perturb it, and watch the equations answer back.

f′(x) = …

Calculus f′(x) = limh→0 Δf/h

The tangent line sliding along that curve is the derivative. Once you see slope as a moving quantity, limits, optimization and related rates stop being tricks.

limits · derivatives · integrals · series · multivariable · AP/IB/A-level

double pendulum — tap to perturb

Mechanics F = ma

A double pendulum, integrated from Newton's laws in real time. Tap it: two nearly identical starts diverge — that's chaos, and it falls straight out of F = ma.

kinematics · dynamics · energy · rotation · Lagrangians · olympiad problems

|ψ(x,t)|² — particle in a box

Quantum iħ ∂ψ/∂t = Ĥψ

A superposition of the first three eigenstates, evolving under the Schrödinger equation. The probability density breathes because the energies differ — interference you can point at.

wavefunctions · operators · spin · uncertainty · intro QM for college & curious minds

n = 0 drops

Statistics X ~ 𝒩(μ, σ²)

A Galton board: each ball makes ten coin-flip decisions, and the bell curve assembles itself. The central limit theorem, demonstrated instead of asserted.

probability · distributions · inference · regression · stats for data science & ML

det M = 1.00

Linear Algebra Av = λv

A matrix warps the entire plane — yet the two dashed eigenvector lines never leave their span. They only stretch by λ. That one picture is half of machine learning.

vectors · matrices · eigenvalues · SVD · the math underneath ML & quant work

square wave from 5 spinning circles

Fourier Analysis f(θ) = 4⁄π Σ sin(nθ)/n

Five circles, each spinning at an odd multiple of the first, add up to a square wave. Every signal decomposes this way — sound, images, markets, quantum states.

series · transforms · ODEs · waves & signals · from music to JPEG compression

θ = 0.00

Trigonometry sin²θ + cos²θ = 1

One point circling is the whole subject: its shadow on each axis gives sine and cosine, and the wave writes itself. Identities stop being flashcards once you see where they live.

unit circle · identities · triangles · precalculus · SAT/ACT foundations

dipole field — straight from Coulomb's law

Electricity E = kq/r²

A dipole's field, computed from Coulomb's law: lines leave +, land on −, and test charges ride the field. Circuits, potential and Maxwell's equations all start from this picture.

Coulomb's law · fields & potential · circuits · magnetism · AP Physics E&M

T_left > T_right

Thermodynamics ΔS ≥ 0

A hot gas (gold) meets a cold one (teal). Elastic collisions share the energy until both sides read the same temperature — the second law, running live, one bounce at a time.

heat & work · gas laws · entropy · engines · statistical mechanics

How a lesson runs

Diagnose. Derive. Drill.

The same loop I use with olympiad students and college classes — scaled to wherever you are now.

STEP 1

Diagnose

We find the exact load-bearing idea that's missing. It's almost never "all of calculus" — it's one definition or one picture, a few chapters back.

find x such that understanding(x) = false

STEP 2

Derive

We rebuild the result from scratch, together, on a shared board. If you can derive it, you can never un-know it — and exams become pattern recognition.

axioms → lemma → the formula you were told to memorize

STEP 3

Drill

Curated problems, olympiad-style: minimum count, maximum coverage. You leave each session with a short set chosen for your specific gaps.

limn→∞ P(solved | n deliberate reps) = 1

Why trust me with this

I've sat on every side of the desk.

Competitor

Olympiad medalist

I've been the student staring at a problem nobody in the room could do. I know what the top of the curve demands — and what it feels like to climb it.

Coach

Olympiad coach

Training competitors means teaching problem-solving itself: invariants, extremal arguments, when to compute and when to think. Those habits transfer to every exam you'll ever take.

Teacher

Schools & colleges

Years of real classrooms, from first-time calculus students to university courses. I've explained the chain rule a thousand ways; one of them will be yours.

Practitioner

Science & AI Lead @ $QUBT

I use this math at work, daily, leading science and AI. You'll hear where linear algebra shows up in machine learning and where statistics earns its keep — not just where it shows up on the test.

Who I work with

From first derivative to first research problem.

∫Exam prep

AP · IB · A-level · SAT/ACT math. Score targets, past-paper strategy, and the understanding that makes the strategy stick.

≡Olympiad training

AMC → AIME → olympiad pipeline, and physics olympiads. Proof technique, problem taste, and a training plan.

ĤUniversity courses

Calc I–III, linear algebra, ODEs, classical mechanics, intro quantum, probability & statistics. Survive the weeder; enjoy the subject.

σProfessionals

The math behind ML and quant work — refreshed properly. Gradients, distributions, estimators, and why the formulas are what they are.

Office hours are open

Bring me the problem you're stuck on.

∃ an explanation that works for you. We'll find it.

First intro session is free: we diagnose, sketch a plan, and you decide. Lessons online, worldwide, on a shared whiteboard.

@your_handle on X