Mathematics
Mathematics: step-by-step Socratic AI tutors, core formulas, worked examples, and exam prep across High School, CÉGEP, and University.
High School & AP
y = mx + b📐 Algebra 1 & Foundations
Linear equations, inequalities, slope, graphing lines, systems, quadratics
Open Course Track & Prompts →a² + b² = c²📏 Geometry & Proofs
Triangle congruence, Pythagorean theorem, circles, perimeter, area, volume
Open Course Track & Prompts →sin²θ + cos²θ = 1⚡ Algebra 2 & Trig
Quadratic formula, polynomials, logarithms, unit circle, trig identities
Open Course Track & Prompts →lim(x→a) f(x)🎯 Pre-Calculus
Rational functions, vectors, parametric curves, sequences & series, intro to limits
Open Course Track & Prompts →dy/dx∫ AP Calculus (AB / BC)
Limits, chain rule, implicit differentiation, optimization, integration, series
Open Course Track & Prompts →z = (x - μ)/σ📊 Intro to Statistics
Normal distributions, z-scores, confidence intervals, linear regression
Open Course Track & Prompts →A = P(1 + r/n)ⁿᵗ💰 Everyday & Financial Math
Compound interest, mortgage payments, credit cards, budgeting, sales tax
Open Course Track & Prompts →CÉGEP & College
dy/dx📈 Calculus 1: Differential
Limits, continuity, product/quotient/chain rules, curve sketching, optimization, related rates
Open Course Track & Prompts →∫ f(x)dx∫ Calculus 2: Integral
Integration by parts, trig substitutions, partial fractions, revolution volumes
Open Course Track & Prompts →Ax = λx🔢 Linear Algebra & Vectors
3D geometric vectors, dot & cross products, lines & planes, matrices, Gauss-Jordan, determinants
Open Course Track & Prompts →MR = MC📊 Calculus for Social Science
Marginal revenue, marginal cost, profit optimization, demand elasticity, growth models
Open Course Track & Prompts →(I - A)X = D📑 Linear Algebra for Commerce
Systems of equations, matrix operations, Leontief economic input-output models, simplex method
Open Course Track & Prompts →p → q ≡ ¬p ∨ q💻 Math for Computer Science
Discrete math: truth tables, boolean logic, set theory, binary/hex, induction, graphs & trees
Open Course Track & Prompts →NPV = ∑ CFₜ/(1+r)ᵗ🏦 Business & Financial Math
Simple & compound interest, annuities, loan amortization, Net Present Value (NPV)
Open Course Track & Prompts →t = (x̄ - μ)/(s/√n)📊 Quantitative Methods & Stats
Normal distribution, hypothesis testing (z-test, t-test), chi-square, linear correlation & regression
Open Course Track & Prompts →N(t) = N₀ e⁻ᵏᵗ🫀 Math for Health & Life Sciences
Drug decay curves, half-life, logarithmic pH scaling, biostatistics, sensitivity, specificity
Open Course Track & Prompts →c² = a² + b² - 2ab cos C⚙️ Technical & Trades Math
Right-triangle trigonometry, oblique laws of sines/cosines, force vector resolution, conversions
Open Course Track & Prompts →University & Honours
∇f = λ∇g🌐 Multivariable Calculus (Calc 3)
Partial derivatives, gradient vectors, directional derivatives, double/triple integrals
Open Course Track & Prompts →∮ F · dr🌀 Vector Calculus & Fields
Vector fields, line integrals, work, surface flux, Green's theorem, Stokes' theorem, Divergence theorem
Open Course Track & Prompts →A = UΣVᵀ🔢 Linear Algebra & Matrices
Vector spaces, linear independence, basis, dimension, eigenvalues, eigenvectors, SVD
Open Course Track & Prompts →y'' + py' + qy = 0🔄 Differential Equations (ODEs)
First/second-order ODEs, undetermined coefficients, variation of parameters, Laplace transforms
Open Course Track & Prompts →∂u/∂t = α∇²u🌊 Partial Differential Equations
Heat equation, wave equation, Laplace equation, separation of variables, Fourier series
Open Course Track & Prompts →V - E + F = 2🌳 Discrete Math & Graph Theory
Combinatorics, generating functions, recurrence relations, graph coloring, paths
Open Course Track & Prompts →L(θ) = ∏ f(xᵢ)🎲 Probability & Math Statistics
Joint distributions, marginals, Central Limit Theorem, Maximum Likelihood Estimation
Open Course Track & Prompts →∮ f(z)dz = 2πi ∑Res⚙️ Engineering Applied Math
Complex analysis, residue theorem, Fourier transforms, transfer functions, state-space models
Open Course Track & Prompts →d(ln S) = (μ - ½σ²)dt + σdW📈 Financial & Actuarial Math
Brownian motion, Itô's lemma, Black-Scholes PDE, risk-neutral pricing
Open Course Track & Prompts →min f(x) s.t. g(x) ≤ 0🎯 Optimization & Operations
Linear programming, simplex algorithm, convex optimization, Karush-Kuhn-Tucker (KKT) conditions
Open Course Track & Prompts →xₙ₊₁ = xₙ - f/f'💻 Numerical Methods
Newton-Raphson method, LU decomposition, Runge-Kutta ODE solvers, numerical quadrature
Open Course Track & Prompts →|G| = |H|[G : H]🏛️ Abstract Algebra & Proofs
Proof techniques, group theory, subgroups, cyclic groups, Lagrange theorem, rings, fields
Open Course Track & Prompts →1-Page Exam Sheet: Integration by Parts
Always set u = x (Algebraic) before e^(2x) (Exponential) so u differentiates down to 1 in one step.
- 1. Set u = x → du = dx; set dv = e^(2x) dx → v = ½e^(2x)
- 2. Apply uv - ∫v du: ½x·e^(2x) - ∫ ½e^(2x) dx
- 3. Final Exam Answer: ½x·e^(2x) - ¼e^(2x) + C
Which function becomes "u" in ∫ x·ln(x) dx?
u = ln(x), because Logarithmic (L) beats Algebraic (A) in LIATE.
Why do students lose 2 points on the final step?
Forgetting to divide by the inner derivative (½ twice → ¼) and omitting + C.
When should you use Tabular Integration instead?
Whenever u is a polynomial (like x³) paired with sin(x) or e^(kx).