48 lessons in Algebra

Variables & expressionsLinear equationsLinear inequalitiesReading $\in$ and $\subset$Set-builder & interval notationRatio, proportion & variationRate, work & mixture problemsReading $f(x)$FunctionsLinear models in contextSystems of equationsAbsolute value & piecewiseExponent rulesPolynomialsFactoring quadraticsSolving quadraticsCompleting the square & quadratic formulaQuadratic applicationsReading $\sum$ and $\prod$Vieta's formulasPolynomial long & synthetic divisionRational expressionsRadical expressions & equationsSurds: conjugates & denestingReading $f \circ g$ and $f^{-1}$Function composition & inversesExponential & logarithmic equationsChoosing a model: linear vs exponentialReading the arrow $\to$Arithmetic & geometric progressionsSequences & arithmetic/geometric seriesThe arithmetic, geometric & harmonic meansPartial fractionsProofs in algebra (selected)The AM–GM inequalityThe Cauchy–Schwarz inequalityThe rearrangement inequalityPower mean & Jensen's inequalityPascal's identity & binomial theorem proofMultinomial & exponential theoremsTheory of equations: roots & Descartes' ruleSymmetric polynomials & Newton's identitiesPolynomial GCD, resultants & discriminantsLagrange interpolation & finite differencesLinear recurrences & closed formsRoots of unityContinued fractions & convergentsFunctional equations

Built to be understood — and remembered.

Every idea is taught with motivation and a worked example before the drills, and an FSRS spaced-repetition engine schedules each review for the day its model predicts you would forget it. A short placement check finds what you already know, so you start Algebra exactly where it's useful.

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