Expressions & equations
Symbols, operations, equivalence, inequalities and solution sets.
MATHEMATICS · CORE SUBJECT
Algebra
Algebra studies mathematical structure through symbols, operations and relationships. Start with equations and functions, then move toward systems, polynomials, vectors, matrices and abstract algebra.
LEARNING PATH
Build algebra in layers.
Each layer introduces ideas that support the next one.
Functions & systems
Represent how quantities depend on each other and solve several constraints together.
Polynomials & linear algebra
Study roots, vector spaces, matrices, transformations and deeper algebraic structure.
CORE ALGEBRA
Start with the most useful topics.
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Equations
Linear, quadratic and higher-order equations, solution sets and solving strategies.
Explore equations →{ }Systems of equations
Linear and nonlinear systems, elimination, Gaussian methods and geometric meaning.
Explore systems →P(x)Polynomials
Factorisation, roots, division and polynomial structure.
Explore polynomials →≤Inequalities
Intervals, sign analysis, absolute values and systems of inequalities.
Explore inequalities →x²Expressions & transformations
Powers, fractions, radicals, identities and algebraic simplification.
Explore expressions →fFunctions
Domain, range, graphs, transformations, inverses and composition.
Explore functions →LINEAR ALGEBRA
Move from equations to spaces and transformations.
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Vectors & spaces
Vector spaces, basis, dimension, subspaces and coordinates.
Explore vectors →AMatrices & determinants
Rank, inverses, determinants, eigenvalues and eigenvectors.
Explore matrices →TLinear transformations
Mappings, kernels, images, diagonalisation and normal forms.
Explore transformations →BEST STARTING POINT
Learn the connected core first.
The strongest path currently available on Tabellenbuch is already connected from equation fundamentals through linear and quadratic equations to systems of linear equations.
ADVANCED ALGEBRA