https://mathematics.wyattau.com Free mathematics study notes and revision guide with worked examples covering algebra, analysis, geometry, and more. en Wed, 22 Jul 2026 00:00:00 +0000 https://mathematics.wyattau.com/favicon.svg https://mathematics.wyattau.com https://mathematics.wyattau.com/1-abstract-algebra/groups-and-subgroups Definition of groups, examples of common groups, subgroups, subgroup tests, and closure properties with worked exercises. Tue, 21 Jul 2026 00:00:00 +0000 https://mathematics.wyattau.com/1-abstract-algebra/groups-and-subgroups https://mathematics.wyattau.com/1-abstract-algebra/normal-subgroups-and-quotient-groups Normal subgroups, coset decomposition, quotient groups, and the first isomorphism theorem with detailed proofs. Mon, 20 Jul 2026 00:00:00 +0000 https://mathematics.wyattau.com/1-abstract-algebra/normal-subgroups-and-quotient-groups https://mathematics.wyattau.com/2-linear-algebra/vector-spaces-and-linear-independence Axioms of vector spaces, spanning sets, linear independence, bases, dimension, and the replacement theorem. Sun, 19 Jul 2026 00:00:00 +0000 https://mathematics.wyattau.com/2-linear-algebra/vector-spaces-and-linear-independence https://mathematics.wyattau.com/2-linear-algebra/eigenvalues-and-diagonalisation Characteristic polynomial, algebraic and geometric multiplicity, diagonalisation conditions, and applications to matrix powers. Sat, 18 Jul 2026 00:00:00 +0000 https://mathematics.wyattau.com/2-linear-algebra/eigenvalues-and-diagonalisation https://mathematics.wyattau.com/3-real-analysis/sequences-and-limits Convergence of sequences, monotone convergence theorem, Bolzano-Weierstrass theorem, and Cauchy sequences with epsilon-delta proofs. Fri, 17 Jul 2026 00:00:00 +0000 https://mathematics.wyattau.com/3-real-analysis/sequences-and-limits https://mathematics.wyattau.com/3-real-analysis/continuity-and-differentiation Continuous functions on metric spaces, differentiability, the mean value theorem, and L'Hopital's rule with rigorous proofs. Thu, 16 Jul 2026 00:00:00 +0000 https://mathematics.wyattau.com/3-real-analysis/continuity-and-differentiation https://mathematics.wyattau.com/4-multivariable-calculus/partial-derivatives-and-the-chain-rule Partial derivatives, directional derivatives, gradient vectors, and the multivariable chain rule with worked examples. Wed, 15 Jul 2026 00:00:00 +0000 https://mathematics.wyattau.com/4-multivariable-calculus/partial-derivatives-and-the-chain-rule https://mathematics.wyattau.com/5-ordinary-differential-equations/first-order-differential-equations Separable equations, exact equations, integrating factors, and existence and uniqueness theorems for first order ODEs. Tue, 14 Jul 2026 00:00:00 +0000 https://mathematics.wyattau.com/5-ordinary-differential-equations/first-order-differential-equations https://mathematics.wyattau.com/6-complex-analysis/complex-numbers-and-functions Complex plane, modulus and argument, Euler's formula, elementary complex functions, and the Cauchy-Riemann equations. Mon, 13 Jul 2026 00:00:00 +0000 https://mathematics.wyattau.com/6-complex-analysis/complex-numbers-and-functions https://mathematics.wyattau.com/7-number-theory/modular-arithmetic-and-congruences Definition of congruence, Chinese remainder theorem, Fermat's little theorem, Euler's theorem, and applications to cryptography. Sun, 12 Jul 2026 00:00:00 +0000 https://mathematics.wyattau.com/7-number-theory/modular-arithmetic-and-congruences https://mathematics.wyattau.com/8-probability-and-statistics/probability-spaces-and-random-variables Axioms of probability, sigma-algebras, measurable spaces, discrete and continuous random variables, and probability mass and density functions. Sat, 11 Jul 2026 00:00:00 +0000 https://mathematics.wyattau.com/8-probability-and-statistics/probability-spaces-and-random-variables https://mathematics.wyattau.com/9-topology/topological-spaces-and-continuity Open sets, topologies generated by bases, continuous functions between topological spaces, homeomorphisms, and Hausdorff spaces. Fri, 10 Jul 2026 00:00:00 +0000 https://mathematics.wyattau.com/9-topology/topological-spaces-and-continuity https://mathematics.wyattau.com/10-measure-theory/lebesgue-measure-and-integration Lebesgue outer measure, measurable sets, the Lebesgue integral, convergence theorems, and comparison with Riemann integration. Thu, 09 Jul 2026 00:00:00 +0000 https://mathematics.wyattau.com/10-measure-theory/lebesgue-measure-and-integration https://mathematics.wyattau.com/11-functional-analysis/normed-vector-spaces-and-banach-spaces Norms, equivalence of norms, Banach spaces, bounded linear operators, the open mapping theorem, and the Hahn-Banach theorem. Wed, 08 Jul 2026 00:00:00 +0000 https://mathematics.wyattau.com/11-functional-analysis/normed-vector-spaces-and-banach-spaces https://mathematics.wyattau.com/12-differential-geometry/manifolds-and-tangent-spaces Smooth manifolds, charts and atlases, tangent vectors, the tangent bundle, and smooth maps between manifolds with worked examples. Tue, 07 Jul 2026 00:00:00 +0000 https://mathematics.wyattau.com/12-differential-geometry/manifolds-and-tangent-spaces https://mathematics.wyattau.com Free mathematics study notes covering abstract algebra, linear algebra, real analysis, multivariable calculus, ODEs, complex analysis, number theory, probability, topology, measure theory, functional analysis, and differential geometry. Mon, 06 Jul 2026 00:00:00 +0000 https://mathematics.wyattau.com