Algebra
Algebra studies mathematical structures such as groups, rings, fields, and vector spaces. It generalizes arithmetic and provides the language for modern mathematics.Key Topics
- Linear Algebra — vectors, matrices, linear transformations, eigenvalues
- Group Theory — groups, subgroups, homomorphisms, symmetry
- Ring Theory — rings, ideals, polynomial rings
- Field Theory — fields, extensions, Galois theory
- Vector Spaces — bases, dimension, inner product spaces
- Matrix Decompositions — LU, QR, SVD, eigendecomposition
- Systems of Equations — Gaussian elimination, rank, nullity
- Abstract Algebra Applications — coding theory, cryptography