Residue Fields and Quadratic Forms

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Elliptical Distributions: Properties and Applications

Covers elliptical distributions, including properties, applications, and risk management implications.

Quadratic Forms: Definitions, Examples

Covers the definition of quadratic forms in R^n with examples in R^2 and R^3.

Irreducible Polynomials and Finite Fields

Explores irreducible polynomials, finite fields, and the construction of unique finite fields from irreducible polynomials.

The Quadratic Linking Degree

Introduces the quadratic linking degree in motivic knot theory, covering knot theory basics, algebraic geometry, and intersection theory.

Algebraic Closure of Qp

Covers the algebraic closure of Qp and the definition of p-adic complex numbers, exploring roots' continuous dependence on coefficients.

Frobenius Theorems in Number Theory

Explores Frobenius theorems in number theory, ideal class groups, norm properties, and geometry of numbers.

Quadratic Forms and Symmetries

Explores quadratic forms, symmetries, representations, and orthogonal sums in mathematics.

Iterative Methods for Linear Equations

Introduces iterative methods for linear equations, convergence criteria, gradient of quadratic forms, and classical force fields in complex atomistic systems.

Algebraic Curves: Normalization

Covers the normalization process of plane algebraic curves, focusing on irreducible polynomials and affine curves.

Decomposition & Inertia: Group Actions and Galois Theory

Explores decomposition groups, inertia subgroups, Galois theory, unramified primes, and cyclotomic fields in group actions and field extensions.