Measures

Desire for the additivity of the measure between disjoint sets.

Measurable, Borel and Lebesgue.

Interesting scientific or quantitative thoughts or ideas!

Measures

Desire for the additivity of the measure between disjoint sets.

Measurable, Borel and Lebesgue.

Matroids

A finite set E with the properties:

(i) The empty set is independent

(ii) Every subset of an independent set is independent

(iii) If A and B are independent sets, with the number of elements of A being (at least) one less than the number of elements of B, then there is some x in B that is not in A such that A union {x} is also independent.

Property (iii) is the exchange axiom.

This idea may be applied to many vector as well as non-vector space problems.

Local and Global in Number Theory, by Fernando Q. Gouvea.

p-adic Numbers.

The Local-Global Principle.

The Mandelbrot Set.

Manifolds.

III.50 Linear Operators and Their Properties.

Properties of Operators Defined on a Hilbert Space.

Unitary and Orthogonal Maps.

Hermitian and Self-Adjoint Maps.

Properties of Matrices.

The Spectral Theorem.

Projections.

III.51 Local and Global in Number Theory, by Fernando Q. Gouvea.

Studying Functions Locally.

Numbers are Like Functions.

Lie Theory by Mark Ronan, Classification of Lie Algebras.

Linear and Nonlinear Waves and Solitons, by Richard S. Palais.

The Korteweg-de Vries Equation.

Some Model Equations.

Split-Stepping.

Solitons and Their Interactions.

Linear Operators and Their Properties.

Algebras of Operators.

Lie Theory by Mark Ronan, Classification of Lie Algebras.

Lie Theory by Mark Ronan, Lie Algebras.

Knot Polynomials, W. B. R. Lickorish, HOMEFLY Calculations

Other Polynomial Invariants

Application to Alternating Knots

Physics

K-Theory

Lagrange Multipliers

The Leech Lattice

L-Functions, Kevin Buzzard

Packaging number sequences

Good Properties

What is the point of L-Functions?

Lie Theory, by Mark Ronan

Lie Groups

Knot Polynomials, W. B. R. Lickorish.

Knots and Links.

The HOMEFLY Polynomial.

The Heat Equation, Igor Rodnianski

Hilbert Spaces

Homology and Cohomology

Homotopy Groups

The Ideal Class Group

Irrational and Transcendental Numbers, Ben Green

Ising Model

Jordan Normal Form