## Archive for July, 2010

### III.55 Measures: Pages 246 – 247.

Tuesday, July 20th, 2010

Measures

Desire for the additivity of the measure between disjoint sets.

Measurable, Borel and Lebesgue.

### III.54 Matroids by Dominic Welsh: Page 245.

Monday, July 19th, 2010

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.

### III.51 Local and Global in Number Theory, by Fernando Q. Gouvea, p-adic Numbers, The Local-Global Principle, III.52 The Mandelbrot Set, III.53 Manifolds: Pages 242 – 244.

Sunday, July 18th, 2010

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

The Local-Global Principle.

The Mandelbrot Set.

Manifolds.

### III.50 Linear Operators and Their Properties, Properties of Operators Defined on a Hilbert Space, III.51 Local and Global in Number Theory, by Fernando Q. Gouvea, Studying Functions Locally and Numbers are Like Functions: Pages 240 – 241.

Friday, July 16th, 2010

III.50 Linear Operators and Their Properties.

Properties of Operators Defined on a Hilbert Space.

Unitary and Orthogonal 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.

### III.48 Lie Theory by Mark Ronan, Classification of Lie Algebras, III.49 Linear and Nonlinear Waves and Solitons, by Richard S. Palais, The Korteweg-de Vries Equation, Some Model Equations, Split-Stepping, Solitons and Their Interactions, III.50 Linear Operators and Their Properties, Algebras of Operators: Pages 234 – 239.

Thursday, July 15th, 2010

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.

### III.48 Lie Theory by Mark Ronan, Classification of Lie Algebras: Pages 232 – 233.

Wednesday, July 14th, 2010

Lie Theory by Mark Ronan, Classification of Lie Algebras.

### III.48 Lie Theory by Mark Ronan, Lie Algebras: Page 231.

Tuesday, July 13th, 2010

Lie Theory by Mark Ronan, Lie Algebras.

### III.44 Knot Polynomials, W. B. R. Lickorish, HOMEFLY Calculations, Other Polynomial Invariants, Application to Alternating Knots, Physics, III.45 K-Theory, Lagrange Multipliers, III.46 The Leech Lattice, III.47 L-Functions by Kevin Buzzard, Packaging Number Sequences, Good Properties, Point, III.48 Lie Theory by Mark Ronan, Lie Groups: Pages 226 – 230.

Monday, July 12th, 2010

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

### III.44 Knot Polynomials, W. B. R. Lickorish, Knots and Links, The HOMEFLY Polynomial: Page 225.

Thursday, July 8th, 2010

Knot Polynomials, W. B. R. Lickorish.

The HOMEFLY Polynomial.

### III.36 The Heat Equation, Igor Rodnianski, III.37 Hilbert Spaces, III.38 Homology and Cohomology, III.39 Homotopy Groups, III.40 The Ideal Class Group, III.41 Irrational and Transcendental Numbers, Ben Green, III.42 Ising Model, III.43 Jordan Normal Form: Pages 216 – 224.

Wednesday, July 7th, 2010

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