Archive for October, 2010

IV.1 Algebraic Numbers by Barry Mazur, Presentation of Algebraic Numbers and Roots of Unity: Pages 326 – 327.

Friday, October 29th, 2010

Algebraic Numbers by Barry Mazur.

Presentation of Algebraic Numbers.

Roots of Unity.

IV.1 Algebraic Numbers by Barry Mazur, Algebraic Numbers and Algebraic Integers: Page 326.

Friday, October 22nd, 2010

Algebraic numbers by Barry Mazur.

Algebraic numbers and algebraic integers.

IV.1 Algebraic Numbers by Barry Mazur, Splitting Laws and the Race Between Residues and Nonresidues: Page 325.

Wednesday, October 20th, 2010

Algebraic Numbers by Barry Mazur.

Splitting laws and the race between residues and nonresidues.

IV.1 Algebraic Numbers by Barry Mazur: Page 325.

Tuesday, October 19th, 2010

Algebraic Numbers by Barry Mazur.

Representations of prime numbers by binary quadratic forms.

IV.1 Algebraic Numbers by Barry Mazur: Pages 322 – 324.

Monday, October 18th, 2010

Class numbers and the unique factorization property.

The elliptic modular function and the unique factorization property.

EXP(p√163) = 262,537,412,640,768,744 – ε with ε < .00000000000075 .

Using Mathematica:

n=N[E^(Pi*(163)^(1/2)),50]

2.6253741264076874399999999999925007259719818568888×1017

N[262537412640768744-n,50]

7.4992740280181431112×10-13

IV.1 Algebraic Numbers by Barry Mazur: Pages 317 – 322.

Friday, October 15th, 2010

Rings and Fields.

The Rings Rd of Quadratic Integers.

Binary Quadratic Forms and the Unique Factorization Property.

Class Numbers and the Unique Factorization Property.

IV: Mathematical Concepts, IV.1 Algebraic Numbers by Barry Mazur: Pages 315 – 317.

Thursday, October 14th, 2010

Mathematical Concepts.

Algebraic Numbers by Barry Mazur.

The Square Root of 2.

The Golden Mean.

Quadratic Irrationalities.

III.99 Zermelo-Fraenkel Axioms: Page 314.

Wednesday, October 13th, 2010

Zermelo-Fraenkel Axioms.

End of Section III Mathematical Concepts!

III.96 Vector Bundles, III.97 Von Neumann Algebras, III.98 Wavelets: Pages 313 – 314.

Tuesday, October 12th, 2010

Vector Bundles.

Von Neumann Algebras.

Wavelets.

III.94 Variational Methods by Lawrence C. Evans, III.95 Varieties: Pages 311 – 313.

Monday, October 11th, 2010

Variational Methods by Lawrence C. Evans.

Generalization: The Euler-Lagrange Equations.

Systems such as geodesics.

Higher dimensional problems, least area, the Euler-Lagrange equations and further issues in the calculus of variations.

The Laplacian in the non-linear Poisson equation.

Varieties.