## 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.

### 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.