Algebraic Numbers by Barry Mazur.
Presentation of Algebraic Numbers.
Roots of Unity.
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, 2010IV.1 Algebraic Numbers by Barry Mazur, Algebraic Numbers and Algebraic Integers: Page 326.
Friday, October 22nd, 2010Algebraic 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, 2010Algebraic 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, 2010Algebraic 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, 2010Class 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, 2010Rings 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, 2010Mathematical 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, 2010Zermelo-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, 2010Vector Bundles.
Von Neumann Algebras.
Wavelets.
III.94 Variational Methods by Lawrence C. Evans, III.95 Varieties: Pages 311 – 313.
Monday, October 11th, 2010Variational 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.