1568811195
IR
EN-53619
انگلیسی
IR
Algebraic number theory and Fermat's last theorem
[Book]
/ Ian Stewart, David Tall
3rd ed.
Natick, Mass.
: AK Peters,
, c2002.
xix, 313 p. , ill. , 24 cm.
Rev. ed. of: Algebraic number theory. 2nd. 1987.
Electronic
Includes bibliographical references (p. 303-308) and index.
The Origins of Algebraic Number Theory -- Algebraic Methods -- Algebraic Background -- Rings and Fields -- Factorization of Polynomials -- Field Extensions -- Symmetric Polynomials -- Modules -- Free Abelian Groups -- Algebraic Numbers -- Conjugates and Discriminants -- Algebraic Integers -- Integral Bases -- Norms and Traces -- Rings of Integers -- Quadratic and Cyclotomic Fields -- Factorization into Irreducibles -- Historical Background -- Trivial Factorizations -- Factorization into Irreducibles -- Examples of Non-Unique Factorization into Irreducibles -- Prime Factorization -- Euclidean Domains -- Euclidean Quadratic Fields -- Consequences of Unique Factorization -- The Ramanujan-Nagell Theorem -- Ideals -- Historical Background -- Prime Factorization of Ideals -- The Norm of an Ideal -- Nonunique Factorization in Cyclotomic Fields -- Geometric Methods -- Lattices -- The Quotient Torus -- Minkowski's Theorem -- The Two-Squares Theorem -- The Four-Squares Theorem -- Geometric Representation of Algebraic Numbers -- The Space mathb f L[superscript st] -- Class-Group and Class-Number -- The Class-Group -- An Existence Theorem -- Finiteness of the Class-Group -- How to Make an Ideal Principal -- Unique Factorization of Elements in an Extension Ring -- Number-Theoretic Applications -- Computational Methods -- Factorization of a Rational Prime -- Minkowski's Constants -- Some Class-Number Calculations -- Kummer's Special Case of Fermat's Last Theorem -- Some History -- Elementary Considerations -- Kummer's Lemma -- Kummer's Theorem -- Regular Primes -- The Path to the Final Breakthrough -- The Wolfskehl Prize -- Other Directions -- Modular Functions and Elliptic Curves -- The Taniyama-Shimura-Weil Conjecture -- Frey's Elliptic Equation -- The Amateur who Became a Model Professional -- Technical Hitch -- Flash of Inspiration -- Elliptic Curves -- Review of Conics -- Projective Space -- Rational Conics and the Pythagorean Equation -- The Tangent/Secant Process -- Group Structure on an Elliptic Curve -- Applications to Diophantine Equations -- Elliptic Functions -- Trigonometry Meets Diophantus -- Elliptic Functions -- Legendre and Weierstrass -- Modular Functions -- The Frey Elliptic Curve -- The Taniyama-Shimura-Weil Conjecture -- Sketch Proof of Fermat's Last Theorem -- Recent Developments -- Quadratic Residues -- Quadratic Equations in Z[subscript m] -- The Units of Z[subscript m] -- Quadratic Residues -- Dirichlet's Units Theorem -- Logarithmic Space -- Embedding the Unit Group in Logarithmic Space -- Dirichlet's Theorem.
Algebraic number theory
Fermat's last theorem
E-BOOK
Stewart, Ian, 1945-
Tall, David Orme
Stewart, Ian, 1945- Algebraic number theory
ایران
1568811195.pdf
عادی
عادی
1568811195.pdf
متن
old catalog
e
BL
1
a
Y
