Mathematics and Its History by John Stillwell

By John Stillwell

From the studies of the second one edition:

"This e-book covers many attention-grabbing issues now not frequently lined in a gift day undergraduate direction, in addition to convinced easy themes resembling the advance of the calculus and the answer of polynomial equations. the truth that the subjects are brought of their historic contexts will allow scholars to raised savour and comprehend the mathematical rules involved...If one constructs an inventory of subject matters imperative to a heritage path, then they'd heavily resemble these selected here."

(David Parrott, Australian Mathematical Society)

"The book...is awarded in a full of life sort with no pointless aspect. it's very stimulating and should be preferred not just by means of scholars. a lot cognizance is paid to difficulties and to the advance of arithmetic earlier than the top of the 19th century... This ebook brings to the non-specialist attracted to arithmetic many fascinating effects. it may be prompt for seminars and may be loved by way of the wide mathematical community."

(European Mathematical Society)

"Since Stillwell treats many issues, so much mathematicians will research much from this publication in addition to they're going to locate friendly and quite transparent expositions of customized fabrics. The e-book is offered to scholars that experience already skilled calculus, algebra and geometry and should supply them a superb account of ways different branches of arithmetic interact."

(Denis Bonheure, Bulletin of the Belgian Society)

This 3rd version comprises new chapters on basic teams and combinatorics, and new sections on a number of subject matters, together with the Poincare conjecture. The publication has additionally been enriched by means of further exercises.

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Unsolved Problems in Number Theory by Richard Guy

By Richard Guy

Mathematics is saved alive via the looks of latest unsolved difficulties, difficulties posed from inside arithmetic itself, and in addition from the expanding variety of disciplines the place arithmetic is utilized. This ebook presents a gentle provide of simply understood, if no longer simply solved, difficulties that are thought of in various depths through mathematicians in any respect degrees of mathematical maturity.

For this re-creation, the writer has integrated new difficulties on symmetric and uneven primes, sums of upper powers, Diophantine m-tuples, and Conway’s RATS and palindromes. the writer has additionally integrated an invaluable new characteristic on the finish of a number of of the sections: lists of references to OEIS, Neil Sloane’s on-line Encyclopedia of Integer Sequences.

About the 1st Edition:

"…many gifted younger mathematicians will write their first papers beginning out from difficulties present in this book."

- András Sárközi, MathSciNet

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Some famous problems of the theory of numbers by G. H. (Godfrey Harold) Hardy

By G. H. (Godfrey Harold) Hardy

Initially released in 1920. This quantity from the Cornell collage Library's print collections was once scanned on an APT BookScan and switched over to JPG 2000 layout by means of Kirtas applied sciences. All titles scanned conceal to hide and pages may well comprise marks notations and different marginalia found in the unique quantity.

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Nombre et répartition de points de hauteur bornée by Emmanuel Peyre (ed.)

By Emmanuel Peyre (ed.)

"Ce quantity est issu de deux séminaires qui ont ecu lieu en avril et en mai 1996".- Préf.
Articles en français ou en anglais ; résumés en français et en anglais.

4ème de couverture:

Si les issues rationnels d'une variété définie sur un corps de
nombres sont denses pour l. a. topologie de Zariski, il est naturel
de munir cette variété de hauteurs qui, du element de vue de los angeles
géométrie d'Arakelov, s'interprètent comme degrés
d'intersection avec des fibres en droites munis de métriques. L'objectif est
alors d'étudier de manière asymptotique l'ensemble des issues
dont los angeles hauteur est inférieure à un nombre réel donné, et cela en
des termes aussi géométriques que attainable.
Ce quantity est issu de deux séminaires qui ont european lieu en avril et
en mai 1996. Il contient des articles de Slater et Swinnerton-
Dyer, de Heath-Brown, de Fouvry et de los angeles Bretèche centrés sur
le cas des surfaces cubiques, un texte de Billard sur les modèles
minimaux des surfaces rationnelles, ainsi que des contributions
de Salberger, de Peyre et de Batyrev et Tschinkel dont le
principal objet est l'interprétation du terme dominant dans l'étude
asymptotique du nombre de issues de hauteur bornée.

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Arithmetic Geometry: Conference on Arithmetic Geometry With by Conference on Arithmetic Geometry With an Emphasis on

By Conference on Arithmetic Geometry With an Emphasis on Iwasawa Theory, Nancy Childress, John W. Jones

This booklet resulted from a examine convention in mathematics geometry held at Arizona kingdom college in March 1993. The papers describe very important contemporary advances in mathematics geometry. numerous articles care for p-adic modular kinds of half-integral weight and their roles in mathematics geometry. the amount additionally comprises fabric at the Iwasawa conception of cyclotomic fields, elliptic curves, and serve as fields, together with p-adic L-functions and p-adic peak pairings. different articles concentrate on the inverse Galois challenge, fields of definition of abelian kinds with actual multiplication, and computation of torsion teams of elliptic curves. the quantity additionally encompasses a formerly unpublished letter of John Tate, written to J.-P. Serre in 1973, touching on Serre's conjecture on Galois representations. With contributions by way of many of the prime specialists within the box, this booklet offers a glance on the state-of-the-art in mathematics geometry.

Readership: Researchers and complicated graduate scholars operating in quantity thought and mathematics geometry.

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Number Theory 2: Introduction to Class Field Theory by K. Kato

By K. Kato

This booklet, the second one of 3 comparable volumes on quantity idea, is the English translation of the unique eastern e-book. the following, the belief of sophistication box idea, a spotlight in algebraic quantity conception, is first defined with many concrete examples. a close account of proofs is punctiliously exposited within the ultimate bankruptcy. The authors additionally clarify the local-global technique in quantity concept, together with using ideles and adeles. easy homes of zeta and $L$-functions are proven and used to end up the leading quantity theorem and the Dirichlet theorem on major numbers in mathematics progressions. With this booklet, the reader can benefit from the fantastic thing about numbers and procure primary wisdom of recent quantity concept. the interpretation of the 1st quantity used to be released as quantity conception 1: Fermat's Dream, Translations of Mathematical Monographs (Iwanami sequence in smooth Mathematics), vol. 186, American Mathematical Society, 2000.

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Problems and Theorems in Analysis: Theory of Functions. by Polya G.

By Polya G.

From the experiences: "... long ago, extra of the major mathematicians proposed and solved difficulties than this day, and there have been challenge departments in lots of journals. Pólya and Szego should have combed the entire huge challenge literature from approximately 1850 to 1925 for his or her fabric, and their choice of the easiest in research is a background of lasting worth. The paintings is unashamedly dated. With few exceptions, all of its fabric comes from sooner than 1925. we will be able to pass judgement on its classic via a quick examine the writer indices (combined)"

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Pi and the AGM: A Study in Analytic Number Theory and by Jonathan M. Borwein

By Jonathan M. Borwein

Offers new learn revealing the interaction among classical research and sleek computation and complexity idea. in detail interwoven threads run even though the textual content: the arithmetic-geometric suggest (AGM) new release of Gauss, Lagrange, and Legendre and the calculation of pi[l.c. Greek letter]. those threads are carried in 3 instructions. the 1st results in nineteenth century research, specifically, the transformation thought of elliptic integrals, which necessitates a quick dialogue of such subject matters as elliptic integrals and services, theta features, and modular features. the second one takes the reader into the area of analytic complexity - simply how intrinsically tricky is it to calculate algebraic features, basic services and constants, and the wide-spread features of mathematical physics? The solutions are fabulous, for the established tools are usually faraway from optimum. The 3rd course leads via functions and ancillary fabric - fairly the wealthy interconnections among the functionality conception and the quantity conception. incorporated are Rogers-Ramanujan identities, algebraic sequence for pi[l.c. Greek letter], effects on sums of 2 and 4 squares, the transcendence of pi[l.c. Greek letter] and e[ital.], and a dialogue of Madelung's consistent, lattice sums, and elliptic invariants. workouts.

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BASIC NUMBER THEORY by ANDRE WEIL

By ANDRE WEIL

From the experiences: "L.R. Shafarevich confirmed me the 1st version […] and acknowledged that this booklet could be any longer the publication approximately type box conception. in reality it really is via a ways the main entire therapy of the most theorems of algebraic quantity thought, together with functionality fields over finite consistent fields, that seemed in ebook form." Zentralblatt MATH

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