Drawn from the Foreword: (...) On the other hand, since much of the material in this volume seems suitable for inclusion in elementary courses, it may not be superfluous to point out that it is almost entirely self-contained. Even the basic facts about trigonometric functions are treated ab initio in Ch. II, according to Eisenstein's method. It would have been both logical and convenient to treat the gamma -function similarly in Ch. VII; for the sake of brevity, this has not been done, and a knowledge of some elementary properties of T(s) has been assumed. One further prerequisite in Part II is Dirichlet's theorem on Fourier series, together with the method of Poisson summation which is only a special case of that theorem; in the case under consideration (essentially no more than the transformation formula for the theta-function) this presupposes the calculation of some classical integrals. (...) As to the final chapter, it concerns applications to number theory (...).

Elliptic functions according to Eisenstein and Kronecker (Ergebnisse der Mathematik und ihrer Grenzgebiete)

Science & Math

Weil, André

Mathematics

Springer, Verlag

certain rational varieties (spaces of straight lines, of conics, etc. ), whereas we shall emphasize the geometry on an arbitrary variety, or at least on a variety without multiple points. The theory of intersection-multiplicities, however, occupies such a centrat position among the topics which constitute the founda tions of algebraic geometry, that a complete treatment of it necessarily supplies the tools by which many other such topics can be dealt with. In deciding be tween alternative methods of proof for the theorems in this book, consistency, and the possibility of applying these methods to further problems, have been the main considerations; for instance, one will find here all that is needed for the proof of Bertini's theorems, for a detailed ideal-theoretic study (by geometric means) of the quotient-ring of a simple point, for the elementary part of the theory of linear series, and for a rigorous definition of the various concepts of equivalence. In consequence, the author has deliberately avoided a few short cuts; this is not to say that there may not be many more which he did not notice, and which our readers, it is hoped, may yet discover. Our method of exposition will be dogmatic and unhistorical throughout, formal proofs, without references, being given at every step.

Oeuvres Scientifiques / Collected Papers: Volume 1 (1926-1951). Volume 2 (1951-1964). Volume 3 (1964-1978) (French, English and German Edition)

History

Europe

Springer

In the summer quarter of 1949, I taught a ten-weeks introductory course on number theory at the University of Chicago; it was announced in the catalogue as "Alge bra 251". What made it possible, in the form which I had planned for it, was the fact that Max Rosenlicht, now of the University of California at Berkeley, was then my assistant. According to his recollection, "this was the first and last time, in the his tory of the Chicago department of mathematics, that an assistant worked for his salary". The course consisted of two lectures a week, supplemented by a weekly "laboratory period" where students were given exercises which they were. asked to solve under Max's supervision and (when necessary) with his help. This idea was borrowed from the "Praktikum" of German universi ties. Being alien to the local tradition, it did not work out as well as I had hoped, and student attendance at the problem sessions so on became desultory. v vi Weekly notes were written up by Max Rosenlicht and issued week by week to the students. Rather than a literal reproduction of the course, they should be regarded as its skeleton; they were supplemented by references to stan dard text-books on algebra. Max also contributed by far the larger part of the exercises. None of ,this was meant for publication.

Number Theory for Beginners

The author, a mathematician whose horizons have never been limited to mathematics, recalls a career that led him to numerous continents: to Italy and Germany first of all; then to India where he lived and taught at a critical time in the history of that country, and where he met with Gandhi and Jawaharlal Nehru; to Russia when Stalinism seemed to be waning only to then rise up again with increased ferocity; to Princeton, the modern "clearing house" of mathematical ideas, called at times a mathematician's paradise; to a prison in Finland where, taken for a Soviet spy, he narrowly escaped execution; to France, where he was convicted for dodging his military obligations (the draft) and where, in the prison of Rouen, he had time to write one of his best mathematical works; to England, where he lived through the Battle of London before returning to France and then to the United States; and finally to Brasil, scene of the last of his vicissitudes, before returning permanently to the United States. Through these often picturesque episodes, the destiny of a mathematician is unfolded, of which perhaps the most salient event was his participation in the foundation of the Bourbaki Group, an auteur collectif , of a treatise that has long since become a classic.  Translated from the French by Jennifer Gage, with assistance of the author.

The Apprenticeship of a Mathematician

Birkhäuser Verlag

This book presents a historical overview of number theory. It examines texts that span some thirty-six centuries of arithmetical work, from an Old Babylonian tablet to Legendre’s Essai sur la Théorie des Nombres, written in 1798. Coverage employs a historical approach in the analysis of problems and evolving methods of number theory and their significance within mathematics. The book also takes the reader into the workshops of four major authors of modern number theory: Fermat, Euler, Lagrange and Legendre and presents a detailed and critical examination of their work.

Number Theory: An approach through history From Hammurapi to Legendre

History & Philosophy

Birkhauser

Number Theory: An Approach Through History from Hammurapi to Legendre (Modern Birkhäuser Classics Series)

Reference

This classic is one of the cornerstones of modern algebraic geometry. At the same time, it is entirely self-contained, assuming no knowledge whatsoever of algebraic geometry, and no knowledge of modern algebra beyond the simplest facts about abstract fields and their extensions, and the bare rudiments of the theory of ideals.

Foundations of Algebraic Geometry

Amer Mathematical Society

Mein Leben, oder zumindest das, was diesen Namen verdient -ein außer­ gewöhnlich glückliches Leben mit einigen Schicksalsschlägen -erstreckte sich auf die Zeit zwischen dem 6. Mai 1906, dem Tag meiner Geburt, und dem 24. Mai 1986, dem Todestag meiner Frau und Gefährtin Eveline. Wenn auf diesen Seiten, die ihr gewidmet sind, von meiner Frau recht wenig die Rede sein wird, heißt das nicht, daß sie in meinem Leben und in meinen Gedanken einen geringen Platz eingenommen hätte. Sie war im Gegenteil, beinahe vom Tag unserer ersten Begegnung an, so eng damit verwoben, daß von mir oder von ihr zu sprechen ein und dasselbe ist. Ihre Anwesenheit beziehungsweise ihre Abwesenheit bestimmte die Textur meines ganzen Lebens. Was könnte ich anderes dazu sagen, als daß unsere Ehe eine von jenen war, die La Rochefoucauld Lügen strafen? »Fulsere vere candidi mihi soles . . . . « Ebenso wird meine Schwester kaum erwähnt werden. Es ist schon lange her, daß ich meine Erinnerungen an sie Simone Petrement mitgeteilt habe, die sie in ihre gute Biographie La vie de Simone Weil einfließen ließ, wo man viele Einzelheiten über unsere gemeinsame Kindheit erfahren kann, und es wäre unnötig, dies hier zu wiederholen. Als Kinder waren wir unzertrennlich, aber ich war der große Bruder und sie die kleine Schwester. Später waren wir selten zusammen, und meist sprachen wir in scherzhaftem Ton miteinander, denn sie hatte ein fröhliches und humorvolles Naturell, wie alle, die sie kannten, bestätigt haben.

Lehr- und Wanderjahre eines Mathematikers: Aus dem Französischen von Theresia Übelhör (German Edition)

Biological Sciences

From reviews: "Extremely readable... rare testimony of a period of the history of 20th century mathematics. Includes very interesting recollections on the author's participation in the formation of the Bourbaki Group, tells of his meetings and conversations with leading mathematicians, reflects his views on mathematics. The book describes an extraordinary career of an exceptional man and mathematicians. Strongly recommended to specialists as well as to the general public." --EMS Newsletter (1992)

Biographies & Memoirs

Drawn from the Foreword: (...) On the other hand, since much of the material in this volume seems suitable for inclusion in elementary courses, it may not be superfluous to point out that it is almost entirely self-contained. Even the basic facts about trigonometric functions are treated ab initio in Ch. II, according to Eisenstein's method. It would have been both logical and convenient to treat the gamma -function similarly in Ch. VII; for the sake of brevity, this has not been done, and a knowledge of some elementary properties of T(s) has been assumed. One further prerequisite in Part II is Dirichlet's theorem on Fourier series, together with the method of Poisson summation which is only a special case of that theorem; in the case under consideration (essentially no more than the transformation formula for the theta-function) this presupposes the calculation of some classical integrals. (...) As to the final chapter, it concerns applications to number theory (...).

Elliptic Functions according to Eisenstein and Kronecker (Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge)

See the best price to sell, buy, or rent books by Weil, André. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Weil, André

See the best price to sell, buy, or rent books by Weil, André. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Elliptic functions according to Eisenstein and Kronecker (Ergebnisse der Mathematik und ihrer Grenzgebiete)

Oeuvres Scientifiques / Collected Papers: Volume 1 (1926-1951). Volume 2 (1951-1964). Volume 3 (1964-1978) (French, English and German Edition)

Number Theory for Beginners

The Apprenticeship of a Mathematician

Number Theory: An approach through history From Hammurapi to Legendre

Number Theory: An Approach Through History from Hammurapi to Legendre (Modern Birkhäuser Classics Series)

Foundations of Algebraic Geometry

Lehr- und Wanderjahre eines Mathematikers: Aus dem Französischen von Theresia Übelhör (German Edition)

The Apprenticeship of a Mathematician

Elliptic Functions according to Eisenstein and Kronecker (Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge)