Lesebuch Mathematik für das erste Studienjahr by Joachim Hilgert

By Joachim Hilgert

Dieses Buch ist eine Begleitlektüre zum ersten Jahr des Mathematikstudiums und darüber hinaus. Im Mittelpunkt stehen Motivation und Erläuterung der zentralen Begriffsbildungen anhand von Beispielen und exemplarischen Resultaten.

Ausgehend von den elementarsten und historisch frühesten mathematischen Konzepten des Messens und Zählens werden Sie zu modernen Begriffen wie Metriken, Maßen und Vektorräumen geführt, die dann zur Lösung konkreter Probleme einsetzt werden. Die Stoffauswahl ist so angelegt, dass die Querverbindungen zwischen den unterschiedlichen Anfängervorlesungen, die im regulären Studienbetrieb oft eher ausgeblendet werden, deutlich hervortreten.

Das Buch richtet sich an Leser, die mit der elementaren Mengenlehre als Sprache zur Beschreibung von mathematischen Inhalten sowie mit den reellen Zahlen als mathematischem Konzept vertraut sind.

Das entspricht etwa dem Kenntnisstand, der von Studierenden der Mathematik nach etwa einen Monat Studium erwartet wird.

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Visions in mathematics: GAFA 2000 Special vol. by Noga Alon, Jean Bourgain, Alain Connes, Misha Gromov, Vitali

By Noga Alon, Jean Bourgain, Alain Connes, Misha Gromov, Vitali D. Milman

"Visions in arithmetic - in the direction of 2000" used to be essentially the most impressive mathematical conferences in recent times. It used to be held in Tel Aviv from August twenty fifth to September third, 1999, and united a number of the prime mathematicians around the world. The ambitions of the convention have been to debate the significance, the tools, the earlier and the way forward for arithmetic as we input the twenty first century and to contemplate the relationship among arithmetic and similar components. The goals of the convention are mirrored within the current set of survey articles, documenting the country of paintings and destiny customers in lots of branches of arithmetic of present curiosity. this is often the second one a part of a two-volume set that may serve any study mathematician or complicated pupil as an summary and guide throughout the multifaceted physique of mathematical examine within the current and close to destiny.

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From Kant to Hilbert Volume 1: A Source Book in the by William Bragg Ewald

By William Bragg Ewald

Immanuel Kant's Critique of natural cause is greatly taken to be the place to begin of the trendy interval of arithmetic whereas David Hilbert was once the final nice mainstream mathematician to pursue very important 19th century rules. This two-volume paintings offers an summary of this crucial period of mathematical study via a gently selected collection of articles. they supply an perception into the rules of every of the most branches of arithmetic - algebra, geometry, quantity conception, research, good judgment, and set concept - with narratives to teach how they're associated. vintage works by way of Bolzano, Riemann, Hamilton, Dedekind, and Poincare are reproduced in trustworthy translations and plenty of choices from writers akin to Gauss, Cantor, Kronecker, and Zermelo are right here translated for the 1st time. the gathering is a useful resource for an individual wishing to achieve an figuring out of the root of recent arithmetic.

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Elliptic Curves: Diophantine Analysis by Serge Lang

By Serge Lang

It is feasible to write down forever on elliptic curves. (This isn't a threat.) We deal right here with diophantine difficulties, and we lay the rules, particularly for the speculation of critical issues. We evaluation in short the analytic conception of the Weierstrass functionality, after which care for the mathematics points of the addition formulation, over entire fields and over quantity fields, giving upward thrust to the idea of the peak and its quadraticity. We observe this to fundamental issues, overlaying the inequalities of diophantine approximation either at the multiplicative workforce and at the elliptic curve at once. therefore the booklet splits clearly in components. the 1st half offers with the normal mathematics of the elliptic curve: The transcendental parametrization, the p-adic parametrization, issues of finite order and the gang of rational issues, and the relief of convinced diophantine difficulties by way of the speculation of heights to diophantine inequalities concerning logarithms. the second one half offers with the proofs of chosen inequalities, at the least powerful adequate to procure the finiteness of vital points.

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Sophus Lie and Felix Klein: The Erlangen Program and Its by Lizhen Ji, Athanase Papadopoulos

By Lizhen Ji, Athanase Papadopoulos

The Erlangen software expresses a basic perspective at the use of teams and transformation teams in arithmetic and physics. This quantity is the 1st glossy complete booklet on that application and its influence in modern arithmetic and physics. Klein spelled out this system, and Lie, who contributed to its formula, is the 1st mathematician who made it powerful in his paintings. The theories that those authors constructed also are associated with their own historical past and to their family members with one another and with different mathematicians, incuding Hermann Weyl, Élie Cartan, Henri Poincaré, and so on. these types of features of the Erlangen application seem during this quantity. The publication is written via famous specialists in geometry, physics and the heritage of arithmetic and physics. A e-book of the eu Mathematical Society. disbursed in the Americas via the yank Mathematical Society.

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