Mathematics : History & Philosophy

Jeder kennt die Kreiszahl p = 3,14159, viele kennen auch e = 2,71828, die Basis der natrlichen Logarithmen, und die imaginre Einheit i. Und dann? Die viertwichtigste" Konstante ist die Eulersche Zahl g = 0,5772156, benannt nach dem genialen Leonhard Euler (1707-1783). p und e sind transzendent, aber bis heute ist unbekannt, ob g eine rationale Zahl ist. Das Buch lotet diese obskure" Konstante aus. Die Reise beginnt mit Logarithmen und der harmonischen Reihe. Es folgen Zeta-Funktionen und Eulers wunderbare Identitt, Bernoulli-Zahlen, Madelungsche Konstanten, Fettfinger in Wrterbchern, elende mathematische Wrmer und Jeeps in der Wste. Harmonien in der Geometrie, in der Musik und bei Primzahlen! Unterwegs begegnen wir Euklid und Tschebyschew, Napier und Kepler, Gau und Riemann, Hardy und Littlewood, den Hilbertschen Problemen, Hadamard und dem Primzahlsatz, Erdos und von Mangoldts expliziter Formel. Die Krnung ist die Riemannsche Vermutung, das bedeutendste ungelste Problem der Mathematik. Besser kann man nicht ber Mathematik schreiben, als dies Julian Havil in seinem Buch ber Gamma, die Euler-Konstante, tut. Wohl jeder Mathematikstudent kennt diese Zahl, aber was Havil an Zusammenhngen in den verschiedensten Mathematikgebieten dazu zu sagen hat ist spektakulr, und die Darstellung ist exzellent. Jeder Mathematik- und Physikstudent sollte dieses Buch lesen, und auch professionelle Mathematiker werden in dem Buch viel Neues finden. more...

Price: $39.95

Greek, Indian and Arabic Logic marks the initial appearance of the multi-volume Handbook of the History of Logic. Additional volumes will be published when ready, rather than in strict chronological order. Soon to appear are The Rise of Modern Logic: From Leibniz to Frege. Also in preparation are Logic From Russell to Gödel, The Emergence of Classical Logic, Logic and the Modalities in the Twentieth Century, and The Many-Valued and Non-Monotonic Turn in Logic. Further volumes will follow, including Mediaeval and Renaissance Logic and Logic: A History of its Central. In designing the Handbook of the History of Logic, the Editors have taken the view that the history of logic holds more than an antiquarian interest, and that a knowledge of logic's rich and sophisticated development is, in various respects, relevant to the research programmes of the present day. Ancient logic is no exception. The present volume attests to the distant origins of some of modern logic's most important features, such as can be found in the claim by the authors of the chapter on Aristotle's early logic that, from its infancy, the theory of the syllogism is an example of an intuitionistic, non-monotonic, relevantly paraconsistent logic. Similarly, in addition to its comparative earliness, what is striking about the best of the Megarian and Stoic traditions is their sophistication and originality. Logic is an indispensably important pivot of the Western intellectual tradition. But, as the chapters on Indian and Arabic logic make clear, logic's parentage extends more widely than any direct line from the Greek city states. It is hardly surprising, therefore, that for centuries logic has been an unfetteredly international enterprise, whose research programmes reach to every corner of the learned world. Like its companion volumes, Greek, Indian and Arabic Logic is the result of a design that gives to its distinguished authors as much space as would be needed to produce highly more...

Price: $185.00

Presents a comprehensive treatment of the history of Banach spaces and (abstract bounded) linear operators. This book talks about Banach space theory as a part of a broad mathematics context, using tools from such areas as set theory, topology, algebra, combinatorics, probability theory, logic, etc. more...

Price: $129.00

The Quine-Putnam indispensability argument in the philosophy of mathematics urges us to place mathematical entities on the same ontological footing as other theoretical entities indispensable to certain scientific theories. This text examines the issues. more...

Price: $41.00

In 1611, Johannes Kepler proposed that the best way to pack spheres as densely as possible was to pile them up in the same way that grocers stack oranges or tomatoes. This proposition, known as Kepler's Conjecture, seemed obvious to everyone except mathematicians, who seldom take anyone's word for anything. In the tradition of Fermat's Enigma , George Szpiro shows how the problem engaged and stymied many men of genius over the centuries, Sir Walter Raleigh, astronomer Tycho Brahe, Sir Isaac Newton, mathematicians C. F. Gauss and David Hilbert, and R. Buckminster Fuller, to name a few until Thomas Hales of the University of Michigan submitted what seems to be a definitive proof in 1998. more...

Price: $24.95