By Martin Aigner, Günter M. Ziegler, Karl H. Hofmann
Diese deutlich erweiterte dritte deutsche Auflage von "Das BUCH der Beweise" enthält fünf neue Kapitel, in denen es um Klassiker geht wie den "Fundamentalsatz der Algebra", um kombinatorisch-geometrische Zerlegungsprobleme, aber auch um Beweise aus letzter Zeit, etwa für die "Kneser-Vermutung" in der Graphentheorie.
Die Neuausgabe wartet auch mit weiteren Verbesserungen und Überraschungen auf - darunter ein neuer Beweis für "Hilberts drittes Problem".
Aus den Rezensionen der bisherigen Ausgaben:
"Ein prächtiges, äußerst sorgfältig und liebevoll gestaltetes Buch! Erdös hatte die Idee DES BUCHES, in dem Gott die perfekten Beweise mathematischer Sätze eingeschrieben hat. Das hier gedruckte Buch will eine "very modest approximation" an dieses BUCH sein.... Das Buch von Aigner und Ziegler ist gelungen ..." Mathematische Semesterberichte, November 1999
"Unermüdlich reiste Paul Erdös durch die Welt und stellte neue Theoreme auf. Jetzt haben zwei seiner Kollegen sein schönstes Werk vollendet: Das BUCH der Beweise - ein Feuerwerk mathematischer Geistesblitze. ......" Die Weltwoche 18. April 2002
"... Martin Aigner ... und Günter Ziegler referieren sympathisch einige dieser gottgefälligen Geistesblitze. ... Der Beweis selbst, seine Ästhetik, seine Pointe geht ins Geschichtsbuch der Königin der Wissenschaften ein. Ihre Anmut offenbart sich in dem gelungenen und geschickt illustrierten Buch über das BUCH. Um sie genießen zu können, lohnt es sich, das bißchen Mathe nachzuholen, das wir vergessen haben oder das uns von der Schule vorenthalten wurde." Die Zeit, 13.August 1998
...Hier ist es additionally, das BUCH der Beweise in der wunderbaren model von Martin Aigner und Günter Ziegler ....Wer (wie ich) bislang vergeblich versucht hat, einen Blick ins BUCH zu werfen, wird begierig in Aigners und Zieglers BUCH der Beweise schmökern. ... www.mathematik.de, Mai 2002
By Frank Morgan
Geometric degree idea presents the framework to appreciate the constitution of a crystal, a cleaning soap bubble cluster, or a universe. degree thought: A Beginner's advisor is vital to any pupil who desires to study geometric degree conception, and should entice researchers and mathematicians operating within the box. Morgan emphasizes geometry over proofs and technicalities offering a quick and effective perception into many features of the topic. New to the 4th edition:* ample illustrations, examples, workouts, and solutions.* the most recent effects on cleaning soap bubble clusters, together with a brand new bankruptcy on "Double Bubbles in Spheres, Gauss area, and Tori."* a brand new bankruptcy on "Manifolds with Density and Perelman's facts of the Poincar? Conjecture."* Contributions by means of undergraduates.
By William Aspray, Philip Kitcher
Goldfarb, "Poincaré opposed to the Logicists." Poincaré complained that makes an attempt to outline mathematics officially really presupposed it, for instance in utilizing the idea that "in no case" while defining 0. Goldfarb claims to "defeat" this objection as follows. "Poincaré is ... construing the venture of the rules of arithmetic as worrying with issues of the psychology of mathemtics and faulting logicism for buying it wrong." (p. 67). yet "it is a important guideline on antipshychologism that such stipulations are inappropriate to the rational grounds for a proposition. hence the objection is defeated." (p. 70). yet what in regards to the query, principal to Poincaré etc, of if it is attainable to minimize mathematics to good judgment? Goldfarb is seemingly satisfied to brush aside this as an "irrelevant" topic of "pshychologism."
Dauben, "Abraham Robinson and Nonstandard Analysis." i've got in basic terms learn the incompetent part on Lakatos (section 2) of this bankruptcy. the following Dauben deals a groundless and ideologically encouraged assault on Lakatos' paper on Cauchy. First there's the nonsense approximately Robinson's non-standard research. Dauben writes appropriately that: "There is not anything within the language or considered Leibniz, Euler, or Cauchy (to whom Lakatos devotes such a lot of his realization) that might cause them to early Robinsonians" (p. 180). this can be all actual, however it is usually actual that Lakatos by no means claimed differently, that is why Dauben needs to inn to underhand insinuations like this. Leaving this straw guy apart, Lakatos wrote accurately that: "The downfall of Leibnizian thought was once no longer seeing that it was once inconsistent, yet that it was once able merely of restricted development. It was once the heuristic strength of growth---and explanatory power---of Weierstrass's conception that caused the downfall of infinitesimals" (p. 181). Dauben foolishly claims that "Lakatos it sounds as if had now not made up his brain" and "even contradicts himself" (p. 182) in acknowledging that Leibnizian calculus is inconsistent. This is senseless. there's no contradiction. The inconsistency of Leibnizian calculus is even often called a truth within the first citation. Dauben additionally claims that Lakatos is incorrect simply because "the actual stumbling block to infinitesimals used to be their stated inconsistency" (p. 181). Why, then, did the calculus "stumble" in basic terms after 200 years? If Dauben thinks that classical infinitesimal calculus "stumbled" sooner than it had dried up, I recommend that he exhibits us what theorems it can have reached have been it no longer for this obstacle.
Askey, "How can mathematicians and mathematical historians support each one other?" such a lot of this text offers with haphazard and vague notes concerning Askey's personal historic examine and does not anything to reply to the identify query. Askey's easy point of view is that mathematicians are well-meaning saints who do not anything flawed yet that mathematical historians are incompetent and prejudiced in quite a few methods. for instance, Askey amuses himself with discovering error in Kline's heritage, and concludes that "it is apparent that mathematical historians desire all of the aid they could get" (p. 212). however it is senseless guilty historians, for Kline was once a mathematician. He got his Ph.D. in arithmetic and was once a professor of arithmetic at a arithmetic division all his profession. in other places Askey writes: "One can't shape an sufficient photograph of what's particularly very important at the foundation of present undergraduate curriculum and first-year graduate classes. particularly, i believe there's a ways an excessive amount of emphasis at the emergence of rigor and the principles of the maths in a lot of what's released at the heritage of mathematics." (p. 203). the most obvious lesson is for mathematicians to prevent educating awful classes that trick scholars into pondering that rigour is a big deal, and so forth. yet no. that may entail admitting a flaw one of the glorified mathematicians that Askey loves a lot. So as a substitute he nonsensically blames historians with out extra dialogue.
By Mircea V. Soare, Petre P. Teodorescu, Ileana Toma (auth.)
The current e-book has its resource within the authors’ desire to create a bridge among the mathematical and the technical disciplines, which desire a stable wisdom of a robust mathematical instrument. the need of such an interdisciplinary paintings drove the authors to submit a primary publication to this objective with Editura Tehnica, Bucharest, Romania.
The current booklet is a brand new, English version of the quantity released in 1999. It includes many advancements in regards to the theoretical (mathematical) info, in addition to new themes, utilizing enlarged and up-to-date references. merely usual differential equations and their options in an analytical body have been thought of, leaving apart their numerical approach.
The problem is to start with acknowledged in its mechanical body. Then the mathematical model is determined up, emphasizing at the one hand the actual significance enjoying the a part of the unknown functionality and however the legislation of mechanics that result in a standard differential equation or procedure. The solution is then bought through specifying the mathematical tools defined within the corresponding theoretical presentation. ultimately a mechanical interpretation of the answer is equipped, this giving upward thrust to a whole wisdom of the studied phenomenon.
The variety of functions used to be elevated, and plenty of of those difficulties look presently in engineering.
Mechanical and civil engineers, physicists, utilized mathematicians, astronomers and scholars. the must haves are classes of straight forward research and algebra, as given at a technical college. On a bigger scale, all these attracted to utilizing mathematical types and strategies in numerous fields, like mechanics, civil and mechanical engineering, and folks fascinated about educating or layout will locate this paintings indispensable.
By Howard Anton, Chris Rorres
Be aware: The textual content this is often used with is on the market the following: http://bibliotik.org/torrents/4530
This vintage therapy of linear algebra provides the basics within the clearest real way, analyzing simple rules via computational examples and geometrical interpretation. It proceeds from widely used suggestions to the strange, from the concrete to the summary. Readers regularly compliment this impressive textual content for its expository sort and readability of presentation.
* The functions model encompasses a wide array of fascinating, modern applications.
* transparent, obtainable, step by step reasons make the fabric crystal clear.
* tested the difficult thread of relationships among structures of equations, matrices, determinants, vectors, linear adjustments and eigenvalues.