Cepts such as the topological invariants represented by the Euler characteristic and orientability A beautiful introduction to the theory of manifolds including concepts such as associated differentiation structures is also a real enjoyment to read Mind blowing facts such as the peculiar richness and complexity of the 4 dimensional space as opposed to all other dimensional situations are also presented beautifully By the way the four color problem is also nicely treated The final two chapters are nothing of particular brilliance but decently good anyway they explain Fermat s last theorem and some introductory concepts about the efficiency of algorithmsOverall a pretty good
overview of some selected recent in modern maths targeted at the competent amateur with some pretty good chapters 4 star This book sketches the beauty and wonders of mathematics L anno scorso Bollati Boringhieri ha molto opportunamente ripubblicato la seconda edizione di uesto saggio di Keith Devlin il cui titolo inglese che fa pi o meno Matematica la nuova et dell oro molto pi incisivo Il testo racconta alcune scoperte matematiche avvenute tra il 1960 e il 1995 Occhei racconta un termine un po fuorviante purtroppo la matematica che si fa oggi troppo astratta per poter essere spiegata anche A Chi Ha Una Cultura chi ha una cultura di base figuriamoci a lettori acculturati s ma non certo specialisti del campo Tanto per dare un idea nell introduzione Devlin spiega che ha dovuto chiedere consulenze ad alcuni suoi colleghi uello che per si pu fare e che Devlin ha fatto egregiamente dare un idea di come si arrivati ai problemi trattati nel libro dare una spiegazione dell enunciato del problema cosa che non sempre cos facile come nel caso dell Ultimo Teorema di Fermat e infine raccontare uali sono state le linee di attacco che hanno infine portato alla soluzione Il risultato finale un bell affresco che permette al lettore di comprendere come l avanzamento della matematica non sia un azione continua e lineare ma proceda in un certo senso come le altre scienze per tentativi ed errori e nuove idee prese da rami a prima vista scorrelati La traduzione di Annarosa Giannetti Agnese Manassero e Laura Servidei generalmente chiara anche per chi non ha una formazione matematica specifica peccato che nella riedizione non siano stati corretti alcuni refusi 1010 This is a great read for people with even the tiniest interest in mathematics It s precise and clearly writte. Lly accessible In this book he offers a glimpse of the extraordinary vistas and bizarre universes opened up by contemporary mathemati. Ent the full result can only be understood by specialists The resulting frustration "is compounded by the fact that the bibliographic references are very limited and unsatisfactory But this is "compounded by the fact that the bibliographic references are very limited and unsatisfactory But this is minor fault Let s get into the actual contents of this book after an initial introductory chapter about prime numbers and number theory there is a pretty nice chapter still at pretty introductory level unfortunately about axiomatic set theory and Cantor s famous continuum problem To be honest I was expecting detail here for example when talking about axiomatic set theories such as Zermelo Fraenkel the axiom of choice is not discussed and the axioms of the ZF theory itself are not discussed Either Real Pity As We Real pity as we dealing with the foundational basis of the whole of mathematics here There is then a section about complex numbers While complex numbers are explained in a reasonable way there is no complex analysis and the uaternions are touched only very briefly This is a real pity and a missed opportunity as complex analysis is one of the most beautiful as well as useful branches of Mathematics This is followed by a really nice chapter titled beauty from chaos which explains in a really beautiful and approachable way the concepts of fractional dimensions chaotic dynamics and the amazingly beauty of fractals The Menger Sponge D27268 an amazing object which has zero volume enclosed by an infinite surface area is also presented Fractals are not just beautiful but also useful and we can see examples of fractals in in the realms of engineering electronics chemistry medicine even urban planning and public policy We have then another very enjoyable chapter about the critically important to science in general not just maths concept of symmetry and symmetry groups The author even manages to explain at conceptual level and in a very approachable way the classification theorem of finite simple groups The monster sporadic simple group consisting of complex matrices of order 196833 is also explained Galois groups and the solution to the general uintic euation are also explained uite well There is then a very nice chapter about the famous Hilbert s Tenth Problem solution to Diophantine Euations The degree 25 prime generating polynomial discovered in 1977 is also explained This is followed by couple of very nice chapters about some fundamental concepts and results in topology where the author manages to beautifully explain in a clear and precise manner fundamental con. Dr Devlin's television appearances and popular GUARDIAN column have revealed his remarkable gift for making difficult topics beautifu. .INTRODUCTORY OVERVIEW OF SOME SELECTED RECENT
Nice general historical survey This is a book I
READ MOSTLY JUST FOR FUN AS WELL AS TOmostly just for fun as well as to about how interest in mathematics can be developed in hound studentsAlthough I have some grasp and appreciation of elementary mathematics having done the obligatory 10000 hours to This had a set of decent descriptions on the important open some are no open problems of mathematics The premise of the book was at least it appeared so to me that the problems and proofs would be described in a pop science ok pop maths way to an average skilled mathematics enthusiast I m well aware that this is an impossible task So enthusiast I m well aware that this is an impossible task So wonder I ended up with having a little bit knowledge on the peripheral aspects of the problems and their proofs However the initial chapters were easily comprehensible But when it comes to advanced topology and number theory things started to go out of hand from me As mentioned somewhere in the book the open problems seem to be deceptively simple and very inviting to be examined only later to be realized how complex they are in factSo the book is uite OK if ou are looking for the thrill of examining some tough problems without being insistent to understand them in detail In my opinion if Out of My Comfort Zone: The Autobiography you want to appreciate them for all the beauty thenou need to go through the proper proof explained in the reference books note to self KIV by the Stanford prof who just won the Carl Sagan Prize for popularizing science Un libro che riesce a descrivere perfettamente la bellezza della matematica This book represents a compendium of some of the major development in modern higher mathematics in areas such as number theory topology group theoryThis book is really good at conveying the fascinating and sometime totally unexpected inter connectedness between apparently unrelated fields in mathematics Moreover the author s love for mathematics as something not just extremely useful to progress but inherently beautiful and fun is visible and contagious What I like about this book is also that it goes into the math to a much significant extent than most popular science books et managing to keep things at a level sufficiently easy to understand The target audience is the competent maths amateur interested in the relatively recent say after WWII developments in higher mathematicsThe only issue I have is that the author in some cases gets so infuriatingly and tantalizingly close to the actual details of a major result and then it just closes with the statem. This lively and comprehensive new survey sets out to show just how mistaken people who think they can't enjoy mathematics really are.