A Mathematical Odyssey: Journey from the Real to the Complex 2014th Edition by Steven G. Krantz (PDF)

Description

Mathematics is a poem. It is a lucid, sensual, precise exposition of beautiful ideas directed to specific goals. It is worthwhile to have as broad a cross-section of mankind as possible be conversant with what goes on in mathematics. Just as everyone knows that the Internet is a powerful and important tool for communication, so everyone should know that the Poincaré conjecture gives us important information about the shape of our universe. Just as every responsible citizen realizes that the mass-production automobile was pioneered by Henry Ford, so everyone should know that the P/NP problem has implications for security and data manipulation that will affect everyone.This book endeavors to tell the story of the modern impact of mathematics, of its trials and triumphs and insights, in language that can be appreciated by a broad audience. It endeavors to show what mathematics means for our lives, how it impacts all of us, and what new thoughts it should cause us to entertain. It introduces new vistas of mathematical ideas and shares the excitement of new ideas freshly minted. It discusses the significance and impact of these ideas, and gives them meaning that will travel well and cause people to reconsider their place in the universe.Mathematics is one of mankind’s oldest disciplines. Along with philosophy, it has shaped the very modus of human thought. And it continues to do so. To be unaware of modern mathematics is to miss out on a large slice of life. It is to be left out of essential modern developments. We want to address this point, and do something about it. This is a book to make mathematics exciting for people of all interests and all walks of life. Mathematics is exhilarating, it is ennobling, it is uplifting, and it is fascinating. We want to show people this part of our world, and to get them to travel new paths.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐A real odyssey for the mind

⭐Having read a couple of books which Krantz wrote co-authored, I bought this book of Krantz and Parksbook “blind”, not knowing at all what was inside not even bothering to look at thetable of content. My spontaneous buy was triggeredby the book cover, which features the Mandelbulb set, the probably most beautifulmathematical object currently known and which is constructed like the Mandelbrot set but byreplacing polar coordinates with spherical coordinates in space.Having shown off this YouTube star in my own classes and lamented that despite its beauty,nothing mathematical is known yet, I was curious. Maybe a first breakthrough onestablishing some topological? The book does not provide that as the bulb is only mentionedon page 85. But the book provides plenty of stimulation and shows off some modernmathematics. For me it is a great background library book. It is accessible, still not dumbeddown. Countless many math books for a more general audience have been written recently.This is a valuable addition and it contains some unique gems and excellent references. I likethe style that the individual chapters can be read independently. So, the book can actually beread in a non-linear way. A nice addendum to the library.

⭐The preface states, “One of the main purposes of this book is to provide the uninitiated reader with some insights into modern mathematics”; and further on, “The book has few prereqisites beyond a good grounding in basic mathematics”. The authors modestly state, “This is likely to be a hard book to put down”.In the main, I would agree with these statements, and some chapters cover considerable ground (eg Ramsey Theory), accessible to anyone prepared to think.But a serious complaint is the sheer laziness with which this book has been cobbled together, with little regard to the reader’s needs. I’d better back this up:1 Considering the book’s avoidance of anything technically demanding or advanced, the ‘References and Further Reading’ sections at the end of each chapter are in urgent need of annotating. Examples abound, such as that following the ‘Special Relativity’ chapter, where the recommended reading includes Sean Carroll’s ‘Space-time and Geometry’, a tensor-laden general relativity text written for well-qualified university graduates, alongside David Mermin’s ‘It’s About Time’, a book suited to capable school pupils; both super books, but the “uninitiated reader” would be oblivious to the gigantic chasm between their mathematical requirements. Likewise, at the end of the chapter on wavelets, itself totally devoid of equations, we are recommended to follow up with Ingrid Daubechies’ classic text, ‘Ten Lecture on Wavelets’, which is pitched at the advanced graduate level! (No mention of the perfectly suitable ‘World According to Wavelets’ by Barbara Hubbard). In fact, leafing back through the book right now, I find the recommended reading lists utterly barmy: all fine books in themselves, but totally inappropriate here (Husemoller’s ‘Elliptic Curves’, Osserman’s ‘Survey of Minimal Surfaces’…. And I could list dozens more).2 Laziness? For example, there’s an anecdote about Erdos on page 63, only to be repeated on page 77. Several other sections caused similar irritation, giving the impression that the book had been rushed and not properly proof-read.There are also one or two technical quibbles, such as the argument establishing upper bounds for certain Ramsey numbers, which could be quite simply ‘tweaked’ to give half the values cited.The text and illustrations are clear, and the few graphics (eg the minimal surface of Costa, Hoffman and Meeks) attractive – no doubt tempting selling-points for the “uninitiated”.

⭐It seems to me must be good stuffs inside when I just make a browse of concepts

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