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Title: Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics
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Manufacturer: Plume
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| Customer Reviews: |
| Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics by Plume Simply breathtaking |
Wauw, never thought the prime principles and theories behind it could be explained so well and most of all so easy to understand.
With this book, the writer makes one of the most mysterious and complex theories in mathematics easy to understand for the common man.
Simply great! |
| Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics by Plume An Excellence Introduction to the Riemann Hypothesis |
John Derbyshire's "Prime Obsession: Bernhard Riemannand the Greatest Unsolved Problem in Mathematics" has two parts. Part I is about The Prime Number Theorem and has ten chapters (Ch1-10). Part II is about The Riemann Hypothesis and has twelve chapters (Ch11-22). "The odd-numbered chapters...contain mathematical exposition...The even-numbered chapters offer historical and biographical background matter." One of the aims of the book is to explain the Riemann Hypothesis through elementary high school math. "...so if you don't understand the Hypothesis after finishing my book, you can be pretty sure you will never understand it."
Right at the first page of the book, the author introduced the origin of the Riemann Hypothesis. The hypothesis was first introduced by Bernhard Riemann's paper "On the Number of Prime Numbers Less Than a Given Quantity" in August 1859. The paper leads to the proof of the Prime Number Theorem (PNT) in 1896. PNT states that the number of prime numbers less than a given number x is approximated by x/ln(x). "If either...or...could have proved the truth of the [Riemann] Hypothesis, the PNT would have followed at once...They couldn't of course...The PNT [could] follows from a much weaker result...: All non-trivial zeros of the zeta function have real part less than one." Riemann Hypothesis is similar to the above weaker result: all non-trivial zeros of the zeta function have real part one-half. In 1914, Hardy proved that "there is infinity of non-trivial zeros...infinitely many of them have real part one-half." But "this did not settle the Hypothesis." Since then, mathematicians discovered or conjectured that the zeta function has relationships with the Mobius function, the J step function, the Li function, field theory, and with some Hermitian operator. The zeta function is also related to quantum mechanics through the Montgomery-Odlyzko Law (GUE operator). However, nobody is able to prove or disprove the hypothesis yet.
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| Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics by Plume My first review |
Really good book for beginners,it explains basic concepts for all audiences, the way of mixing history and concepts is original (i prefer The Music of the Primes: Searching to Solve the Greatest Mystery in Mathematics) , but sometimes slow for advanced readers.
ugly/strange typography of ecuations and errors. |
| Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics by Plume A wonderful read for the inclined |
| For the person with an interest in mathematics this book is a wonderful read. It is written for the general lay person, but I would generally recommend the book to someone who has already completed high school level calculus. The author does a wonderful job of breaking down the Riemann Hypothesis and presenting it in the easiest way possible. I preferred the actual math explanations more than the math history sections myself. The only real complaint I can make are the poorly presented graphs, which are often so small to make the axis or values unreadable. |
| Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics by Plume The calculation of the very first example is wrong! |
I just start reading this book. The writing is very good and easy to understand. However, I am upset by the fact that the author calculated wrongly the very first example he gave: the maximum length of the deck of cards.
The error started from the third card. The total length of the top three cards is (1 + 1/4 + 1/2) = 7/4. So the center of their gravity is (7/4)/2 = 7/8. This means that the third card can be pushed by (1 - 7/8) = 1/8 without falling, not 1/6 as stated by the author! The total overhang of the 52-card deck is 1/2 + 1/4 + 1/8 + ... + 1/(2^51). So we get the same series as the second example (the ruler working) given by the author. And with infinite number of cards, the lenght of the above series is 1!
The author wanted to use the example to introduce the harmonic series (1/2 + 1/3 + 1/4 + 1/5 + ...), which can go infinite given infinite cards. Unfortunately, he needs to find another one. |
| Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics by Plume Product Description |
| In 1859, Bernhard Riemann, a little-known thirty-two year old mathematician, made a hypothesis while presenting a paper to the Berlin Academy titled “On the Number of Prime Numbers Less Than a Given Quantity.” Today, after 150 years of careful research and exhaustive study, the Riemann Hyphothesis remains unsolved, with a one-million-dollar prize earmarked for the first person to conquer it. Alternating passages of extraordinarily lucid mathematical exposition with chapters of elegantly composed biography and history, Prime Obsession is a fascinating and fluent account of an epic mathematical mystery that continues to challenge and excite the world. |
| Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics by Plume Amazon.com |
| Bernhard Riemann was an underdog of sorts, a malnourished son of a parson who grew up to be the author of one of mathematics' greatest problems. In Prime Obsession, John Derbyshire deals brilliantly with both Riemann's life and that problem: proof of the conjecture, "All non-trivial zeros of the zeta function have real part one-half." Though the statement itself passes as nonsense to anyone but a mathematician, Derbyshire walks readers through the decades of reasoning that led to the Riemann Hypothesis in such a way as to clear it up perfectly. Riemann himself never proved the statement, and it remains unsolved to this day. Prime Obsession offers alternating chapters of step-by-step math and a history of 19th-century European intellectual life, letting readers take a breather between chunks of well-written information. Derbyshire's style is accessible but not dumbed-down, thorough but not heavy-handed. This is among the best popular treatments of an obscure mathematical idea, inviting readers to explore the theory without insisting on page after page of formulae. In 2000, the Clay Mathematics Institute offered a one-million-dollar prize to anyone who could prove the Riemann Hypothesis, but luminaries like David Hilbert, G.H. Hardy, Alan Turing, André Weil, and Freeman Dyson have all tried before. Will the Riemann Hypothesis ever be proved? "One day we shall know," writes Derbyshire, and he makes the effort seem very worthwhile. --Therese Littleton |
