Number-Crunching: Taming Unruly Computational Problems from Mathematical Physics to Science Fiction by Paul J. Nahin (PDF)

Description

More stimulating mathematics puzzles from bestselling author Paul NahinHow do technicians repair broken communications cables at the bottom of the ocean without actually seeing them? What’s the likelihood of plucking a needle out of a haystack the size of the Earth? And is it possible to use computers to create a universal library of everything ever written or every photo ever taken? These are just some of the intriguing questions that best-selling popular math writer Paul Nahin tackles in Number-Crunching. Through brilliant math ideas and entertaining stories, Nahin demonstrates how odd and unusual math problems can be solved by bringing together basic physics ideas and today’s powerful computers. Some of the outcomes discussed are so counterintuitive they will leave readers astonished.Nahin looks at how the art of number-crunching has changed since the advent of computers, and how high-speed technology helps to solve fascinating conundrums such as the three-body, Monte Carlo, leapfrog, and gambler’s ruin problems. Along the way, Nahin traverses topics that include algebra, trigonometry, geometry, calculus, number theory, differential equations, Fourier series, electronics, and computers in science fiction. He gives historical background for the problems presented, offers many examples and numerous challenges, supplies MATLAB codes for all the theories discussed, and includes detailed and complete solutions.Exploring the intimate relationship between mathematics, physics, and the tremendous power of modern computers, Number-Crunching will appeal to anyone interested in understanding how these three important fields join forces to solve today’s thorniest puzzles.

User’s Reviews

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

⭐This is an excellent author; interesting and entertaining. The illustrations depict the complexity and difficulty of problems that we have all heard about; but, haven’t had to deal with personally [unless you are a talented engineer / scientist]. The tools he uses to approach these problems are a highlight of the book — should you desire to tackle a difficult problem, you can make an enlightened choice from his experiments with different techniques.

⭐All of his books are great ! His books are somewhat like puzzle books but instead of a short answer, he works through the whole issue and presents the history, logic and mathematics. You learn alot from the way he works out these but I think he would admit there was a lot of thought in developing the analysis—both his and other authors [who he credits].I could not more highly recommend his books.

⭐Great Book! Anything written by Paul Nahin is just super. He gives detailed historical as well as mathematical background in all his books. I wish I had them when I was going to school in electrical engineering at Michigan State U. – Much easier learned when taught by Paul Nahin

⭐If you enjoy applied mathematics, MATLAB, fun with numbers, physics and electrical engineering, buy this book.You’ll appreciate his MATLAB treatment of the three body problem as well as his discussions of ladder networks.

⭐Kurt Vonnegut,

⭐– Question: If Farmer A can plant 300 potatoes an hour, and Farmer B can plant potatoes fifty percent faster, and Farmer C can plant potatoes one third as fast as farmer B, and 10,000 potatoes are to be planted to an acre, how many nine-hour days will it take Farmers A, B, and C, working simultaneously, to plant 25 acres? Answer: I think I’ll blow my brains out.That’s the opening quote. The author suggests that if your reaction was less extreme than Vonnegut’s, and you started working out an answer, then his book is probably for you! I’ve enjoyed his other books, about

⭐, and

⭐, so I tried out this one.The book has sample tricky problems involving boundary conditions, electric circuits, chaos theory, differential amplifiers, heat transfer, n-body problems, and predator-prey equations. These are all explained well.Unfortunately, the book isn’t really cutting edge. For example, page 329, on zeros of the Riemann Zeta function: “Trillions of complex zeros have been calculated since 1859, and every last one of them does indeed have a real part of 1/2.” The actual story is more recent. The Zetagrid project calculated 935.7 billion nontrivial zeros by the year 2004. Xavier Gourdon then found a much faster method, and calculated the first 10 trillion zeros that same year.The computers of today are roughly a billion times more powerful than computers of 1980 or earlier. Most of the book deals with problems solved by computers 1940-1980. Myself, I looked at the Mrs. Perkins Quilt problem, which involves cutting a square into a minimal number of smaller squares. I brought very little new to the problem, using the same 1940’s methods as the author describes in his book

⭐. However, I had a *hundred trillion* times as much computer power. Their old programs on my 2009-era computer vastly extended the known results. Any problem subject to computer attack that hasn’t been seriously studied in the past 20 years will yeild new results to anyone using a modern computer.I just reviewed

⭐, and in that book five college students and their programs found new discoveries on what could be folded from the Latin cross.Number-Crunching is good enough to recommend, but a follow-up book that only has stunning number-crunching results from the last decade would be appreciated.

⭐Great book….for math lovers 🙂

⭐a good read on Monte Carlo

⭐He can make quite difficult maths entertaining. I have previously preferred pure maths and especially number theory or combinatorics to exemplify the computer approach but someday we have to look at the real world! His examples of programs to crunch numbers are written in MATLAB but where I could understand the maths I found it an absorbing education to translate these into the free SageMath with its access to R (runif) for Monte Carlo ideas. A book I will come back to.

⭐Good book.

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