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When Least Is Best By Paul Nahin BRAND NEW - Picture 1 of 1
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When Least Is Best By Paul Nahin BRAND NEW

Rich's Riches & Trinkets
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Located in: Lake Placid, New York, United States
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eBay item number:333253206520
Last updated on 27 Dec, 2021 23:44:01 GMTView all revisionsView all revisions

Item specifics

Condition
New: A new, unread, unused book in perfect condition with no missing or damaged pages. See the ...
ISBN
9780691130521

About this product

Product Identifiers

Publisher
Princeton University Press
ISBN-10
0691130523
ISBN-13
9780691130521
eBay Product ID (ePID)
59043562

Product Key Features

Number of Pages
392 Pages
Language
English
Publication Name
When Least Is Best : How Mathematicians Discovered Many Clever Ways to Make Things As Small (or As Large) As Possible
Publication Year
2007
Subject
History & Philosophy, Mathematical Analysis
Features
Revised
Type
Textbook
Subject Area
Mathematics
Author
Paul J. Nahin
Format
Perfect

Dimensions

Item Height
0.9 in
Item Weight
20 Oz
Item Length
9.1 in
Item Width
6.6 in

Additional Product Features

Intended Audience
College Audience
Reviews
"A valuable and stimulating introduction to problems that have fascinated mathematicians and physicists for millennia."-- D.R. Wilkins, Contemporary Physics, This book was terrific fun to read! I thought I would skim the chapters to write my review, but I was hooked by the preface, and read through the first 100 pages in one sitting. . . . [Nahin shows] obvious delight and enjoyment--he is having fun and it is contagious. -- Bonnie Shulman, MAA Online, Anyone with a modest command of calculus, a curiosity about how mathematics developed, and a pad of paper for calculations will enjoy Nahin's lively book. His enthusiasm is infectious, his writing style is active and fluid, and his examples always have a point. . . . [H]e loves to tell stories, so even the familiar is enjoyably refreshed. -- Donald R. Sherbert, SIAM Review, "This book was terrific fun to read! I thought I would skim the chapters to write my review, but I was hooked by the preface, and read through the first 100 pages in one sitting. . . . [Nahin shows] obvious delight and enjoyment--he is having fun and it is contagious." --Bonnie Shulman, MAA Online, [ When Least is Best is] a wonderful sourcebook from projects and is just plain fun to read. -- Choice, "A valuable and stimulating introduction to problems that have fascinated mathematicians and physicists for millennia." --D.R. Wilkins, Contemporary Physics, When Least is Bestis clearly the result of immense effort. . . . [Nahin] just seems to get better and better. . . . The book is really a popular book of mathematics that touches on a broad range of problems associated with optimization., When Least is Bestis clearly the result of immense effort. . . . [Nahin] just seems to get better and better. . . . The book is really a popular book of mathematics that touches on a broad range of problems associated with optimization. -- Dennis S. Bernstein, IEEE Control Systems Magazine, Anyone with a modest command of calculus, a curiosity about how mathematics developed, and a pad of paper for calculations will enjoy Nahin's lively book. His enthusiasm is infectious, his writing style is active and fluid, and his examples always have a point. . . . [H]e loves to tell stories, so even the familiar is enjoyably refreshed., "[ When Least is Best is] a wonderful sourcebook from projects and is just plain fun to read."-- Choice, [When Least is Bestis] a wonderful sourcebook from projects and is just plain fun to read. -- Choice, A valuable and stimulating introduction to problems that have fascinated mathematicians and physicists for millennia. -- D.R. Wilkins, Contemporary Physics, "Anyone with a modest command of calculus, a curiosity about how mathematics developed, and a pad of paper for calculations will enjoy Nahin's lively book. His enthusiasm is infectious, his writing style is active and fluid, and his examples always have a point. . . . [H]e loves to tell stories, so even the familiar is enjoyably refreshed."-- Donald R. Sherbert, SIAM Review, "Anyone with a modest command of calculus, a curiosity about how mathematics developed, and a pad of paper for calculations will enjoy Nahin's lively book. His enthusiasm is infectious, his writing style is active and fluid, and his examples always have a point. . . . [H]e loves to tell stories, so even the familiar is enjoyably refreshed." ---Donald R. Sherbert, SIAM Review, "This is a delightful account of how the concepts of maxima, minima, and differentiation evolved with time. The level of mathematical sophistication is neither abstract nor superficial and it should appeal to a wide audience." --Ali H. Sayed, University of California, Los Angeles, This book was terrific fun to read! I thought I would skim the chapters to write my review, but I was hooked by the preface, and read through the first 100 pages in one sitting. . . . ÝNahin shows¨ obvious delight and enjoyment--he is having fun and it is contagious. -- Bonnie Shulman "MAA Online", When Least is Best is clearly the result of immense effort. . . . [Nahin] just seems to get better and better. . . . The book is really a popular book of mathematics that touches on a broad range of problems associated with optimization., A valuable and stimulating introduction to problems that have fascinated mathematicians and physicists for millennia. ---D.R. Wilkins, Contemporary Physics, When Least is Best is clearly the result of immense effort. . . . [Nahin] just seems to get better and better. . . . The book is really a popular book of mathematics that touches on a broad range of problems associated with optimization. -- Dennis S. Bernstein, IEEE Control Systems Magazine, " When Least Is Best is an illustrative historical walk through optimization problems as solved by mathematicians and scientists. Although many of us associate solving optimization with calculus, Paul J. Nahin shows here that many key problems were posed and solved long before calculus was developed." --Mary Ann B. Freeman, Math Team Development Manager, Mathworks, A valuable and stimulating introduction to problems that have fascinated mathematicians and physicists for millennia., "A valuable and stimulating introduction to problems that have fascinated mathematicians and physicists for millennia." ---D.R. Wilkins, Contemporary Physics, "Nahin delivers maximal mathematical enjoyment with minimal perplexity and boredom. . . . [He lets] general readers in on the thrill of riding high-school geometry and algebra to breakthrough insights. . . . A refreshingly lucid and humanizing approach to mathematics."-- Booklist, " When Least is Best is clearly the result of immense effort. . . . [Nahin] just seems to get better and better. . . . The book is really a popular book of mathematics that touches on a broad range of problems associated with optimization."-- Dennis S. Bernstein, IEEE Control Systems Magazine, "This book was terrific fun to read!... ÝNahin shows¨ obvious delight and enjoyment--he is having fun and it is contagious." -- Bonnie Shulman, Anyone with a modest command of calculus, a curiosity about how mathematics developed, and a pad of paper for calculations will enjoy Nahin's lively book. His enthusiasm is infectious, his writing style is active and fluid, and his examples always have a point. . . . [H]e loves to tell stories, so even the familiar is enjoyably refreshed. ---Donald R. Sherbert, SIAM Review, Nahin delivers maximal mathematical enjoyment with minimal perplexity and boredom. . . . [He lets] general readers in on the thrill of riding high-school geometry and algebra to breakthrough insights. . . . A refreshingly lucid and humanizing approach to mathematics. -- Booklist, This book was terrific fun to read! I thought I would skim the chapters to write my review, but I was hooked by the preface, and read through the first 100 pages in one sitting. . . . [Nahin shows] obvious delight and enjoyment--he is having fun and it is contagious., "Nahin delivers maximal mathematical enjoyment with minimal perplexity and boredom. . . . [He lets] general readers in on the thrill of riding high-school geometry and algebra to breakthrough insights. . . . A refreshingly lucid and humanizing approach to mathematics." -- Booklist, Nahin delivers maximal mathematical enjoyment with minimal perplexity and boredom. . . . [He lets] general readers in on the thrill of riding high-school geometry and algebra to breakthrough insights. . . . A refreshingly lucid and humanizing approach to mathematics., When Least Is Bestis an illustrative historical walk through optimization problems as solved by mathematicians and scientists. Although many of us associate solving optimization with calculus, Paul J. Nahin shows here that many key problems were posed and solved long before calculus was developed., "This book was terrific fun to read! I thought I would skim the chapters to write my review, but I was hooked by the preface, and read through the first 100 pages in one sitting. . . . [Nahin shows] obvious delight and enjoyment--he is having fun and it is contagious."-- Bonnie Shulman, MAA Online, When Least is Best is clearly the result of immense effort. . . . [Nahin] just seems to get better and better. . . . The book is really a popular book of mathematics that touches on a broad range of problems associated with optimization. ---Dennis S. Bernstein, IEEE Control Systems Magazine, " When Least is Best is clearly the result of immense effort. . . . [Nahin] just seems to get better and better. . . . The book is really a popular book of mathematics that touches on a broad range of problems associated with optimization." ---Dennis S. Bernstein, IEEE Control Systems Magazine, This book was terrific fun to read! I thought I would skim the chapters to write my review, but I was hooked by the preface, and read through the first 100 pages in one sitting. . . . [Nahin shows] obvious delight and enjoyment--he is having fun and it is contagious. ---Bonnie Shulman, MAA Online, "Anyone with a modest command of calculus, a curiosity about how mathematics developed, and a pad of paper for calculations will enjoy Nahin's lively book. His enthusiasm is infectious, his writing style is active and fluid, and his examples always have a point. . . . [H]e loves to tell stories, so even the familiar is enjoyably refreshed." --Donald R. Sherbert, SIAM Review, " When Least is Best is clearly the result of immense effort. . . . [Nahin] just seems to get better and better. . . . The book is really a popular book of mathematics that touches on a broad range of problems associated with optimization." --Dennis S. Bernstein, IEEE Control Systems Magazine, "[ When Least is Best is] a wonderful sourcebook from projects and is just plain fun to read." -- Choice, "This book was terrific fun to read! I thought I would skim the chapters to write my review, but I was hooked by the preface, and read through the first 100 pages in one sitting. . . . [Nahin shows] obvious delight and enjoyment--he is having fun and it is contagious." ---Bonnie Shulman, MAA Online
Dewey Edition
23
Illustrated
Yes
Dewey Decimal
511/.66
Edition Description
Revised edition
Table Of Content
Preface xiii 1. Minimums, Maximums, Derivatives, and Computers 1 1.1 Introduction 1 1.2 When Derivatives Don't Work 4 1.3 Using Algebra to Find Minimums 5 1.4 A Civil Engineering Problem 9 1.5 The AM-GM Inequality 13 1.6 Derivatives from Physics 20 1.7 Minimizing with a Computer 24 2. The First Extremal Problems 37 2.1 The Ancient Confusion of Length and Area 37 2.2 Dido' Problem and the Isoperimetric Quotient 45 2.3 Steiner '"Solution" to Dido' Problem 56 2.4 How Steiner Stumbled 59 2.5 A "Hard "Problem with an Easy Solution 62 2.6 Fagnano' Problem 65 3. Medieval Maximization and Some Modern Twists 71 3.1 The Regiomontanus Problem 71 3.2 The Saturn Problem 77 3.3 The Envelope-Folding Problem 79 3.4 The Pipe-and-Corner Problem 85 3.5 Regiomontanus Redux 89 3.6 The Muddy Wheel Problem 94 4. The Forgotten War of Descartes and Fermat 99 4.1 Two Very Different Men 99 4.2 Snell' Law 101 4.3 Fermat, Tangent Lines, and Extrema 109 4.4 The Birth of the Derivative 114 4.5 Derivatives and Tangents 120 4.6 Snell' Law and the Principle of Least Time 127 4.7 A Popular Textbook Problem 134 4.8 Snell' Law and the Rainbow 137 5. Calculus Steps Forward, Center Stage 140 5.1 The Derivative:Controversy and Triumph 140 5.2 Paintings Again, and Kepler' Wine Barrel 147 5.3 The Mailable Package Paradox 149 5.4 Projectile Motion in a Gravitational Field 152 5.5 The Perfect Basketball Shot 158 5.6 Halley Gunnery Problem 165 5.7 De L' Hospital and His Pulley Problem, and a New Minimum Principle 171 5.8 Derivatives and the Rainbow 179 6. Beyond Calculus 200 6.1 Galileo'Problem 200 6.2 The Brachistochrone Problem 210 6.3 Comparing Galileo and Bernoulli 221 6.4 The Euler-Lagrange Equation 231 6.5 The Straight Line and the Brachistochrone 238 6.6 Galileo' Hanging Chain 240 6.7 The Catenary Again 247 6.8 The Isoperimetric Problem, Solved (at last!) 251 6.9 Minimal Area Surfaces, Plateau' Problem, and Soap Bubbles 259 6.10 The Human Side of Minimal Area Surfaces 271 7. The Modern Age Begins 279 7.1 The Fermat/Steiner Problem 279 7.2 Digging the Optimal Trench, Paving the Shortest Mail Route, and Least-Cost Paths through Directed Graphs 286 7.3 The Traveling Salesman Problem 293 7.4 Minimizing with Inequalities (Linear Programming) 295 7.5 Minimizing by Working Backwards (Dynamic Programming) 312 Appendix A. The AM-GM Inequality 331 Appendix B. The AM-QM Inequality, and Jensen' Inequality 334 Appendix C. "The Sagacity of the Bees" 342 Appendix D. Every Convex Figure Has a Perimeter Bisector 345 Appendix E. The Gravitational Free-Fall Descent Time along a Circle 347 Appendix F. The Area Enclosed by a Closed Curve 352 Appendix G. Beltrami 'Identity 359 Appendix H. The Last Word on the Lost Fisherman Problem 361 Acknowledgments 365 Index 367
Synopsis
Shows how life often works at the extremes - with values becoming as small (or as large) as possible - and how mathematicians over the centuries have struggled to calculate these problems of minima and maxima. This is the book on optimization for math enthusiasts of all backgrounds., What is the best way to photograph a speeding bullet? Why does light move through glass in the least amount of time possible? How can lost hikers find their way out of a forest? What will rainbows look like in the future? Why do soap bubbles have a shape that gives them the least area? By combining the mathematical history of extrema with contemporary examples, Paul J. Nahin answers these intriguing questions and more in this engaging and witty volume. He shows how life often works at the extremes--with values becoming as small (or as large) as possible--and how mathematicians over the centuries have struggled to calculate these problems of minima and maxima. From medieval writings to the development of modern calculus to the current field of optimization, Nahin tells the story of Dido's problem, Fermat and Descartes, Torricelli, Bishop Berkeley, Goldschmidt, and more. Along the way, he explores how to build the shortest bridge possible between two towns, how to shop for garbage bags, how to vary speed during a race, and how to make the perfect basketball shot.Written in a conversational tone and requiring only an early undergraduate level of mathematical knowledge, When Least Is Best is full of fascinating examples and ready-to-try-at-home experiments. This is the first book on optimization written for a wide audience, and math enthusiasts of all backgrounds will delight in its lively topics., What is the best way to photograph a speeding bullet? Why does light move through glass in the least amount of time possible? How can lost hikers find their way out of a forest? What will rainbows look like in the future? Why do soap bubbles have a shape that gives them the least area? By combining the mathematical history of extrema with contemporary examples, Paul J. Nahin answers these intriguing questions and more in this engaging and witty volume. He shows how life often works at the extremes--with values becoming as small (or as large) as possible--and how mathematicians over the centuries have struggled to calculate these problems of minima and maxima. From medieval writings to the development of modern calculus to the current field of optimization, Nahin tells the story of Dido's problem, Fermat and Descartes, Torricelli, Bishop Berkeley, Goldschmidt, and more. Along the way, he explores how to build the shortest bridge possible between two towns, how to shop for garbage bags, how to vary speed during a race, and how to make the perfect basketball shot. Written in a conversational tone and requiring only an early undergraduate level of mathematical knowledge, When Least Is Best is full of fascinating examples and ready-to-try-at-home experiments. This is the first book on optimization written for a wide audience, and math enthusiasts of all backgrounds will delight in its lively topics., By combining the mathematical history of extrema with contemporary examples, Nahin answers intriguing questions in this engaging and witty volume. He shows how life often works at the extremes--with values becoming as small (or as large) as possible--and how mathematicians over the centuries have struggled to calculate these problems of minima and maxima.
LC Classification Number
QA306.N34 2007

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Rich's Riches & Trinkets

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Joined Dec 1999
Registered as a private sellerThereby, consumer rights stemming from EU consumer protection law do not apply. eBay buyer protection still applies to most purchases.
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