An engaging collection of intriguing problems that shows you how to think like a mathematical physicist
Paul Nahin is a master at explaining odd phenomena through straightforward mathematics. In this collection of twenty-six intriguing problems, he explores how mathematical physicists think. Always entertaining, the problems range from ancient catapult conundrums to the puzzling physics of a very peculiar kind of glass called NASTYGLASS―and from dodging trucks to why raindrops fall slower than the rate of gravity. The questions raised may seem impossible to answer at first and may require an unexpected twist in reasoning, but sometimes their solutions are surprisingly simple. Nahin’s goal, however, is always to guide readers―who will need only to have studied advanced high school math and physics―in expanding their mathematical thinking to make sense of the curiosities of the physical world.
The problems are in the first part of the book and the solutions are in the second, so that readers may challenge themselves to solve the questions on their own before looking at the explanations. The problems show how mathematics―including algebra, trigonometry, geometry, and calculus―can be united with physical laws to solve both real and theoretical problems. Historical anecdotes woven throughout the book bring alive the circumstances and people involved in some amazing discoveries and achievements.
More than a puzzle book, this work will immerse you in the delights of scientific history while honing your math skills.
Author(s): Paul J. Nahin
Publisher: Princeton University Press
Year: 2018
Language: English
Pages: 282
Tags: Puzzle Book
Cover
Title
Copyright
Dedication
Contents
Preface
PART I. THE PROBLEMS
Problem 1. A Military Question: Catapult Warfare
Problem 2. A Seemingly Impossible Question: A Shocking Snow Conundrum
Problem 3. Two Math Problems: Algebra and Differential Equations Save the Day
Problem 4. An Escape Problem: Dodge the Truck
Problem 5. The Catapult Again: Where Dead Cows Can’t Go!
Problem 6. Another Math Problem: This One Requires Calculus
Problem 7. If Theory Fails: Monte Carlo Simulation
Problem 8. Monte Carlo and Theory: The Drunkard’s One-Dimensional Random Walk
Problem 9. More Monte Carlo: A Two-Dimensional Random Walk in Paris
Problem 10. Flying with (and against) the Wind: Math for the Modern Traveler
Problem 11. A Combinatorial Problem with Physics Implications: Particles, Energy Levels, and Pauli Exclusion
Problem 12. Mathematical Analysis: By Physical Reasoning
Problem 13. When an Integral Blows Up: Can a Physical Quantity Really Be Infinite?
Problem 14. Is This Easier Than Falling Off a Log? Well, Maybe Not
Problem 15. When the Computer Fails: When Every Day Is a Birthday
Problem 16. When Intuition Fails: Sometimes What Feels Right, Just Isn’t
Problem 17. Computer Simulation of the Physics of NASTYGLASS: Is This Serious? . . . Maybe
Problem 18. The Falling-Raindrop, Variable-Mass Problem: Falling Slower Than Gravity
Problem 19. Beyond the Quadratic: A Cubic Equation and Discontinuous Behavior in a Physical System
Problem 20. Another Cubic Equation: This One Inspired by Jules Verne
Problem 21. Beyond the Cubic: Quartic Equations, Crossed Ladders, Undersea Rocket Launches, and Quintic Equations
Problem 22. Escaping an Atomic Explosion: Why the Enola Gay Survived
Problem 23. “Impossible’’ Math Made Easy: Gauss’s Congruence Arithmetic
Problem 24. Wizard Math: Fourier’s Series, Dirac’s Impulse, and Euler’s Zeta Function
Problem 25. The Euclidean Algorithm: The Zeta Function and Computer Science
Problem 26. One Last Quadratic: Heaviside Locates an Underwater Fish Bite!
PART II. THE SOLUTIONS
Appendix 1. MATLAB, Primes, Irrationals, and Continued Fractions
Appendix 2. A Derivation of Brouncker’s Continued Fraction for 4/π
Appendix 3. Landen’s Calculus Solution to the Depressed Cubic Equation
Appendix 4. Solution to Lord Rayleigh’s Rotating-Ring Problem of 1876
Acknowledgments
Index
Also by Paul J. Nahin
