I am a Research Assistant Professor of Computer Science at Stony Brook University learning/teaching/researching mathematics/algorithms/puzzles. In these fields, I have published a book, published 15+ papers in conferences/journals, been granted a US patent, won two Outstanding Paper Awards, taught 10+ courses in 25+ offerings, and have supervised 90+ master's/bachelor students. I am a puzzle addict involved in this field for 25 years and puzzles are my religion/God. Puzzles are the main form of supreme energy in this universe that can consistently give me infinite peace.
This continuously-updated free online book presents serious mathematical and algorithmic puzzles that are mostly counterintuitive. The presented puzzles are simultaneously entertaining, challenging, intriguing, and haunting. This book introduces counterintuitive mathematical ideas and revolutionary algorithmic insights from a wide variety of topics.
This book uses a puzzle-centric approach and multiple ways of attacking the same puzzle are presented which teach the application of elegant problem-solving strategies. Many of these counterintuitive solutions are intriguing to a degree that they shatter our preconceived notions, shake our long-held belief systems, debunk our fundamental intuitions, and finally rob us of sleep and haunt us for a lifetime. This book gives deep and generalized solutions to several puzzles, which you cannot find elsewhere.
Peter Winkler is famous for his collections of counterintuitive puzzles. Thousands of people, including me, have spent many sleepless nights trying to understand the mysteries in these puzzles, for which, I am forever grateful.
Haunting puzzles in the book include hats and infinity, all right or all wrong, comparing numbers version 1/2, wild guess, laser gun, precarious picture, names in boxes, sleeping beauty, and dot-town exodus.
Most puzzle books exclude counterintuitive puzzles for unknown reasons. So, many people incorrectly assume that counterintuitive puzzles are majorly found in paradoxes. Peter Winkler in this book shows that counterintuition can come from either puzzles or solutions or both, and they need not come from paradoxes alone.
Finally, reading Winkler's statements is an absolute delight due to its enjoyable and entertaining nature.
Research in mathematics is much more than solving puzzles, but most people will agree that solving puzzles is not just fun: it helps focus the mind and increases one's armory of techniques for doing mathematics. Mathematical Puzzles makes this connection explicit by isolating important mathematical methods, then using them to solve puzzles and prove a theorem.
Features
A collection of the world's best mathematical puzzles
Each chapter features a technique for solving mathematical puzzles, examples, and finally a genuine theorem of mathematics that features that technique in its proof
Puzzles that are entertaining, mystifying, paradoxical, and satisfying; they are not…
This is one of the first books in the entire puzzles literature that gave multiple detailed solutions to several beautiful mathematical puzzles.
Some of today's most famous puzzles were either popularized or introduced in this book. For example, truck in the desert, start of the snow, the rookie electrician, hole in a sphere, captivating problem in navigation, the hunter and his dog, the counterfeit coin, and common birthdays.
This book with its multiple-solutions feature taught me that we should never stop searching for more solutions as there can always be a better solution. Furthermore, when 1- or 2-paragraph solutions were the norm, this book illustrated the beauty of having multi-page detailed solutions.
Interestingly, this book is a crowd-written book as most of the puzzles and solutions presented in this book are contributed by readers of a magazine. This implies that it is possible to write great crowd-written books.
For two decades, an international readership of workers in applied mathematics submitted their favorite puzzles to a mid-twentieth-century column, The Graham Dial. This original collection features 100 of the publication's very best problems, with themes ranging from logic and engineering situations to number theory and geometry. Each problem was specifically selected for its widely differing modes of solution, and most include several methods of solution plus assessments of their efficacy. In checking their solutions against the book's, readers may find that their interest in the puzzles increases. The search for an answer can develop into a challenge to improve upon…
Anany Levitin introduced me to algorithmics – my second love (my first love is mathematics), through his legendary algorithmics textbook. He was one of my superheroes in my young adult life and he got me addicted to algorithms. His book is my favorite because it is beautifully organized based on design techniques, well-written, and uses nice puzzles to teach algorithms.
Levitin went much deeper and wrote this book on algorithmic puzzles. This book is the first mainstream book in the puzzle literature that taught beautiful algorithmic puzzles via various algorithm technique techniques. Levitin claimed several mathematical puzzles as algorithmic focusing on aspects of the solutions that are automatable.
Elegant puzzles (with extensive references) in this book that I have enjoyed include missionaries and cannibals, bridge crossing, circle of lights, MU puzzle, turning on a light bulb, chameleons, poisoned wine, game of life, twelve coins, fifteen puzzle, hats with numbers, and one coin for freedom.
Algorithmic puzzles are puzzles involving well-defined procedures for solving problems. This book will provide an enjoyable and accessible introduction to algorithmic puzzles that will develop the reader's algorithmic thinking.
The first part of this book is a tutorial on algorithm design strategies and analysis techniques. Algorithm design strategies - exhaustive search, backtracking, divide-and-conquer and a few others - are general approaches to designing step-by-step instructions for solving problems. Analysis techniques are methods for investigating such procedures to answer questions about the ultimate result of the procedure or how many steps are executed before the procedure stops. The discussion is an…
If you want a mathematical high, then the special theory of relativity is your cannabis. This out-of-the-world book by Tatsu Takeuchi gives us the key to the gateway to the heavens. This book beautifully teaches the special theory of relativity using hundreds of pleasing diagrams.
The special theory of relativity leads to the most counterintuitive concept that there is no "now". A's now can be the past of B's now and the future of C's now. This and several other counterintuitive ideas arise out of the fact that light travels at a finite speed. This book does an amazing job of teaching the mathematical theory that deals with time, space, and motion.
In many world religions there is a concept of heaven that is reachable after death. For puzzle addicts like me, the puzzle world itself is heaven, and I have been there an unlimited number of times when I am alive. This book is one way to go to that heaven.
Aimed at both physics students and non-science majors, this unique book explains Einstein's special theory of relativity pictorially, using diagrams rather than equations. The diagrams guide the reader, step-by-step, from the basics of relativity to advanced topics including the addition of velocities, Lorentz contraction, time dilation, the twin paradox, Doppler shift, and Einstein's famous equation E=mc(2). The distinctive figures throughout the book enable the reader to visualize the theory in a way that cannot be fully conveyed through equations alone. The illustrative explanations in this book maintain the logic and rigour necessary for physics students, yet are simple enough to…
This book is full of beautiful puzzles on a mathematical topic called pursuit evasion. Its author Paul Nahin has written tens of books in physics and mathematics.
Nahin's writing can be described as a captivating reading experience pulling readers into his world like a whirlpool. His appreciation of mathematics, physics, and the people who discover them is unmatchable. It seems like the physics of motion and the mathematics of calculus is inseparable, as can be witnessed in the book.
The calculus used in this book is heavy. Nevertheless, Nahin makes his readers fall in love with this big beast. Almost every puzzle in this book is aesthetically beautiful and gives readers a deep sense of satisfaction. My favorites include Lady in the Lake, and Lion and Man.
We all played tag when we were kids. What most of us don't realize is that this simple chase game is in fact an application of pursuit theory, and that the same principles of games like tag, dodgeball, and hide-and-seek are also at play in military strategy, high-seas chases by the Coast Guard, and even romantic pursuits. In Chases and Escapes, Paul Nahin gives us the first complete history of this fascinating area of mathematics, from its classical analytical beginnings to the present day. Drawing on game theory, geometry, linear algebra, target-tracking algorithms, and much more, Nahin also offers an…
When Lara was four years old, her father moved from Rochester, New York, to Anchorage, Alaska, a distance of over 4,000 miles. She spent her childhood chasing after him, flying a quarter of the way around the world to tug at the hem of his jacket.
Now that he is in his eighties, she contemplates her obligation to an absentee father. The Truth About Unringing Phones is an exploration of responsibility and culpability told in experimental and fragmented essays.
When Lara was four years old, her father moved from Rochester, New York, to Anchorage, Alaska, a distance of over 4,000 miles. She spent her childhood chasing after him, flying a quarter of the way around the world to tug at the hem of his jacket. Now that he is in his eighties, she contemplates her obligation to an absentee father.
The Truth About Unringing Phones: Essays on Yearning is an exploration of responsibility and culpability told in experimental and fragmented essays.
