Here are 100 books that How to Solve It fans have personally recommended if you like
How to Solve It.
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I’m a professor of computer science at Oregon State University. My research focus is on programming languages, but I also work on computer science education and outreach. I grew up in Germany and moved to the United States in 2000. Since computer science is a fairly new and not widely understood discipline, I am interested in explaining its core ideas to the general public. I believe that in order to attract a more diverse set of people to the field we should emphasize that coding is only a small part of computer science.
This book is not about computing, but it is relevant in an indirect way. I love this book, since it is written in such an engaging style and illustrates with many examples that math is not a dry subject to be practiced only by mathematicians but helps everyone to solve real-world problems. The book shows how important it is to be precise in describing problems and that applying a little mathematical rigor goes a long way in solving them. Ellenberg describes mathematics as the “extension of common sense by other means.” In a similar way, I view computer science as the extension of problem-solving methods (aka “algorithms”) by other means.
"Witty, compelling, and just plain fun to read . . ." -Evelyn Lamb, Scientific American
The Freakonomics of math-a math-world superstar unveils the hidden beauty and logic of the world and puts its power in our hands
The math we learn in school can seem like a dull set of rules, laid down by the ancients and not to be questioned. In How Not to Be Wrong, Jordan Ellenberg shows us how terribly limiting this view is: Math isn't confined to abstract incidents that never occur in real life, but rather touches everything we do-the whole world is shot through…
Most of my books (101 Philosophy Problems, Wittgenstein's Beetle, Critical Thinking for Dummies, and so on) are on thinking skills, in the broad sense. However, I'm always a bit uncomfortable when I'm presented as an expert on thinking, as people tend to imagine I must have some brainy strategies for thinking better when my interest is also in the ways we "think badly." Because logic is really a blunt tool, compared to the brilliant insights that come with intuition. Yet how do you train your intuition? So the books I've chosen here are all ones that I've found don't so much tell you how to think, but actually get you thinking. And that's always been my aim in my books too.
Raymond Smullyan is a riddler, a puzzler, well-known for various Knights and Knaves puzzles, a type of logic game where some characters can only answer questions truthfully, and others only falsely. However, I recommend this book as here he offers not only logical tricks but many insights too. One section offers the World's shortest explanation of Gödel's theorem which is a magnificent achievement but frankly, reminds me why I like long explanations sometimes.
Basically, this is an examination of boolean logic, which is (rather boringly) a branch of algebra in which all operations are either true or false, and relationships are expressed with logical operators such as and, or, or not. So it’s serious stuff, but also pretty funny along the way.
"The most original, most profound, and most humorous collection of recreational logic and math problems ever written." — Martin Gardner, Scientific American "The value of the book lies in the wealth of ingenious puzzles. They afford amusement, vigorous exercise, and instruction." — Willard Van Orman Quine, The New York Times Book Review If you're intrigued by puzzles and paradoxes, these 200 mind-bending logic puzzles, riddles, and diversions will thrill you with challenges to your powers of reason and common sense. Raymond M. Smullyan — a celebrated mathematician, logician, magician, and author — presents a logical labyrinth of more than 200…
I became a scientist because I enjoyed the puzzles in Scientific American. I loved the notion that through mere thought, one could solve a question that at first glance seemed impossible to solve. When I had to design methods to detect ephemeral failures in electronic circuits underlying a mainframe computer, I created a puzzle having occasional liars. When I thought about ways to understand global wars, I constructed a puzzle about bullies in a playground. Some of my puzzles have been very computational, some purely paper and pencil. Over the years, my puzzles have appeared in Scientific American, Dr. Dobb’s Journal, and the Communications of the ACM.
Abraham Lincoln famously had little formal education but was capable of sophisticated logical thinking in his arguments. He credits his ability to form his arguments to his encounter with Euclid’s writings about geometry. He felt in awe by the notion of “demonstration” and went on to apply that notion to his compelling arguments about the injustice and hypocrisy of slavery.
This volume presents nearly 250 of Lincoln's most important speeches, state papers, and letters in their entirety. Here are not only the masterpieces,the Gettysburg Address, the Inaugural Addresses, the 1858 Republican Convention Speech, the Emancipation Proclamation,but hundreds of lesser-known gems. Alfred Kazin has written that Lincoln was "not just the greatest writer among our Presidents . . . but the most telling and unforgettable of all American'public' writer-speakers," and it's never been cleaner than in this comprehensive edition.
I became a scientist because I enjoyed the puzzles in Scientific American. I loved the notion that through mere thought, one could solve a question that at first glance seemed impossible to solve. When I had to design methods to detect ephemeral failures in electronic circuits underlying a mainframe computer, I created a puzzle having occasional liars. When I thought about ways to understand global wars, I constructed a puzzle about bullies in a playground. Some of my puzzles have been very computational, some purely paper and pencil. Over the years, my puzzles have appeared in Scientific American, Dr. Dobb’s Journal, and the Communications of the ACM.
Peter Winkler is an outstanding theoretical computer scientist, which is another way of saying that he is a mathematician who loves combinatorics and logic. He brings the precision and clarity of a mathematician to both the presentation and the solutions of his puzzles. The book consists of great puzzles from the centuries. Professor Winkler has excellent taste.
Collected over several years by Peter Winkler, of Bell Labs, dozens of elegant, intriguing challenges are presented in Mathematical Puzzles. The answers are easy to explain, but without this book, devilishly hard to find. Creative reasoning is the key to these puzzles. No involved computation or higher mathematics is necessary, but your ability to construct a mathematical proof will be severly tested--even if you are a professional mathematician. For the truly adventurous, there is even a chapter on unsolved puzzles.
I became a scientist because I enjoyed the puzzles in Scientific American. I loved the notion that through mere thought, one could solve a question that at first glance seemed impossible to solve. When I had to design methods to detect ephemeral failures in electronic circuits underlying a mainframe computer, I created a puzzle having occasional liars. When I thought about ways to understand global wars, I constructed a puzzle about bullies in a playground. Some of my puzzles have been very computational, some purely paper and pencil. Over the years, my puzzles have appeared in Scientific American, Dr. Dobb’s Journal, and the Communications of the ACM.
In the history of science, fields of studies have evolved from empirical to principled. In linguistics, field linguists had understood the need to construct grammars of languages they encountered. Noam Chomsky understood the need to place grammars into a mathematical hierarchy of formalisms, showing through brilliant counter-examples which grammatical constructs could be handled by each formalism. For example, Chomsky showed that finite state automata model noun phrases beautifully but fail with if-then sentences. He showed that context-free grammars handle if-then, but fail at passive constructions. The book offered a new way to think about language.
Noam Chomsky's first book on syntactic structures is one of the first serious attempts on the part of a linguist to construct within the tradition of scientific theory-construction a comprehensive theory of language which may be understood in the same sense that a chemical, biological theory is understood by experts in those fields. It is not a mere reorganization of the data into a new kind of library catalogue, nor another specualtive philosophy about the nature of man and language, but rather a rigorus explication of our intuitions about our language in terms of an overt axiom system, the theorems…
Saying just the right words in just the right way can cause a box of electronics to behave however you want it to behave… that’s an idea that has captivated me ever since I first played around with a computer at Radio Shack back in 1979. I’m always on the lookout for compelling ways to convey the topic to people who are open-minded, but maybe turned off by things that are overly technical. I teach computer science and study artificial intelligence as a way of expanding what we can get computers to do on our behalf.
I always find myself applying algorithmic thinking in my everyday life—it affects the way I put away dishes, navigate to the store, and organize my to-do lists. And I think others could benefit from that mindset.
So, when I read this book, my reaction was "Yes! That's what I want people to know. I just wish I could have said it that well!" The authors (who I know, but didn't know they wrote a book together), did a fantastic job of selecting algorithms with deep human connections. Really! And they explain them just right, without getting too mathematical but while still hitting the key ideas with clarity and accuracy. Fantastic!
A fascinating exploration of how computer algorithms can be applied to our everyday lives.
In this dazzlingly interdisciplinary work, acclaimed author Brian Christian and cognitive scientist Tom Griffiths show us how the simple, precise algorithms used by computers can also untangle very human questions. Modern life is constrained by limited space and time, limits that give rise to a particular set of problems. What should we do, or leave undone, in a day or a lifetime? How much messiness should we accept? The authors explain how to have better hunches and when to leave things to chance, how to deal…
I am Professor of Computer Science at Stony Brook University, and have spent the past thirty years thinking/teaching/writing about algorithms. Algorithms are the really cool thing about computer science, for they form the ideas behind any interesting computer program. And algorithms turn out to be the ideas behind many interesting aspects of life that have nothing to do with computers. I have written six books on algorithms, programming, gambling, and history –including the ranking of the historical significance of all the people in Wikipedia.
Knuth’s unique mix of playfulness and rigor came to define computer science as an intellectual discipline: computer science didn’t really have anything to do with computers, but everything to do with a particular way of seeing the world. Just browse and wonder at the beauty and precision achieved in these books.
Volume 3 (Sorting and Searching) is my personal favorite, and I encourage you to start there. During the pandemic, I finally got around to reading Volume 4A (Combinatorial Algorithms), which was published thirty plus years after Volume 3. It was the same feeling I had watching the movie The Phantom Menace years after growing up with the original Star Wars trilogy. I had forgotten just how unique and distinctive Knuth’s Art of Computer Programming is.
The bible of all fundamental algorithms and the work that taught many of today's software developers most of what they know about computer programming.
-Byte, September 1995
I can't begin to tell you how many pleasurable hours of study and recreation they have afforded me! I have pored over them in cars, restaurants, at work, at home... and even at a Little League game when my son wasn't in the line-up.
-Charles Long
If you think you're a really good programmer... read [Knuth's] Art of Computer Programming... You should definitely send me a resume if you can read the whole…
I love mathematics and truly believe that “Functions Describe the World.” I'm deeply satisfied that I've spent my professional life discovering new mathematics and explaining known mathematics to others. I was an undergraduate at the University of Texas, Austin, got my PhD from Brown University, then spent three years as a G.C. Evans Instructor at Rice University, before moving to Williams, where I've been ever since. Besides writing All the Math You Missed (But Need to Know for Graduate School), I've also written Algebraic Geometry: A Problem Solving Approach (with a number of co-authors) and Electricity and Magnetism for Mathematicians: A Guided Path from Maxwell’s Equations to Yang-Mills, and a number of research articles.
Ulam was a Polish mathematical prodigy, publishing significant mathematics by the time he was 20. He was part of the rich Polish math community centered around Stefan Banach. Unlike most, he was heading to the United States in 1939 (with his younger brother) when Germany invaded Poland. All the rest of his family were murdered by the Nazis. He on the other hand ended up in Los Alamos, providing critical help on the Manhattan Project. Later in life, he wrote this book, his autobiography. Based on his history, one could well think that it would be a book full of tragic grief. Instead, it is a pean to the joys of doing mathematics and of living a life full of mathematics, without downplaying the horrors of the mid-twentieth century.
This autobiography of mathematician Stanislaw Ulam, one of the great scientific minds of the twentieth century, tells a story rich with amazingly prophetic speculations and peppered with lively anecdotes. As a member of the Los Alamos National Laboratory from 1944 on, Ulam helped to precipitate some of the most dramatic changes of the postwar world. He was among the first to use and advocate computers for scientific research, originated ideas for the nuclear propulsion of space vehicles, and made fundamental contributions to many of today's most challenging mathematical projects. With his wide-ranging interests, Ulam never emphasized the importance of his…
I'm a British writer, (though I now live and work in California) and a Stanford professor who is passionate about helping everyone know they have endless potential and that math is a subject of creativity, connections, and beautiful ideas. I spend time battling against math elitism, systemic racism, and the other barriers that have stopped women and people of color from going forward in STEM. I am the cofounder of youcubed, a site that inspires millions of educators and their students, with creative mathematics and mindset messages. I've also made a math app, designed to help students feel good about struggling, called Struggly.com. I love to write books that help people develop their mathematical superpowers!
This is a beautiful book filled with glossy color photos, that would be a lovely gift for any girl or woman interested in mathematics, or really, any human.
Inside the book are the “rebel women” who have specialized in mathematics (and yes it seems you still need to be a rebel to succeed in this male-dominated field). I learned so much about the mathematics the women studied and created, as well as the ways they battled for recognition to be able to contribute to mathematics.
The book is filled with powerful and creative mathematics produced by inspirational women.
From rocket scientists to code breakers, discover the incredibly inspiring stories of more than 30 women who fought through the obstacles, shattered the stereotypes, and embraced their STEM passions.
Prepare to be inspired. With more than 200 photos and original interviews with several of the amazing women covered, Power in Numbers: The Rebel Women of Mathematics is a full-color volume that takes aim at the forgotten influence of women on the development of mathematics over the last two millennia.
Each biography reveals the amazing life of a different female mathematician, from her childhood and early influences, to the obstacles she…
Philosophy’s core questions have always obsessed me: What is real? What makes life worth living? Can knowledge be made secure? In graduate school at the University of Virginia I was drawn to mathematically formalized approaches to such questions, especially those of C. S. Peirce and Alain Badiou. More recently, alongside colleagues at Endicott College’s Center for Diagrammatic and Computational Philosophy and GCAS College Dublin I have explored applications of diagrammatic logic, category theory, game theory, and homotopy type theory to such problems as abductive inference and artificial intelligence. Philosophers committed to the perennial questions have much to gain today from studying the new methods and results of contemporary mathematics.
Zalamea’s book is the perfect introduction and survey if you want to understand how developments in contemporary mathematics are relevant to current philosophy.
Zalamea’s own approach follows closely in the steps of Peirce, Lautman, and Grothendieck, merging pragmatism, dialectics, and sheaf theory, but he also engages the work of dozens of other key mathematicians and philosophers coming from different points of view, sometimes cursorily, always tantalizingly.
No philosopher can read this book without a quickened heartbeat and eager plans to clear shelf space for some of the many volumes of mathematics and philosophy of mathematics canvassed here by Zalamea.
A panoramic survey of the vast spectrum of modern and contemporary mathematics and the new philosophical possibilities they suggest.
A panoramic survey of the vast spectrum of modern and contemporary mathematics and the new philosophical possibilities they suggest, this book gives the inquisitive non-specialist an insight into the conceptual transformations and intellectual orientations of modern and contemporary mathematics.
The predominant analytic approach, with its focus on the formal, the elementary and the foundational, has effectively divorced philosophy from the real practice of mathematics and the profound conceptual shifts in the discipline over the last century. The first part discusses the…
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