We've ranked the best math books using expert recommendations, sales data, and millions of reader ratings. At Shortform, we know books. Our book guides are the best in the world. Learn why.
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1
Gödel, Escher, Bach: An Eternal Golden Braid
Douglas R. Hofstadter
5.0
Douglas Hofstadter's book is concerned directly with the nature of “maps” or links between formal systems. However, according to Hofstadter, the formal system that underlies all mental activity transcends the system that supports it. If life can grow out of the formal chemical substrate of the cell, if consciousness can emerge out of a formal system of firing neurons, then so too will computers attain human intelligence. Gödel, Escher, Bach is a wonderful exploration of fascinating ideas at the heart of cognitive science: meaning, reduction, recursion, and much more.
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Recommended by Steve Jurvetson, Seth Godin, Cory Zue, and 2 others.
Steve Jurvetson
Steve Jurvetson recommended this book on the podcast "The Tim Ferriss Show". [source]
In the last week, I discovered that at least two of my smart friends hadn't read Godel, Escher, Bach. They have now. You should too. [source]
Cory Zue
More recently books like Godel, Escher, Bach and Sapiens have influenced my thinking a lot. [source]
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2
Fermat's Enigma: The Epic Quest to Solve the World's Greatest Mathematical Problem
Simon Singh
4.9
"I have discovered a truly marvelous proof, which this margin is too narrow to contain". With these tantalizing words the seventeenth-century French mathematician Pierre de Fermat threw down the gauntlet to future generations. What came to be known as Fermat's Last Theorem looked simple, yet the finest mathematical minds would be baffled for more than three and a half centuries.Fermat's Last Theorem became the Holy Grail of mathematics. Whole and colorful lives were devoted, and even sacrificed, to finding a solution. Leonhard Euler, the greatest mathematician of the 18th century, had to admit defeat. Sophie Germain had to take on the identity of a man to do research in a field forbidden to females, and made the most significant breakthrough of the 19th century. The clashing Evariste Galois scribbled down the results of his research deep into the night before venturing out to die in a duel in 1832. Yutaka Taniyama, whose insights would lead directly to the ultimate solution to Fermat, tragically killed himself in despair. On the other hand, Paul Wolfskehl, a famous German industrialist, claimed Fermat had saved him from suicide, and established a rich prize for the first person to prove the theorem.
And then came Princeton Professor Andrew Wiles, who had dreamed of proving Fermat ever since he first read of it as a boy of ten in his local library. In 1993, some 356 years after Fermat's challenge, and after seven years of working in isolation and secrecy, Wiles stunned the world by announcing a proof -- though his own journey would be far from over.
"Fermat's Enigma" is the story of the epic quest to solve the greatest math problem of all time. Written by the award-winningfilm-maker who has had more access to Andrew Wiles than any other journalist, it is a human drama of high dreams, intellectual brilliance, and extraordinary determination.
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Recommended by Kirk Borne and Sarah-Jayne Blakemore.
Kirk Borne
New Perspective on Fermat's Last Theorem: https://t.co/YeaHQ6iadB by @granvilleDSC @DataScienceCtrl #abdsc #Mathematics See the best-selling book "Fermat's Enigma: The Epic Quest to Solve the World's Greatest Mathematical Problem": https://t.co/dqenmvUw0A by @SLSingh https://t.co/deyMhQTQLU [source]
Sarah-Jayne Blakemore
The book is great because Simon Singh has this ability to write about the driest and most complex scientific or mathematical concepts and issues, and somehow make them come alive. [source]
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3
How Not to Be Wrong: The Power of Mathematical Thinking
Jordan Ellenberg
4.8
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 with it.
Math allows us to see the hidden structures underneath the messy and chaotic surface of our world. It’s a science of not being wrong, hammered out by centuries of hard work and argument. Armed with the tools of mathematics, we can see through to the true meaning of information we take for granted: How early should you get to the airport? What does “public opinion” really represent? Why do tall parents have shorter children? Who really won Florida in 2000? And how likely are you, really, to develop cancer?
How Not to Be Wrong presents the surprising revelations behind all of these questions and many more, using the mathematician’s method of analyzing life and exposing the hard-won insights of the academic community to the layman—minus the jargon. Ellenberg chases mathematical threads through a vast range of time and space, from the everyday to the cosmic, encountering, among other things, baseball, Reaganomics, daring lottery schemes, Voltaire, the replicability crisis in psychology, Italian Renaissance painting, artificial languages, the development of non-Euclidean geometry, the coming obesity apocalypse, Antonin Scalia’s views on crime and punishment, the psychology of slime molds, what Facebook can and can’t figure out about you, and the existence of God.
Ellenberg pulls from history as well as from the latest theoretical developments to provide those not trained in math with the knowledge they need. Math, as Ellenberg says, is “an atomic-powered prosthesis that you attach to your common sense, vastly multiplying its reach and strength.” With the tools of mathematics in hand, you can understand the world in a deeper, more meaningful way. How Not to Be Wrong will show you how.
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Recommended by Bill Gates, Auston Bunsen, and Nick Ganju.
The writing is funny, smooth, and accessible -- not what you might expect from a book about math. What Ellenberg has written is ultimately a love letter to math. If the stories he tells add up to a larger lesson, it’s that 'to do mathematics is to be, at once, touched by fire and bound by reason' -- and that there are ways in which we’re all doing math, all the time. [source]
Auston Bunsen
I’ve got a few, one book that really impacted me early on as someone coming from a middle-class family was “Rich dad, Poor dad”. Since then I’ve read many books but one that really stands out is “How not to be wrong” by Jordan Ellenberg which really reignited my appetite & appreciation for math. [source]
Nick Ganju
Written for an audience of people who have historically been intimidated by math … and introduces things in a very simple way, and then works up to more complex concepts. [source]
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4
Flatland: A Romance of Many Dimensions
Edwin A. Abbott
4.7
This masterpiece of science (and mathematical) fiction is a delightfully unique and highly entertaining satire that has charmed readers for more than 100 years. The work of English clergyman, educator and Shakespearean scholar Edwin A. Abbott (1838-1926), it describes the journeys of A. Square [sic – ed.], a mathematician and resident of the two-dimensional Flatland, where women-thin, straight lines-are the lowliest of shapes, and where men may have any number of sides, depending on their social status. Through strange occurrences that bring him into contact with a host of geometric forms, Square has adventures in Spaceland (three dimensions), Lineland (one dimension) and Pointland (no dimensions) and ultimately entertains thoughts of visiting a land of four dimensions—a revolutionary idea for which he is returned to his two-dimensional world. Charmingly illustrated by the author, Flatland is not only fascinating reading, it is still a first-rate fictional introduction to the concept of the multiple dimensions of space. "Instructive, entertaining, and stimulating to the imagination." — Mathematics Teacher.
Bryan Johnson recommended this book on Twitter. [source]
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Zero: The Biography of a Dangerous Idea
Charles Seife
4.7
The Babylonians invented it, the Greeks banned it, the Hindus worshipped it, and the Church used it to fend off heretics. For centuries, the power of zero savored of the demonic; once harnessed, it became the most important tool in mathematics. Zero follows this number from its birth as an Eastern philosophical concept to its struggle for acceptance in Europe and its apotheosis as the mystery of the black hole. Today, zero lies at the heart of one of the biggest scientific controversies of all time, the quest for the theory of everything. Elegant, witty, and enlightening, Zero is a compelling look at the strangest number in the universe and one of the greatest paradoxes of human thought.
Unlike Ifrah, Charles Seife is a brilliant popular science writer who has here written the ‘biography’ of zero. And even though he doesn’t talk that much about India, it works well as a handbook to Ifrah’s sections on India. Because Seife talks about how zero is mathematically very close to the idea of infinity, which is another mathematical idea that the Indians thought about differently. Seife gives you the context and it explains why, really, without zero, you can’t do anything. The difficulty of understanding zero is similar to the difficulty of understanding infinity. The Greeks had no zero, Roman numerals have no zero, and they had no infinity. He plays with this idea that we were afraid of infinity and then gradually we learnt not to be afraid of it. [source]
Chronicles how hard it was for humanity to come up with and hold onto the concept of zero. No zero, no math. No zero, no engineering. No zero, no modern world as we know it... [source]
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6
Math Curse
Jon Scieszka, Lane Smith
4.7
Did you ever wake up to one of those days where everything is a problem? You have 10 things to do, but only 30 minutes until your bus leaves. Is there enough time? You have 3 shirts and 2 pairs of pants. Can you make 1 good outfit? Then you start to wonder: Why does everything have to be such a problem? Why do 2 apples always have to be added to 5 oranges? Why do 4 kids always have to divide 12 marbles? Why can't you just keep 10 cookies without someone taking 3 away? Why? Because you're the victim of a Math Curse. That's why. But don't despair. This is one girl's story of how that curse can be broken.
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Recommended by Daniel Munro.
Daniel Munro
Book 15: Math Curse! A favourite for 20 years. My kids loved this book instantly when I introduced them to it. Great illustrations, fun math challenges and jokes. https://t.co/MdYEXKyz76 [source]
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7
How to Solve It: A New Aspect of Mathematical Method
George Pólya
4.6
A perennial bestseller by eminent mathematician G. Polya, How to Solve It will show anyone in any field how to think straight. In lucid and appealing prose, Polya reveals how the mathematical method of demonstrating a proof or finding an unknown can be of help in attacking any problem that can be "reasoned" out--from building a bridge to winning a game of anagrams. Generations of readers have relished Polya's deft--indeed, brilliant--instructions on stripping away irrelevancies and going straight to the heart of the problem.
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8
The Doorbell Rang
Pat Hutchins
4.6
Each ring of the doorbell brings more friends to share the delicious cookies Ma has made in this beloved classic.
This enjoyable read-aloud picture book about friendship, sharing, and cookies can also be used to introduce basic math concepts to young children.
The Doorbell Rang was named a Notable Book for Children by the American Library Association.
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The Greedy Triangle
Marilyn Burns, Gordon Silveria
4.6
In this lively introduction to shapes and polygons, a bored triangle is turned into a quadrilateral after a visit to the shapeshifter. Delighted with his new career opportunities--as a TV screen and a picture frame--he decides the more angles the better, until an accident teaches him a lesson. Includes special teaching section. Full color.
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10
The Code Book: The Science of Secrecy from Ancient Egypt to Quantum Cryptography
Simon Singh
4.6
In his first book since the bestselling Fermat's Enigma, Simon Singh offers the first sweeping history of encryption, tracing its evolution and revealing the dramatic effects codes have had on wars, nations, and individual lives. From Mary, Queen of Scots, trapped by her own code, to the Navajo Code Talkers who helped the Allies win World War II, to the incredible (and incredibly simple) logistical breakthrough that made Internet commerce secure, The Code Book tells the story of the most powerful intellectual weapon ever known: secrecy.
Throughout the text are clear technical and mathematical explanations, and portraits of the remarkable personalities who wrote and broke the world's most difficult codes. Accessible, compelling, and remarkably far-reaching, this book will forever alter your view of history and what drives it. It will also make yo wonder how private that e-mail you just sent really is.
Whether you are a student struggling to fulfill a math or science requirement, or you are embarking on a career change that requires a higher level of math competency, A Mind for Numbers offers the tools you need to get a better grasp of that intimidating but inescapable field. Engineering professor Barbara Oakley knows firsthand how it feels to struggle with math. She flunked her way through high school math and science courses, before enlisting in the army immediately after graduation. When she saw how her lack of mathematical and technical savvy severely limited her options—both to rise in the military and to explore other careers—she returned to school with a newfound determination to re-tool her brain to master the very subjects that had given her so much trouble throughout her entire life.
In A Mind for Numbers, Dr. Oakley lets us in on the secrets to effectively learning math and science—secrets that even dedicated and successful students wish they’d known earlier. Contrary to popular belief, math requires creative, as well as analytical, thinking. Most people think that there’s only one way to do a problem, when in actuality, there are often a number of different solutions—you just need the creativity to see them. For example, there are more than three hundred different known proofs of the Pythagorean Theorem. In short, studying a problem in a laser-focused way until you reach a solution is not an effective way to learn math. Rather, it involves taking the time to step away from a problem and allow the more relaxed and creative part of the brain to take over. A Mind for Numbers shows us that we all have what it takes to excel in math, and learning it is not as painful as some might think!
CEO/MikeRoweWorks Foundation, Former TV Host/Dirty Jobs
A good teacher will leave you educated. But a great teacher will leave you curious. Well, Barbara Oakley is a great teacher. Not only does she have a mind for numbers, she has a way with words, and she makes every one of them count [source]
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12
The Man Who Loved Only Numbers: The Story of Paul Erdős and the Search for Mathematical Truth
Paul Hoffman
4.5
Based on a National Magazine Award-winning article, this masterful biography of Hungarian-born Paul Erdos is both a vivid portrait of an eccentric genius and a layman's guide to some of this century's most startling mathematical discoveries.
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13
The Black Swan: The Impact of the Highly Improbable
A black swan is a highly improbable event with three principal characteristics: It is unpredictable; it carries a massive impact; and, after the fact, we concoct an explanation that makes it appear less random, and more predictable, than it was.
The astonishing success of Google was a black swan; so was 9/11. For Nassim Nicholas Taleb, black swans underlie almost everything about our world, from the rise of religions to events in our own personal lives.
Why do we not acknowledge the phenomenon of black swans until after they occur? Part of the answer, according to Taleb, is that humans are hardwired to learn specifics when they should be focused on generalities.
We concentrate on things we already know and time and time again fail to take into consideration what we don’t know. We are, therefore, unable to truly estimate opportunities, too vulnerable to the impulse to simplify, narrate, and categorize, and not open enough to rewarding those who can imagine the “impossible.”
For years, Taleb has studied how we fool ourselves into thinking we know more than we actually do. We restrict our thinking to the irrelevant and inconsequential, while large events continue to surprise us and shape our world. Now, in this revelatory book, Taleb explains everything we know about what we don’t know. He offers surprisingly simple tricks for dealing with black swans and benefiting from them.
Elegant, startling, and universal in its applications The Black Swan will change the way you look at the world. Taleb is a vastly entertaining writer, with wit, irreverence, and unusual stories to tell. He has a polymathic command of subjects ranging from cognitive science to business to probability theory.
The Black Swan is a landmark book – itself a black swan.
The book also contains a 4-page glossary; 19 pages of notes; and, a 28-page bibliography in addition to an index.
From the book "The Everything Store: and the Age of Amazon" “The scholar argues that people are wired to see patterns in chaos while remaining blind to unpredictable events, with massive consequences. Experimentation and empiricism trumps the easy and obvious narrative,” Stone writes. [source]
And throw in “The Black Swan” and “Fooled by Randomness”. “Fragile” means if you hit something might break. “Resilient” means if you hit something, it will stay the same. On my podcast Nassim discusses “Antifragility” – building a system, even on that works for you on a personal level, where you if you harm your self in some way it becomes stronger. That podcast changed my life He discusses Antifragility throughout history, up to our current economic situation, and even in our personal situations. [source]
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14
The Signal and the Noise: Why So Many Predictions Fail - But Some Don't
One of Wall Street Journal's Best Ten Works of Nonfiction in 2012
New York Times Bestseller
"Not so different in spirit from the way public intellectuals like John Kenneth Galbraith once shaped discussions of economic policy and public figures like Walter Cronkite helped sway opinion on the Vietnam War…could turn out to be one of the more momentous books of the decade." -New York Times Book Review
"Nate Silver's The Signal and the Noise is The Soul of a New Machine for the 21st century." -Rachel Maddow, author of Drift
"A serious treatise about the craft of prediction-without academic mathematics-cheerily aimed at lay readers. Silver's coverage is polymathic, ranging from poker and earthquakes to climate change and terrorism." -New York Review of Books
Nate Silver built an innovative system for predicting baseball performance, predicted the 2008 election within a hair's breadth, and became a national sensation as a blogger-all by the time he was thirty. He solidified his standing as the nation's foremost political forecaster with his near perfect prediction of the 2012 election. Silver is the founder and editor in chief of FiveThirtyEight.com.
Drawing on his own groundbreaking work, Silver examines the world of prediction, investigating how we can distinguish a true signal from a universe of noisy data. Most predictions fail, often at great cost to society, because most of us have a poor understanding of probability and uncertainty. Both experts and laypeople mistake more confident predictions for more accurate ones. But overconfidence is often the reason for failure. If our appreciation of uncertainty improves, our predictions can get better too. This is the "prediction paradox": The more humility we have about our ability to make predictions, the more successful we can be in planning for the future.
In keeping with his own aim to seek truth from data, Silver visits the most successful forecasters in a range of areas, from hurricanes to baseball, from the poker table to the stock market, from Capitol Hill to the NBA. He explains and evaluates how these forecasters think and what bonds they share. What lies behind their success? Are they good-or just lucky? What patterns have they unraveled? And are their forecasts really right? He explores unanticipated commonalities and exposes unexpected juxtapositions. And sometimes, it is not so much how good a prediction is in an absolute sense that matters but how good it is relative to the competition. In other cases, prediction is still a very rudimentary-and dangerous-science.
Silver observes that the most accurate forecasters tend to have a superior command of probability, and they tend to be both humble and hardworking. They distinguish the predictable from the unpredictable, and they notice a thousand little details that lead them closer to the truth. Because of their appreciation of probability, they can distinguish the signal from the noise.
With everything from the health of the global economy to our ability to fight terrorism dependent on the quality of our predictions, Nate Silver's insights are an essential read.
Anyone interested in politics may be attracted to Nate Silver’s The Signal and the Noise: Why So Many Predictions Fail—but Some Don't. Silver is the New York Times columnist who got a lot of attention last fall for predicting—accurately, as it turned out–the results of the U.S. presidential election. This book actually came out before the election, though, and it’s about predictions in many domains besides politics. Silver knows a lot about baseball, and I especially liked his explanation of hold’em poker. A few pages – where he talks about how early computers supposedly made everything less efficient—are utter nonsense. I wish he had gone into more depth on some things, like why it is that voters are increasingly polarized. I liked the book, though I wish he’d gone deeper on a number of topics. [source]
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15
The Joy of x: A Guided Tour of Math, from One to Infinity
Steven Strogatz
4.5
A world-class mathematician and regular contributor to the New York Times hosts a delightful tour of the greatest ideas of math, revealing how it connects to literature, philosophy, law, medicine, art, business, even pop culture in ways we never imagined
Did O.J. do it? How should you flip your mattress to get the maximum wear out of it? How does Google search the Internet? How many people should you date before settling down? Believe it or not, math plays a crucial role in answering all of these questions and more.
Math underpins everything in the cosmos, including us, yet too few of us understand this universal language well enough to revel in its wisdom, its beauty — and its joy. This deeply enlightening, vastly entertaining volume translates math in a way that is at once intelligible and thrilling. Each trenchant chapter of The Joy of x offers an “aha!” moment, starting with why numbers are so helpful, and progressing through the wondrous truths implicit in π, the Pythagorean theorem, irrational numbers, fat tails, even the rigors and surprising charms of calculus. Showing why he has won awards as a professor at Cornell and garnered extensive praise for his articles about math for the New York Times, Strogatz presumes of his readers only curiosity and common sense. And he rewards them with clear, ingenious, and often funny explanations of the most vital and exciting principles of his discipline.
Whether you aced integral calculus or aren’t sure what an integer is, you’ll find profound wisdom and persistent delight in The Joy of x.
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16
Sir Cumference and the First Round Table: A Math Adventure
Cindy Neuschwander, Wayne Geehan
4.5
Join Sir Cumference, Lady Di of Ameter, and their son Radius for wordplay, puns, and problem solving in this geometry-packed math adventure. King Arthur was a good ruler, but now he needs a good ruler. What would you do if the neighboring kingdom were threatening war? Naturally, you'd call your strongest and bravest knights together to come up with a solution. But when your conference table causes more problems than the threat of your enemy, you need expert help. Enter Sir Cumference, his wife Lady Di of Ameter, and their son Radius. With the help of the carpenter, Geo of Metry, this sharp-minded team designs the perfect table conducive to discussing the perfect plan for peace. The first in Sir Cumference series, SIR CUMFERENCE AND THE FIRST ROUND TABLE makes math fun and accessible for everyone.
In this stunning new book, Malcolm Gladwell takes us on an intellectual journey through the world of "outliers"--the best and the brightest, the most famous and the most successful. He asks the question: what makes high-achievers different?
His answer is that we pay too much attention to what successful people are like, and too little attention to where they are from: that is, their culture, their family, their generation, and the idiosyncratic experiences of their upbringing. Along the way he explains the secrets of software billionaires, what it takes to be a great soccer player, why Asians are good at math, and what made the Beatles the greatest rock band.
Gladwell is not the first person to come up with the 10,000 hour rule. Nor is he the first person to document what it takes to become the best in the world at something. But his stories are so great as he explains these deep concepts. How did the Beatles become the best? Why are professional hockey players born in January, February and March? And so on. [source]
Alex Circei
Question: What five books would you recommend to young people interested in your career path & why? Answer: Screw It, Let's Do It: Lessons In Life by Richard Branson Outliers: The Story of Success by Malcolm Gladwell Start With Why: How Great Leaders Inspire Everyone To Take Action by Simon Sinek The Hard Thing About Hard Things: Building a Business When There Are No Easy Answers by Ben Horowitz Rich Dad Poor Dad: What the Rich Teach Their Kids About Money That the Poor and Middle Class Do Not! by Robert T. Kiyosaki [source]
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18
Factfulness: Ten Reasons We're Wrong About the World – and Why Things Are Better Than You Think
Factfulness: The stress-reducing habit of only carrying opinions for which you have strong supporting facts.
When asked simple questions about global trends—what percentage of the world’s population live in poverty; why the world’s population is increasing; how many girls finish school—we systematically get the answers wrong. So wrong that a chimpanzee choosing answers at random will consistently outguess teachers, journalists, Nobel laureates, and investment bankers.
In Factfulness, Professor of International Health and global TED phenomenon Hans Rosling, together with his two long-time collaborators, Anna and Ola, offers a radical new explanation of why this happens. They reveal the ten instincts that distort our perspective—from our tendency to divide the world into two camps (usually some version of us and them) to the way we consume media (where fear rules) to how we perceive progress (believing that most things are getting worse).
Our problem is that we don’t know what we don’t know, and even our guesses are informed by unconscious and predictable biases.
It turns out that the world, for all its imperfections, is in a much better state than we might think. That doesn’t mean there aren’t real concerns. But when we worry about everything all the time instead of embracing a worldview based on facts, we can lose our ability to focus on the things that threaten us most.
Inspiring and revelatory, filled with lively anecdotes and moving stories, Factfulness is an urgent and essential book that will change the way you see the world and empower you to respond to the crises and opportunities of the future.
As 2018 draws to a close, I’m continuing a favorite tradition of mine and sharing my year-end lists. It gives me a moment to pause and reflect on the year through the books I found most thought-provoking, inspiring, or just plain loved. It also gives me a chance to highlight talented authors – some who are household names and others who you may not have heard of before. Here’s my best of 2018 list. [source]
This was a breakthrough to me. The framework Hans enunciates is one that took me decades of working in global development to create for myself, and I could have never expressed it in such a clear way. I’m going to try to use this model moving forward. [source]
Aidan Connolly
I would suggest Hans Rosling’s Factfulness on the real world of statistics. [source]
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19
The Tipping Point: How Little Things Can Make a Big Difference
The tipping point is that magic moment when an idea, trend, or social behavior crosses a threshold, tips, and spreads like wildfire. Just as a single sick person can start an epidemic of the flu, so too can a small but precisely targeted push cause a fashion trend, the popularity of a new product, or a drop in the crime rate. This widely acclaimed bestseller, in which Malcolm Gladwell explores and brilliantly illuminates the tipping point phenomenon, is already changing the way people throughout the world think about selling products and disseminating ideas.
Gladwell introduces us to the particular personality types who are natural pollinators of new ideas and trends, the people who create the phenomenon of word of mouth. He analyzes fashion trends, smoking, children's television, direct mail, and the early days of the American Revolution for clues about making ideas infectious, and visits a religious commune, a successful high-tech company, and one of the world's greatest salesmen to show how to start and sustain social epidemics.
Bunch of really good information in here on how to make ideas go viral. This could be good to apply to any kind of products or ideas you may have. Definitely, check out The Tipping Point, which is one of my favorites. [source]
Malcolm Gladwell's breakthrough insight was to focus on the micro-relationships between individuals, which helped organizations realize that it's not about the big ads and the huge charity balls... it's about setting the stage for the buzz to start. [source]
Andy Stern
I think that when we talk about making change, it is much more about macro change, like in policy. This book reminds you that at times when you're building big movements, or trying to elect significant decision-makers in politics, sometimes it's the little things that make a difference. Ever since the book was written, we've become very used to the idea of things going viral unexpectedly and then having massive impact. The Tipping Point, to me, is really an appreciation that very small things can rearrange thinking in ways – like infectious diseases – that have huge implications. While we're always searching for the big policy changes – and we think we have to do that in very traditional ways of building coalitions against constituencies, movements and the media – sometimes it's the little things that actually tip the situation. Like the story of a person and their unique set of circumstances that really captures an issue about health care or housing. So it's trying to remember, while you're thinking about the grand and the glorious, that thinking about the small things can equally bring about change. [source]
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20
What Is Mathematics?: An Elementary Approach to Ideas and Methods
Richard Courant, Herbert Robbins, Ian Stewart
4.5
For more than two thousand years a familiarity with mathematics has been regarded as an indispensable part of the intellectual equipment of every cultured person. Today, unfortunately, the traditional place of mathematics in education is in grave danger. The teaching and learning of mathematics has degenerated into the realm of rote memorization, the outcome of which leads to satisfactory formal ability but does not lead to real understanding or to greater intellectual independence. This new edition of Richard Courant's and Herbert Robbins's classic work seeks to address this problem. Its goal is to put the meaning back into mathematics.
Written for beginners and scholars, for students and teachers, for philosophers and engineers, What is Mathematics? Second Edition is a sparkling collection of mathematical gems that offers an entertaining and accessible portrait of the mathematical world. Covering everything from natural numbers and the number system to geometrical constructions and projective geometry, from topology and calculus to matters of principle and the Continuum Hypothesis, this fascinating survey allows readers to delve into mathematics as an organic whole rather than an empty drill in problem solving. With chapters largely independent of one another and sections that lead upward from basic to more advanced discussions, readers can easily pick and choose areas of particular interest without impairing their understanding of subsequent parts.
Brought up to date with a new chapter by Ian Stewart, What is Mathematics? Second Edition offers new insights into recent mathematical developments and describes proofs of the Four-Color Theorem and Fermat's Last Theorem, problems that were still open when Courant and Robbins wrote this masterpiece, but ones that have since been solved.
Formal mathematics is like spelling and grammar - a matter of the correct application of local rules. Meaningful mathematics is like journalism - it tells an interesting story. But unlike some journalism, the story has to be true. The best mathematics is like literature - it brings a story to life before your eyes and involves you in it, intellectually and emotionally. What is Mathematics is like a fine piece of literature - it opens a window onto the world of mathematics for anyone interested to view.
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21
Journey through Genius: The Great Theorems of Mathematics
William Dunham
4.5
Like masterpieces of art, music, and literature, great mathematical theorems are creative milestones, works of genius destined to last forever. Now William Dunham gives them the attention they deserve.Dunham places each theorem within its historical context and explores the very human and often turbulent life of the creator — from Archimedes, the absentminded theoretician whose absorption in his work often precluded eating or bathing, to Gerolamo Cardano, the sixteenth-century mathematician whose accomplishments flourished despite a bizarre array of misadventures, to the paranoid genius of modern times, Georg Cantor. He also provides step-by-step proofs for the theorems, each easily accessible to readers with no more than a knowledge of high school mathematics.
A rare combination of the historical, biographical, and mathematical, Journey Through Genius is a fascinating introduction to a neglected field of human creativity.
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22
The Drunkard's Walk: How Randomness Rules Our Lives
Leonard Mlodinow
4.4
Recommended by David Spiegelhalter and Gabriel Coarna.
David Spiegelhalter
This is a general introduction to the history of probability and the way it comes into everyday life. It intersperses the historical development with modern applications, and looks at finance, sport, gambling, lotteries and coincidences. [source]
Gabriel Coarna
Leonard Mlodinow's "The Drunkarkd's Walk" -more precisely, the section on the "Monty Hall" problem- totally changed how I look-at/think-about probabilities and choices in general; this has impacted almost every real-life choice I've made since I read this book. [source]
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23
How Much Is a Million?
David M Schwartz, Steven Kellogg
4.4
“A jubilant, original picture book.” —Booklist (starred review)
Ever wonder just what a million of something means? How about a billion? Or a trillion? Marvelosissimo the mathematical magician can teach you!
How Much Is a Million? knocks complex numbers down to size in a fun, humorous way, helping children conceptualize a difficult mathematical concept. It's a math class you'll never forget.
This classic picture book is an ALA Notable Book, a Reading Rainbow Feature Selection, and a Boston Globe/Horn Book Honor Book for Illustration.
The repackage of this fun look at math concepts includes a letter from the author that features several ways for children to find a million everyday things.
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24
The Princeton Companion to Mathematics
Timothy Gowers, June Barrow-Green, Imre Leader
4.4
This is a one-of-a-kind reference for anyone with a serious interest in mathematics. Edited by Timothy Gowers, a recipient of the Fields Medal, it presents nearly two hundred entries, written especially for this book by some of the world's leading mathematicians, that introduce basic mathematical tools and vocabulary; trace the development of modern mathematics; explain essential terms and concepts; examine core ideas in major areas of mathematics; describe the achievements of scores of famous mathematicians; explore the impact of mathematics on other disciplines such as biology, finance, and music--and much, much more.
Unparalleled in its depth of coverage, The Princeton Companion to Mathematics surveys the most active and exciting branches of pure mathematics. Accessible in style, this is an indispensable resource for undergraduate and graduate students in mathematics as well as for researchers and scholars seeking to understand areas outside their specialties.
Features nearly 200 entries, organized thematically and written by an international team of distinguished contributors Presents major ideas and branches of pure mathematics in a clear, accessible style Defines and explains important mathematical concepts, methods, theorems, and open problems Introduces the language of mathematics and the goals of mathematical research Covers number theory, algebra, analysis, geometry, logic, probability, and more Traces the history and development of modern mathematics Profiles more than ninety-five mathematicians who influenced those working today Explores the influence of mathematics on other disciplines Includes bibliographies, cross-references, and a comprehensive index Contributors incude:
Graham Allan, Noga Alon, George Andrews, Tom Archibald, Sir Michael Atiyah, David Aubin, Joan Bagaria, Keith Ball, June Barrow-Green, Alan Beardon, David D. Ben-Zvi, Vitaly Bergelson, Nicholas Bingham, Bela Bollobas, Henk Bos, Bodil Branner, Martin R. Bridson, John P. Burgess, Kevin Buzzard, Peter J. Cameron, Jean-Luc Chabert, Eugenia Cheng, Clifford C. Cocks, Alain Connes, Leo Corry, Wolfgang Coy, Tony Crilly, Serafina Cuomo, Mihalis Dafermos, Partha Dasgupta, Ingrid Daubechies, Joseph W. Dauben, John W. Dawson Jr., Francois de Gandt, Persi Diaconis, Jordan S. Ellenberg, Lawrence C. Evans, Florence Fasanelli, Anita Burdman Feferman, Solomon Feferman, Charles Fefferman, Della Fenster, Jose Ferreiros, David Fisher, Terry Gannon, A. Gardiner, Charles C. Gillispie, Oded Goldreich, Catherine Goldstein, Fernando Q. Gouvea, Timothy Gowers, Andrew Granville, Ivor Grattan-Guinness, Jeremy Gray, Ben Green, Ian Grojnowski, Niccolo Guicciardini, Michael Harris, Ulf Hashagen, Nigel Higson, Andrew Hodges, F. E. A. Johnson, Mark Joshi, Kiran S. Kedlaya, Frank Kelly, Sergiu Klainerman, Jon Kleinberg, Israel Kleiner, Jacek Klinowski, Eberhard Knobloch, Janos Kollar, T. W. Korner, Michael Krivelevich, Peter D. Lax, Imre Leader, Jean-Francois Le Gall, W. B. R. Lickorish, Martin W. Liebeck, Jesper Lutzen, Des MacHale, Alan L. Mackay, Shahn Majid, Lech Maligranda, David Marker, Jean Mawhin, Barry Mazur, Dusa McDuff, Colin McLarty, Bojan Mohar, Peter M. Neumann, Catherine Nolan, James Norris, Brian Osserman, Richard S. Palais, Marco Panza, Karen Hunger Parshall, Gabriel P. Paternain, Jeanne Peiffer, Carl Pomerance, Helmut Pulte, Bruce Reed, Michael C. Reed, Adrian Rice, Eleanor Robson, Igor Rodnianski, John Roe, Mark Ronan, Edward Sandifer, Tilman Sauer, Norbert Schappacher, Andrzej Schinzel, Erhard Scholz, Reinhard Siegmund-Schultze, Gordon Slade, David J. Spiegelhalter, Jacqueline Stedall, Arild Stubhaug, Madhu Sudan, Terence Tao, Jamie Tappenden, C. H. Taubes, Rudiger Thiele, Burt Totaro, Lloyd N. Trefethen, Dirk van Dalen, Richard Weber, Dominic Welsh, Avi Wigderson, Herbert Wilf, David Wilkins, B. Yandell, Eric Zaslow, Doron Zeilberger
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25
Chaos: Making a New Science
James Gleick
4.4
Few writers distinguish themselves by their ability to write about complicated, even obscure topics clearly and engagingly. In Chaos, James Gleick, a former science writer for the New York Times, shows that he resides in this exclusive category. Here he takes on the job of depicting the first years of the study of chaos--the seemingly random patterns that characterise many natural phenomena.
This is not a purely technical book. Instead, it focuses as much on the scientists studying chaos as on the chaos itself. In the pages of Gleick's book, the reader meets dozens of extraordinary and eccentric people. For instance, Mitchell Feigenbaum, who constructed and regulated his life by a 26-hour clock and watched his waking hours come in and out of phase with those of his coworkers at Los Alamos National Laboratory.
As for chaos itself, Gleick does an outstanding job of explaining the thought processes and investigative techniques that researchers bring to bear on chaos problems. Rather than attempt to explain Julia sets, Lorenz attractors and the Mandelbrot Set with gigantically complicated equations, Chaos relies on sketches, photographs and Gleick's wonderful descriptive prose. --Christine Buttery
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Recommended by Adam Maloof and Pedro G Ferreira.
Adam Maloof
James Gleick is a former science writer for the New York Times and in this book Gleick describes the science of chaos, and how complex systems can also be interpreted in terms of simple rules and simple (but interacting) behaviours. [source]
Pedro G Ferreira
It turns out that even simple equations can have such complicated behaviour that, in practice, it’s impossible to predict the outcome, which is described as ‘chaotic’. [source]
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26
Grapes Of Math
Greg Tang, Harry Briggs
4.4
Let Scholastic Bookshelf be your guide through the whole range of your child's experiences-laugh with them, learn with them, read with them!
Eight classic, best-selling titles are available now!
Category: Math Skills "How many grapes are on the vine? Counting each takes too much time. Never Fear, I have a hunch There is a match for every bunch!"
Greg Tang, a lifelong lover of math, shares the techniques that have helped him solve problems in the most creative ways! Harry Briggs's vibrant & inviting illustrations create a perfect environment for these innovative games. So open your mind-and have fun!
"This...clever math book uses rhyming couplets... riddles...visual clues to help the reader find new ways to group numbers for quick counting...A winning addition!" --Kirkus
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27
Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics
John Derbyshire
4.4
In 1859, Bernhard Riemann, a little-known thirty-two year old mathematician, made a hypothesis while presenting a paper to the Berlin Academy titled “On the Number of Prime Numbers Less Than a Given Quantity.” Today, after 150 years of careful research and exhaustive study, the Riemann Hypothesis remains unsolved, with a one-million-dollar prize earmarked for the first person to conquer it. Alternating passages of extraordinarily lucid mathematical exposition with chapters of elegantly composed biography and history, Prime Obsession is a fascinating and fluent account of an epic mathematical mystery that continues to challenge and excite the world.
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28
Innumeracy: Mathematical Illiteracy and Its Consequences
John Allen Paulos
4.4
Recommended by Sophie Scott.
Sophie Scott
If you were listening to #themathsoflife on today’s @laurenlaverne show and you’d like to know more about how we can misperceive numbers and magnitude, I recommend @JohnAllenPaulos and his brilliant book, Innumeracy. [source]
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29
The Very Hungry Caterpillar
Eric Carle
4.4
THE all-time classic story, from generation to generation, sold somewhere in the world every 30 seconds! Have you shared it with a child or grandchild in your life?
One sunny Sunday, the caterpillar was hatched out of a tiny egg. He was very hungry. On Monday, he ate through one apple; on Tuesday, he ate through three plums--and still he was hungry. When full at last, he made a cocoon around himself and went to sleep, to wake up a few weeks later wonderfully transformed into a butterfly!
The brilliantly innovative Eric Carle has dramatized the story of one of Nature's commonest yet loveliest marvels, the metamorphosis of the butterfly. This audiobook will delight as well as instruct the very youngest listener.
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30
Logicomix: An Epic Search for Truth
Apostolos Doxiadis, Christos Papadimitriou
4.3
An innovative, dramatic graphic novel about the treacherous pursuit of the foundations of mathematics. This graphic novel recounts the spiritual odyssey of philosopher Bertrand Russell. In his agonized search for absolute truth, he crosses paths with thinkers like Gottlob Frege, David Hilbert & Kurt Gödel, & finds a passionate student in Ludwig Wittgenstein. But his most ambitious goal—to establish unshakable logical foundations of mathematics—continues to loom before him. Thru love & hate, peace & war, he persists in the mission threatening to claim both his career & happiness, finally driving him to the brink of insanity. This story is at the same time a historical novel & an accessible explication of some of the biggest ideas of mathematics & modern philosophy. With rich characterizations & atmospheric artwork, it spins the pursuit of such ideas into a satisfying tale. Probing, layered, the book throws light on Russell’s inner struggles while setting them in the context of the timeless questions he tried to answer. At its heart, Logicomix is a story about the conflict between ideal rationality & the flawed fabric of reality.
This is quite a recent publication and I saw the first inklings of this graphic novel when I went to a meeting in Mykonos on maths and narrative and it really looked an incredibly exciting project. I enjoy the graphic novel as an art form and I’ve always enjoyed Tintin and this has a very Tintinesque line to it, the illustration. But it brings alive one of the great stories of 20th-century mathematics, which is the crisis that happened when Gödel proved that there are statements about numbers which are true but which will never be proved. And this went against the whole ethos of mathematics since the ancient Greeks. If something is true, we should be able to prove why it’s true. If there are infinitely many primes, we can prove that there are infinitely many primes. But we don’t know that there are infinitely many twin primes: Primes that are two apart, like 17 and 19. Maybe that’s a true statement that doesn’t have a proof and we’re trying to chase something that doesn’t exist. Gödel’s theorem, proved in the 1930s, was a real bombshell for the philosophy of mathematics. [source]
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31
Here's Looking at Euclid: A Surprising Excursion Through the Astonishing World of Math
Alex Bellos
4.3
Too often math gets a bad rap, characterized as dry and difficult. But, Alex Bellos says, "math can be inspiring and brilliantly creative. Mathematical thought is one of the great achievements of the human race, and arguably the foundation of all human progress. The world of mathematics is a remarkable place."Bellos has traveled all around the globe and has plunged into history to uncover fascinating stories of mathematical achievement, from the breakthroughs of Euclid, the greatest mathematician of all time, to the creations of the Zen master of origami, one of the hottest areas of mathematical work today. Taking us into the wilds of the Amazon, he tells the story of a tribe there who can count only to five and reports on the latest findings about the math instinct--including the revelation that ants can actually count how many steps they've taken. Journeying to the Bay of Bengal, he interviews a Hindu sage about the brilliant mathematical insights of the Buddha, while in Japan he visits the godfather of Sudoku and introduces the brainteasing delights of mathematical games.Exploring the mysteries of randomness, he explains why it is impossible for our iPods to truly randomly select songs. In probing the many intrigues of that most beloved of numbers, pi, he visits with two brothers so obsessed with the elusive number that they built a supercomputer in their Manhattan apartment to study it. Throughout, the journey is enhanced with a wealth of intriguing illustrations, such as of the clever puzzles known as tangrams and the crochet creation of an American math professor who suddenly realized one day that she could knit a representation of higher dimensional space that no one had been able to visualize. Whether writing about how algebra solved Swedish traffic problems, visiting the Mental Calculation World Cup to disclose the secrets of lightning calculation, or exploring the links between pineapples and beautiful teeth, Bellos is a wonderfully engaging guide who never fails to delight even as he edifies. "Here's Looking at Euclid "is a rare gem that brings the beauty of math to life.
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32
The Music of the Primes: Searching to Solve the Greatest Mystery in Mathematics
Marcus du Sautoy
4.3
In 1859, German mathematician Bernhard Riemann presented a paper to the Berlin Academy that would forever change the history of mathematics. The subject was the mystery of prime numbers. At the heart of the presentation was an idea that Riemann had not yet proved but one that baffles mathematicians to this day.
Solving the Riemann Hypothesis could change the way we do business, since prime numbers are the lynchpin for security in banking and e-commerce. It would also have a profound impact on the cutting-edge of science, affecting quantum mechanics, chaos theory, and the future of computing. Leaders in math and science are trying to crack the elusive code, and a prize of $1 million has been offered to the winner. In this engaging book, Marcus du Sautoy reveals the extraordinary history behind the holy grail of mathematics and the ongoing quest to capture it.
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33
Concrete Mathematics: A Foundation for Computer Science
Ronald L. Graham, Donald E. Knuth, et al.
4.3
Concrete Mathematics is a blending of CONtinuous and disCRETE mathematics. "More concretely," the authors explain, "it is the controlled manipulation of mathematical formulas, using a collection of techniques for solving problems."
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34
A Mathematician's Apology
G. H. Hardy, C. P. Snow
4.3
Written in 1940 as his mathematical powers were declining, G.H. Hardy's apology offers an engaging account of the thoughts of a man known for his eccentricities as well as his brilliance in mathematics.
Yes, it really appealed to me when I read it as a kid because I was interested in music, I played the trumpet, I loved doing theatre, and somehow GH Hardy in that book revealed to me how much mathematics is a creative art as much as a useful science. In fact he probably goes further, he really revels in the beauty of the subject and says he’s not particularly interested in the applications. That really appealed to me at the time – I was still hankering after something that made a lot of logical sense and wasn’t too ambiguous but was creative. That book really brought mathematics alive for me. [source]
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35
Gödel's Proof
Ernest Nagel, James R. Newman, Douglas R. Hofstadter
4.3
In 1931 Kurt Gödel published his fundamental paper, "On Formally Undecidable Propositions of Principia Mathematica and Related Systems." This revolutionary paper challenged certain basic assumptions underlying much research in mathematics and logic. Gödel received public recognition of his work in 1951 when he was awarded the first Albert Einstein Award for achievement in the natural sciences--perhaps the highest award of its kind in the United States. The award committee described his work in mathematical logic as "one of the greatest contributions to the sciences in recent times."
However, few mathematicians of the time were equipped to understand the young scholar's complex proof. Ernest Nagel and James Newman provide a readable and accessible explanation to both scholars and non-specialists of the main ideas and broad implications of Gödel's discovery. It offers every educated person with a taste for logic and philosophy the chance to understand a previously difficult and inaccessible subject.
New York University Press is proud to publish this special edition of one of its bestselling books. With a new introduction by Douglas R. Hofstadter, this book will appeal students, scholars, and professionals in the fields of mathematics, computer science, logic and philosophy, and science.
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36
The Boy Who Loved Math: The Improbable Life of Paul Erdos
Deborah Heiligman, LeUyen Pham
4.3
Most people think of mathematicians as solitary, working away in isolation. And, it's true, many of them do. But Paul Erdos never followed the usual path. At the age of four, he could ask you when you were born and then calculate the number of seconds you had been alive in his head. But he didn't learn to butter his own bread until he turned twenty. Instead, he traveled around the world, from one mathematician to the next, collaborating on an astonishing number of publications. With a simple, lyrical text and richly layered illustrations, this is a beautiful introduction to the world of math and a fascinating look at the unique character traits that made "Uncle Paul" a great man.
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37
Weapons of Math Destruction: How Big Data Increases Inequality and Threatens Democracy
Longlisted for the National Book Award New York Times Bestseller
A former Wall Street quant sounds an alarm on the mathematical models that pervade modern life -- and threaten to rip apart our social fabric
We live in the age of the algorithm. Increasingly, the decisions that affect our lives--where we go to school, whether we get a car loan, how much we pay for health insurance--are being made not by humans, but by mathematical models. In theory, this should lead to greater fairness: Everyone is judged according to the same rules, and bias is eliminated.
But as Cathy O'Neil reveals in this urgent and necessary book, the opposite is true. The models being used today are opaque, unregulated, and uncontestable, even when they're wrong. Most troubling, they reinforce discrimination: If a poor student can't get a loan because a lending model deems him too risky (by virtue of his zip code), he's then cut off from the kind of education that could pull him out of poverty, and a vicious spiral ensues. Models are propping up the lucky and punishing the downtrodden, creating a "toxic cocktail for democracy." Welcome to the dark side of Big Data.
Tracing the arc of a person's life, O'Neil exposes the black box models that shape our future, both as individuals and as a society. These "weapons of math destruction" score teachers and students, sort resumes, grant (or deny) loans, evaluate workers, target voters, set parole, and monitor our health.
O'Neil calls on modelers to take more responsibility for their algorithms and on policy makers to regulate their use. But in the end, it's up to us to become more savvy about the models that govern our lives. This important book empowers us to ask the tough questions, uncover the truth, and demand change.
-- Longlist for National Book Award (Non-Fiction) -- Goodreads, semi-finalist for the 2016 Goodreads Choice Awards (Science and Technology) -- Kirkus, Best Books of 2016 -- New York Times, 100 Notable Books of 2016 (Non-Fiction) -- The Guardian, Best Books of 2016 -- WBUR's "On Point," Best Books of 2016: Staff Picks -- Boston Globe, Best Books of 2016, Non-Fiction
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Recommended by Paula Boddington and Ramesh Srinivasan.
Paula Boddington
How the use of algorithms has affected people’s lives and occasionally ruined them. [source]
Ramesh Srinivasan
This book is a really fantastic analysis of how quantification, the collection of data, the modelling around data, the predictions made by using data, the algorithmic and quantifiable ways of predicting behaviour based on data, are all built by elites for elites and end up, quite frankly, screwing over everybody else. [source]
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38
Freakonomics: A Rogue Economist Explores the Hidden Side of Everything
Which is more dangerous, a gun or a swimming pool? What do schoolteachers and sumo wrestlers have in common? Why do drug dealers still live with their moms? How much do parents really matter? What kind of impact did Roe v. Wade have on violent crime? Freakonomics will literally redefine the way we view the modern world.
These may not sound like typical questions for an economist to ask. But Steven D. Levitt is not a typical economist. He is a much heralded scholar who studies the stuff and riddles of everyday life -- from cheating and crime to sports and child rearing -- and whose conclusions regularly turn the conventional wisdom on its head. He usually begins with a mountain of data and a simple, unasked question. Some of these questions concern life-and-death issues; others have an admittedly freakish quality. Thus the new field of study contained in this book: freakonomics.
Through forceful storytelling and wry insight, Levitt and co-author Stephen J. Dubner show that economics is, at root, the study of incentives -- how people get what they want, or need, especially when other people want or need the same thing. In Freakonomics, they set out to explore the hidden side of ... well, everything. The inner workings of a crack gang. The truth about real-estate agents. The myths of campaign finance. The telltale marks of a cheating schoolteacher. The secrets of the Ku Klux Klan.
What unites all these stories is a belief that the modern world, despite a surfeit of obfuscation, complication, and downright deceit, is not impenetrable, is not unknowable, and -- if the right questions are asked -- is even more intriguing than we think. All it takes is a new way of looking. Steven Levitt, through devilishly clever and clear-eyed thinking, shows how to see through all the clutter.
Freakonomics establishes this unconventional premise: If morality represents how we would like the world to work, then economics represents how it actually does work. It is true that readers of this book will be armed with enough riddles and stories to last a thousand cocktail parties. But Freakonomics can provide more than that. It will literally redefine the way we view the modern world. (front flap)
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Recommended by Malcolm Gladwell, Daymond John, Ev Williams, and 12 others.
James Altucher recommended this book on the podcast "The Tim Ferriss Show". [source]
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39
The Golden Ratio: The Story of Phi, the World's Most Astonishing Number
Mario Livio
4.3
Throughout history, thinkers from mathematicians to theologians have pondered the mysterious relationship between numbers and the nature of reality. In this fascinating book, Mario Livio tells the tale of a number at the heart of that mystery: phi, or 1.6180339887...This curious mathematical relationship, widely known as "The Golden Ratio," was discovered by Euclid more than two thousand years ago because of its crucial role in the construction of the pentagram, to which magical properties had been attributed. Since then it has shown a propensity to appear in the most astonishing variety of places, from mollusk shells, sunflower florets, and rose petals to the shape of the galaxy. Psychological studies have investigated whether the Golden Ratio is the most aesthetically pleasing proportion extant, and it has been asserted that the creators of the Pyramids and the Parthenon employed it. It is believed to feature in works of art from Leonardo da Vinci's Mona Lisa to Salvador Dali's The Sacrament of the Last Supper, and poets and composers have used it in their works. It has even been found to be connected to the behavior of the stock market!
The Golden Ratio is a captivating journey through art and architecture, botany and biology, physics and mathematics. It tells the human story of numerous phi-fixated individuals, including the followers of Pythagoras who believed that this proportion revealed the hand of God; astronomer Johannes Kepler, who saw phi as the greatest treasure of geometry; such Renaissance thinkers as mathematician Leonardo Fibonacci of Pisa; and such masters of the modern world as Goethe, Cezanne, Bartok, and physicist Roger Penrose. Wherever his quest for the meaning of phi takes him, Mario Livio reveals the world as a place where order, beauty, and eternal mystery will always coexist.
From the Hardcover edition.
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Recommended by Kirk Borne.
Kirk Borne
Some Fun with Gentle Chaos, the Golden Ratio, and Stochastic Number Theory, with Gaming Applications: https://t.co/oQG0y3vA22 #abdsc by @granvilleDSC @DataScienceCtrl #Mathematics #Statistics ————— Learn all about the Golden Ratio in this fantastic book: https://t.co/9QxN9ECpH7 https://t.co/Mt45UZFFHH [source]
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40
Sir Cumference and the Dragon of Pi
Cindy Neuschwander, Wayne Geehan
4.3
Sir Cumference, Lady Di of Ameter, and Radius are back in their second Math Adventure! This time, a potion has changed Sir Cumference into a fire-breathing dragon. Can Radius change him back? Join Radius on his quest through the castle to solve a riddle that will reveal the cure. It lies in discovering the magic number that is the same for all circles.
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41
The Math Book: From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics
Clifford A. Pickover
4.3
Math's infinite mysteries unfold in this paperback edition of the bestselling TheMath Book. Beginning millions of years ago with ancient “ant odometers” and moving through time to our modern-day quest for new dimensions, prolific polymath Clifford Pickover covers 250 milestones in mathematical history. Among the numerous concepts readers will encounter as they dip into this inviting anthology: cicada-generated prime numbers, magic squares, and the butterfly effect. Each topic is presented in a lavishly illustrated spread, including formulas and real-world applications of the theorems.
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42
Euclid's Elements
Euclid, Dana Densmore, T.L. Heath
4.3
Green Lion Press has prepared a new one-volume edition of T.L. Heath's translation of the thirteen books of Euclid's Elements. In keeping with Green Lion's design commitment, diagrams have been placed on every spread for convenient reference while working through the proofs; running heads on every page indicate both Euclid's book number and proposition numbers for that page; and adequate space for notes is allowed between propositions and around diagrams. The all-new index has built into it a glossary of Euclid's Greek terms.
Heath's translation has stood the test of time, and, as one done by a renowned scholar of ancient mathematics, it can be relied upon not to have inadvertantly introduced modern concepts or nomenclature.
We have excised the voluminous historical and scholarly commentary that swells the Dover edition to three volumes and impedes classroom use of the original text. The single volume is not only more convenient, but less expensive as well.
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43
Infinite Powers: How Calculus Reveals the Secrets of the Universe
Steven Strogatz
4.3
Without calculus, we wouldn’t have cell phones, TV, GPS, or ultrasound. We wouldn’t have unraveled DNA or discovered Neptune or figured out how to put 5,000 songs in your pocket.
Though many of us were scared away from this essential, engrossing subject in high school and college, Steven Strogatz’s brilliantly creative, down‑to‑earth history shows that calculus is not about complexity; it’s about simplicity. It harnesses an unreal number—infinity—to tackle real‑world problems, breaking them down into easier ones and then reassembling the answers into solutions that feel miraculous.
Infinite Powers recounts how calculus tantalized and thrilled its inventors, starting with its first glimmers in ancient Greec e and bringing us right up to the discovery of gravitational waves (a phenomenon predicted by calculus). Strogatz reveals how this form of math rose to the challenges of each age: how to determine the area of a circle with only sand and a stick; how to explain why Mars goes “backwards” sometimes; how to make electricity with magnets; how to ensure your rocket doesn’t miss the moon; how to turn the tide in the fight against AIDS.
As Strogatz proves, calculus is truly the language of the universe. By unveiling the principles of that language, Infinite Powers makes us marvel at the world anew.
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Recommended by John Urschel, Kirk Borne, and Nigel Shadbolt.
John Urschel
I hope they enjoy it as much as I did. If you or someone you know is studying Calculus, this book is highly recommended. https://t.co/s2yVt6SwTx [source]
Kirk Borne
"Infinite Powers: How Calculus Reveals the Secrets of the Universe" book by @stevenstrogatz https://t.co/wy91xAEqlS Great #Mathematics book that explores the History of Modern Science from this amazing perspective! https://t.co/M4obTvpnbe [source]
Nigel Shadbolt
Infinite Powers is a wonderful motivational for anyone taking a course in calculus. For those readers who remember calculus with dread from maths classes of yore, here is a text that explains just why the material has always had such a key place in our curricula. It charts a history of ideas that sought to make sense of the world through mathematics—to develop methods that find the deep laws and patterns that govern nature and enable us to build everything from computers to jet engines, televisions to microwaves. [source]
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44
One Hundred Hungry Ants
Elinor J Pinczes, Bonnie MacKain
4.3
One hundred hungry ants march off single file to sample a picnic, but when the going gets too slow, they divide into two rows of fifty, then four rows of twenty . . . until they take so long that the picnic is gone!
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45
How to Prove It: A Structured Approach
Daniel J. Velleman
4.3
Geared to preparing students to make the transition from solving problems to proving theorems, this text teaches them the techniques needed to read and write proofs. The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. To help students construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. Previous Edition Hb (1994) 0-521-44116-1 Previous Edition Pb (1994) 0-521-44663-5
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46
One Grain of Rice: A Mathematical Folktale
Demi
4.3
A reward of one grain of rice doubles day by day into millions of grains of rice when a selfish raja is outwitted by a clever village girl.
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47
The Man Who Knew Infinity: A Life of the Genius Ramanujan
Robert Kanigel
4.2
The tale of a relationship between a young Indian mathematics genius, Ramanujan, and his tutor at Cambridge University, G.H. Hardy, in the years before World War I. Through their eyes the reader is taken on a journey through numbers theory. Ramanujan would regularly telescope 12 steps of logic into two - the effect is said to be like Dr Watson in the train of some argument by Sherlock Holmes. The language of symbols and infinitely large (and small) regions of mathematics should be rendered with clarity for the general reader.
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48
The Number Devil: A Mathematical Adventure
Hans Magnus Enzensberger, Rotraut Susanne Berner, Michael Henry Heim
4.2
The international best-seller that makes mathematics a thrilling exploration.
In twelve dreams, Robert, a boy who hates math, meets a Number Devil, who leads him to discover the amazing world of numbers: infinite numbers, prime numbers, Fibonacci numbers, numbers that magically appear in triangles, and numbers that expand without. As we dream with him, we are taken further and further into mathematical theory, where ideas eventually take flight, until everyone - from those who fumble over fractions to those who solve complex equations in their heads - winds up marveling at what numbers can do.
Hans Magnus Enzensberger is a true polymath, the kind of superb intellectual who loves thinking and marshals all of his charm and wit to share his passions with the world. In The Number Devil, he brings together the surreal logic of Alice in Wonderland and the existential geometry of Flatland with the kind of math everyone would love, if only they had a number devil to teach it to them.
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49
Spaghetti and Meatballs for All!
Marilyn Burns, Debbie Tilley
4.2
Mr. and Mrs. Comfort have arranged tables and chairs to seat 32 people at their family reunion. But the guests have their own ideas for seating. Area and perimeter come alive as the family makes room for everyone. Used in Math By All Means: Area and Perimeter, Grades 5-6.
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50
Measuring Penny
Loreen Leedy
4.2
Lisa has an important homework assignment--to measure something in several different ways. She has to use standard units like inches and nonstandard units like paper clips to find out height, width, length, weight, volume, temperature, and time. Lisa decides to measure her dog, Penny, and finds out ...
Penny's nose = 1 inch long Penny's tail = 1 dog biscuit long Penny's paw print = 3 centimeters wide
... and that's only the beginning! Lisa learns a lot about her dog and about measuring, and even has fun doing it.
This clear and engaging concept book, delivered with a sense of humor, is certain to win over the most reluctant mathematician.
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51
A Mathematician's Lament: How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form
Paul Lockhart, Keith Devlin
4.2
“One of the best critiques of current mathematics education I have ever seen.”—Keith Devlin, math columnist on NPR’s Morning Edition
A brilliant research mathematician who has devoted his career to teaching kids reveals math to be creative and beautiful and rejects standard anxiety-producing teaching methods. Witty and accessible, Paul Lockhart’s controversial approach will provoke spirited debate among educators and parents alike and it will alter the way we think about math forever.
Paul Lockhart, has taught mathematics at Brown University and UC Santa Cruz. Since 2000, he has dedicated himself to K-12 level students at St. Ann’s School in Brooklyn, New York.
The history of pi, says the author, though a small part of the history of mathematics, is nevertheless a mirror of the history of man. Petr Beckmann holds up this mirror, giving the background of the times when pi made progress -- and also when it did not, because science was being stifled by militarism or religious fanaticism.
Recommended by Alex Bellos.
Alex Bellos
Petr Beckmann was a Czech electrical engineer who lived in Czechoslovakia until he was 39 in 1963, when he went to America as a visiting professor and just stayed there. [source]
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53
Inch by Inch
Leo Lionni
4.2
Can a song be measured?
Meet a winning, winsome inchworm, proud of his ability to measure anything under the sun, from a robin's tail to a toucan's beak. When a hungry nightingale threatens to eat him for breakfast unless he can measure her song, the inchworm calls on his craft and skill to creatively solve the dilemma.
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54
Hidden Figures: The American Dream and the Untold Story of the Black Women Mathematicians Who Helped Win the Space Race
Set against the backdrop of the Jim Crow South and the civil rights movement, the never-before-told true story of NASA’s African-American female mathematicians who played a crucial role in America’s space program—and whose contributions have been unheralded, until now.
Before John Glenn orbited the Earth or Neil Armstrong walked on the moon, a group of professionals worked as “Human Computers,” calculating the flight paths that would enable these historic achievements. Among these were a coterie of bright, talented African-American women. Segregated from their white counterparts by Jim Crow laws, these “colored computers,” as they were known, used slide rules, adding machines, and pencil and paper to support America’s fledgling aeronautics industry, and helped write the equations that would launch rockets, and astronauts, into space.
Drawing on the oral histories of scores of these “computers,” personal recollections, interviews with NASA executives and engineers, archival documents, correspondence, and reporting from the era, Hidden Figures recalls America’s greatest adventure and NASA’s groundbreaking successes through the experiences of five spunky, courageous, intelligent, determined, and patriotic women: Dorothy Vaughan, Mary Jackson, Katherine Johnson, Christine Darden, and Gloria Champine.
Moving from World War II through NASA’s golden age, touching on the civil rights era, the Space Race, the Cold War, and the women’s rights movement, Hidden Figures interweaves a rich history of scientific achievement and technological innovation with the intimate stories of five women whose work forever changed the world—and whose lives show how out of one of America’s most painful histories came one of its proudest moments.
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55
Secrets of Mental Math: The Mathemagician's Guide to Lightning Calculation and Amazing Math Tricks
Arthur Benjamin, Michael Shermer, et al.
4.2
These simple math secrets and tricks will forever change how you look at the world of numbers.
Secrets of Mental Math will have you thinking like a math genius in no time. Get ready to amaze your friends—and yourself—with incredible calculations you never thought you could master, as renowned “mathemagician” Arthur Benjamin shares his techniques for lightning-quick calculations and amazing number tricks. This book will teach you to do math in your head faster than you ever thought possible, dramatically improve your memory for numbers, and—maybe for the first time—make mathematics fun.
Yes, even you can learn to do seemingly complex equations in your head; all you need to learn are a few tricks. You’ll be able to quickly multiply and divide triple digits, compute with fractions, and determine squares, cubes, and roots without blinking an eye. No matter what your age or current math ability, Secrets of Mental Math will allow you to perform fantastic feats of the mind effortlessly. This is the math they never taught you in school.
Also available as an eBook
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56
Pete the Cat and His Four Groovy Buttons
James Dean, Eric Litwin
4.2
An award-winning and bestselling Pete the Cat hardcover picture book!
Count down with Pete in this rocking story that makes counting fun! Pete the Cat is wearing his favorite shirt—the one with the four totally groovy buttons.
But when one falls off, does Pete cry? Goodness, no! He just keeps on singing his song—after all, what could be groovier than three groovy buttons? The winner of the Theodor Seuss Geisel Honor Award.
The fun never stops—download the free groovin’ song!
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57
The Grouchy Ladybug
Eric Carle
4.2
From Eric Carle, New York Times bestselling author of The Very Hungry Caterpillar and From Head to Toe, comes the classic story of one very grouchy ladybug. Eric Carle's bright artwork and signature style will charm both ardent fans and new readers alike.
As children follow the Grouchy Ladybug on her journey, they will learn the important concepts of time, size, and shape, as well as the benefits of friendship and good manners.
For generations, The Grouchy Ladybug has delighted readers of all ages with the story of a bad-tempered bug who won't say "please" or "thank you," won't share, and thinks she is bigger and better than anyone else. Readers will love how this testy ladybug introduces them to many new animals and learns that maybe being grouchy isn’t always the best option.
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58
In Pursuit of the Unknown: 17 Equations That Changed the World
Ian Stewart
4.2
In In Pursuit of the Unknown, celebrated mathematician Ian Stewart uses a handful of mathematical equations to explore the vitally important connections between math and human progress. We often overlook the historical link between mathematics and technological advances, says Stewart—but this connection is integral to any complete understanding of human history.Equations are modeled on the patterns we find in the world around us, says Stewart, and it is through equations that we are able to make sense of, and in turn influence, our world. Stewart locates the origins of each equation he presents—from Pythagoras's Theorem to Newton's Law of Gravity to Einstein's Theory of Relativity—within a particular historical moment, elucidating the development of mathematical and philosophical thought necessary for each equation's discovery. None of these equations emerged in a vacuum, Stewart shows; each drew, in some way, on past equations and the thinking of the day. In turn, all of these equations paved the way for major developments in mathematics, science, philosophy, and technology. Without logarithms (invented in the early 17th century by John Napier and improved by Henry Briggs), scientists would not have been able to calculate the movement of the planets, and mathematicians would not have been able to develop fractal geometry. The Wave Equation is one of the most important equations in physics, and is crucial for engineers studying the vibrations in vehicles and the response of buildings to earthquakes. And the equation at the heart of Information Theory, devised by Claude Shannon, is the basis of digital communication today.
An approachable and informative guide to the equations upon which nearly every aspect of scientific and mathematical understanding depends, In Pursuit of the Unknown is also a reminder that equations have profoundly influenced our thinking and continue to make possible many of the advances that we take for granted.
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Recommended by Ante Shoda and Nick Higham.
Ante Shoda
This is written by a professor of mathematics from the United Kingdom, and it describes a number of mathematical breakthroughs and their consequences related to engineering and the practical usage of mathematics in machines and other things that we use every day. It’s a great introduction to the underlying principles of engineering. [source]
Nick Higham
He is a brilliant writer and one of the most famous people in the world for popularising mathematics. [source]
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59
Love and Math: The Heart of Hidden Reality
Edward Frenkel
4.2
A New York Times Science Bestseller
What if you had to take an art class in which you were only taught how to paint a fence? What if you were never shown the paintings of van Gogh and Picasso, weren’t even told they existed? Alas, this is how math is taught, and so for most of us it becomes the intellectual equivalent of watching paint dry.
In Love and Math, renowned mathematician Edward Frenkel reveals a side of math we’ve never seen, suffused with all the beauty and elegance of a work of art. In this heartfelt and passionate book, Frenkel shows that mathematics, far from occupying a specialist niche, goes to the heart of all matter, uniting us across cultures, time, and space.
Love and Math tells two intertwined stories: of the wonders of mathematics and of one young man’s journey learning and living it. Having braved a discriminatory educational system to become one of the twenty-first century’s leading mathematicians, Frenkel now works on one of the biggest ideas to come out of math in the last 50 years: the Langlands Program. Considered by many to be a Grand Unified Theory of mathematics, the Langlands Program enables researchers to translate findings from one field to another so that they can solve problems, such as Fermat’s last theorem, that had seemed intractable before.
At its core, Love and Math is a story about accessing a new way of thinking, which can enrich our lives and empower us to better understand the world and our place in it. It is an invitation to discover the magic hidden universe of mathematics.
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60
How Big Is a Foot?
Rolf Myller
4.2
The King wants to give the Queen something special for her birthday. The Queen has everything, everything except a bed. The trouble is that no one in the Kingdom knows the answer to a very important question: How Big is a Bed? because beds at the time had not yet been invented. The Queen's birthday is only a few days away. How can they figure out what size the bed should be?
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61
Alexander, Who Used to Be Rich Last Sunday
Judith Viorst
4.2
Last Sunday, Alexander's grandparents gave him a dollar -- and he was rich. There were so many things that he could do with all of that money!
He could buy as much gum as he wanted, or even a walkie-talkie, if he saved enough. But somehow the money began to disappear...
Readers of all ages will be delighted by this attractive new edition of Judith Viorst's beloved picture book.
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62
Principles of Mathematical Analysis
Walter Rudin
4.2
The third edition of this well known text continues to provide a solid foundation in mathematical analysis for undergraduate and first-year graduate students. The text begins with a discussion of the real number system as a complete ordered field. (Dedekind's construction is now treated in an appendix to Chapter I.) The topological background needed for the development of convergence, continuity, differentiation and integration is provided in Chapter 2. There is a new section on the gamma function, and many new and interesting exercises are included. This text is part of the Walter Rudin Student Series in Advanced Mathematics.
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63
Fooled by Randomness: The Hidden Role of Chance in Life and in the Markets
Fooled by Randomness is a standalone book in Nassim Nicholas Taleb’s landmark Incerto series, an investigation of opacity, luck, uncertainty, probability, human error, risk, and decision-making in a world we don’t understand. The other books in the series are The Black Swan, Antifragile, and The Bed of Procrustes.
Now in a striking new hardcover edition, Fooled by Randomness is the word-of-mouth sensation that will change the way you think about business and the world. Nassim Nicholas Taleb–veteran trader, renowned risk expert, polymathic scholar, erudite raconteur, and New York Times bestselling author of The Black Swan–has written a modern classic that turns on its head what we believe about luck and skill.
This book is about luck–or more precisely, about how we perceive and deal with luck in life and business. Set against the backdrop of the most conspicuous forum in which luck is mistaken for skill–the world of trading–Fooled by Randomness provides captivating insight into one of the least understood factors in all our lives. Writing in an entertaining narrative style, the author tackles major intellectual issues related to the underestimation of the influence of happenstance on our lives.
The book is populated with an array of characters, some of whom have grasped, in their own way, the significance of chance: the baseball legend Yogi Berra; the philosopher of knowledge Karl Popper; the ancient world’s wisest man, Solon; the modern financier George Soros; and the Greek voyager Odysseus. We also meet the fictional Nero, who seems to understand the role of randomness in his professional life but falls victim to his own superstitious foolishness.
However, the most recognizable character of all remains unnamed–the lucky fool who happens to be in the right place at the right time–he embodies the “survival of the least fit.” Such individuals attract devoted followers who believe in their guru’s insights and methods. But no one can replicate what is obtained by chance.
Are we capable of distinguishing the fortunate charlatan from the genuine visionary? Must we always try to uncover nonexistent messages in random events? It may be impossible to guard ourselves against the vagaries of the goddess Fortuna, but after reading Fooled by Randomness we can be a little better prepared.
PRAISE FOR FOOLED BY RANDOMNESS:
Named by Fortune One of the Smartest Books of All Time
A Financial Times Best Business Book of the Year
“[Fooled by Randomness] is to conventional Wall Street wisdom approximately what Martin Luther’s ninety-five theses were to the Catholic Church.” –Malcolm Gladwell, author of Blink
“The book that rolled down Wall Street like a hand grenade.” –Maggie Mahar, author of Bull! A History of the Boom, 1982—1999
“Fascinating . . . Taleb will grab you.” –Peter L. Bernstein, author of Capital Ideas Evolving
“Recalls the best of scientist/essayists like Richard Dawkins . . . and Stephen Jay Gould.” –Michael Schrage, author of Serious Play: How the World’s Best Companies Simulate to Innovate
“We need a book like this. . . . Fun to read, refreshingly independent-minded.” –Robert J. Shiller, author of Irrational Exuberance
“Powerful . . . loaded with crackling little insights [and] extreme brilliance.” –National Review
And throw in “The Black Swan” and “Fooled by Randomness”. “Fragile” means if you hit something might break. “Resilient” means if you hit something, it will stay the same. On my podcast Nassim discusses “Antifragility” – building a system, even on that works for you on a personal level, where you if you harm your self in some way it becomes stronger. That podcast changed my life He discusses Antifragility throughout history, up to our current economic situation, and even in our personal situations. [source]
Anant Jain
The five-book series, "Incerto", by Nassim Nicholas Taleb has had a profound impact on how I think about the world. There’s some overlap across the books — but you'll likely find the repetition helpful in retaining the content better. [source]
Art De Vany
I used this book is a class I taught on the economics of uncertainty. [source]
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64
Sir Cumference and All the King's Tens
Cindy Neuschwander, Wayne Geehan
4.1
A clever introduction to place value.
Sir Cumference and Lady Di planned a surprise birthday party for King Arthur, but they didn’t expect so many guests to show up. How many lunches will they need? And with more guests arriving by the minute, what about dinner? Sir Cumference and Lady Di have to figure out a quick way to count the guests to bring order to the party.
Sir Cumference and his friends have been entertaining young and old alike for years as they introduce important math concepts with clarity and humor.
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65
A Remainder of One
Elinor J Pinczes
4.1
Hup, two, three, four! We're in the 25th Army Corps. Queen's count! Two, three! We are the marching infantry! Poor Joe! He wants to march in the parade, but every time the lines are uneven, he must stand aside. What's a poor bug to do? Joe is determined. He studies the problem, relining the twenty-five bugs in his squadron from two lines to three lines to four lines, until inspiration and fortitude result in five lines of five -- and Joe fits in the last.
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66
Things to Make and Do in the Fourth Dimension
Matt Parker
4.1
- Cut pizzas in new and fairer ways! - Fit a 2p coin through an impossibly small hole! - Make a perfect regular pentagon by knotting a piece of paper! - Tie your shoes faster than ever before, saving literally seconds of your life! - Use those extra seconds to contemplate the diminishing returns of an exclamation-point at the end of every bullet-point! - Make a working computer out of dominoes!
Maths is a game. This book can be cut, drawn in, folded into shapes and will even take you to the fourth dimension.
So join stand-up mathematician Matt Parker on a journey through narcissistic numbers, optimal dating algorithms, at least two different kinds of infinity and more.
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67
How Many Seeds in a Pumpkin?
Margaret McNamara, G. Brian Karas
4.1
For curious kids, this explores skip counting and estimation in a fun pumpkin-themed classroom experiment. "How many seeds are in a pumpkin?" Mr. Tiffin asks his class as they gather around the big, medium, and small pumpkins on his desk. Robert, the biggest kid, guesses that the largest one has a million seeds; Elinor, sounding like she knows what she's talking about, guesses the medium one has 500 seeds; and Anna, who likes even numbers better than odd ones, guesses that the little one has 22. Charlie, the smallest boy in the class, doesn't have a guess. Counting pumpkin seeds is messy business, but once the slimy job is done, ... well, you'll have to read and find out!
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68
A Beautiful Mind
Sylvia Nasar
4.1
Stories of famously eccentric Princetonians abound—such as that of chemist Hubert Alyea, the model for The Absent-Minded Professor, or Ralph Nader, said to have had his own key to the library as an undergraduate. Or the "Phantom of Fine Hall," a figure many students had seen shuffling around the corridors of the math and physics building wearing purple sneakers and writing numerology treatises on the blackboards. The Phantom was John Nash, one of the most brilliant mathematicians of his generation, who had spiraled into schizophrenia in the 1950s. His most important work had been in game theory, which by the 1980s was underpinning a large part of economics. When the Nobel Prize committee began debating a prize for game theory, Nash's name inevitably came up—only to be dismissed, since the prize clearly could not go to a madman. But in 1994 Nash, in remission from schizophrenia, shared the Nobel Prize in economics for work done some 45 years previously.
Economist and journalist Sylvia Nasar has written a biography of Nash that looks at all sides of his life. She gives an intelligent, understandable exposition of his mathematical ideas and a picture of schizophrenia that is evocative but decidedly unromantic. Her story of the machinations behind Nash's Nobel is fascinating and one of very few such accounts available in print (the CIA could learn a thing or two from the Nobel committees).
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Recommended by Ariel Rubinstein and Diane Coyle.
Ariel Rubinstein
The story of John Nash is really a human story – I don’t think it sheds much light on game theory. But it gives hope to people dealing with this disease. [source]
Diane Coyle
This is a terrific book for just saying something about what game theory helps to do, without plunging you into all the complicated mathematics of how to do it in practice. [source]
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69
Proofs from THE BOOK
Martin Aigner, Günter M. Ziegler, Karl H. Hofmann
4.1
This revised and enlarged sixth edition of Proofs from THE BOOK features an entirely new chapter on Van der Waerden's permanent conjecture, as well as additional, highly original and delightful proofs in other chapters.
From the citation on the occasion of the 2018 "Steele Prize for Mathematical Exposition"
"... It is almost impossible to write a mathematics book that can be read and enjoyed by people of all levels and backgrounds, yet Aigner and Ziegler accomplish this feat of exposition with virtuoso style. [...] This book does an invaluable service to mathematics, by illustrating for non-mathematicians what it is that mathematicians mean when they speak about beauty."
From the Reviews
"... Inside PFTB (Proofs from The Book) is indeed a glimpse of mathematical heaven, where clever insights and beautiful ideas combine in astonishing and glorious ways. There is vast wealth within its pages, one gem after another. ... Aigner and Ziegler... write: "... all we offer is the examples that we have selected, hoping that our readers will share our enthusiasm about brilliant ideas, clever insights and wonderful observations." I do. ... "
Notices of the AMS, August 1999
"... This book is a pleasure to hold and to look at: ample margins, nice photos, instructive pictures and beautiful drawings ... It is a pleasure to read as well: the style is clear and entertaining, the level is close to elementary, the necessary background is given separately and the proofs are brilliant. ..."
LMS Newsletter, January 1999
"Martin Aigner and G�nter Ziegler succeeded admirably in putting together a broad collection of theorems and their proofs that would undoubtedly be in the Book of Erd�s. The theorems are so fundamental, their proofs so elegant and the remaining open questions so intriguing that every mathematician, regardless of speciality, can benefit from reading this book. ... "
SIGACT News, December 2011
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70
Our Mathematical Universe: My Quest for the Ultimate Nature of Reality
Max Tegmark
4.1
Our Mathematical Universe is a journey to explore the mysteries uncovered by cosmology and to discover the nature of reality. Our Big Bang, our distant future, parallel worlds, the sub-atomic and intergalactic - none of them are what they seem. But there is a way to understand this immense strangeness - mathematics. Seeking an answer to the fundamental puzzle of why our universe seems so mathematical, Tegmark proposes a radical idea: that our physical world not only is described by mathematics, but that it is mathematics. This may offer answers to our deepest questions: How large is reality? What is everything made of? Why is our universe the way it is?
Table of Contents Preface
1 What Is Reality? Not What It Seems • What’s the Ultimate Question? • The Journey Begins
Part One: Zooming Out
2 Our Place in Space Cosmic Questions • How Big Is Space? • The Size of Earth • Distance to the Moon • Distance to the Sun and the Planets • Distance to the Stars • Distance to the Galaxies • What Is Space?
3 Our Place in Time Where Did Our Solar System Come From? • Where Did the Galaxies Come From? • Where Did the Mysterious Microwaves Come From? • Where Did the Atoms Come From?
4 Our Universe by Numbers Wanted: Precision Cosmology • Precision Microwave-Background Fluctuations • Precision Galaxy Clustering • The Ultimate Map of Our Universe • Where Did Our Big Bang Come From?
5 Our Cosmic Origins What’s Wrong with Our Big Bang? • How Inflation Works • The Gift That Keeps on Giving • Eternal Inflation
6 Welcome to the Multiverse The Level I Multiverse • The Level II Multiverse • Multiverse Halftime Roundup
Part Two: Zooming In
7 Cosmic Legos Atomic Legos • Nuclear Legos • Particle-Physics Legos • Mathematical Legos • Photon Legos • Above the Law? • Quanta and Rainbows • Making Waves • Quantum Weirdness • The Collapse of Consensus • The Weirdness Can’t Be Confined • Quantum Confusion
8 The Level III Multiverse The Level III Multiverse • The Illusion of Randomness • Quantum Censorship • The Joys of Getting Scooped • Why Your Brain Isn’t a Quantum Computer • Subject, Object and Environment • Quantum Suicide • Quantum Immortality? • Multiverses Unified • Shifting Views: Many Worlds or Many Words?
Part Three: Stepping Back
9 Internal Reality, External Reality and Consensus Reality External Reality and Internal Reality • The Truth, the Whole Truth and Nothing but the Truth • Consensus Reality • Physics: Linking External to Consensus Reality
10 Physical Reality and Mathematical Reality Math, Math Everywhere! • The Mathematical Universe Hypothesis • What Is a Mathematical Structure?
11 Is Time an Illusion? How Can Physical Reality Be Mathematical? • What Are You? • Where Are You? (And What Do You Perceive?) • When Are You?
12 The Level IV Multiverse Why I Believe in the Level IV Multiverse • Exploring the Level IV Multiverse: What’s Out There? • Implications of the Level IV Multiverse • Are We Living in a Simulation? • Relation Between the MUH, the Level IV Multiverse and Other Hypotheses •Testing the Level IV Multiverse
13 Life, Our Universe and Everything How Big Is Our Physical Reality? • The Future of Physics • The Future of Our Universe—How Will It End? • The Future of Life •The Future of You—Are You Insignificant?
Acknowledgments Suggestions for Further Reading Index
Bryan Johnson recommended this book on Twitter. [source]
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72
Calculus Made Easy
Silvanus P. Thompson, Martin Gardner
4.1
Calculus Made Easy has long been the most popular calculus primer, and this major revision of the classic math text makes the subject at hand still more comprehensible to readers of all levels. With a new introduction, three new chapters, modernized language and methods throughout, and an appendix of challenging and enjoyable practice problems, Calculus Made Easy has been thoroughly updated for the modern reader.
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73
Ten Apples Up On Top!
Dr. Seuss, Roy McKie
4.1
Learning to count has never been more fun than in this crazy tale of a dog, a lion and a tiger all showing off how many apples they can balance on their heads as they skip, walk the tightrope and roller skate their way through the book.
This delightful book forms part of the second stage in HarperCollins’ major Dr. Seuss rebrand programme. With the relaunch of 10 more titles in August 2003, such all-time favourites as How the Grinch Stole Christmas!, Mr. Brown Can Moo! Can You? and Dr. Seuss’ Sleep Book boast bright new covers that incorporate much needed guidance on reading levels: Blue Back Books are for parents to share with young children, Green Back Books are for budding readers to tackle on their own, and Yellow Back Books are for older, more fluent readers to enjoy. Ten Apples Up On Top belongs to the Green Back Book range.
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74
Sir Cumference and the Great Knight of Angleland
Cindy Neuschwander, Wayne Geehan
4.1
Radius is on a quest to earn his knighthood! With only a circular medallion, a mysterious poem, and his own wits to guide him, he must find and rescue a missing king.
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75
Linear Algebra Done Right
Sheldon Axler
4.1
This text for a second course in linear algebra is aimed at math majors and graduate students. The novel approach taken here banishes determinants to the end of the book and focuses on the central goal of linear algebra: understanding the structure of linear operators on vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. For example, the book presents - without having defined determinants - a clean proof that every linear operator on a finite-dimensional complex vector space (or an odd-dimensional real vector space) has an eigenvalue. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. This second edition includes a new section on orthogonal projections and minimization problems. The sections on self-adjoint operators, normal operators, and the spectral theorem have been rewritten. New examples and new exercises have been added, several proofs have been simplified, and hundreds of minor improvements have been made throughout the text.
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76
Humble Math - 100 Days of Timed Tests: Multiplication: Grades 3-5, Math Drills, Digits 0-12, Reproducible Practice Problems
Humble Math
4.1
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77
Naked Statistics: Stripping the Dread from the Data
Once considered tedious, the field of statistics is rapidly evolving into a discipline Hal Varian, chief economist at Google, has actually called “sexy.” From batting averages and political polls to game shows and medical research, the real-world application of statistics continues to grow by leaps and bounds. How can we catch schools that cheat on standardized tests? How does Netflix know which movies you’ll like? What is causing the rising incidence of autism? As best-selling author Charles Wheelan shows us in Naked Statistics, the right data and a few well-chosen statistical tools can help us answer these questions and more. For those who slept through Stats 101, this book is a lifesaver. Wheelan strips away the arcane and technical details and focuses on the underlying intuition that drives statistical analysis. He clarifies key concepts such as inference, correlation, and regression analysis, reveals how biased or careless parties can manipulate or misrepresent data, and shows us how brilliant and creative researchers are exploiting the valuable data from natural experiments to tackle thorny questions.
And in Wheelan’s trademark style, there’s not a dull page in sight. You’ll encounter clever Schlitz Beer marketers leveraging basic probability, an International Sausage Festival illuminating the tenets of the central limit theorem, and a head-scratching choice from the famous game show Let’s Make a Deal—and you’ll come away with insights each time. With the wit, accessibility, and sheer fun that turned Naked Economics into a bestseller, Wheelan defies the odds yet again by bringing another essential, formerly unglamorous discipline to life.
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78
e: the Story of a Number
Eli Maor
4.1
The story of [pi] has been told many times, both in scholarly works and in popular books. But its close relative, the number e, has fared less well: despite the central role it plays in mathematics, its history has never before been written for a general audience. The present work fills this gap. Geared to the reader with only a modest background in mathematics, the book describes the story of e from a human as well as a mathematical perspective. In a sense, it is the story of an entire period in the history of mathematics, from the early seventeenth to the late nineteenth century, with the invention of calculus at its center. Many of the players who took part in this story are here brought to life. Among them are John Napier, the eccentric religious activist who invented logarithms and - unknowingly - came within a hair's breadth of discovering e; William Oughtred, the inventor of the slide rule, who lived a frugal and unhealthful life and died at the age of 86, reportedly of joy when hearing of the restoration of King Charles II to the throne of England; Newton and his bitter priority dispute with Leibniz over the invention of the calculus, a conflict that impeded British mathematics for more than a century; and Jacob Bernoulli, who asked that a logarithmic spiral be engraved on his tombstone - but a linear spiral was engraved instead! The unifying theme throughout the book is the idea that a single number can tie together so many different aspects of mathematics - from the law of compound interest to the shape of a hanging chain, from the area under a hyperbola to Euler's famous formula e superscript i[pi++ = -1, from the inner structure of a nautilus shell to Bach's equal-temperedscale and to the art of M. C. Escher. The book ends with an account of the discovery of transcendental numbers, an event that paved the way for Cantor's revolutionary ideas about infinity. No knowledge of calculus is assumed, and the few places where calculus is used are fully exp
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79
Everything You Need to Ace Math in One Big Fat Notebook: The Complete Middle School Study Guide
Workman Publishing, Ouida Newton, et al.
4.1
It’s the revolutionary math study guide just for middle school students from the brains behind Brain Quest.
Everything You Need to Ace Math . . . covers everything to get a student over any math hump: fractions, decimals, and how to multiply and divide them; ratios, proportions, and percentages; geometry; statistics and probability; expressions and equations; and the coordinate plane and functions.
The BIG FAT NOTEBOOK™ series is built on a simple and irresistible conceit—borrowing the notes from the smartest kid in class. There are five books in all, and each is the only book you need for each main subject taught in middle school: Math, Science, American History, English Language Arts, and World History. Inside the reader will find every subject’s key concepts, easily digested and summarized: Critical ideas highlighted in neon colors. Definitions explained. Doodles that illuminate tricky concepts in marker. Mnemonics for memorable shortcuts. And quizzes to recap it all.
The BIG FAT NOTEBOOKS meet Common Core State Standards, Next Generation Science Standards, and state history standards, and are vetted by National and State Teacher of the Year Award–winning teachers. They make learning fun and are the perfect next step for every kid who grew up on Brain Quest.
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80
An Imaginary Tale: The Story of the Square Root of Minus One
Paul J. Nahin
4.1
In An Imaginary Tale, Paul Nahin tells the 2000-year-old history of one of mathematics' most elusive numbers, the square root of minus one, also known as i, re-creating the baffling mathematical problems that conjured it up and the colorful characters who tried to solve them. Addressing readers with both a general and scholarly interest in mathematics, Nahin weaves into this narrative entertaining historical facts, mathematical discussions, and the application of complex numbers and functions to important problems.
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81
Letters to a Young Mathematician
Ian Stewart
4.1
The first scientific entry in the acclaimed Art of Mentoring series from Basic Books, Letters to a Young Mathematician tells readers what Ian Stewart wishes he had known when he was a student and young faculty member. Subjects ranging from the philosophical to the practical--what mathematics is and why it's worth doing, the relationship between logic and proof, the role of beauty in mathematical thinking, the future of mathematics, how to deal with the peculiarities of the mathematical community, and many others--are dealt with in Stewart's much-admired style, which combines subtle, easygoing humor with a talent for cutting to the heart of the matter. In the tradition of G.H. Hardy's classic A Mathematician's Apology, this book is sure to be a perennial favorite with students at all levels, as well as with other readers who are curious about the frequently incomprehensible world of mathematics.
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82
Mathematics: Its Content, Methods and Meaning
A. D. Aleksandrov, A. N. Kolmogorov, M. A. Lavrent’ev
4.1
". . . Nothing less than a major contribution to the scientific culture of this world." — The New York Times Book Review This major survey of mathematics, featuring the work of 18 outstanding Russian mathematicians and including material on both elementary and advanced levels, encompasses 20 prime subject areas in mathematics in terms of their simple origins and their subsequent sophisticated developement. As Professor Morris Kline of New York University noted, "This unique work presents the amazing panorama of mathematics proper. It is the best answer in print to what mathematics contains both on the elementary and advanced levels." Beginning with an overview and analysis of mathematics, the first of three major divisions of the book progresses to an exploration of analytic geometry, algebra, and ordinary differential equations. The second part introduces partial differential equations, along with theories of curves and surfaces, the calculus of variations, and functions of a complex variable. It furthur examines prime numbers, the theory of probability, approximations, and the role of computers in mathematics. The theory of functions of a real variable opens the final section, followed by discussions of linear algebra and nonEuclidian geometry, topology, functional analysis, and groups and other algebraic systems. Thorough, coherent explanations of each topic are further augumented by numerous illustrative figures, and every chapter concludes with a suggested reading list. Formerly issued as a three-volume set, this mathematical masterpiece is now available in a convenient and modestly priced one-volume edition, perfect for study or reference. "This is a masterful English translation of a stupendous and formidable mathematical masterpiece . . ." — Social Science
There is something admirable about the school of the Russians: they are thinkers doing math, with remarkable clarity, minimal formalism, and total absence of unnecessary pedantry one finds in more modern texts (in the post Bourbaki era). This is of course surprising as one would have expected the exact opposite from the products of the communist era. Mathematicians should be using this book as a model for their own composition. You can read it and reread it. Professors should assign this in addition to modern texts, as readers can get intutions, something alas absent from modern texts. [source]
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83
Proofs and Refutations: The Logic of Mathematical Discovery
Imre Lakatos, John Worrall, Elie Zahar
4.1
A novel introduction to the philosophy of mathematics, mostly in the form of a discussion between a group of students and their teacher. It combats the positivist picture and develops a much richer, more dramatic progression.
Recommended by Alf Coles.
Alf Coles
I first came across this book at university in a course on the philosophy of mathematics. Looking back, it was one of my first experiences of how maths could be different to how I was taught it. In the book, Lakatos takes a particular area of mathematics to do with shape and recreates an imaginary dialogue where he and the characters in the book go through this extraordinary process of developing what mathematicians would call conjectures. So they are developing predictions about how a particular property of a shape might operate, or which types of shape it might be true for. There’s this amazing description of a process which, for me, is at the heart of doing mathematics, which is coming up with conjectures, coming up with predictions and then the search for counter-examples that don’t fit that conjecture, and, as a result of that, the refinement of the conjecture itself. It’s quite a scientific process: you come up with an idea and you try and refute it. [source]
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84
Calculus
Michael Spivak
4.1
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85
Zero the Hero
Joan Holub, Tom Lichtenheld
4.1
Zero. Zip. Zilch. Nada. That's what all the other numbers think of Zero. He doesn't add anything in addition. He's of no use in division. And don't even ask what he does in multiplication. (Hint: Poof!) But Zero knows he's worth a lot, and when the other numbers get into trouble, he swoops in to prove that his talents are innumerable.
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86
The Colossal Book of Mathematics
Martin Gardner
4.1
s/t: Classic Puzzles, Paradoxes & Problems Whether discussing hexaflexagons or number theory, Klein bottles or the essence of "nothing," Martin Gardner has single-handedly created the field of "recreational mathematics." The Colossal Book of Mathematics collects together Gardner's most popular pieces from his legendary "Mathematical Games" column, which ran in Scientific American for twenty-five years. Gardner's array of absorbing puzzles and mind-twisting paradoxes opens mathematics up to the world at large, inspiring people to see past numbers and formulas and experience the application of mathematical principles to the mysterious world around them. With articles on topics ranging from simple algebra to the twisting surfaces of Mobius strips, from an endless game of Bulgarian solitaire to the unreachable dream of time travel, this volume comprises a substantial and definitive monument to Gardner's influence on mathematics, science, and culture.
In its twelve sections, The Colossal Book of Math explores a wide range of areas, each startlingly illuminated by Gardner's incisive expertise. Beginning with seemingly simple topics, Gardner expertly guides us through complicated and wondrous worlds: by way of basic algebra we contemplate the mesmerizing, often hilarious, linguistic and numerical possibilities of palindromes; using simple geometry, he dissects the principles of symmetry upon which the renowned mathematical artist M. C. Escher constructs his unique, dizzying universe. Gardner, like few thinkers today, melds a rigorous scientific skepticism with a profound artistic and imaginative impulse. His stunning exploration of "The Church of the Fourth Dimension," for example, bridges the disparate worlds of religion and science by brilliantly imagining the spatial possibility of God's presence in the world as a fourth dimension, at once "everywhere and nowhere."
With boundless wisdom and his trademark wit, Gardner allows the reader to further engage challenging topics like probability and game theory which have plagued clever gamblers, and famous mathematicians, for centuries. Whether debunking Pascal's wager with basic probability, making visual music with fractals, or uncoiling a "knotted doughnut" with introductory topology, Gardner continuously displays his fierce intelligence and gentle humor. His articles confront both the comfortingly mundane—"Generalized Ticktacktoe" and "Sprouts and Brussel Sprouts"—and the quakingly abstract—"Hexaflexagons," "Nothing," and "Everything." He navigates these staggeringly obscure topics with a deft intelligence and, with addendums and suggested reading lists, he informs these classic articles with new insight.
Admired by scientists and mathematicians, writers and readers alike, Gardner's vast knowledge and burning curiosity reveal themselves on every page. The culmination of a lifelong devotion to the wonders of mathematics, The Colossal Book of Mathematics is the largest and most comprehensive math book ever assembled by Gardner and remains an indispensable volume for the amateur and expert alike.
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87
God Created the Integers: The Mathematical Breakthroughs That Changed History
Stephen Hawking
4.1
In this collection of landmark mathematical works, editor Stephen Hawking has assembled the greatest feats humans have ever accomplished using just numbers and their brains.
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88
Sir Cumference and the Sword in the Cone
Cindy Neuschwander, Wayne Geehan
4.1
King Arthur has issued a challenge. The first knight to find the sword Edgecalibur will be the next king. Join Sir Cumference, Lady Di of Ameter, and their son, Radius, as they race to help their friend, Vertex, find the sword and discover the secrets of cubes, pyramids, cylinders, and cones.
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89
One Fish, Two Fish, Red Fish, Blue Fish
Dr. Seuss
4.1
One Fish Two Fish Red Fish Blue Fish is a 1960 children's book by Dr. Seuss (Theodor Seuss Geisel). A simple rhyming book for learner readers, it is a book with a freewheeling plot about a boy and a girl, and the many amazing creatures they have for friends and pets. One Fish Two Fish Red Fish Blue Fish was part of the Beginner Book Video series which included Oh, the Thinks You Can Think! and The Foot Book.
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90
Pigs Will Be Pigs: Fun with Math and Money
Amy Axelrod, Sharon McGinley-Nally
4.1
Join the pig family as they add, subtract, multiply, divide, and think about how money works in order to satisfy their big pig appetites!
The pigs are very hungry, and there’s no food in the house. Mr. Pig suggests eating out—but oh, no! The Pigs are out of money!
So the family goes on a money hunt. In beds, under the carpet, even in the washing machine the coins and bills add up, and soon it’s off to the Enchanted Enchilada.
How much money did the Pigs find? What can they afford to order from the menu? Join the fun and pig out on math and money concepts with the Pigs!
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91
Big Book of Math Practice Problems Addition and Subtraction: Single Digit Facts / Drills, Double Digits, Triple Digits, Arithmetic With & Without Regrouping, Grades 1-3
Stacy Otillio and Frank Otillio
4.0
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92
Chicka Chicka 1, 2, 3
Bill Martin Jr., Michael Sampson, Lois Ehlert
4.0
1 told 2 and 2 told 3, "I'll race you to the top of the apple tree." One hundred and one numbers climb the apple tree in this bright, rollicking, joyous book for young children. As the numerals pile up and bumblebees threaten, what's the number that saves the day? (Hint: It rhymes with "hero.") Read and count and play and laugh to learn the surprising answer.
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93
Measurement
Paul Lockhart
4.0
For seven years, Paul Lockhart s "A Mathematician s Lament" enjoyed a samizdat-style popularity in the mathematics underground, before demand prompted its 2009 publication to even wider applause and debate. An impassioned critique of K 12 mathematics education, it outlined how we shortchange students by introducing them to math the wrong way. Here Lockhart offers the positive side of the math education story by showing us how math should be done. "Measurement "offers a permanent solution to math phobia by introducing us to mathematics as an artful way of thinking and living.
In conversational prose that conveys his passion for the subject, Lockhart makes mathematics accessible without oversimplifying. He makes no more attempt to hide the challenge of mathematics than he does to shield us from its beautiful intensity. Favoring plain English and pictures over jargon and formulas, he succeeds in making complex ideas about the mathematics of shape and motion intuitive and graspable. His elegant discussion of mathematical reasoning and themes in classical geometry offers proof of his conviction that mathematics illuminates art as much as science.
Lockhart leads us into a universe where beautiful designs and patterns float through our minds and do surprising, miraculous things. As we turn our thoughts to symmetry, circles, cylinders, and cones, we begin to see that almost anyone can do the math in a way that brings emotional and aesthetic rewards. "Measurement" is an invitation to summon curiosity, courage, and creativity in order to experience firsthand the playful excitement of mathematical work."
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94
Probability Theory
E. T. Jaynes, G. Larry Bretthorst
4.0
Going beyond the conventional mathematics of probability theory, this study views the subject in a wider context. It discusses new results, along with applications of probability theory to a variety of problems. The book contains many exercises and is suitable for use as a textbook on graduate-level courses involving data analysis. Aimed at readers already familiar with applied mathematics at an advanced undergraduate level or higher, it is of interest to scientists concerned with inference from incomplete information.
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95
Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering
Steven H. Strogatz
4.0
This textbook is aimed at newcomers to nonlinear dynamics and chaos. The presentation stresses analytical methods, concrete examples, and geometric intuition. A unique feature of the book is its emphasis on applications. These include mechanical vibrations, lasers, biological rhythms, superconducting circuits, insect outbreaks, chemical oscillators, genetic control systems, chaotic waterwheels, and even a technique for using chaos to send secret messages. In each case, the scientific background is explained at an elementary level and closely integrated with mathematical theory.
About the Author: Steven Strogatz is in the Center for Applied Mathematics and the Department of Theoretical and Applied Mathematics at Cornell University. Since receiving his Ph.D. from Harvard university in 1986, Professor Strogatz has been honored with several awards, including the E.M. Baker Award for Excellence, the highest teaching award given by MIT.
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96
The Man Who Counted: A Collection of Mathematical Adventures
Malba Tahan is the creation of a celebrated Brazilian mathematician who was looking for a way to bring some of the mysteries and delights of mathematics to a wider public. He turned out to be a born storyteller.
The adventures of Beremiz Samir, The Man Who Counted, take the reader on an exotic journey in which, time and again, he summons his extraordinary mathematical powers to settle disputes, give wise advice, overcome dangerous enemies, and win for himself fame and fortune. as we accompany him, we learn much of the history of famous mathematicisns who preceded him; we undergo a series of trials at the hands of the wise men of the day; and we come to admire the warm wisdom and patience that earn him the respect and affection of those whose problems he resolves so astutely. In the grace of their telling, these stories hold unusual delights for the reader.
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Recommended by Alex Bellos.
Alex Bellos
The author Malba Tahan is a fictional character, the pen name of Júlio César de Mello e Sousa, and the book is set in Arabia as a mixture of One Thousand and One Nights and a maths book – it’s coming out of the most populous Catholic country in the world and yet it’s as much a love story to Arab culture as to maths itself. There were lots of Arab immigrants in Brazil and they love Arab culture – one of the most popular fast food chains is called Habib’s. The story here is presented as if the author, who I believe only went to Lisbon once and virtually never left Brazil, has just stumbled upon or discovered this Arab text. [source]
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97
Math for All Seasons
Greg Tang, Harry Briggs
4.0
Let the Scholastic bookshelf be your guide through the whole range of your child's reading experience--laugh with them, learn with them, read with them! Category: Math Skills Your challenge is to find the sum Without counting one by one Why not count? It's much too slow -- Adding is the way to go! Make clever groups before you start -- Then add them in a way that's smart! MATH FOR ALL SEASONS will challenge every kid -- and every parent -- to open their minds and solve problems in new and unexpected ways. By looking for patterns, symmetries, and familiar number combinations within eye-catching pictures, math will become easier, quicker, and more fun than anyone could have imagined!
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98
The Phantom Tollbooth
Norton Juster, Jules Feiffer
4.0
Hailed as “a classic. . . . humorous, full of warmth and real invention” (The New Yorker), this beloved story -first published more than fifty years ago- introduces readers to Milo and his adventures in the Lands Beyond.
For Milo, everything’s a bore. When a tollbooth mysteriously appears in his room, he drives through only because he’s got nothing better to do. But on the other side, things seem different. Milo visits the Island of Conclusions (you get there by jumping), learns about time from a ticking watchdog named Tock, and even embarks on a quest to rescue Rhyme and Reason! Somewhere along the way, Milo realizes something astonishing. Life is far from dull. In fact, it’s exciting beyond his wildest dreams. . . .
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Recommended by Clara Jeffery and Julie Zhuo.
Clara Jeffery
The best kids book ever https://t.co/9f3UGfmPdi [source]
Julie Zhuo
To this day, I can think of no better book that captures the imagination, wonder and adventure of life that children so intuitively grasp. [source]
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99
Apple Fractions
Jerry Pallotta, Rob Bolster
4.0
Best-selling author Jerry Pallotta turns his talents to teaching fractions to kids by using a healthy snack food: apples!
Author Jerry Pallotta and illustrator Rob Bolster use a variety of different apples to teach kids all about fractions in this innovative and enjoyable book. Playful elves demonstrate how to divide apples into halves, thirds, fourths, and more. Young readers will also learn about varieties of apples, including Golden and Red Delicious, Granny Smiths, Cortlands, and even Asian Pears.
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100
Introduction to Linear Algebra
Gilbert Strang
4.0
Linear algebra is something all mathematics undergraduates and many other students, in subjects ranging from engineering to economics, have to learn. The fifth edition of this hugely successful textbook retains all the qualities of earlier editions while at the same time seeing numerous minor improvements and major additions. The latter include: - A new chapter on singular values and singular vectors, including ways to analyze a matrix of data - A revised chapter on computing in linear algebra, with professional-level algorithms and code that can be downloaded for a variety of languages - A new section on linear algebra and cryptography - A new chapter on linear algebra in probability and statistics. A dedicated and active website also offers solutions to exercises as well as new exercises from many different sources (e.g. practice problems, exams, development of textbook examples), plus codes in MATLAB, Julia, and Python.
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