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The Joy of X: A Guided Tour of Math, from One to Infinity
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 p, 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 .
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 p, 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 .
316 pages, Hardcover
First published October 2, 2012
About the author
Steven H. Strogatz
17 books891 followersSteven Strogatz is the Schurman Professor of applied mathematics at Cornell University. A renowned teacher and one of the world’s most highly cited mathematicians, he has been a frequent guest on National Public Radio’s Radiolab. Among his honors are MIT's highest teaching prize, membership in the American Academy of Arts and Sciences, and a lifetime achievement award for communication of math to the general public, awarded by the four major American mathematical societies. He also wrote a popular New York Times online column, “The Elements of Math,” which formed the basis for his new book, The Joy of x. He lives in Ithaca, New York with his wife and two daughters.
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Displaying 1 - 30 of 895 reviews
August 12, 2012
I will be the first to admit that I'm not good at math. Despite taking Higher Maths in IB (I just practiced so many times that I somehow knew how to solve the question), I still didn't understand a lot of concepts. And despite all the quotes about how math was beautiful in my textbooks, I still just don't get it. And I suspect that this problem isn't unique to me a lone. So, I was really intrigued by the promise of this book to be a guided (and fun) tour of math.
The Joy of X, unlike what the name suggests, doesn't start from algebra. Instead, it starts from what we all consider basic - the concept of numbers. From there, we move on to addition and subtraction, and the book gets progressively harder as we head into algebra, geometry, calculus, statistics and finally, the biggest number of them all, infinity.
If you're looking for a "how-to" guide book, then this book probably isn't for you. After reading it, I can't say that I fully understand all the basic concepts in maths, but I am much more interested in them now. Each chapter is short and sweet, and I suspect that the fact that each chapter is fairly short means that there is less time to understand each concept. So what we do get is a very interesting introduction to the concept, designed to spark your interest.
And really, with the internet (and all the math textbooks lying around. Oh, you already burned yours?), you can always study the topics that interest you in-depth by yourself. To me, the true gem of this book is how it encouraged me to regain hope that math can be fun and rewarding.
I would say, that if you're looking for a fun and interesting explanation on one particular topic, you should check out the "manga-guide" series (e.g. The Manga Guide to Statistics). But if you're looking to encourage yourself after feeling like you will never understand mathematics, or simply want to regain a spark of curiosity in maths (doesn't it too often feel like the mere memorisation of formulae?), then you should definitely pick up this book.
Disclaimer: I got this book free from NetGalley in exchange for a free and honest review.
First posted at Inside the mind of a Bibliophile
The Joy of X, unlike what the name suggests, doesn't start from algebra. Instead, it starts from what we all consider basic - the concept of numbers. From there, we move on to addition and subtraction, and the book gets progressively harder as we head into algebra, geometry, calculus, statistics and finally, the biggest number of them all, infinity.
If you're looking for a "how-to" guide book, then this book probably isn't for you. After reading it, I can't say that I fully understand all the basic concepts in maths, but I am much more interested in them now. Each chapter is short and sweet, and I suspect that the fact that each chapter is fairly short means that there is less time to understand each concept. So what we do get is a very interesting introduction to the concept, designed to spark your interest.
And really, with the internet (and all the math textbooks lying around. Oh, you already burned yours?), you can always study the topics that interest you in-depth by yourself. To me, the true gem of this book is how it encouraged me to regain hope that math can be fun and rewarding.
I would say, that if you're looking for a fun and interesting explanation on one particular topic, you should check out the "manga-guide" series (e.g. The Manga Guide to Statistics). But if you're looking to encourage yourself after feeling like you will never understand mathematics, or simply want to regain a spark of curiosity in maths (doesn't it too often feel like the mere memorisation of formulae?), then you should definitely pick up this book.
Disclaimer: I got this book free from NetGalley in exchange for a free and honest review.
First posted at Inside the mind of a Bibliophile
April 12, 2023
To many he is the Jacob Gould Schurman Professor of Applied mathematics at Cornell University, but to me he is a man making the complex palatable in small pieces manifesting into vibrating works of art. He likes Archimedes. We then played on table with “kinder augen.” Seagulls watched as we replicated Archimedes lever using a fork, saltshaker and finger while Pacific salty breezes blew the blue linen corner of the linen—so oft kissed by salty breezes.
“The Joy of X: A Guided Tour of Math, from one to Infinity” is not a rollercoaster ride in math. Yet it is a rather elegant meandering from algebra to vector calculus. In the smallest and rudimentary forms of life math leaves its indelible signature on little things like dragonflies to large black and white zebra stripes. Discovery within how number three is not naked. How is the correct formula for Y = 3G really F = 3Y?
"Princeton rejected his application... His best option (though he found it depressing) was MIT... In physicist Gell-Mann's eyes, MIT was a grubby technological institute, beneath his rarefied taste... He could always go to MIT and commit suicide later if he had to, but not the other way around."
---Steven Henry Strogatz
Harvard man Steven has us brushing up against Galileo and Georg Cantor in realizing that infinity could occupy three varied types. Math and mental illness (for Georg) seemed to be bitter common companions despite his orchestration of set theory. Royal Society awarded him the Sylvester Medal in 1904 post hospitalization.
Word etymology is fascinating as the light shines brightly on algebra and how the word is Arabic from the word “al Jabr” meaning restoring---taking term on one side of equation and restoring balance by moving it to the other side. Who knew algebra came out of the need to solve Islamic law fair division issues? Find wisdom within (giving clarity to the blind). Buy.
“The Joy of X: A Guided Tour of Math, from one to Infinity” is not a rollercoaster ride in math. Yet it is a rather elegant meandering from algebra to vector calculus. In the smallest and rudimentary forms of life math leaves its indelible signature on little things like dragonflies to large black and white zebra stripes. Discovery within how number three is not naked. How is the correct formula for Y = 3G really F = 3Y?
"Princeton rejected his application... His best option (though he found it depressing) was MIT... In physicist Gell-Mann's eyes, MIT was a grubby technological institute, beneath his rarefied taste... He could always go to MIT and commit suicide later if he had to, but not the other way around."
---Steven Henry Strogatz
Harvard man Steven has us brushing up against Galileo and Georg Cantor in realizing that infinity could occupy three varied types. Math and mental illness (for Georg) seemed to be bitter common companions despite his orchestration of set theory. Royal Society awarded him the Sylvester Medal in 1904 post hospitalization.
Word etymology is fascinating as the light shines brightly on algebra and how the word is Arabic from the word “al Jabr” meaning restoring---taking term on one side of equation and restoring balance by moving it to the other side. Who knew algebra came out of the need to solve Islamic law fair division issues? Find wisdom within (giving clarity to the blind). Buy.
This entire review has been hidden because of spoilers.
January 24, 2019
This book is based on Strogatz's online New York Times column, "The Elements of Math," and on the whole I found it a little underwhelming.
I typically rate pop-math books based on how many "fuck, that's cool" moments they elicit, and that's a game of diminishing returns - many of my "fuck, that's cool" resources were spent on books I read previously (and recommend more heartily), like Bellos's Here's Looking at Euclid and The Grapes of Math, Parker's Things to Make and Do in the Fourth Dimension, and Cochrane's The Secret Life of Equations. My well of fucks hath run dry, I suppose.
Still, this book has some nice moments, like a very cool and very ancient graphical breakdown of the quadratic formula (chapter 10), a visual method showing why the area of a circle is πr^2 (chapter 16), a few nifty brainteasers on probability (chapter 23), and some almost poetic commentary on the strange qualities of prime numbers (chapter 25). And I'm so glad this book introduced me to Vi Hart's mathtastic YouTube channel.
There's more cool stuff in here (visual proofs of the Pythagorean theorem never fail to enchant me, for instance), but I had come across them before. So if this is the first pop-math book you've picked up, it's probably not a bad choice! But it wouldn't be my first recommendation.
I typically rate pop-math books based on how many "fuck, that's cool" moments they elicit, and that's a game of diminishing returns - many of my "fuck, that's cool" resources were spent on books I read previously (and recommend more heartily), like Bellos's Here's Looking at Euclid and The Grapes of Math, Parker's Things to Make and Do in the Fourth Dimension, and Cochrane's The Secret Life of Equations. My well of fucks hath run dry, I suppose.
Still, this book has some nice moments, like a very cool and very ancient graphical breakdown of the quadratic formula (chapter 10), a visual method showing why the area of a circle is πr^2 (chapter 16), a few nifty brainteasers on probability (chapter 23), and some almost poetic commentary on the strange qualities of prime numbers (chapter 25). And I'm so glad this book introduced me to Vi Hart's mathtastic YouTube channel.
There's more cool stuff in here (visual proofs of the Pythagorean theorem never fail to enchant me, for instance), but I had come across them before. So if this is the first pop-math book you've picked up, it's probably not a bad choice! But it wouldn't be my first recommendation.
January 10, 2013
I wish I could have read this book during that hell year of first year university, when I barely passed calculus despite devoting more time to studying it then the other 4 subjects combined (or maybe it just seemed like that -- very long nights in the library, writing out reams of papers of formulae, the table strewn with my hair and tears).
Now sufficient time has passed and, like childbirth, I forget the pain and remember only those good moments, the eureka! ones.
This isn't a book for geeks and nerds, coz they already get this stuff. But for the rest of us who might still be curious, it is just as advertised in the blurb.
One of my favourites was the explanation of the quadratic formula. I learned how to solve it, but never understood "...the cleverness packed into that porcupine of symbols." He says that "The quadratic formula is the Rodney Dangerfield of algebra. Even though it's one of the all-time greats, it don't get no respect." He then goes on to provide and illustrate the history and concept of the equation with elegant passages such as, "The upshot is that x² and 10x are now moving gracefully as a couple, rather than stepping on each other’s toes, by being paired within the single expression (x + 5)². That’s what will soon enable us to solve for x."
And then there's this excerpt from the discussion of π, and infinity to the rescue:
"What’s so charming about this calculation is the way infinity comes to the rescue. At every finite stage, the scalloped shape looks weird and unpromising. But when you take it to the limit—when you finally get to the wall—it becomes simple and beautiful, and everything becomes clear. That’s how calculus works at its best."
and
"This approach is known as the method of exhaustion because of the way it traps the unknown number pi between two known numbers that squeeze it from either side. The bounds tighten with each doubling, thus exhausting the wiggle room for pi."
This man loves math, and the reader can't help being caught up in the passionate and well-written explanations.
Now sufficient time has passed and, like childbirth, I forget the pain and remember only those good moments, the eureka! ones.
This isn't a book for geeks and nerds, coz they already get this stuff. But for the rest of us who might still be curious, it is just as advertised in the blurb.
One of my favourites was the explanation of the quadratic formula. I learned how to solve it, but never understood "...the cleverness packed into that porcupine of symbols." He says that "The quadratic formula is the Rodney Dangerfield of algebra. Even though it's one of the all-time greats, it don't get no respect." He then goes on to provide and illustrate the history and concept of the equation with elegant passages such as, "The upshot is that x² and 10x are now moving gracefully as a couple, rather than stepping on each other’s toes, by being paired within the single expression (x + 5)². That’s what will soon enable us to solve for x."
And then there's this excerpt from the discussion of π, and infinity to the rescue:
"What’s so charming about this calculation is the way infinity comes to the rescue. At every finite stage, the scalloped shape looks weird and unpromising. But when you take it to the limit—when you finally get to the wall—it becomes simple and beautiful, and everything becomes clear. That’s how calculus works at its best."
and
"This approach is known as the method of exhaustion because of the way it traps the unknown number pi between two known numbers that squeeze it from either side. The bounds tighten with each doubling, thus exhausting the wiggle room for pi."
This man loves math, and the reader can't help being caught up in the passionate and well-written explanations.
November 16, 2012
Are you the type of person who spent hours on the bus on the way to school working out multiplication tables for prime numbers only? When you're having sex do you find that the earth may not move, but images of numbers and mathematical symbols appear in your head when things are going great? OK, I'm getting a little too personal here, but if you're a numbers geek, you'll love this book.
Steven Strogatz writes in a very chatty, entertaining style about the nature of mathematics, from number theory all the way through calculus. This book is the perfect present to give to your geeky nephew/niece/husband/wife/son/daughter who majored in electrical engineering/math/comp sci/physics. They will be thoroughly amused and maybe even laugh out loud at some of the clever descriptions of the math they know so well.
I knew some of the stories and anecdotes told here, but certainly not most of them. The Joy of x would be an excellent beach read for a geek. I'm knocking off one star only because I doubt someone who isn't as numbers obsessed as I am will find this book, lighthearted and witty though it may be, accessible.
Steven Strogatz writes in a very chatty, entertaining style about the nature of mathematics, from number theory all the way through calculus. This book is the perfect present to give to your geeky nephew/niece/husband/wife/son/daughter who majored in electrical engineering/math/comp sci/physics. They will be thoroughly amused and maybe even laugh out loud at some of the clever descriptions of the math they know so well.
I knew some of the stories and anecdotes told here, but certainly not most of them. The Joy of x would be an excellent beach read for a geek. I'm knocking off one star only because I doubt someone who isn't as numbers obsessed as I am will find this book, lighthearted and witty though it may be, accessible.
September 28, 2018
فهم ریاضی هرچقدر بزرگتر میشویم و بیشتر با حوزه های مرتبط و کاربردها آشنا میشویم، اگر در مسیر درست قرار گیرد میتواند بسیار جذاب باشد. استروگاتز از ساده ترین و قدیمی ترین مسایل آغاز میکند. شاید پیش پا افتاده به نظر برسند، اما در نوع نگاهش مسایل جالبی وجود دارد. اینکه چرا اصلا راه حلهایی ایجاد شدند و ریاضیدانها به همین مسایلی که امروزه ساده به نظر میرسند جور دیگری نگاه کردند
اما هرچه گذشت مفاهیم و راه حلها پیچیده تر شدند. در برخی فصول نیاز به تمرکز و جستجو و حتی تمرین هست تا زیبایی مدنظر نویسنده آشکار شود و البته سطح دانش ریاضیاتی خواننده و میزان مواجهه قبلی اش با مفاهیم هم بی تاثیر نیستند. حتی در فصل موبیوس به سراغ آزمایش عملی رفتم که پدر فرد اشاره شده در کتاب طراحی کرد و بسیار لذتبخش بود و حال برای متعجب کردن اطرافیان در جمعهای دوستانه ترفند جدیدی بلدم :)
در کل به نظرم به سختی میتوان از کتبی که همزمان قصد آموزش دادن و سرگرم کردن را دارند متنفر بود
اما هرچه گذشت مفاهیم و راه حلها پیچیده تر شدند. در برخی فصول نیاز به تمرکز و جستجو و حتی تمرین هست تا زیبایی مدنظر نویسنده آشکار شود و البته سطح دانش ریاضیاتی خواننده و میزان مواجهه قبلی اش با مفاهیم هم بی تاثیر نیستند. حتی در فصل موبیوس به سراغ آزمایش عملی رفتم که پدر فرد اشاره شده در کتاب طراحی کرد و بسیار لذتبخش بود و حال برای متعجب کردن اطرافیان در جمعهای دوستانه ترفند جدیدی بلدم :)
در کل به نظرم به سختی میتوان از کتبی که همزمان قصد آموزش دادن و سرگرم کردن را دارند متنفر بود
March 13, 2014
Всегда белой завистью завидовал тем, кто на "ты" с математикой. Мне "царица наук" всегда давалась очень трудно, требуя больших затрат энергии и выдающихся усилий моска)))
Я прошёл долгий путь от слабеньких "троечек" по алгебре в старших классах до преподавания методов мат.статистики в ВУЗе. Но путь этот давался мне "потом и кровью": весь дом был постоянно завален какими-то продвинутыми пособиями по математике; за свою жизнь я закончил примерно с десяток (кроме учебных предметов в школе и ВУЗе) математических курсов - кружков, физ.-мат. школ, семинаров и т.п.
Но как только мне казалось, что я хоть что-то начинаю понимать, математика самым коварным образом доказывала мне обратное :) История из жизни: второй год после университета; браво докладываю на научной конференции результаты факторного анализа. ФА, кстати, проведён с помощью программы Statgraphics (один из самых первых пакетов, под DOS ещё))).
И тут в конце моего выступления один уважаемый человек (доктор наук, математик) говорит, что такой резу��ьтат получить невозможно, что где-то в моих вычислениях ошибка. Я в панике. Коллега забирает у меня исходные данные (+ листинг встроенного в программу алгоритма ФА); сутки (!!!) перепроверяет их "вручную", и с гордостью сообщает, что нашёл в алгоритме ошибку!
Но самое ужасное было потом... Понадобилась неделя (!!!) и ещё два уважаемых математика (!!!), чтобы растолковать мне (ощущавшему тогда свою полную тупость и никчёмность))), в чём же именно заключалась данная ошибка. В итоге я разобрался, но, чёрт, как это было нелегко!
Подозреваю, что ещё с младых лет у меня в голове сложилось какое-то неправильное ;) равенство: "математика = трудно, сложно, тяжело". И вообще, откуда тогда берутся люди (а их немало), для которых "математика = легко, просто, весело"? Думаю, что причина в том, как мы познаём математику...
Нужны талантливые учителя, которые умеют просто, наглядно и эмоционально рассказывать о сложном. Когда в книге Стивен Строгац приводит множество примеров о том, как он ставит математические эксперименты с детьми, красиво и просто объясняя им серьёзные математические формулы - очень чётко понимаешь, что это "правильная" книга! :)
Думаю, что книгу: а) просто в обязательном порядке надо читать старшеклассникам и студентам, чтобы понять изящество "царицы наук" и преодолеть свои математические фобии :)
б) читать всем, кто желает "размять мозги", т.к. книга не просто про математику, а, скорее, про математический образ мышления, про творческий и нешаблонный (не школярский) подход к изучению/применению математики.
Основные "плюсы" книги:
1) Очень широкий (хотя и поверхностный) охват практически всех разделов математики: буквально от философских оснований ("что есть число") и арифметики, заканчивая дифференциальным и интегральным исчислением, теорией групп, топологией, векторными исчислениями и т.п.
2) Это книга для расширения кругозора :) Во многих главах экскурсы в историю математики; живой рассказ о том, откуда и как появилась та или иная формула, как менялось её понимание с течением времени и т.п.
3) Главная задача автора: "дарить читателю радость самостоятельного открытия". И это ему прекрасно удаётся: книга напичкана задачами, которые можно попробовать решить самостоятельно; но при этом для каждой из задачек автор даёт 2-3 варианта решения. Причём это не готовые решения, а пошаговый мыслительный процесс, в который автор (с помощью вопросов) втягивает и читателя.
Процесс этот увлекает :) Тем более что автор показывает много "хитрых" способов решения, к примеру, стандартных школьных примеров/задачек. Я отчётливо помню с каким трудом мне давались в школе квадратные уравнения, а описанный автором геометрический способ решения - просто прекрасен! Как жаль, что я не знал его в школе :(
4) Книга написана очень легко, простым языком, и полна различными "житейскими" примерами. Например, рассказывая о различных функциях, автор постоянно приводит примеры из сферы управления личными финансами. Как вкладывать деньги, чтобы это было действительно прибыльно? :)
При этом очень импонирует мягкая ирония автора над "одержимостью математикой", и его постоянные напоминания о том, что в применении любых формул нужна аккуратность и осторожность, что реальность обычно гораздо сложнее тех формул, в которые мы пытаемся её "упаковать".
Вывод: читать обязательно! Очень хорошая научно-популярная книга по математике (а для желающих "углубиться в детали" в конце книги роскошные примечания с пруфлинками).
/Лучше не торопясь; лучше с карандашом и бумагой; лучше вместе со своими детьми (12+)/
Я прошёл долгий путь от слабеньких "троечек" по алгебре в старших классах до преподавания методов мат.статистики в ВУЗе. Но путь этот давался мне "потом и кровью": весь дом был постоянно завален какими-то продвинутыми пособиями по математике; за свою жизнь я закончил примерно с десяток (кроме учебных предметов в школе и ВУЗе) математических курсов - кружков, физ.-мат. школ, семинаров и т.п.
Но как только мне казалось, что я хоть что-то начинаю понимать, математика самым коварным образом доказывала мне обратное :) История из жизни: второй год после университета; браво докладываю на научной конференции результаты факторного анализа. ФА, кстати, проведён с помощью программы Statgraphics (один из самых первых пакетов, под DOS ещё))).
И тут в конце моего выступления один уважаемый человек (доктор наук, математик) говорит, что такой резу��ьтат получить невозможно, что где-то в моих вычислениях ошибка. Я в панике. Коллега забирает у меня исходные данные (+ листинг встроенного в программу алгоритма ФА); сутки (!!!) перепроверяет их "вручную", и с гордостью сообщает, что нашёл в алгоритме ошибку!
Но самое ужасное было потом... Понадобилась неделя (!!!) и ещё два уважаемых математика (!!!), чтобы растолковать мне (ощущавшему тогда свою полную тупость и никчёмность))), в чём же именно заключалась данная ошибка. В итоге я разобрался, но, чёрт, как это было нелегко!
Подозреваю, что ещё с младых лет у меня в голове сложилось какое-то неправильное ;) равенство: "математика = трудно, сложно, тяжело". И вообще, откуда тогда берутся люди (а их немало), для которых "математика = легко, просто, весело"? Думаю, что причина в том, как мы познаём математику...
Нужны талантливые учителя, которые умеют просто, наглядно и эмоционально рассказывать о сложном. Когда в книге Стивен Строгац приводит множество примеров о том, как он ставит математические эксперименты с детьми, красиво и просто объясняя им серьёзные математические формулы - очень чётко понимаешь, что это "правильная" книга! :)
Думаю, что книгу: а) просто в обязательном порядке надо читать старшеклассникам и студентам, чтобы понять изящество "царицы наук" и преодолеть свои математические фобии :)
б) читать всем, кто желает "размять мозги", т.к. книга не просто про математику, а, скорее, про математический образ мышления, про творческий и нешаблонный (не школярский) подход к изучению/применению математики.
Основные "плюсы" книги:
1) Очень широкий (хотя и поверхностный) охват практически всех разделов математики: буквально от философских оснований ("что есть число") и арифметики, заканчивая дифференциальным и интегральным исчислением, теорией групп, топологией, векторными исчислениями и т.п.
2) Это книга для расширения кругозора :) Во многих главах экскурсы в историю математики; живой рассказ о том, откуда и как появилась та или иная формула, как менялось её понимание с течением времени и т.п.
3) Главная задача автора: "дарить читателю радость самостоятельного открытия". И это ему прекрасно удаётся: книга напичкана задачами, которые можно попробовать решить самостоятельно; но при этом для каждой из задачек автор даёт 2-3 варианта решения. Причём это не готовые решения, а пошаговый мыслительный процесс, в который автор (с помощью вопросов) втягивает и читателя.
Процесс этот увлекает :) Тем более что автор показывает много "хитрых" способов решения, к примеру, стандартных школьных примеров/задачек. Я отчётливо помню с каким трудом мне давались в школе квадратные уравнения, а описанный автором геометрический способ решения - просто прекрасен! Как жаль, что я не знал его в школе :(
4) Книга написана очень легко, простым языком, и полна различными "житейскими" примерами. Например, рассказывая о различных функциях, автор постоянно приводит примеры из сферы управления личными финансами. Как вкладывать деньги, чтобы это было действительно прибыльно? :)
При этом очень импонирует мягкая ирония автора над "одержимостью математикой", и его постоянные напоминания о том, что в применении любых формул нужна аккуратность и осторожность, что реальность обычно гораздо сложнее тех формул, в которые мы пытаемся её "упаковать".
Вывод: читать обязательно! Очень хорошая научно-популярная книга по математике (а для желающих "углубиться в детали" в конце книги роскошные примечания с пруфлинками).
/Лучше не торопясь; лучше с карандашом и бумагой; лучше вместе со своими детьми (12+)/
June 13, 2017
If you feel that Mathematics is not for you, please read this book. Strogatz deftly guides the reader through some of the most important ideas in the field, using easily digestible examples. I was able to grasp concepts that eluded me all through graduate school with ease.
Most people think Math is about numbers, but it is much more than that. When used properly it is more akin to a language or a philosophy, a way to understand the world we can see and the many worlds we cannot. Some scenarios are clearly memorable, such as his explanation of how Google's PageMark works (that is the algorithm that assigns relative weights to the almost infinite web addresses).
Definitely a worthwhile read!
Most people think Math is about numbers, but it is much more than that. When used properly it is more akin to a language or a philosophy, a way to understand the world we can see and the many worlds we cannot. Some scenarios are clearly memorable, such as his explanation of how Google's PageMark works (that is the algorithm that assigns relative weights to the almost infinite web addresses).
Definitely a worthwhile read!
March 3, 2016
You wouldn’t know it, but maths permeates everything we do and touch. Your smartphone would not be able to operate without maths, nor would the internet. You couldn’t buy anything risk free if we didn’t have the primes. Things as unlikely as the correct time to flip a mattress, the number of people to date before settling down, the best path from A to B, that if you look hard enough you can see sine waves everywhere all have some element of maths in them.
He does manage to take a subject that many people find confusing and make it manageable and understandable and possibly a tiny bit less scary. There is the odd subject that will make non mathematical readers blanch a bit (it involves quadratic equations), but you’ll be pleased to hear that there are not many subjects that he cannot clearly illuminate. It is packed with photos, picture and diagrams to help illustrate each of the short punchy subjects. Overall a good introduction to maths for those who need to brush up a little when staring at their children’s homework in a bemused fashion.
He does manage to take a subject that many people find confusing and make it manageable and understandable and possibly a tiny bit less scary. There is the odd subject that will make non mathematical readers blanch a bit (it involves quadratic equations), but you’ll be pleased to hear that there are not many subjects that he cannot clearly illuminate. It is packed with photos, picture and diagrams to help illustrate each of the short punchy subjects. Overall a good introduction to maths for those who need to brush up a little when staring at their children’s homework in a bemused fashion.
October 2, 2012
Struggling through several years of higher math in engineering school in the 1960s didn't engender a love of mathematics in me. It wasn't until years later that I began to value the beauty and elegance of mathematics. A big part of my appreciation came from mathematicians like Steven Strogatz who wrote about math for readers who appreciated the concepts but had no desire to wade into a morass of complex equations.
In The Joy of x, Strogatz has done a masterful job as our tour guide through the elements of mathematics, and he's done it without "dumbing it down" or making it just another refresher course for the subject. He presented the various mathematical elements and concepts in fresh new ways, but he clearly expected the reader to exercise their mind to understand. The reward was a new appreciation of the beauty of mathematics and for how our knowledge of the subject advanced in fits and starts over several thousand years.
The book has six parts, each presenting certain elements of mathematics: Numbers, Relationships, Shapes, Change, Data, and Frontiers. These sections represent a grand tour through the history and development of mathematics, including the practical - and some whimsical - applications. Never again will I fall into the trap of bungling the answer to the classic "If three men paint three fences in three hours, how long will it take for one man to paint one fence?" (answer: 3 hours). Now I understand why a piece of paper can't be folded in half more than 7-8 times, and how a high school junior was able to beat the record using a monstrously long roll of... toilet paper! I know how Luke could guarantee himself a win over Darth Vader in a game of laser tag (hint: it involves a conic section). For young lovers, mathematics could help in finding the perfect mate (if you make a few simplistic assumptions, that is). And if the prosecution in the O.J. Simpson murder trial had understood probability and statistics, could they have gotten a conviction?
As enjoyable as the first five sections of the book were, my favorite section was the last, "Frontiers," where the author covered topics including prime numbers, where I learned that no one has ever found an exact formula to find primes; group theory, which bridges the arts and sciences; topology; spherical geometry; and infinite series. This section presented some fascinating ideas. For example, group theory suggests how to get the most even wear from a mattress and confirms the old mnemonic "spin in the spring, flip in the fall." For topology, the famous Möbius strip is examined. I thought I understood the properties of a Möbius strip, but they're actually more remarkable than I would have guessed. And the most mind-blowing concept was that some infinities are larger than others. This finding, which was bitterly contested at the time, is brilliantly demonstrated with a parable named the Hilbert Hotel.
I don't always read all of the footnotes or endnotes in a book, but the endnotes in The Joy of x are not to be missed. There are dozens of links to websites and online videos that demonstrate or expound on the concepts presented in the book. Some of these were so intriguing that I spent a couple of hours being spellbound by them.
For anyone who's been disappointed by other math books written for laypersons, The Joy of x may be the book they've been hoping for. With keen insight, a light touch, and a bit of humor, author Steven Strogatz has written a splendid book for anyone who wants a broader understanding of mathematics.
Note: I read an advance reader copy of this book provided by the publisher through NetGalley.
In The Joy of x, Strogatz has done a masterful job as our tour guide through the elements of mathematics, and he's done it without "dumbing it down" or making it just another refresher course for the subject. He presented the various mathematical elements and concepts in fresh new ways, but he clearly expected the reader to exercise their mind to understand. The reward was a new appreciation of the beauty of mathematics and for how our knowledge of the subject advanced in fits and starts over several thousand years.
The book has six parts, each presenting certain elements of mathematics: Numbers, Relationships, Shapes, Change, Data, and Frontiers. These sections represent a grand tour through the history and development of mathematics, including the practical - and some whimsical - applications. Never again will I fall into the trap of bungling the answer to the classic "If three men paint three fences in three hours, how long will it take for one man to paint one fence?" (answer: 3 hours). Now I understand why a piece of paper can't be folded in half more than 7-8 times, and how a high school junior was able to beat the record using a monstrously long roll of... toilet paper! I know how Luke could guarantee himself a win over Darth Vader in a game of laser tag (hint: it involves a conic section). For young lovers, mathematics could help in finding the perfect mate (if you make a few simplistic assumptions, that is). And if the prosecution in the O.J. Simpson murder trial had understood probability and statistics, could they have gotten a conviction?
As enjoyable as the first five sections of the book were, my favorite section was the last, "Frontiers," where the author covered topics including prime numbers, where I learned that no one has ever found an exact formula to find primes; group theory, which bridges the arts and sciences; topology; spherical geometry; and infinite series. This section presented some fascinating ideas. For example, group theory suggests how to get the most even wear from a mattress and confirms the old mnemonic "spin in the spring, flip in the fall." For topology, the famous Möbius strip is examined. I thought I understood the properties of a Möbius strip, but they're actually more remarkable than I would have guessed. And the most mind-blowing concept was that some infinities are larger than others. This finding, which was bitterly contested at the time, is brilliantly demonstrated with a parable named the Hilbert Hotel.
I don't always read all of the footnotes or endnotes in a book, but the endnotes in The Joy of x are not to be missed. There are dozens of links to websites and online videos that demonstrate or expound on the concepts presented in the book. Some of these were so intriguing that I spent a couple of hours being spellbound by them.
For anyone who's been disappointed by other math books written for laypersons, The Joy of x may be the book they've been hoping for. With keen insight, a light touch, and a bit of humor, author Steven Strogatz has written a splendid book for anyone who wants a broader understanding of mathematics.
Note: I read an advance reader copy of this book provided by the publisher through NetGalley.
October 16, 2014
I love this book. My only regret is that I couldn't read it in high school, when I was *actually* struggling with math. At this point (having degrees & math & math education & have spent over a decade teaching the subject and/or teachers of it), I read it more from the point of view of, "How could I use pieces of this with students and/or the teachers that I work with?"
In these 30 short essays--a couple of which I had read before in his Time column--Strogatz begins at the beginning (with the concept of counting) and winds his way through everything from basic algebra to calculus to advanced topics like group theory and topology, discussing each topic in a way that is not only friendly and approachable for the mathematical neophite (or phobic), but fascinating. And for all that the book is aimed at a general audience, I have to admit that I learned a few fascinating things about some topics that I didn't even learn in my advanced semester-long college classes. (Did you know there are real-world applications from infinite series? I didn't!)
So yes, this is a book about math, but it isn't just for math lovers. In fact, it's probably more for people who felt like they "never really got it" in school but are maybe just a little intrigued and kind of want another crack at it (in a way that doesn't involve doing homework). I also think it makes a GREAT resource for math teachers. (I used the two calculus essays as introductions to each semester of the course, differential & integral respectively. They give a really great, 30,000 ft overview that I thought might help the students see what it was we were really doing and why before we got bogged down in problem sets.)
June 28, 2020
Колись я любила математику.
У школі класу до десятого я дуже любила математику і краще б вирішувала рівняння, ніж писала твори. Якось легше вирішити і знайти потрібну схему, ніж створювати щось з нуля. Але потім неочікувано вирішила вступати на журналістику, тому на математику забила.
Беручись за «Екскурсію математикою» мені хотілося відновити чи принаймні пригадати ту шкільну любов до матема��ики. Схоже, любов була не такою сильною, як пригадувалося.
Перша частина була доволі нудною (хоч і не повністю вся). Так, цікаво, як можна пояснити процеси додавання, віднімання, множення і ділення дуже просто, аби зацікавити дитину. У моїй голові це вже автоматизовані процеси і доволі зрозумілі, тому захвату від першої частини не було.
Деякі глави книжки були дійсно цікавими і зрозумілими: про еліпси, параболи, гіперболи чи навіть про звичайні вже нам квадрати і трикутники. Ще було цікаво про статистику, теорію ймовірності та алгоритми. Мабуть, у моїй голові підсвідомо навіть відклалася якась інформація.
Та все ж під час прочитання більшості глав я діставала Дениса, який би мені пояснив, що саме намагається сказати автор книжки. Тоді ставало зрозуміліше, але любов до математики не поверталася.
Власне, я весь час забувала, що назва книжки «Екскурсія математикою», тому читачі буквально отримують екскурсію від найпростішого до складнішого, дуже побіжно зупиняючись на кожній темі. Автор не стільки хотів щось дійсно пояснити, скільки показати «диви, як воно може бути цікаво». Хоча мені місцями здавалося, що це екскурсія по картинній галереї, в якій немає картин. Але розумію, що місцями пояснювати щось формулами було б ще важче, бо вони довгі й складні (хоча незрозуміло, для чого таку красиву формулу коренів квадратного рівняння було так складно пояснювати).
⠀
Мені б ця книжка сподобалася у школі паралельно з роками вивчення математики. Чи якби в університеті мала курс з математики, то ця б книжка переконала, що математика цікава і лекції варто послухати. Але якщо вже 10 років пересікатися з математикою лише на базовому рівні, то книжка Стівена Строґаца не відновить знання, які ви колись отримали (чи ні) у школі.
3,5 ⭐️ з 5-ти.
У школі класу до десятого я дуже любила математику і краще б вирішувала рівняння, ніж писала твори. Якось легше вирішити і знайти потрібну схему, ніж створювати щось з нуля. Але потім неочікувано вирішила вступати на журналістику, тому на математику забила.
Беручись за «Екскурсію математикою» мені хотілося відновити чи принаймні пригадати ту шкільну любов до матема��ики. Схоже, любов була не такою сильною, як пригадувалося.
Перша частина була доволі нудною (хоч і не повністю вся). Так, цікаво, як можна пояснити процеси додавання, віднімання, множення і ділення дуже просто, аби зацікавити дитину. У моїй голові це вже автоматизовані процеси і доволі зрозумілі, тому захвату від першої частини не було.
Деякі глави книжки були дійсно цікавими і зрозумілими: про еліпси, параболи, гіперболи чи навіть про звичайні вже нам квадрати і трикутники. Ще було цікаво про статистику, теорію ймовірності та алгоритми. Мабуть, у моїй голові підсвідомо навіть відклалася якась інформація.
Та все ж під час прочитання більшості глав я діставала Дениса, який би мені пояснив, що саме намагається сказати автор книжки. Тоді ставало зрозуміліше, але любов до математики не поверталася.
Власне, я весь час забувала, що назва книжки «Екскурсія математикою», тому читачі буквально отримують екскурсію від найпростішого до складнішого, дуже побіжно зупиняючись на кожній темі. Автор не стільки хотів щось дійсно пояснити, скільки показати «диви, як воно може бути цікаво». Хоча мені місцями здавалося, що це екскурсія по картинній галереї, в якій немає картин. Але розумію, що місцями пояснювати щось формулами було б ще важче, бо вони довгі й складні (хоча незрозуміло, для чого таку красиву формулу коренів квадратного рівняння було так складно пояснювати).
⠀
Мені б ця книжка сподобалася у школі паралельно з роками вивчення математики. Чи якби в університеті мала курс з математики, то ця б книжка переконала, що математика цікава і лекції варто послухати. Але якщо вже 10 років пересікатися з математикою лише на базовому рівні, то книжка Стівена Строґаца не відновить знання, які ви колись отримали (чи ні) у школі.
3,5 ⭐️ з 5-ти.
June 10, 2020
I wish all math was taught with the passion and insight Strogatz brings to the subject. This was not as fantastic as Infinite Powers, which ended up becoming a favorite book of all time for me, but it made me wish I could go back in time and make all the connections outlined in this book before learning the math taught to me from middle school through college. I spent so much time memorizing. If only I had looked at foci from the point of Luke Skywalker trying to hit Darth Vader with a light saber. I think I would have understood things in a more intuitive manner.
Strogatz takes his reader through the most basic math through calculus by helping the reader make the necessary connections to understand not just what a theorem says so that you can solve a problem, but connections so that you start seeing the world in mathematical terms. Then no matter what problems comes your way, you solve it not from memorization of a rule but from a true understanding of what the problem is actually asking you about the world and universe in which you live. Strogatz teaching style is second to none.
Strogatz takes his reader through the most basic math through calculus by helping the reader make the necessary connections to understand not just what a theorem says so that you can solve a problem, but connections so that you start seeing the world in mathematical terms. Then no matter what problems comes your way, you solve it not from memorization of a rule but from a true understanding of what the problem is actually asking you about the world and universe in which you live. Strogatz teaching style is second to none.
June 10, 2021
If Steven Strogatz can't make you fall in love with mathematics, then probably nobody can. I have never studied math after my school but recently my curiosity got better of me and I've been reading about different math and science topics. That is when I stumbled upon this book. In this book, the author strives to communicate what mathematics is about to a set of people who might be otherwise intimidated by the very name of 'math'. The book is divided into six sections - Numbers, Relationships, Shapes, Change, Data and “Frontiers. Strogatz’s writing style and use of visuals and anecdotes makes the book very interesting. Each chapter is very short and about a particular topic of mathematics. He covers so much of the basic ethos of the topics like algebra, geometry, trigonometry, calculus, probability etc. often by stressing upon intuition and visualization. It’s a great book for the curious mind.
April 26, 2020
The main premise of the Joy of X is to explain mathematical concepts for adults in a way that they can relate to it to now (as opposed to rote learning in schools). The other premise is to basically answer the question which most adults (who have found maths to be a nightmare) have - why should I learn this topic? I think the book succeeds in some areas while falling flat in others. The Joy of X is a collection of articles written for a magazine about various topics in mathematics. While a few were interesting and offered insights, I found the overall quality to be a hit or miss. So overall, it is worth a read but I don't think it lives up to its goals.
March 31, 2022
I am a math and science tutor and I have always loved math. So I looked forward to this book with great anticipation. It was obvious to me that this author shares a similar love and I really enjoyed listening to him talk about different concepts from the various branches of mathematics. However, I think I would have enjoyed it even more if I had been able to follow along with a written version because as much as I love and can do the math, I am very much a visual learner and I need to see the equations in order to follow them. Some of what he talked about were very familiar to me, so even though I didn't have the equations in front of me I was able to jot down notes and follow his reasoning very easily. In others, especially the chapters on calculus and series, I needed to pause and jot things down and go back and relisten to what he was saying to make sure I was following everything correctly. Despite these shortcomings, I don't regret purchasing this audiobook (it was one of the deals of the day) and I wouldn't mind listening to it again, this time following along with the written book. I am definitely part of the target audience, so I am a bit biased. Even if you're not a math expert, I still think you could get something out if this book, if only to see how mathematics can be part of every day life.
October 29, 2012
I applaud you, Stephen Strogatz, for truly putting the joy back in math! My life might have been very different if I had read this book in high school. Biology was my passion, but I avoided the field because of the math courses required for a bachelor of science degree.
My father was a calculus professor and he made math interesting and approachable. He died when I was 13 and afterwards numbers became a challenge because my teachers never explained them with flair and passion. My dad said, "If you can't explain it simply, you don't understand it." Strogatz understands it and effectively communicates so that YOU will understand.
Words and art have been my passion all my life, but the world of numbers left me cold. After of life time of being intimidated by numbers, I'm falling in love with math again.
If you, or anyone you know is intimidated by numbers, find a copy of this book and settle in for a delightful spin on the world of math!
My father was a calculus professor and he made math interesting and approachable. He died when I was 13 and afterwards numbers became a challenge because my teachers never explained them with flair and passion. My dad said, "If you can't explain it simply, you don't understand it." Strogatz understands it and effectively communicates so that YOU will understand.
Words and art have been my passion all my life, but the world of numbers left me cold. After of life time of being intimidated by numbers, I'm falling in love with math again.
If you, or anyone you know is intimidated by numbers, find a copy of this book and settle in for a delightful spin on the world of math!
September 7, 2012
A wonderful book of short essays displaying the elegance of math in a grand and easily digestible format. This book started life as a series of columns in the New York Times as an introduction to and has been expanded on a bit. Each chapter is the length of a typical column, and while the book is by no means comprehensive, there are copious notes and reading lists in the back should one want to explore topics further.
The book starts with basics like numbers and addition and continues right on to infinity. Filled with history, anecdotes and *gasp* how we actually use each type of math in our daily lives, the book is written in a very comfortable style. Filled with humor and the joy of learning, I found it refreshing and inviting to it's approach.
The book starts with basics like numbers and addition and continues right on to infinity. Filled with history, anecdotes and *gasp* how we actually use each type of math in our daily lives, the book is written in a very comfortable style. Filled with humor and the joy of learning, I found it refreshing and inviting to it's approach.
September 26, 2012
I know what "i" (make that italics) does to something in a practical manner now!!!! Took me twenty-eight years to make it 30 minutes into a book that explained it to me.. but.. I KNOW!! Wooohooooo
Really, I loved reading this book, it was a super fun journey. Now, I'm going to sit down and make a mobius strip with my five-year old daughter!!
(Won this off of Goodreads first reads btw. Going to purchase two more copies for Christmas presents. So fun!)
Really, I loved reading this book, it was a super fun journey. Now, I'm going to sit down and make a mobius strip with my five-year old daughter!!
(Won this off of Goodreads first reads btw. Going to purchase two more copies for Christmas presents. So fun!)
January 26, 2013
Rare is the occasion to have math thrown at your brain in a direct and pedagogical manner after, say, college calculus. The Joy of X is math made quick and fun, replete with dad jokes, groaners that make an appearance at the close of each chapter. Typically, they reference a social touchstone that is out of date or just sort of lame. After a certain point, though, their earnestness infected my mind and I began to unironically enjoy them, even attempting to anticipate when, where, and in what form they might appear:
There’s a lot of math to cover, and, like any good course, the subject matter gets more difficult the further into thesemester book you go. The chapters, which are either adapted or pulled en masse from the author's prior column, do not have the heft of a full-novel’s chapter pacing. Which, given the subject matter, is a benefit. Illustrations abound and while the actual symbols-in-your-face math is kept to a minimum, the concepts and their implications are given free reign:
The only other thing that I could ask of The Joy of X is some historical context, maybe a few well-placed digressions within the streamlined chapter/niblets.
Rather than close out on a dad joke, this sample problem should let you know whether The Joy of X is right for you: “If the cold-water faucet can fill the tub in a half-hour, and the hot-water faucet can fill it in an hour, how long will it take to fill the tub when they’re running together?” Whether or not you can solve it in your head, The Joy of X is a great opportunity to let you soak in some math.
The great innovation here is that even though this system is based on the number 10, there is no single symbol reserved for 10. Ten is marked by a position—the tens place—instead of a symbol. The same is true for 100, or 1,000, or any other power of 10. Their distinguished status is signified not by a symbol but by a parking spot, a reserved piece of real estate. Location, location, location.You can almost hear the author chuckle as your read these bons mots; maybe you will hear them in the voice of your dad as he assures you that, “You’d be disappointed if I didn’t say it,” while you roll your eyes from teenaged embarrassment. I sure did.
There’s a lot of math to cover, and, like any good course, the subject matter gets more difficult the further into the
As the numbers inside the logarithms grew multiplicatively, increasing tenfold each time from 100 to 1,000 to 10,000, their logarithms grew additively, increasing from 2 to 3 to 4. Our brains perform a similar trick when we listen to music. The frequencies of the notes in a scale—do,re, mi, fa, sol, la, ti, do—sound to us like they’re rising in equal steps. But objectively their vibrational frequencies are rising by equal multiples. We perceive pitch logarithmically.But The Joy of X is not simply information transfer sweetened with sincerity. There is a dark side to math, the spooky forest of numbers and incomprehensibility that frightened so many of us into a B.A. in English Lit. For those willing to return to the road not taken, there are forty pages of endnotes:
The analysts of the 1800s identified the underlying mathematical cause of the Gibbs phenomenon. For functions (or, nowadays, images) displaying sharp edges or other mild types of jump discontinuities, the partial sums of the sine waves were proven to converge pointwise but not uniformly to the original function. Pointwise convergence means that at any particular point x, the partial sums get arbitrarily close to the original function as more terms are added. So in that sense, the series does converge, as one would hope. The catch is that some points are much more finicky than others. The Gibbs phenomenon occurs near the worst of those points—the edges in the original function.These notes are here to remind a reader, flush with feelings that math is for the people—doable by everyone in an egalitarian utopia of numbers and equations and formulae—that maybe math is not quite that simple. The Joy of X just makes it seem so clear and enjoyable, like an organized hike up gentle mountain trail. The path has been worn clear of debris by the generations of travelers before you, and your tour guide is so witty and knowledgeable that before you know it you're standing next to a sign marked "Scenic Overlook," posing in front of the same backdrop as countless other tourists before you. You feel like you've done something: "I've hiked a mountain!" But no. You've trod a path that's existed for millennia, and while it may be a good first tour, experienced outdoorsy-types would cluck their tongues and shake their heads if you started calling yourself a hiker. As time passes, only the photo remains; a vague memory of the brief moment your comprehension of mathematics sufficed for a picturesque vista. By contrast, the endnotes lead you to a sheer cliff, toss you a rope, a compass, and a pocket knife, and ditch you in the middle of the Appalachians. Just like this extended metaphor, math is a struggle. Unlike this metaphor, math can often be elegant.
The only other thing that I could ask of The Joy of X is some historical context, maybe a few well-placed digressions within the streamlined chapter/niblets.
In the early part of the ninth century, Muhammad ibn Mus al-Khwarizmi, a mathematician working in Baghdad, wrote a seminal textbook in which he highlighted the usefulness of restoring a quantity being subtracted by adding it to the other side of the equation. He called this process al-jabr (Arabic for “restoring”), which later morphed into “algebra.” Then, long after his death, he hit the etymological jackpot again. His own name, al-khwarizmi, lives on today in the word “algorithm.”Well, good, then. One would think this would be common knowledge. Really, both algebra and algorithm from the same person? That's impressive. "Restoring" even makes sense—it's what you do while balancing equations in algebra. Many students, past and present, might benefit from having context to frame the math ex nihilo that is constantly being smashed into their faces.
Rather than close out on a dad joke, this sample problem should let you know whether The Joy of X is right for you: “If the cold-water faucet can fill the tub in a half-hour, and the hot-water faucet can fill it in an hour, how long will it take to fill the tub when they’re running together?” Whether or not you can solve it in your head, The Joy of X is a great opportunity to let you soak in some math.
February 8, 2017
This book, written in a plain and enjoyable form, with humoristic touchs ,is aimed to people with little background in mathematics , but that have some interest in its concepts and play roled in everyday life.
I think that the book fulfil its goals, from elementary arithmetic till goup theory ,crossing by elementary notions of euclidean geometry in special Pitagoras theorem,(it gives two demostrations ,grafic and algebraic),elementary trigonometry (sine function),conics and it properties,a curious naive demostration of the surface of a circle,distributions of probability (including the normal distribution),the concept and meaning of conditioned probability and Bayes rule,prime numbers and some results,the concept of complex numbers and complex plane,fractals,e number and logaritmic and exponential function and basic concepts of topology including geodesics.
Makes some excursion in more advances topics as calculus,diferential equations,Mobius strip and Maxwel equations,all with a lot of pictures and examples of daily life
Where the book is no so good is in explaining the concept of differential equation and Maxwell equations,a very difficul task at this level.
Has a valuable appendix with notes ,references and further reading bibliography.
A recomendable book for those that think that maths are boring and difficult per se.
I think that the book fulfil its goals, from elementary arithmetic till goup theory ,crossing by elementary notions of euclidean geometry in special Pitagoras theorem,(it gives two demostrations ,grafic and algebraic),elementary trigonometry (sine function),conics and it properties,a curious naive demostration of the surface of a circle,distributions of probability (including the normal distribution),the concept and meaning of conditioned probability and Bayes rule,prime numbers and some results,the concept of complex numbers and complex plane,fractals,e number and logaritmic and exponential function and basic concepts of topology including geodesics.
Makes some excursion in more advances topics as calculus,diferential equations,Mobius strip and Maxwel equations,all with a lot of pictures and examples of daily life
Where the book is no so good is in explaining the concept of differential equation and Maxwell equations,a very difficul task at this level.
Has a valuable appendix with notes ,references and further reading bibliography.
A recomendable book for those that think that maths are boring and difficult per se.
April 5, 2021
Книжка для тих, хто не дружить з математикою про основні принципи цієї науки, щось на кшталт філософії математики. Автор дуже старається і придумує всякі різні приклади, наприклад пояснює диференційні рівняння через історію Ромео і Джульєтти, а безкінечність через метафору готелю з безкінечними кімнатами і безкінечною кількістю гостей. Я все ж часто губила нитку розповіді і не те щоб якось сильно наблизилася до розуміння інтегралів, але загалом приємне читання, яке урізноманітнило мій звичний набір текстів.
August 9, 2019
Ірині Олексіївні ця книга не сподобалася! В мене скільки претензій, питань і нерозуміння автора, що я навіть не знаю як написати адекватний відгук. Але спробую.
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Перша частина починається з розділу про те, що замість того аби говорити «риба, риба, риба, риба, риба, риба» можна сказати «6 рибин». Так з’являюся числа. Далі розповідається про дії з числами. І останній розділ які бувають ще числа 😕 Серйозно? Мій внутрішній критик обурився, бо якось не логічно після арифметичних дій, казати «ааа, ну є ще римські числа і двійкова система числення»! І паралельно обурилася вчителька в мені: як можна починати розділ, розповідаючи на рівні дитячого садка, а закінчити принципом невизначеності Гейзенберга!! 😩
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І такого багато! Автор згадує щось «розумне», без пояснення для простих людей! Хоч би два слова сказав у виносках! А стоп, їх же немає 😕. Є Примітки в кінці, де пояснення на кшталт такого: «хочете дізнатися про це більше, почитайте в тій то книзі» 😕👍
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Ні, ну я спершу навіть стікери клеїла! Взяла для себе пояснення як утворюється квадрат числа (з допомогою камінців) та навіщо нам формули скороченого множення. Й дві крутезні цитати (2 фото в стрічці).
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А далі пішло... Перший курс мехмату... третій курс... п`ять перездач... пані Осіпкова, яка різниця між зліченою і скінченною множиною... доведіть абсолютну збіжність ряду Фур‘є... ви не знаєте як розв’язати це диференціальне рівняння... так, це топологічний простір... аааааа 🤯
І читаючи про все це я, ніби, знову пережила «найкращі» моменти свого студентського життя 😅 Радію, що це вже позаду 🙂 і Доббі вільний!
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Так, повернімося до того, що це не книга «Настальгія за мехматом», а екскурсія математикою. Екскурсія на транспорті зі швидкість 300м/с, бо тобі просто кажуть якісь факти, які є в природі і все. Ну О’кей, будемо знати
що поведінку Ромео і Джульєти можна описати простим гармонічним осцилятором. А найпрекрасніше описав прості числа Паоло Джордано, тому гріх не вставити в розділ пару абзаців з його «Самотність простих чисел» 😕
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І насамкінець, найжахливіша, на мою думку, помил��а в книзі, це запис логарифмів😤!!! Можливо, в Америці так прийнято, що log (100)=2, але в нас тут має бути основа! Я розумію, що тут основа 10, але де вона написана?? Існує інше, спеціальне позначення, для логарифмів з основою 10 - lg !!! Lg(100)=2!! А для log треба писати основу!!
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То для кого, взагалі, ця «екскурсія»?? Я без поняття. Школярі зрозуміють 40% книги, дорослі без математичної освіти 60%, з математичною освітою - 90%, люди з червоним дипломом мехмату, скажуть що воно як тепле пиво в спекотний день (в мене немає червоного диплому, але це не заважає мені робити такі порівняння 😆).
Короче 😓 якщо я помиляюся, або ви хочете посперечатися про крутість цієї книги, пишіть в коментарях! Я з радістю вступлю в дискусію ☺️
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Перша частина починається з розділу про те, що замість того аби говорити «риба, риба, риба, риба, риба, риба» можна сказати «6 рибин». Так з’являюся числа. Далі розповідається про дії з числами. І останній розділ які бувають ще числа 😕 Серйозно? Мій внутрішній критик обурився, бо якось не логічно після арифметичних дій, казати «ааа, ну є ще римські числа і двійкова система числення»! І паралельно обурилася вчителька в мені: як можна починати розділ, розповідаючи на рівні дитячого садка, а закінчити принципом невизначеності Гейзенберга!! 😩
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І такого багато! Автор згадує щось «розумне», без пояснення для простих людей! Хоч би два слова сказав у виносках! А стоп, їх же немає 😕. Є Примітки в кінці, де пояснення на кшталт такого: «хочете дізнатися про це більше, почитайте в тій то книзі» 😕👍
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Ні, ну я спершу навіть стікери клеїла! Взяла для себе пояснення як утворюється квадрат числа (з допомогою камінців) та навіщо нам формули скороченого множення. Й дві крутезні цитати (2 фото в стрічці).
⠀
А далі пішло... Перший курс мехмату... третій курс... п`ять перездач... пані Осіпкова, яка різниця між зліченою і скінченною множиною... доведіть абсолютну збіжність ряду Фур‘є... ви не знаєте як розв’язати це диференціальне рівняння... так, це топологічний простір... аааааа 🤯
І читаючи про все це я, ніби, знову пережила «найкращі» моменти свого студентського життя 😅 Радію, що це вже позаду 🙂 і Доббі вільний!
⠀
Так, повернімося до того, що це не книга «Настальгія за мехматом», а екскурсія математикою. Екскурсія на транспорті зі швидкість 300м/с, бо тобі просто кажуть якісь факти, які є в природі і все. Ну О’кей, будемо знати
що поведінку Ромео і Джульєти можна описати простим гармонічним осцилятором. А найпрекрасніше описав прості числа Паоло Джордано, тому гріх не вставити в розділ пару абзаців з його «Самотність простих чисел» 😕
⠀
І насамкінець, найжахливіша, на мою думку, помил��а в книзі, це запис логарифмів😤!!! Можливо, в Америці так прийнято, що log (100)=2, але в нас тут має бути основа! Я розумію, що тут основа 10, але де вона написана?? Існує інше, спеціальне позначення, для логарифмів з основою 10 - lg !!! Lg(100)=2!! А для log треба писати основу!!
⠀
То для кого, взагалі, ця «екскурсія»?? Я без поняття. Школярі зрозуміють 40% книги, дорослі без математичної освіти 60%, з математичною освітою - 90%, люди з червоним дипломом мехмату, скажуть що воно як тепле пиво в спекотний день (в мене немає червоного диплому, але це не заважає мені робити такі порівняння 😆).
Короче 😓 якщо я помиляюся, або ви хочете посперечатися про крутість цієї книги, пишіть в коментарях! Я з радістю вступлю в дискусію ☺️
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September 1, 2019
This book started out so strong, and drew me in. I was excited to be learning about math as an adult - to create a new relationship with it.
But very quickly it became too much for this math-phobe. The gentle guiding ended by being thrown into the deep end with i, and it didn’t get better. I hung in for over 50%. But I hung it up when I admitted to myself I was absorbing nothing.
If you already like math and just wish to get reacquainted, this might be the book for you. For everyone else, it’s a reminder of struggles best forgotten.
But very quickly it became too much for this math-phobe. The gentle guiding ended by being thrown into the deep end with i, and it didn’t get better. I hung in for over 50%. But I hung it up when I admitted to myself I was absorbing nothing.
If you already like math and just wish to get reacquainted, this might be the book for you. For everyone else, it’s a reminder of struggles best forgotten.
April 12, 2014
Pretty dull. The book's structure parallel's that of a standard math education, and offers little added value. I wanted a greater appreciation of math's beauty, instead I god a folksy re-hash over concepts I was generally aware of, and competent and applying (the exceptions being topology, group theory, the hilbert hotel, and a few other odds and ends).
In the end, it wasn't worth my time.
Disclaimer: I have a math minor, so I know only enough math to be marginally dangerous.
In the end, it wasn't worth my time.
Disclaimer: I have a math minor, so I know only enough math to be marginally dangerous.
February 19, 2021
4 Stars // 82%
As a fact-based thinker, I've always done fairly well in math. However, I don't think I've ever considered it all that fascinating or a subject to be pondered over deep into the night—until now. Strogatz has opened my mind to a whole new level of thinking, and for that, I am infinitely grateful.
As a fact-based thinker, I've always done fairly well in math. However, I don't think I've ever considered it all that fascinating or a subject to be pondered over deep into the night—until now. Strogatz has opened my mind to a whole new level of thinking, and for that, I am infinitely grateful.
April 25, 2016
Q:
... clue to the ubiquity of e. It ofthen arises when something changes through the cumulative effect of many tiny events.
... clue to the ubiquity of e. It ofthen arises when something changes through the cumulative effect of many tiny events.
April 22, 2019
I admit it: I bought Joy of X: A Guided Tour of Math, from One to Infinity for the title, although the concept also engaged me (the joy of it). I love watching people doing anything that they are passionate about: skating and gymnastics during the Olympics, performing, philosophy, science, cooking.
And, apparently, Mathematics. The goal is to give you a better feeling for what math is all about and why it’s so enthralling to those who get it.
As Steven Strogatz said, this is a guided tour, but an idiosyncratic one. All sorts of things are fair game: Sesame Street, Google searches, the OJ Simpson trial, flipping your mattress ... and children's questions.
Today is the 100th day of school. [My son] was very excited and told me everything he knows about the number 100, including that 100 was an even number. He then told me that 101 was an odd number and 1 million was an even number, etc. He then paused and asked: “Is infinity even or odd?” (p. 249)
And, then, Strogatz explored why. In exciting detail, as he did in each essay. These details are engaging. A book that includes things like this, for example, is a book worth reading:
Years later he would explain that he had contemplated suicide at the time but decided against it once he realized that attending MIT and killing himself didn’t commute. He could always go to MIT and commit suicide later if he had to, but not the other way around. (p. 27).
And, in the process, Strogatz demystified Mathematics.
The naive view is that we make our definitions, set them in stone, then deduce whatever theorems happen to follow from them. Not so. That would be much too passive. We’re in charge and can alter the definitions as we please—especially if a slight tweak leads to a tidier theorem, as it does here. (p. 204)
Okay, now I know. Life is good.
And, apparently, Mathematics. The goal is to give you a better feeling for what math is all about and why it’s so enthralling to those who get it.
As Steven Strogatz said, this is a guided tour, but an idiosyncratic one. All sorts of things are fair game: Sesame Street, Google searches, the OJ Simpson trial, flipping your mattress ... and children's questions.
Today is the 100th day of school. [My son] was very excited and told me everything he knows about the number 100, including that 100 was an even number. He then told me that 101 was an odd number and 1 million was an even number, etc. He then paused and asked: “Is infinity even or odd?” (p. 249)
And, then, Strogatz explored why. In exciting detail, as he did in each essay. These details are engaging. A book that includes things like this, for example, is a book worth reading:
Years later he would explain that he had contemplated suicide at the time but decided against it once he realized that attending MIT and killing himself didn’t commute. He could always go to MIT and commit suicide later if he had to, but not the other way around. (p. 27).
And, in the process, Strogatz demystified Mathematics.
The naive view is that we make our definitions, set them in stone, then deduce whatever theorems happen to follow from them. Not so. That would be much too passive. We’re in charge and can alter the definitions as we please—especially if a slight tweak leads to a tidier theorem, as it does here. (p. 204)
Okay, now I know. Life is good.
May 25, 2017
Considering how horrible I am at Calculus, it's surprising how much I enjoyed this book :|
Brilliantly written and covers so many aspects brilliantly, all the way from "kindergarten" math to "University-level" mathematics using a wide variety of interesting examples and tidbits of humour.
The book ended up being a bit of a combination of a mathematics introductory and a refresher course without dumbing anything down or making one feel silly for not previously understanding the topic.
There are also so many external sources referenced that you can quite easily use this book as a stepping stone into a brilliant and well rounded education in mathematics or calculus.
Highly recommend.
Brilliantly written and covers so many aspects brilliantly, all the way from "kindergarten" math to "University-level" mathematics using a wide variety of interesting examples and tidbits of humour.
The book ended up being a bit of a combination of a mathematics introductory and a refresher course without dumbing anything down or making one feel silly for not previously understanding the topic.
There are also so many external sources referenced that you can quite easily use this book as a stepping stone into a brilliant and well rounded education in mathematics or calculus.
Highly recommend.
January 21, 2018
If I could give half stars, this would get 3.5 stars. It was fun to read, but maybe a bit too light and fluffy. I think the purpose of these essays was to skim the surface of a number of ideas though, and the author succeeded at that goal. If you're interested in some different ways to look at math functions, this book is worth the read.
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