Математика

50 Ideas You Really Need to Know

by Tony Crilly, Shashi Martynova (Translator)

Математика, Снежная королева наук, чарует и вызывает священный трепет у каждого, кто соприкасается с ней, даже у самого завзятого гуманитария. Всю математику не под силу знать никому, она слишком многообразна, но основные идеи, что определили и определяют нашу жизнь, надо знать всем. Том «Математика» – сжатый, но идеально выверенный экскурс в эту великую и прекрасную науку, это головокружительный полет над лунным пейзажем ее неумолимой, строгой красоты. Со многими идеями, изложенными в этой книге, читатель наверняка знаком, но «Математика» предлагает то, что не дают учебники, – постичь красоту математических идей, увидеть, как математика связана с жизнью, искусством, политикой, экономикой. Эта книга может стать подспорьем и для тех, кто решил развеять свое математическое невежество, и для тех, кто хочет освежить свои познания в этой самой магической науке. Здесь собраны 50 главных математических идей – как очень простых, так и изумляющих своей великой непостижимостью.

Genres: Science, Nonfiction, Mathematics, Reference, Popular Science, History, Education

208 pages, Hardcover

First published January 1, 2007

Reviews

[Kent · Rating 3 out of 5]

Grabbed this on sale at Borders, and it was worth the discount price. Written by a Brit, it does a good job of highlighting the many mathematical ideas that each of us has probably been exposed over the years, while adding some very interesting history into the mathematicians studying the problem.

Each Idea is exactly four pages long, so they are given equal stature and rank. Some are more obvious than others. Some Ideas are easy, some incredibly advanced. I enjoyed the time line for each Idea.

I would retitle the book "50 Mathematical Ideas You Probably Knew About, but You Don't Really Need to Get By in Real Life." Sending it to the family mathematician Prof. T. Watterson.

[Carlex · Rating 5 out of 5]

An excellent tool to remember mathematical concepts and to know new ones.

[Brian Sison · Rating 2 out of 5]

This book should really be titled "An Introduction to 50 Mathematical Ideas..." Limiting oneself to four pages is very difficult to do even with simple concepts like Zero and fractions. It is downright impossible with broader concepts like Calculus, Game Theory, or Relativity.

Even worse is the fact that these broad introductions to complex ideas contain multiple small, but drastic, errors. This book would be fine for a complete math novice who has no intention of ever using these concepts or thinking about them again in the future. For anyone mathematically inclined, I would skip this for any of the multitude of other books out there with a more focused, refined scope.

[Márcio · Rating 3 out of 5]

Após ler o livro dessa coleção acerca da mecânica quantica, o qual me ajudou a elucidar alguns questões que eu não entendia bem, pensei em ler sobre Matemática. Mas confesso que apesar de ter percebido isso e aquilo um pouquinho melhor, ainda me encontro anos-luz dessa área do conhecimento humano. Não é tanto pelo autor e pela obra em si, que como qualquer livro que visa a apresentar apenas certos aspectos de uma determinada área, deixa a desejar. A questão, na verdade, está em mim, com minha dificuldade de perceber conceitos abstratos e suas formulações. A mente humana tem várias formas de se desenvolver, mas aparentemente, a minha mente não é dada às questões matemáticas 😂

No entanto, uma coisa eu percebi claramente e diz acerca da natureza da Matemática, pois é comum ouvirmos dizer que ela é a linguagem da Natureza, é a forma como o Universo fala conosco. O livro não dá essa resposta, mas deixa claro que a Matemática é uma criação humana para poder entender o Universo, uma forma de linguagem e consiste em uma série de abstrações que nos permitem realizar coisas básicas da vida humana, mas também outras tantas increvelmente complexas.

[Gabriela Pistol · Rating 2 out of 5]

Total neatrăgătoare pentru un umanist și probabil total inutilă pentru cineva cu înclinații și cunoștinte medii-avansate. Combină concepte foarte de bază și ușor de înțeles cu noțiuni avansate și le dedică la fel de mult spațiu ambelor categorii.

[Dai]

Abandonado. No era lo que esperaba

[Björn Bengtsson · Rating 4 out of 5]

This book contains trivia about mathematics.

It contains 50 topics of general interest, and each topic can be read by itself. There is no need to read the book from cover to cover, so it is a great coffee book, or for breakfast reading, etc.

Each topic is explained in an easy and relaxed way, requiring no prior mathematical knowledge, which makes it easy to grasp.

Anyone with the slightest interest in mathematics would enjoy this book.

[Celia · Rating 5 out of 5]

as a math gal this isn't really anything i would put forth for serious math heads...but if you're looking for a book that will introduce a mathophobe to some of the more fascinating mathematical concepts this is the stuff. that's why it got the stars it did.

[John Schneider · Rating 3 out of 5]

When my family saw me reading a math book for fun, they thought I was crazy. I think they are crazy for not wanting to learn more about mathematics. Although far from an advanced course on math, this book is fun and informative for the most part. Every so often it covers a math problem that only a mathematician could love, but such quirkiness make the book. Since mathematics covers so many different topics, this book should enable even the most bitter hater of math to find some part of math to love.

[Lauma · Rating 3 out of 5]

Šo grāmatu vajadzēja lasīt pirms iestāšanās matemātikas fakultātē, vairāk jauna uzzinātu. Visas tēmas, protams, man nebija zināmas, bija arī tādas, kas mani tiešām neinteresēja, bet kopumā tāpat diezgan laba lasāmviela, JA interesē matemātika. Neieteiktu cilvēkiem, kurus tā vispār neaizrauj, pat ar interesi negribas vienmēr pieķerties. It sevišķi, ja ir iesāktas vēl citas aizraujošas grāmatas.
Uzzināju dažus interesantus vēstures faktus un to, ka matemātiķi esot sasodīti dīvaini radījumi, jo viņiem vajadzēja ieviest simbolu, kas apzīmē neko. Kam gan vajag nulli?

[Alan · Rating 3 out of 5]

I learned more about Roman numerals - idea 1 was all about Zero - and how the Romans didn't have nothing.

QED has been replaced with a solid square - how disappointing!

Many of the other ideas I had already come across but I did find them well explained and I liked the style - neither too heavy nor too trivial.

I picked this one for the cover for Summer09 Challenge 30.09 but I thoroughly enjoyed it.

[Marcos · Rating 3 out of 5]

Leitura bem informativa, ajudou-me a rever alguns conceitos e a adquirir uma pequena noção de outros, mais complexos que até então só tinha ouvido falar. As explicações são bem acessíveis, e servem como isca para quem se interessar por algum dos assuntos apresentados. Obviamente que o livro não tem a pretensão de cobrir temas complexos de maneira profunda, mas sim dar algumas pinceladas introdutórias.

[Jonathan Gnagy · Rating 4 out of 5]

Great descriptions of some of very interesting ideas. I read 1 idea a day for 50 days and found all the ideas interesting and explained well enough that I understood (and I learned a bit about their history at times too). A great way to keep the mental juices flowing when not in college or just not taking any serious math.

[Dustin East · Rating 4 out of 5]

<3 Math <3

If you're interested in math beyond Arithmetic, worth a read or at least a skim of the topics that interest you. Talks a lot more about the history and development of various topics than you'd normally get even in most Undergraduate level courses.

[Edkallenn Lima · Rating 5 out of 5]

Excelente livro.
Algumas vezes o autor "exagera" na matemática mostrada (que deve assustar o mais leigo), mas em geral, os conceitos estão corretos e bem apresentados, com poucas pequenas falhas que não comprometem o texto geral.
Recomendo.

[Calvin · Rating 5 out of 5]

Fun book, finished this on a plane trip home.

[ahsen · Rating 4 out of 5]

güzel güzellllll. matematik.

[João Vaz · Rating 4 out of 5]

Fact: Math is beautiful. Fun and quick walkthrough of some of the more important mathematical concepts.

[Maurizio Codogno · Rating 5 out of 5]

Ci sono molte collane divulgative, e anche per quanto riguarda la matematica la Very Short Introduction di Timothy Gowers è insuperabile. Però ogni collana ha un pubblico di riferimento, e secondo me queste "50 grandi idee" sono più adatte al grande pubblico. I temi, in questo caso quelli matematici, sono infatti trattati in pillole, quattro pagine cadauno; la trattazione è naturalmente di base, ma arriva anche a temi non banali tipo l'ultimo teorema di Fermat e l'ipotesi di Riemann (con un erroraccio non so se nel testo originale o nella traduzione, che comunque è scorrevole). Molto bella l'idea della linea temporale in fondo nelle prime due pagine, che dà un'idea di quando e come i concetti si sono sviluppati; meno indovinate a mio parere le frasi chiave che terminano i capitoletti, frasi che a volte mi sembravano piuttosto stupide. Ma a parte questa pecca il libro è assolutamente consigliabile se avete sempre avuto paura che la matematica sia troppo complicata e avete il coraggio di provare a cambiare idea.

[Zhelana · Rating 2 out of 5]

While some of the concepts in this book were explained at a level that I could understand them, many more were not. I found myself confused more often than not. It seemed like it could be some interesting information, but it was not written to a beginner level, which is what I would expect from a book by this title.

[Dan Cohen · Rating 2 out of 5]

It's not a bad book and would be worth reading by someone with a very deficient mathematical education. I found it inaccurate in parts and badly explained in others. I also felt that the selection of ideas was not great (why do writers of books on mathematics for non-mathematicians so often include a section on relativity theory?)

[Sarah · Rating 4 out of 5]

Good clear summary of the ideas. Gets a bit confusing when you reach the last few which are the most complicated ones but not surprising given each idea is given four pages.

[Sadia Mansoor · Rating 4 out of 5]

RECOMMEND TO ALL MATHS RELATED STUDENTS & TEACHERS

Having problems in solving that mathematical formula? Do you feel the need to revise your mathematical equations again? Do you face problems with remembering definitions & find no way to look for? Are you tired of mixing all the theories together?
Worry no more.. because Tony Crilly has brought a basic maths book which teaches you the concepts of mathematical problems, ranging from the simplest fractions to the most complicated lengthy equations. It's a reader friendly book, which gives you the understanding of how every formula or problem is formed & solved. It's not at all boring for anyone. Not only teachers but students can read it easily as well. Also, there are lots of examples with the descriptions of how numbers can be simplified & many different graphs, tables, shapes & charts are available to help you further in getting the idea of your problem.
I wish I had found this book before in my school days. It's a lot easier & helpful to understand..

Have a look at this book.. https://sangu.ge/images/50mathematica...

[Jason Edwards · Rating 3 out of 5]

I would have told you that I’ve always been “good” at math, but now I’m more inclined to tell you that I’ve always been “comfortable” with math. I’ve enjoyed playing around with numbers and shapes and equations and all that. So when I saw 50 Mathematical Ideas on a friend’s shelf it was an easy one to grab and browse.

Which is what you can do with this book: browse. I read it in order, one through fifty and there are overlapping concepts that might have you go read a previous chapter if you haven’t already. But not too often, and Crilly is consistently “light but thorough” in his treatment of each idea, whether it’s The Zero, Infinity, Relativity, or Fractions.

For folks familiar with the concepts, it’s a nice little review, and for those who are new to the ideas, the chapters provide a tidy introduction.

But I don’t know if people who aren’t comfortable with math should even bother.

[Victor Henrique · Rating 3 out of 5]

Tony Crilly's 50 Mathematical Ideas offers a refreshing perspective on math, blending intellectual curiosity with accessible explanations. For those already well-versed in mathematics, the approach may feel unconventional, as Crilly leans heavily on linguistic analogies and conceptual storytelling to explore mathematical principles. However, this unique angle is precisely what makes the book fascinating for readers seeking to reconnect with math from a more mature, contemplative standpoint.

The incorporation of linguistics to elucidate mathematical ideas stands out, as it bridges abstract concepts with relatable, real-world contexts. This method gains an added layer of intrigue when read in different languages, where the nuances of mathematical expression shift subtly yet meaningfully. Ultimately, Crilly’s work is a compelling choice for those curious about the interplay of logic, language, and numbers, offering an engaging journey for rekindling one’s appreciation of mathematics.

[Mariia Filipchenko · Rating 3 out of 5]

WHAT’S IT ABOUT? :: 50 math-related topics arranged in a logical sequence and presented in the form of an encyclopedia.

THOUGHTS :: I don’t have that much to say here. I did like the topics covered in the book, but a lot of them were already familiar to me from school or previous research. That’s probably more my issue than the book’s fault. Overall, I liked the way it’s structured and how convenient it is to use, BUT…

A separate paragraph of my frustration goes to the way the book is bound. I always read carefully, trying to keep the spine intact, BUT MY BOOK STARTED FALLING APART. It’s glued instead of sewn (like it normally should be). So the pages don’t tear – they just unstick ☠️… I have a lot of respect for PWN as a publisher, but this…

RECOMMENDATIONS :: For anyone who wants to have an encyclopedia-style book to pick up and read any time.

[Athena · Rating 5 out of 5]

Be prepared, because I am a maths nerd, so I did, absolutely love this book.

It was simple enough that I could understand it without too much brain work (aka. I could read it just before bed without crying), but was also full of new principles and ideas I'd never heard of, or thought about.

I definitely picked this back up again at the perfect time. I found that I'd read about something, and then be covering it in lessons in the next couple of weeks. It laid the perfect base for my teacher to build on, and helped me pick up principles so much quicker than I normally would.

This book is such an incredible resource for maths students, but also, if you're just a bit nerdy, and want to learn a tiny bit more about maths, it can be super interesting (and not too boring).

[Chris Seltzer · Rating 2 out of 5]

I question who the audience for this book is.

It's not that I think the topics are particularly bad nor do I think the sections are poorly written.

I just wonder if the same person who needs an explanation of pi will also find topology interesting.

Also why is relativity even on the list?

Does the average person on the street really need to know about the parallel postulate?

It's just a hodgepodge of math topics lacking in framing, curation, and organization.

Recommend you skip.

[Sammie McGurl · Rating 1 out of 5]

I had to read this book for school, and I can honestly say that it is possibly THE WORST book I have ever read. Don't get me wrong; I love math. This book; however, KILLED me. It spent four pages per topic talking about some things that should have been learned in kindergarten and some other things that are irrelevant and confusing. DON'T read this book unless you absolutely have to.

You don't have to agree with me; I'm just sharing MY honest opinion.

[Socrate · Rating 3 out of 5]

TONY CRILLY este scriitor freelancer, anterior fiind profesor la Universitatea din Michigan, la City University din Hong Kong, la Open University şi la Middlesex University din Londra. Domeniul său principal de interes este istoria matematicii şi a scris şi a editat numeroase lucrări despre fractali, haos şi aritmetică. Este autorul unei biografii apreciate a matematicianului englez Arthur Cayley şi al unei cărţi de popularizare a matematicii, How Big is Infinity?