Conceptos de matematica moderna/ Concepts of Modern Mathematics

by Ian Stewart

In this charming volume, a noted English mathematician uses humor and anecdote to illuminate the concepts of groups, sets, subsets, topology, Boolean algebra and other mathematical subjects. 200 illustrations.

Genres: Mathematics, Science, Nonfiction, Philosophy, Reference, Textbooks, Physics

Paperback

First published January 1, 1975

About the author

Ian Nicholas Stewart is an Emeritus Professor and Digital Media Fellow in the Mathematics Department at Warwick University, with special responsibility for public awareness of mathematics and science. He is best known for his popular science writing on mathematical themes.
--from the author's website

Librarian Note: There is more than one author in the GoodReads database with this name. See other authors with similar names.

Reviews

[Jose Moa · Rating 5 out of 5]

Ian Stewart is a great maths popularizer,he has a lot of books written with this aim,but this one is in some way special,it is one of the few math popular books that yet introducing math concepts and branchs in a rather rigurous way and in depht one can read them with the mathematical background of the high school,that I know other books of this sort are Mathemathics Methods,Contents and Significance by A.D.Alexandrov and Others and What is Mathematics by Richard Courant.

In this excelent book Ian Stewart introduces with rigor and depht : modular aritmethics,theory of sets,functions,algebraic structures with special atention to groups,linear algebra,infinite cardinality,algebraic topology and algebraic topological invariants as the fundamental groups and Euler charateristic,probability,aplications of mathematics to computer sciences and other fields ,fundations were the book exposes the Russels paradox and a sketch of the proof of the Godels theorems.

In brief,a excelent book for all people with a real,srious interest in whatmathematics is really and its fundamental ideas.

[Stephen · Rating 4 out of 5]

This book should be required to be read by all math teachers in high school. Instead of neglecting to answer questions of "so how is this used in the real world". the teacher can now provide an adequate answer, with this reference text. The mathematics discussed in this text can be thought of high level, but you only need a high school knowledge to understand most of the chapters. There are no real theorems or proofs, but Stewart provides general concepts, which may enlighten the non-mathematician to what it is that mathematicians do.

[William Schram · Rating 4 out of 5]

Professor Ian Stewart brings us the soul of New Math in Concepts of Modern Mathematics. I don’t remember why I chose to buy this book. The description said something about New Math, so I immediately assumed that it might have something to do with Common Core which is a mystery to me. I was incorrect on that account.

This book was originally written in 1975 and published in Great Britain. Modern Mathematics is their term for New Math. The book opens in the prologue with the author apologizing. Well, not really, but with the tone of the Preface, it certainly feels like that. He states that since Modern Mathematics came out, a lot of parents complained since they couldn’t help their children with their homework. This book is an attempt to familiarize the layman with the mathematician’s toolkit so it doesn’t seem so peculiar and terrifying.

The author covers a massive swath of Mathematics. Professor Stewart starts at Euclidean Geometry and moves on from there to cover the Cartesian Coordinate System, the Theory of Sets, Functions, Symmetry, Groups, and more. He explains with lucid prose and clear images. These images appear to be drawn by hand, adding to the overall charm of the book. Eventually, he covers topics such as Probability and what a computer does. Keep in mind that this book was written in 1975 so computers were not commonplace yet. There was another edition of the book in 1981, but that still predates a number of advancements.

The final chapters discuss applications of modern mathematics and discuss overall how the extraordinary has become mundane. Professor Stewart states that Algebra and Geometry being wed by the Cartesian Coordinate system was a surprise. People of the time couldn’t see the links that happened in two separate fields of mathematics. Now it is common to go and start in one field and have to borrow from several other fields to complete your work.

While this book was slightly different from what I expected it to be, it was not disappointing. I enjoyed it well enough and thought it was well done for being written back in the 1980s. For example, one problem that Professor Stewart talks about is that of the Four Color Theorem. It stated that four colors should be sufficient to color any and all maps, but it required a massive amount of computation to prove this. I wonder how long it would take to prove today.

[Daniel Toker · Rating 3 out of 5]

I got this book because I'm frustrated with learning the "how to" of mathematics. For the most part, my mathematical education has been, "Do this. Then this. And that's all you need to know for the test." I never got too thorough an understanding of how some things work, why they work, who came up with them, etc. (No wonder I came into college wanting to be an English major...).

This book does a good job of demonstrating the fundamental notions that underly all branches of math. I would recommend it to someone who's mathematically competent and isn't intimidated by a lot of numbers.

I, on the other hand, am much more comfortable with words than with numbers. Whenever Stewart EXPLAINS a theorem, I understood it without a problem. Unfortunately, this was rare - he spends most of time proving or disproving concepts through demonstrations that were too much for me to handle. Also, he doesn't delve enough into the history behind these mathematical ideas, so it all felt a bit cold to me. I need a human face behind a theorem (this why I love Dantzig's Number: The Language of Science, which does a BRILLIANT job of this).

Well, I got through a good amount of the book. At least I feel like I understand the bare basics of set theory, graph theory, and topology (I had to skip most of the section on how symmetry and group theory relate, which I still fail to understand).

[Mobin Shakeri · Rating 5 out of 5]

Wow! a magnificent book written by Ian Stewart.
the explanation of concepts and the fluency in the book in amazing. a very interesting book that makes you engage with the concepts. it's a great choice for a start on modern mathematics.
read it plenty times. and probably gonna read plenty more times too. totally advice everyone who is interested in the subject to read it.

[Nick Black · Rating 2 out of 5]

Read back in high school just as I was getting into calculus (and beginning to think that a Comparative Literature degree might not, after all, be in my future). Gentle introductions to all kinds of things (vector calculus, topology, group theory etc) but lacking either the detail to make any real sense of them, or the historical data to bring them to life.

[Erickson · Rating 5 out of 5]

Very good, though does not seem like suitable for perfect beginners. This book in my view is more for those who has great interest in mathematics and have some grounds on it.

[rohola zandie · Rating 5 out of 5]

This book is the most elegant book I read in mathematics. It's more fun than reading any novel or story. The amazing Ian Stewart talent in conveying the importance of modern mathematics is just unique. The book is more like a story to me, you can read it all along without interruption. The author sends you to another world which to me is like the Wonderland of Alice. The book starts with set theory and goes through, analytic geometry, abstract algebra, group theory, topology, and probability.
The book published in 1975 but have insights for people in far future.
I strongly recommend the book for mathematics lovers and other who hate it. :)

[Ben Gutierrez · Rating 4 out of 5]

Have you ever wondered what you would learn if you learned mathematics that you didn't need to know? Like, what if you wanted to become a mathematician: what would you be thinking about? I ended up learning a bit of discrete mathematics and some calculus for computer science, but I'd always wondered what I could have studied if I'd kept taking math courses. This book was an overview of some of these topics. Groups, rings, analysis, abstract algebra… that stuff is all talked about in here. Not a lot of rigor or detail, just enough to give an overview of some of the things you might be missing if you stopped with trigonometry or calculus.

It's all very readable and gave me a bit of a roadmap for things I'll want to investigate further.

[Volodymyr · Rating 5 out of 5]

Quick tour de force into the subject, although with some reverence for the topology.
Proofs could be too intuitive sometimes or lack some steps, but the main idea is to show the mathematics as science of patterns and concepts and explain unity and meaning of its concepts, which is fulfilled on whole 100%.
The interesting thing was author's scepticism regarding computer-assisted proofs as too complex and not intuitive, however Stewart has left space for maneuver, telling that maybe the problem is in the increased essential complexity of things to be proved.
Also, the thing I liked the most is the emphasis and explanation of connection between intuition and rigour.

[Amit Kumar · Rating 5 out of 5]

Some of the topics such as the ones related to topology and group theory were difficult to grasp. Maybe because this is the first time I am learning about these. In general the text is very good and makes you understand the concepts at a deeper level.

[Kate Lane · Rating 5 out of 5]

A well-written survey of a broad sweep of mathematical topics. Perfect to introduce students who might not know what direction they'd like to go in their future studies, or for more seasoned mathematicians to review a great many topics without having to jump between many seperate books.

[Ami Iida · Rating 2 out of 5]

it is the modern math. book and it is boring. -;)

[Nitin · Rating 5 out of 5]

Just Beautiful

Just Beautiful. Excellent summary of current mathematics topics for a lay person. I especially liked the last chapter. Love to see more books like this

[Emmalyn Renato · Rating 4 out of 5]

Even though the author has written several SFF novels and stories (and did a bi-monthly column on recreational mathematics in the Scientific American for several years), this was one of his (numerous) popular non-fiction books. It's the book I wish I'd had when I was studying in England for an A level in Pure Mathematics in the early 70's. Ironically (and unbeknownst to me), Stewart was giving an extramural (nowadays it would be called "continuing education") course on these very topics at about the same time, just "up the road" from me, at Warwick University.

This book does a very good job of explaining a lot of the things in the "new math", that I'm convinced my teacher at the time, didn't fully understand himself. There were some places (for example, in the concepts for the abstract algebra chapter), where we went from simple beginner steps, to what felt like expert steps, and I was left with a "and now draw the rest of the owl" feeling. I ended up skipping through those. Parts of the chapter on Computers and Their Uses haven't aged well, and can be ignored (unless you'd like a brief giggle). There also appear to be several mistakes. I wonder whether there is an errata available online somewhere.

[Uladzislau · Rating 5 out of 5]

В школе наше изучение математики ограничивается достижениями 18 века, ну может начала анализа крохотной частью касаются века 19. По сути из всего математического небоскреба, кропотливо возводимого последние лет двести, нами освоено в разной степени пара цокольных помещений.
В этой книге Стюарта дается популярный обзор основных математических концепций по состоянию на вторую половину 20 века. Теория множеств, абстрактная алгебра, топология, теория групп, неэвклидова геометрия, линейное программирование и теорема Геделя о неполноте на закуску - все это вполне доступно пониманию рядового читателя. Причем не только сами эти концепции, но и простейшие доказательства основных положений.
Насколько я знаю, это единственная книга Иэна Стюарта, отобранная для публикации в советскую эпоху, что не может не говорить о ее качестве.

[Omarove · Rating 4 out of 5]

Finallyyyyyyyyy!
I struggled until finishing this book, and don't ask me why but I can't not finish a book!
At the beginning the book started going easy and everything (almost) was comprehensible. Later on, some chapters went crazy while I pretended that I'm following the material. I found myself indulging more in number problems so I skimmed through (ditched) topology and similar topics. But at the end I was relieved by this sentence in the last section written by the author: "It has always seemed to me that the non-specialist is capable of grasping more of the spirit of a subject than is commonly imagined".

Thank you Dr. Miller for lending me this book, it's time to return it to the shelf!

[Roberto Rigolin F Lopes · Rating 5 out of 5]

We are in 1975, Ian is teasing us with bits of modern mathematics. He warm up remembering us that mathematicians are juggling concepts (instead of numbers) for intellectual satisfaction. Impressive jugglers playing with axioms, functions, sets and so on. Everything connected together by powerful, and enjoyable concepts from the queen of the sciences. Here, emphasis on enjoyable because our math majesty is introduced to layperson by a very good teacher. The whole thing is well illustrated with examples and plots in an engaging parade of abstractions; majestic indeed.

[Ong Chen Ping · Rating 4 out of 5]

In this book, Ian Stewart shows readers what real Mathematics is. He talks about several important topics such as sets, algebra, topology & analysis. Although Stewart only provides brief introduction for each topic, I found some topics/concepts hard to grasp. However, I've learned plenty of new stuffs throughout the whole book and got an idea of what 'Modern Mathematics' is. Definitely gonna reread it when I go to highschool.

[Özgür · Rating 4 out of 5]

Bazı bölümlere hiç yabancılık duymazken topoloji, aksiyomatik, hyperspace gibi bazı bölümler gerçekten ilginçti. Kitabı motivasyonumu kaybetmeden bitirdim. En az 20 yıllık bir kitaba göre bence genel bakış ve kapsama güzel. Eksik olarak gördüğüm yanı bazı bölümler bana göre kolaydı ancak anlatabilmek için daha fazla yer harcanmıştı, bazıları ise daha zordu ancak o özen sanki daha az gösterilmişti. Genel olarak kitabı tavsiye ederim, özellikle matematiğe genel olarak bakmak isteyenlere.

[Reid Ginoza · Rating 4 out of 5]

I read this book hoping to get an informal summary of undergraduate mathematics, and the book succeeded! I liked the variety of math topics covered. There are definitely some technical sections that can get dense, and sometimes I found myself wishing Stewart could be either more rigorous with more precision or less rigorous and letting me just take things on faith. But overall, it was worth my time.

[Willem Hoekstra · Rating 4 out of 5]

Ik probeer me een duidelijke doelgroep voor te stellen voor dit boek. Omdat ik veel van wat Stewart beschrijft al eens eerder had gezien, las het makkelijk en vond ik de grote lijnen die hij schetste interessant. Maar na tweederde van het boek sloop er wat verveling in.
Ik vraag me af of het werkt als je het boek langzaam moet bestuderen omdat je niet bekend met met de inhoud.

[Alastair · Rating 5 out of 5]

A superb primer on modern maths for someone with a reasonable bit of experience in the field. Probably not for the uninitiated ...

[Shanley Kearney · Rating 5 out of 5]

this book was SO good. will be referencing a lot

[Jean-Luc · Rating 3 out of 5]

"The reader who has persevered this far must by now be a cultivator of mathematics, even if he was not at the start of the endeavour. He will therefore appreciate that, while it may be ancient and venerable, it is far from complete; that not all of it is dry; and that its reasoning has not always been either unambiguous or irrefutable - nor is it yet."
-Ian Stewart, Appendix

That about sums it up. This book was incredibly easy to read, and despite being written more than 31 years ago, it's still relevant and illuminating. Individual topics are only investigated to the depth that we can see patterns emerge. Simple examples demonstrate why these topics are useful. Subsequent topics will usually refer back to elaborate on how everything is (surprisingly!) interwoven.

I can't recommend this book enough, many thanks to my family for picking it up for me. This book would work best, IMO, if you read it during the summer in between high school and college. I imagine that if I had read this book, specifically the chapters on "Short Cuts in the Higher Arithmetic" and "The Language of Sets", before I took CS 666 (Cryptography) @ Stevens-Tech, then I probably would've done much better in that course... I felt comfortable w/ the author because I had read one of his previous works, The Annotated Flatland.

[Maurizio Codogno · Rating 1 out of 5]

Ogni tanto sbaglio gli acquisti. Questo libro non è nient'altro che un testo scolastico su quella che è diventata di moda come la "nuova matematica". Quello non sarebbe stato poi chissà quale problema, se il testo fosse stato scritto nel modo brillante che mi aspetto da Ian Stewart; purtroppo però questa è probabilmente la sua prima opera - la prima edizione del libro è infatti del 1975 - e si sente che l'autore aveva sì delle potenzialità, ma non erano state ancora espresse. Alla fine, pertanto, il libro non ha nemmeno il fascino di un'opera antica che uno magari legge da un punto di vista storico; se ne può fare tranquillamente a meno.
( da http://xmau.com/notiziole/arch/200608... )

[Daniel · Rating 3 out of 5]

Good general introduction to give you a feel for some diverse areas of modern mathematics. However, the explanations are glossed over too quickly and I found it very difficult to follow some of the details even with a mathematical background. Will still give you the broad ideas but for a more thorough and complete introduction to the topics, topic specific books will be needed.

[Joe · Rating 5 out of 5]

great intro for me to a wide range of mathematics. a huge boost up. great translation from hard-core math land to non mathematicians. a good balance between oversimplifying one the one hand and overwhelm with symbols on the other.

[Mitchell Kember · Rating 5 out of 5]

This was an excellent book. I already knew a bit about set theory and some of the other topics, but this book gave me a much better understanding of how it all fits together. It gave me a great foundation of modern mathematics going into my first year of university. Ian Stewart is a great writer.

[Zhaodan Kong · Rating 4 out of 5]

The book gives a big picture (although somewhat skewed towards topology) view of modern math. I would say it should be a light read for most undergraduate students, especially those who are interested in science and engineering.