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Concepts of Modern Mathematics

4.01  ·  Rating Details ·  344 Ratings  ·  22 Reviews
Some years ago, "new math" took the country's classrooms by storm. Based on the abstract, general style of mathematical exposition favored by research mathematicians, its goal was to teach students not just to manipulate numbers and formulas, but to grasp the underlying mathematical concepts. The result, at least at first, was a great deal of confusion among teachers, stud ...more
Paperback, 352 pages
Published February 1st 1995 by Dover Publications (first published 1975)
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Mar 29, 2009 Stephen rated it really liked it
Shelves: mathematics
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-mathematici ...more
Daniel Toker
Aug 27, 2010 Daniel Toker rated it liked it
Shelves: philosophy, math
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
Ben Gutierrez
Feb 04, 2017 Ben Gutierrez rated it really liked it
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 ...more
Jan 07, 2017 Volodymyr rated it it was amazing
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
Sep 11, 2011 Erickson rated it it was amazing
Recommends it for: Han Zhicheng
Shelves: mathematics
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.
Ami Iida
Aug 31, 2015 Ami Iida rated it it was ok
Shelves: math
it is the modern math. book and it is boring. -;)
Dec 14, 2007 Jean-Luc rated it liked it
"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 r
Maurizio Codogno
Nov 15, 2010 Maurizio Codogno rated it did not like it
Shelves: math, finished
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 ...more
Jun 03, 2013 Daniel rated it liked it
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.
Nick Black
Apr 11, 2009 Nick Black rated it it was ok
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.
Zhaodan Kong
Dec 01, 2014 Zhaodan Kong rated it really liked it
Shelves: research
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.
Mitchell Kember
Nov 01, 2014 Mitchell Kember rated it it was amazing
Recommends it for: anyone interested in math
Recommended to Mitchell by: Amazon
Shelves: favorites
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.
Oct 15, 2007 Joe rated it it was amazing
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.
Feb 25, 2010 Andrewcharles420 rated it it was amazing
Shelves: math-textbooks
Great explanation of how one should think to understand modern mathematical theories--very different from ways I was taught in any schooling.
Jonathanstray Stray
Aug 21, 2009 Jonathanstray Stray rated it liked it
Wouldn't help much if you didn't already know math.
Andrew Thibodeau
Aug 03, 2011 Andrew Thibodeau rated it did not like it
Shelves: mathematics
While the book touched on multiple areas there was not nearly enough depth. That may have been the purpose though.
Juan C Aragon
Cohesion of past reading

Alright definitely the book your looking for if you need a conceptual framework of math......ok ok ok ok ok ok
Jul 12, 2014 Leemaslibros rated it really liked it
Wonderful reading, disastrous (kindle) edition.
Feb 01, 2017 Gus rated it really liked it
Terrific read. Prof. Stewart knows how to talk about mathematics. The breadth of this book was amazing.
Matt Conrad
Jan 27, 2016 Matt Conrad rated it really liked it
A bit difficult to understand for anyone not yet familiar with its concepts.
Feb 04, 2014 Eleanor rated it it was amazing
Shelves: 2014
The most charming book :)
Sep 05, 2008 Michael rated it it was ok
A good review of modern math. Could've used some more rigor though.
Jason Benedict
Jason Benedict rated it liked it
Sep 28, 2014
Dean rated it it was amazing
Jul 04, 2016
Paul Pseudo-Expert
Paul Pseudo-Expert rated it it was amazing
Jan 09, 2016
Bigwickerventriloquist rated it really liked it
Nov 04, 2014
Simon Young
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Mar 30, 2015
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Mar 10, 2012
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Jan 10, 2015
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Raphael Corrêa rated it really liked it
Jul 22, 2013
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Ian 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

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“if a theorem is geometrically obvious why prove it? This was exactly the attitude taken in the eighteenth century. The result, in the nineteenth century, was chaos and confusion: for intuition, unsupported by logic, habitually assumes that everything is much nicer behaved than it really is.     Good” 0 likes
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