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Introduction to Mathematical Thinking

3.89  ·  Rating details ·  401 ratings  ·  27 reviews
In the twenty-first century, everyone can benefit from being able to think mathematically. This is not the same as “doing math.” The latter usually involves the application of formulas, procedures, and symbolic manipulations; mathematical thinking is a powerful way of thinking about things in the world -- logically, analytically, quantitatively, and with precision. It is n ...more
Kindle Edition, 104 pages
Published July 18th 2012 by Keith J. Devlin (first published 2012)
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3.89  · 
Rating details
 ·  401 ratings  ·  27 reviews

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Matthew Dowd
Didn't complete all of the exercises since many of them are nearly the same as the MMOC Devlin teaches through Coursera, and some of them took longer than I had time for (I'll be revisiting, this was a pretty cursory read). Renders poorly on the kindle but very instructive nonetheless.
Olga Grytsenko
Oct 02, 2017 rated it really liked it  ·  review of another edition
Nice read :)
This would work very well if you're about to start a university degree that supposed you did some "higher" mathematics in high school and you need an introduction, or a refresher - you'll learn what all of those Greek symbols do (university-level notation), you'll learn about the kind of precise language you need, how to structure proofs, types of proofs, etc.

The language is the best part. It's never particularly dry or boring, Devlin knows how to structure what he wants to convey. However, mos
Dec 05, 2013 rated it liked it  ·  review of another edition
This was basically a retread of the Coursera course, and while I still really really love the preface to this book with its overview of the difference between school mathematics and actual Mathematics, the details of how to come to an attitude of puzzling over math and logic problems didn't really make for a readable book.
Sep 09, 2013 rated it it was amazing  ·  review of another edition
I've been reading this book while taking Dr. Devlin's Coursera class of the same name. I have greatly enjoyed both the textbook and the online course. If you have any interest in mathematics, I recommend both the course and this textbook.
Patrick Coakley
Aug 21, 2017 rated it really liked it  ·  review of another edition
Great way to jump into mathematical concepts that many people didn't learn in school. I used it as a way to catch up on understanding some of the basics of computer science-oriented math and it helped tremendously. Includes exercises but no answers, which really makes it sort of frustrating to do them because it can feel like a waste of time and there are other meatier books with more problem sets.
Aug 30, 2017 rated it really liked it  ·  review of another edition
This is a book you shouldn't only read but live with it for however long it takes you grasp the content. This includes thinking deeply about almost every sentence, solve or at least try to solve every exercise, even if it costs you many hours of your life. If I follow my own advice I am far from done with the book but intend to start again right away.
Michael Cayley
Aug 09, 2017 rated it it was amazing  ·  review of another edition
Shelves: maths
A good and accessible introduction to mathematical reasoning, with exercises to test your comprehension. It covers logic and mathematical proof, and does not require much previous mathematical knowledge, so it is accessible to lay readers as well as people studying maths at school or university.
Warren Mcpherson
This book has a couple of very good insights and is fairly short.
I think it is useful for getting reacquainted with reading mathematical material.
Alexander Gomez Villa
Although the concepts and explations are pretty good I sincerely think that the book is very short. Anyway it is a must read to any engineering freshman
Minh Nhật
cuôn nay la background reading theo course introduction to mathematical thinking cua stanford, 1/2 đâu noi kha hay vê toan, vơi môt ngươi lân đâu tiên tim hiêu sâu sâu ti vê toan thi thây nhiêu thư rât thu vi.

1/2 sau tâp trung vao phân tich ngôn ngư hơi chan vi minh đa tưng theo 1 lơp khac chuyên sâu va thu vi hơn la Language, Proof and Logic

The dramatic growth in mathematics led in the 1980s to the emergence of a new definition of mathematics as the science of patterns. According to this descr

»You won't learn much new math from this book. But by acquiring the ability to think like a mathematician, you will be able to master new math quickly«

Stanford-Mathematiker & Wissenschaftspopularisierer Devlin erklärt in diesem Heft das neuere, begriffliche (also das Wesen der Sache ergründende/auf sich selbst reflektierende) Denken moderner Hochschulmathematik, das der rechnenden, prozedurenfolgenden Sekundarschule abginge (wie Mathematikern Jahrhunderte zuvor
Dec 21, 2014 rated it really liked it  ·  review of another edition
This was nice - Prof. Devlin throws in some humor, history, and down-to-earth language into this "introduction" to mathematical thinking. I'd say it certainly would work better if used in a class (e.g. a course complementary text) because although for the already initiated the proofs that are given are "basic" -- for those who are truly starting their journey into mathematical thinking it will still be tough and would benefit from the advice of a teacher (for some of the practice problems, for e ...more
Thai Son
The introductory essay on math is great, I got a great deal of insights out of that. The rest was nice, but I was too bored by the time I got through the major half of the book, having learned proofs and other things beforehand. I certainly am not with the camp who thinks a proofs class should be required before taking any math-major course class (e.g. Abstract Algebra, Real Analysis, etc.) . But that is just me, coming from a rich pre-university background, having exposed myself to some interes ...more
Vilém Zouhar
Lousy introduction to formal logic. If you have at lest a basic understanding of the term such as disjunction, conjunction, implication or equivalence, this book is going to be a waste of time. I have deep respect for Keith Devlin. My experience with his other books has been pleasing at least. This, however, I either misunderstood or is not really something worth reading thouroughly.
Apr 03, 2013 rated it really liked it  ·  review of another edition
The first chapter of this short book is a terrific explanation of the value of math and why it matters. As a proponent of the rethinking of education in general and the needs of a changing economy in particular, I found that Devlin really understood what too many people do not. The rest of the book is good, too, but that whole first section was what really piqued my interest!
Jan 22, 2017 rated it really liked it
One of my (multi) NY resolutions is to study the math pretty much from scratch and this is a good first book - the material is pretty simple though even if you took math in college it still going to be a workout.
Violet Marcelo
Most problems at the latter end of the book were too technical for readers who have no background in higher maths. And this is supposed to be 'Intro to mathematical thinking'. The outline is good to follow though, so you can take it from there.
Sep 04, 2014 marked it as to-read  ·  review of another edition
In the present moment I'm thinking: "may be I should learn about mathematics as a hobby".
Izhan Noorzi
Jul 22, 2015 rated it really liked it  ·  review of another edition
It's a good book especially for non-mathematician to learn the essence of mathematics.
The author described in depth how the framework of mathematical thinking deal with every day related matters.
Gnuehc Ecnerwal
It tends to reaffirm the status quo by suggesting ways to be better equipped to handle it. Not what I expected from Devlin, who had been a proponent for reform.
Raymond Lewis
Jan 17, 2017 rated it really liked it
Deceivingly short.
Oct 30, 2016 rated it liked it  ·  review of another edition
Recommends it for: This book is practical for anyone seeking to improve their analytical thinking
#mathematical thinking
#analytical skills
#math exercises
#21st century skills
Alexander Mostovenko
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Börp Madley
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Jan 25, 2016
David N. Violette
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Dr. Keith Devlin is a co-founder and Executive Director of the university's H-STAR institute, a Consulting Professor in the Department of Mathematics, a co-founder of the Stanford Media X research network, and a Senior Researcher at CSLI. He is a World Economic Forum Fellow and a Fellow of the American Association for the Advancement of Science. His current research is focused on the use of differ ...more
“Give a man a fish, he’ll eat for a day. Teach a man to fish, he’ll eat for a lifetime.”? It’s the same for mathematics education for twenty-first century life.” 5 likes
“For all the time schools devote to the teaching of mathematics, very little (if any) is spent trying to
convey just what the subject is about. Instead, the focus is on learning and applying various procedures
to solve math problems. That's a bit like explaining soccer by saying it is executing a series of maneuvers
to get the ball into the goal. Both accurately describe various key features, but they miss the \what?"
and the \why?" of the big picture.”
More quotes…