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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. 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. ...more

Dec 25, 2015 Philipp rated it liked it

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

The language is the best part. It's never particularly dry or boring, Devlin knows how to structure what he wants to convey. However, most of the content I already had back in my "Mathematik Leistungskurs" [in Germany's gymnasium you can kind of "major" in a few classes so you'll have more classes and more depth] so I've had all this before - why did I read it then? Curiosity about the title, I guess. I thought there would be more "how to think", less "how to write". But you've got to start somewhere, I guess.

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Sep 09, 2013 Brian rated it it was amazing

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. 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. ...more

Aug 30, 2017 Sebastian rated it really liked it

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. 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. ...more

Dec 05, 2013 Alison rated it liked it

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. 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. ...more

Oct 30, 2016 Marina rated it liked it

Recommends it for: This book is practical for anyone seeking to improve their analytical thinking

#logicalthinking
#reasoning
#mathematical thinking
#analytical skills
#math exercises
#21st century skills

Apr 21, 2020 Mayur Sinha rated it really liked it

I read this book while taking the Coursera class of Dr. Devlin. Mathematics is not about solving abstract problems with no meaning in real life, it's about the higher-order form of thinking where you combine multiple streams of knowledge to solve a real-world problem. No one can teach you how to think mathematically, one has to learn on his own. The author recommends knowing at least algebra, logic, set theory, and real analysis to be able to be proficient in mathematical thinking but I think he I read this book while taking the Coursera class of Dr. Devlin. Mathematics is not about solving abstract problems with no meaning in real life, it's about the higher-order form of thinking where you combine multiple streams of knowledge to solve a real-world problem. No one can teach you how to think mathematically, one has to learn on his own. The author recommends knowing at least algebra, logic, set theory, and real analysis to be able to be proficient in mathematical thinking but I think he should add Calculus as well. I recommended this book for high school students at least. ...more

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. 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. ...more

This book is good introduction to maths for people who are not familiar with it on university level. When I was reading it I had to skip a lot of parts which I already knew, because people after even one semester of STEM studies have already done that. Besides that, book is very resourceful and exercises are very similar to academic once.

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.

Helped a lot

I never took this course,and had a lot of lightbulb moments reading this before each lecture. That's all I have.

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

Jun 29, 2020 sarah chang rated it it was amazing

I'm grateful for Prof. Keith Devlin. Saved my life from math anxiety inflicted by my high school math Olympics. I'm grateful for Prof. Keith Devlin. Saved my life from math anxiety inflicted by my high school math Olympics. ...more

Very witty for a mathematic book. I'm currently taking Dr. Devlin's MOOC and it was as fun as reading the book and doing the exercise. I thought this course was going to be an easy one because this is an introduction, but the energy required to think in the course is enormous. Very witty for a mathematic book. I'm currently taking Dr. Devlin's MOOC and it was as fun as reading the book and doing the exercise. I thought this course was going to be an easy one because this is an introduction, but the energy required to think in the course is enormous. ...more

cuốn này là background reading theo course introduction to mathematical thinking của stanford, 1/2 đầu nói khá hay về toán, với một người lần đầu tiên tìm hiểu sâu sâu tí về toán thì thấy nhiều thứ rất thú vị.

1/2 sau tập trung vào phân tích ngôn ngữ hơi chán vì mình đã từng theo 1 lớp khác chuyên sâu và thú vị hơn là 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 desc

1/2 sau tập trung vào phân tích ngôn ngữ hơi chán vì mình đã từng theo 1 lớp khác chuyên sâu và thú vị hơn là 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 description, the mathematician identifies and analyzes abstract patterns—numerical patterns, patterns of shape, patterns of motion, patterns of behavior, voting patterns in a population, patterns of repeating chance events, and so on. Those patterns can be either real or imagined, visual or mental, static or dynamic, qualitative or quantitative, utilitarian or recreational. They can arise from the world around us, from the pursuit of science, or from the inner workings of the human mind. Different kinds of patterns give rise to different branches of mathematics. For example:

- Arithmetic and number theory study the patterns of number and counting.
- Geometry studies the patterns of shape.
- Calculus allows us to handle patterns of motion.
- Logic studies patterns of reasoning.
- Probability theory deals with patterns of chance.
- Topology studies patterns of closeness and position.
- Fractal geometry studies the self-similarity found in the natural world

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Dec 21, 2014 Omar rated it really liked it

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 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 example).

Overall, excellent, and Devlin does not stray much from his usual approach in teaching (compared to some of his public university lectures, videos, etc).

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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 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 interesting math. It probably won't work for people from the US public schools system. ...more

Apr 03, 2013 Corin rated it really liked it

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!

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.

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. 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. ...more

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.

Sep 04, 2014 AZ ZA marked it as to-read

In the present moment I'm thinking: "may be I should learn about mathematics as a hobby". In the present moment I'm thinking: "may be I should learn about mathematics as a hobby". ...more

Apr 17, 2017 Othman rated it liked it

a very good book not only for math majors but also for prospective formal semanticists like myself.

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Jul 22, 2015 Izhan Noorzi rated it really liked it

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. 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. ...more

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.

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 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 different media to teach and communicate mathematics to diverse audiences. He also works on the design of information/reasoning systems for intelligence analysis. Other research interests include: theory of information, models of reasoning, applications of mathematical techniques in the study of communication, and mathematical cognition. He has written 26 books and over 80 published research articles. Recipient of the Pythagoras Prize, the Peano Prize, the Carl Sagan Award, and the Joint Policy Board for Mathematics Communications Award. He is "the Math Guy" on National Public Radio. ...more

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"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." — 4 likes

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