Introduction to Mathematical Thinking に戻る

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Learn how to think the way mathematicians do – a powerful cognitive process developed over thousands of years.
Mathematical thinking is not the same as doing mathematics – at least not as mathematics is typically presented in our school system. School math typically focuses on learning procedures to solve highly stereotyped problems. Professional mathematicians think a certain way to solve real problems, problems that can arise from the everyday world, or from science, or from within mathematics itself. The key to success in school math is to learn to think inside-the-box. In contrast, a key feature of mathematical thinking is thinking outside-the-box – a valuable ability in today’s world. This course helps to develop that crucial way of thinking....

Mar 05, 2018

An awesome course. Very easy to follow at the start, becomes more challenging at the end. I have a PhD in economics yet I struggled with the real analysis at the end. And that's just intro level! :-D

Aug 26, 2017

Great course, it's really shows the way how to think in mathematical rigor. It gave me an intuition about what Mathematics is itself.\n\nThank you Profesor Keith Devlin, you are a great teacher !

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by Ho X V

•Jun 21, 2018

My love for Mathematics in the past few years is like the electrocardiogram (Điện tâm đồ) of a near-death patient, which is peaceful as the surface of a calm lake. This does not annoy me at all, despite for the fact that I used to be called the smartest one in class, in this specific topic particularly. Then, how did I end up like this? Fortunately, Professor Keith Devlin points out that this is not exceptional. It is not true that people are born to be good or bad at math by default, and keep up the trend till they die. In fact, there is always a transformation in mathematical thinking from high school to university level, that almost no one was told when they were students. Moving from being taught a fixed set of techniques to solve a problem, now you are asked to be able to abstract things and reason about it, which naturally confuse learners. To prepare for such transformation, this is the exact course you need. My personal opinion: I wish that I have taken this course 5 years ago, so I can learn a bit more about Algebra. First year undergraduate students, mark my words: take it!. Course review: In the first half of the course, Professor teaches the importance of understanding the primitive mathematical notations, how careful you should be when formulate a problem, and do not rush when attack it. The quizzes successfully demonstrate the second and third points. In the second half, it's amazing to see how one can derive mathematical reasoning solely from the truth tables, and apply it to produce appropriate techniques to solve problems. Only now that I know it's not black magic when somebody choose an arbitrary value that I have no idea where it comes from in a proof. In the last 2 weeks, he gives us a few touch on set theory and real analysis, the two subjects that I suddenly feel attracted to, not to mention his sense of humour when introducing them ;) Notably, throughout the whole course, Professor shows us how to evaluate a proof, and I do learn a thing or two about it. As he always says, the point of a proof is 1) establising the truth and 2) explaining it for the readers, math will be interesting once you learn its way of thinking. I now feel more ready than ever to read a mathematical problem; specifically, where to look for in the beginning of a proof, and the abstract idea of how the authors come up with their chain of deduction. Thank you so much Professor.

by Christopher B

•Jan 17, 2019

I found this course to be incomprehensible. The professor was rude and dismissive, when I asked for help.

by Yuliya S

•Jun 12, 2017

Some work is involved and probably a good ideas to start on assignments earlier then later, but it's really thought through material that is being presented and great concepts.

by Alexis H

•Feb 12, 2019

Touches the foundamental parts of mathematics. Really helped with my mathematical thinking.

by Колесник П П

•Feb 15, 2019

Очень сложно сказать, что курс был полезен для меня в карьере или учебе (или как-то крайне интересен), однако благодаря курсу я стал лучше понимать язык математиков и освежил память по некоторым математическим законам. Огромное спасибо создателю курса за отдельные turorial-видео после assignments!

by rajat j

•Sep 27, 2018

I was interested in mathematics till high school. But after that in engineering we have to learn Applied Mathematics(AM) and which is quiet boring for me. Due to these type of mathematics , I decided not to learn math anymore. But this course was very intuitive and focuses more on thinking and logical steps rather than computational parts. Now I love math more than I used to love before Engineering. I will definitely learn more mathematics because of enormous interest in this field. THANK YOU Prof. Keith Devlin for this course. Since, you're the reason why I love Mathematics. Sorry for English because it is not my native language. Sir please reply to my review if you have time :) .

by Joseph J

•May 10, 2018

Really great course. It's aimed at high school students, but I found it valuable even as a college graduate who has taken several math classes but never had a formal introduction to how to think about proofs. I wish I was able to take this class when I was an undergrad.

by Randall G T

•Feb 19, 2018

Good overall, but Dr. Devlin tends to ramble in lectures rather than getting to the point. He also seems somewhat inconsistent in how he evaluates proofs. Since proofs and their evaluating are the core of the course I found it frustrating that there isn't more care given to clarifying what constitutes a good proof.

by Minh D

•Dec 11, 2018

The course name itself is a importance not only for individual but for the world. The development of Mathematic can significanly boost if we not only know calculate, how to calculate the formation, but know how to think (Mathematical Thinking). Huge potential course that can change our community! Thank teacher!

by m.urban

•Dec 10, 2018

I'm sure that I will come back to this course! Thank you very much Profesor Devlin! You are a great teacher! Greeteing from Poland!

by Jordi a

•Nov 29, 2018

This is a fantastic introduction to the world of college-level math. Recommended to HS students, social science majors who are quite analytical, and maybe even some STEM freshmen. While it takes considerable effort to follow the course and assignments, it's quite a learning experience, and I with I had taken it earlier in my life.

by Clotilde C

•Jan 11, 2019

Brilliant and Crystal Clear

by Hussein A

•Jan 08, 2019

great course that make you able to establish proofs and use mathematical notations also it help you in some branches of math like number theory and real analysis.

by Dmitry Z

•Dec 26, 2018

Excellent introductory course! Thank you, Prof. Devlin!

by Omer F U

•Jan 11, 2019

a good course

by patrice m

•Dec 31, 2018

Interesting and easy to follow . But serious work required . Not for the lazy...

by Mougahed S

•Feb 17, 2019

It's simply extraordinary

by Lucas C

•Feb 15, 2019

An excellent course. Sometimes I've had some difficulties, but I've learnt so much. Thanks.

by Pavel K

•Feb 17, 2019

Really powerful course. Thanks to the authors.

by Robert D C

•Feb 22, 2019

A difficult course, but I learned a lot of math!

by Neftalí A

•Mar 25, 2019

Thanks for everything, Dr. Keith.

by Thong D L B

•Mar 26, 2019

I just want to say thanks to Prof. Keith Devlin. I have never been quite comprehend the proof techniques and usually have to prove statements arithmetically directly. Thanks to this course, I finally see how I can approach the problems more systematically, thus being able to find the answers faster and more consistently

by Marcelo L S

•Jan 28, 2019

It is a very didactic course,. I wish I had concluded it earlier in my career.

by Brett A W

•Feb 08, 2019

Great course challenging and worth the effort

by Thai D N D

•Feb 08, 2019

Great Course !!!