Back to Introduction to Mathematical Thinking

4.8

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1,782 ratings

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400 reviews

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

Nov 24, 2019

It was an amazing course! Lots of interesting content. The content is also explained really well, i found it really easy to understand. The assessments are a little challenging, but reasonably sized.

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By Sharad S

•Dec 21, 2017

This was a very good course which helped me to increase my horizons in the field of mathematics. I am no longer intimidated by the complex looking symbols and am able to make statements precise. I also do not rush to find an answer through a structured methodology. Prof. Devlin was superb.

By Buwaneka S

•May 23, 2019

This course starts slowly and clearly with the beginner in mind. I had to refer to other on-line material to really grasp the concept of the material conditional. Nonetheless this is a fantastic course, and any person starting a rigorous study of mathematics should take this course.

By Mohammad M A

•Jan 28, 2017

The course is really awesome and very much help full, as a student I can say every students that they want to go to universities they should join to this nice course which is provided by the coursera the best plat form for education.

Thank you for providing such a help full course.

By CHENG K

•Aug 09, 2017

It is a very interesting course and over my expectation on what I could learn from the course. Apart from various technique taught in the course for solving mathematical problem, as Dr said, the most interesting thing learnt is the way of thinking to approach the problem.

By Sajjad A

•Nov 16, 2017

This course has really changed my way of thinking towards life in general, and Mathematics in particular. I feel every student above the age 14 should take this course, not just once, but should repeat it every year or so! Thank you Coursera. Thank you Professor Keith!

By Brian-Tinh V

•Jul 10, 2018

As an aspiring physicist, this class helped me a lot. I didn't learn any actual physics in this course, but I was able to develop a sense of what to pay attention to when tackling advanced math texts and topics to advance my career. Great summer activity.

By Rafay N A

•Aug 26, 2017

The most amazing and unique course on mathematics! I absolutely love it even though it was immensely challenging as the instructor said. But it is really helpful in letting one think in a very different yet effective way through the lens of mathematics!

By Rajendra K

•Jul 06, 2017

Excellent course to understand how Math "works". The concepts are introduced very gently and clearly. The only thing I would say is that a basic level of high school algebra is needed to do this course and must be specified up front (maybe I missed it).

By Elias D

•Jun 19, 2019

It took me 10 months to complete this. it's fundamental in today's day an age. it was a humble step back to basics, with many comebacks. I recommend to anyone which looks to better enhance his thinking in all walks of life.

The teacher is a funny guy :)

By Nanda K

•Sep 28, 2017

An excellent course, well-designed and well-taught. Prof Devlin made the content, examples and quizzes very interesting and enjoyable. The technical aspects of the platform were handled well making the learning that much more easy and non-distracting.

By Илья

•Jun 05, 2019

Great course from talented teacher. I really enjoyed it. You have to think hard in this course, some exercises were ok for me, some were too hard. But everytihing was interesting. And information about mathematical notation and logic was very helpful

By Vadim

•Jan 14, 2018

The course is awesome! It helped me to recall a lot of stuff from university mathematics. Most importantly, it let me look at everything I knew, from a different point of view, get deeper insight. Great thanks to Dr. Keith Devlin - awesome teacher!

By Leo F

•Oct 06, 2018

Approachable for pretty much anyone and actually complemented a lot of later university math by going into more detail. This is an assignment heavy course, which I liked, but requires a lot more effort than other MOOC (it was worth it though!).

By Mitchel v H

•May 10, 2018

It was a really interesting course up until the end. The way in which language can be ambigious has never been as clear to me. This course wasn't just about math but more or less the world as a working place where you have to make it work.

By oximas

•May 31, 2020

really great course and really great professor, the course made me smarter at writing better proofs and thinking in more formal and smarter ways, it's really an essential course if you are looking to become smarter in all sorts of manner.

By 王映皓

•May 27, 2020

Clear and understandable description about proofs and theorems represented by Dr.Devlin, I had an enjoyable and fruitful learning experience. I strongly recommend this course to those who will enter univerisity or college sooner or later.

By Маханько М А

•Aug 30, 2019

Really changes the mindset! A new way of looking at evidence. I understood the principle of mathematical induction, why it allows to obtain true conclusions. Everything is clear and easily explained. Many thanks for the course!

By felix s

•Apr 14, 2019

Thank you for this course! It is slowly building your new thinking. So dont rush, just take time and let your new thinking grow from the smallest math concepts. It is pretty fantastic what your work is done for me! Thank you!

By himanshu k s

•Aug 27, 2017

Course is well explained. Course should come in two flavour i.e. fast pace course and more advanced for those who have already studied this course in college ,but want to revise it from coursera and this is best for beginner

By Rashmi R

•May 12, 2020

It helped to review and recall all the old content, Was able to get new insight of Natural Number Systems, Quantifiers , Mathematical Reasoning, Sequence,etc.

The Videos, Quizzes, Assignments ,Peer Review were eye openers.

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By Henry L

•Jul 04, 2018

A detailed and thorough course presented in an understandable fashion. It helps you develop critical thinking and problem solving skills by getting you to think in different ways as a mathematician. Highly recommended.

By Srivibhavan B

•Sep 26, 2019

I found this course a great refresher and it helped me fill a lot of gaps that had developed in my ability to understand advanced mathematics. The course helped me move faster with my study of ML and AI algorithms.

By deepak k s

•Jul 08, 2017

This course really helped me notice the subtleties of simple mathematical things in nature and even in daily life which we take for granted or assume to be true. This was my first course and it was a good decision

By Chaitanya K

•May 10, 2020

A fantastic course , professor Keith was extraordinary , I am currently pursuing my Bsc. in Mathematics and this is one course that I recommend for all the students who see their future in fields of mathematics

By Ravi N

•Mar 15, 2017

This was a really good course, making you "think" in general and in particular about mathematical proofs. The professor's exposition was outstanding. The explanation of evaluation of proofs was really nice.