Back to Introduction to Mathematical Thinking

4.8

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1,900 ratings

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443 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 Marin L

•Mar 13, 2017

Wonderful and usable course. I graduated mathematics 20 years ago, and I regret I didn't have such clear and informative lessons back then when I needed them most. Even now, watching tutorials and doing exercises gave me great pleasure and some new insights into the problems and techniques I failed to catch.

Thank you for your effort and dedication!

By Sarah E B

•Aug 10, 2017

So far, this course has changed the way I think and view things. Professor Devlin's genuine enthusiasm is contagious and I love interacting with other students online. The TA is very active. There is a great interview with Prof. Devlin here: https://onbeing.org/programs/keith-devlin-the-joy-of-math-learning-and-what-it-means-to-be-human/

By Paolo I

•Jun 08, 2020

I think classes like these should be mandatory on colleges, for some courses at least. I think many people tend to have trouble with maths not because of the content, but because we have trouble reading and understanding its language. I think a class like this course helps to develop maths skills that helps in maths courses in general

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 bj d

•May 13, 2017

Excellent course! Started off slowly and methodically laying the foundations for successive lessons. Prof. Devlin explains, demonstrates and allows one to "hear" him think through solutions. My math skills got stronger, but more importantly, my approach to the logic of mathematical thinking can be transferred to other disciplines.

By Abhay G

•Jun 17, 2019

I get a new thinking in Mathematics. Now, i get a new approach to tackle mathematical problems.

I learnt some new different methods to prove the theorems and get a paradox(in which we have proved 1 = 2) that give me a new sight to see a problem.

I realise "Mathematics does not depend upon solution, it depends upon a process".

By Mikhail Z

•Sep 18, 2017

This course is a fun, thorough and thoughtful introduction to the basics of mathematical thinking. I've used it as a supplementary course for series of seminars for philosophy of mathematics. The peer-review assignment is a brilliant way to grasp the difference between solving a problem and thinking about solving a problem.

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 Adam M

•Mar 26, 2020

A great assignment-based introduction to discrete math with an emphasis on communication and thinking. This is a course to improve how you approach problems, and although it provides highly useful skills for university math courses, the disciplined thought process outlined in the course is applicable to the real-world.

By Anhad S B

•Oct 28, 2019

Great course for someone trying to get back in touch with college level mathematics after working professionally and/or more usually, someone trying to get started on graduate level mathematics. Dr. Devlin is quite a thorough professor and I wish I had more professors like him during my undergraduate years as well.

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 Elmer N

•Aug 28, 2019

Excellent instruction and pacing. As a veteran Professional Engineer, I found the course challenging and informative. I enjoyed especially the real-world examples. I would recommend this course to anyone with a desire to discover the fundamental principles of number and set theory.

Elmer A. Norvell, PhD, PE

By Vishal

•May 15, 2020

it is a very fantastic course which improves our ability of thinking. It is a easy course at the beginning but little bit challenging in last weeks of this course also assignments some how hard but overall course is very fantastics and also well design. Thank you sir Dr.Keith Devlin for your guidance .

By Sagar P

•Sep 28, 2017

The 9-week mathematical journey taught me a lot and made fall in love with mathematics back again. I wish , I had worked harder and earned a better grade but commitments to my family and job did not let me do so. I await for another opportunity to get tutored by Dr. Keith Devlin and Stanford Univ. again

By Luiz F C S

•Jul 29, 2020

This course is extremely good. I just got out of High school and the vision of mathematics this course gave me is totally different. My way of reasoning certainly changed and now I can recognize the importance of the use of language when comunicating, does not matter in what way it's been doing.

By Chloe L

•Jun 08, 2020

I never appreciated math or thought myself capable of doing math well. Now I am excited about real numbers and integers and solving puzzles! This course was a great life experience, and I am indebted to Prof. Devlin for the excellent design and meaningful principles that he put into the course.

By Assaad E

•Jun 11, 2020

just an awesome course that anyone should take. Since I began in this course, I saw mathematics in a new way that is more brilliant and effective, also my grades at the university goes up as well as my understanding of math and science materials.

Professor Keith Devlin will make you love math!!

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).

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