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Back to Introduction to Mathematical Thinking

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2,498 ratings

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....

PD

Jun 29, 2020

It has help evaluate what I put into decision in any applicable context. Since I've noted what decision I make and how outcome can be made to vary when I consider all components in a isolated manner.

NR

Mar 4, 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

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By Tim G

•Jul 26, 2020

Great course. It ramps up quite steeply towards the end but is arranged to still be doable by someone like me, who will have to work more on even the introductory real analysis.

By 许甲一

•Jan 19, 2022

This course is really instructive. It serves as a pretty good transition from high school math to college math. The knowledge related to logic in it is also very fascinating.

By VIJI B N 2

•Oct 3, 2020

The course is really helpful and easy to understand. It has helped me greatly by improving my understanding of the subject and helped me improve my way of writing mathematics.

By Maojie T

•Nov 26, 2019

What a nice course! I like the logic, interesting and vivid process in this course. I am appreciated to the professor and I will review what I have learned in recent days.

By Kishan V

•Oct 3, 2020

Keith Devlin is a perfect teacher! I wish I could learn under him in real life. Fantastic course for high school seniors who want to study university level mathematics.

By Bartosz W

•Dec 21, 2017

As the name suggests, it is a great introduction to the world of mathematics. No unecessary pressure, which makes it an enjoyable experience for those willing to learn.

By David B

•Apr 5, 2017

Hard work but worth it. I get the feeling I now know something about what maths is about.

Brilliant teacher, although I didn't realize this until completing the course.

By Saayan

•May 27, 2020

Great course. Really teaches you how to think. If you are making the transition to college mathematics. I would highly recommend this course. It could not get better>

By Akinpelu T

•Nov 9, 2020

I had a great time trying to break a mental barrier. This course would not only teach a new way to think but also how to express and communicate your ideas clearly

By Hussein A

•Jan 8, 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 Rahul C

•Jul 2, 2020

Only one word: Brilliant.

Take this course if are aiming to become a Mathematician. You will not regret it. It's absolutely must for all who are entering college.

By Julien C

•Oct 23, 2017

A lot of much time spent on simple things and no enough example with answers to make sure we understand the exercise. (sorry no precise example available handy)

By Carlos M

•Jun 4, 2020

This course convinced me of enrolling for a college degree in mathematics, I don't think I can say much more. Thanks to professor Devlin for this amazing work.

By Seyyed M A D

•Apr 1, 2018

Very dedicated teacher. Very clear and neat teaching method.

The teacher solves a lot of good examples by himself and this makes the course very understandable.

By Olzhas I

•Feb 13, 2018

Sometimes challenging, but very interesting and fascinating course! Keith Devlin is a talented professor and his way of describing topics is well-constructed.

By Matteo F

•Feb 7, 2021

Fantastic course! The lessons are clear and interesting and the forum is active.

The last week is much harder than the other but the satisfaction is high!

By John A

•Sep 21, 2020

Very useful for knowing the basics of number theory and to think mathematically. Slow and Steady wins the race! Concepts explained with good explanation.

By Micael M

•Jul 4, 2021

Excellent teaching style!! Will aid anyone to understand mathematical thinking!! Definitely take this course if you are taking mathematics in university

By Malcolm G

•Apr 19, 2020

Wonderful Course. A great distraction from the Covid19 virus. Much more interesting and exciting than Netflix. Thankyou to all involved in its creation.

By Monica K

•Sep 3, 2021

The content is great, well explained; and If you invest some time in it, surely it will open a hole new way to see Maths. Thanks for the good content.

By luo r

•Jul 27, 2019

It's a pretty good course. I learnt a lot. I hope Stanford open more math courses in math field, such as Number Theory, Analysis, and Abstract Algebra.

By Andres D P P

•Aug 24, 2019

Es un curso muy bien orientado, y el método de enseñanza es excelente. El profesor te enseña a pensar más allá, lo recomiendo para todos los niveles.

By Ronnith N

•Aug 20, 2021

Thanks to Prof. Keith Devlin. This course is a must for everyone planning to undertake an undergraduate program in any field related to mathematics.

By xiexiaoqi

•Nov 23, 2017

很棒的数学课程，适合大学新生在上高等数学时学习。这门课详细介绍了数学证明的方法，并且会告你大学学的数学和高中时不一样，最后一周的互评作业也很有意思，通过批改其他学生的作业我也学到了更多知识。这门课让我对数学有了更大的兴趣，如果你对数学感兴趣或者想学好大学数学的话，你应该来试一下这门课程！

By Oskernel R

•Aug 19, 2018

You don't learn math only; you learn the techniques of logical reasoning.

This course is evaluable and helps me become a more effective thinker.

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