To support our site, Class Central may be compensated by some course providers.

Introduction to Mathematical Thinking

Stanford University via Coursera

students interested
  • Provider Coursera
  • Subject Foundations of Mathematics
  • $ Cost Free Online Course (Audit)
  • Session In progress
  • Language English
  • Certificate Paid Certificate Available
  • Effort 8-10 hours a week
  • Start Date
  • Duration 9 weeks long

Taken this course? Share your experience with other students. Write review

Overview

Sign up to Coursera courses for free Learn how

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.

Taught by

Keith Devlin

Class Central Charts

Help Center

Most commonly asked questions about Coursera Coursera

Reviews for Coursera's Introduction to Mathematical Thinking
4.3 Based on 44 reviews

  • 5 stars 59%
  • 4 stars 27%
  • 3 stars 5%
  • 2 stars 7%
  • 1 star 2%

Did you take this course? Share your experience with other students.

Write a review
  • 1
Anonymous
4.0 6 years ago
Anonymous completed this course.
I enjoyed this course, I am glad I took it. The Professor was very enthusiastic, and the lectures were well done. All the course material was available on time. The material does not lend itself as well to the online format as say the programming courses. I thought the course was well done in spite of that. I think more peer review on the assignments instead of just the final would help.
1 person found
this review helpful
Was this review helpful to you? Yes
Sami L
5.0 4 years ago
Sami completed this course, spending 4 hours a week on it and found the course difficulty to be medium.
An excellent introductory course to mathematical thinking or a companion course to follow while shuffling through your first book about mathematical proofs. Professor Devlin's way of putting out lots of exercises and going through them meticulously afterwards is as challenging as it is rewarding.

If you really want to learn the subject material, active engagement in problem solving is required and all the exercises should be considered as obligatory. While you might learn something by just watching the videos and working with obligatory quizzes, the real beef is in working with optional practice problems. Coming up with even a simple proof on your own, making mistakes on the way, seems to be only way to learn proofs.

In my opinion the practice problems were the best part of the course. Being a fellow with humanities background and thus very little mathematical education, I advanced tremendously when struggling with optional problems and proofs.
36 people found
this review helpful
Was this review helpful to you? Yes
Change N
5.0 5 years ago
Change completed this course and found the course difficulty to be hard.
I think this is one of the most useful, real-world applicable courses on Coursera or the entire Internet, and I would recommend it to anyone. It’s so rare that a course teaches a new way of thinking, rather than new concepts or new data. Prof. Devlin has a clear, friendly style that makes difficult concepts easy to understand. The teaching method where he hand-writes proofs while narrating is the next best thing to actually seeing a brain work. And I’m no longer afraid of a jumble of math symbols when I see them on a page. I can dive in, sort out the meaning, and understand the point the author is trying to make. Which is amazing.
19 people found
this review helpful
Was this review helpful to you? Yes
Seb S
5.0 5 years ago
Seb completed this course, spending 10 hours a week on it.
I am finding the course considerably less discussive than I did Peter Norvig and Sebastian Thrun’s AI course. This is partly because the video lectures are longer and more formal; and partly because there seems to be less active discussion in the course-provided discussion forums, possibly on account of the way in which students have been encouraged to make their own arrangements, which was far less the case with the AI course. But what this course shares with the AI course is the feature that struck me so forcefully in 2011: the feeling that you are getting one-to-one personal tuition from a very skilled and interesting teacher.
10 people found
this review helpful
Was this review helpful to you? Yes
Anonymous
4.0 6 years ago
Anonymous completed this course.
Thank the stars that I bought and read his book, before the course. It's most likely the only reason that I was able to "hang on" and finish the course. The pace was "Stanford full speed ahead."

Professor Devlin paid attention and saw that speed was an issue to some of us. To his credit I note that he plans to now offer the MOOC at varying speeds.

If you really want to understand such thinking buy the book (its small and cheap), read it and then jump into the course with both feet.
8 people found
this review helpful
Was this review helpful to you? Yes
Anonymous
4.0 6 years ago
Anonymous completed this course.
I would say this class is more for people who want to major in mathematics than anything else. It begins with lessons on logic and how to think about the language in a logical fashion. It eventually moves into mathematical proofs. I feel that more of the class should have been spent on proofs, mostly because I have always struggled with them. Professor Keith Devlin seems like someone I would want to have lunch with while discussing math, philosophy, and science in general.
7 people found
this review helpful
Was this review helpful to you? Yes
Elazar N
2.0 2 years ago
by Elazar completed this course, spending 2 hours a week on it and found the course difficulty to be hard.
As a mathematics teacher and a major in mathematics I found this course mostly a waste of time (from the point of view of a student intending to study mathematics) and a far cry from the description given in Mr. Devlin's introduction.

Mr. Devlin seems to have an obsession with formal logic (also known as "sentential logic" )and he dedicates most of the course to this rather negligible (mathematically speaking) subject as if mathematics and "mathematical thinking" depend on it (which they most certainly do not!) . As a result, students of the course expend enormous amounts time and energy in translating sentences into formal logic and vice versa instead of studying actual mathematical content and actual examples of mathematical thinking.
3 people found
this review helpful
Was this review helpful to you? Yes
Anonymous
5.0 3 years ago
Anonymous completed this course.
Instructor is very engaging and thorough, does a very good job of helping to ensure that difficult concepts are understood. Assignments (both graded and practice) are very helpful, instructive, and quite fun, though often challenging. Since the course is essentially pass/fail based on completing the assignments, the challenge is definitely worth it. Overall, a very interesting course taught by a very good professor that would be highly worthwhile for anyone in STEM fields, not to mention the general public.
3 people found
this review helpful
Was this review helpful to you? Yes
Wei E
5.0 4 years ago
Wei completed this course, spending 5 hours a week on it and found the course difficulty to be medium.
An excellent course on mathematical thinking. Prof. Keith Devlin does a great job of going through the material and explaining solutions to the problems. There's also loads of student interaction in this course, though unfortunately, student activity dropped off towards the end as many people dropped out. Going through this course was definitely worth it though -- I have a much better understanding of proofs now.
5 people found
this review helpful
Was this review helpful to you? Yes
Qz Q
5.0 3 years ago
by Qz completed this course, spending 10 hours a week on it and found the course difficulty to be hard.
This was an interesting course. It assumes no understanding of advanced mathematics. It teaches you how to think which is an important skill for possibly every job out there. The time you spend every week depends on your own goals. Sure, you can just do the quizzes and still get a certificate of accomplishment; but to get the most out of it you'll need to utilise study groups and the course discussion forums.
3 people found
this review helpful
Was this review helpful to you? Yes
Mamartin M
4.0 5 years ago
Mamartin completed this course, spending 5 hours a week on it and found the course difficulty to be hard.
Very good and worth doing but hard work. My education has been in history - reading texts from strange times and cultures and weighing half-formed, messy evidence. This was technical; it has real world application but, as with any course in logic, do not expect human color. I will give it another, effortful try at a later time.
2 people found
this review helpful
Was this review helpful to you? Yes
Anonymous
2.0 a year ago
Anonymous is taking this course right now.
This course has, in my opinion, a huge weakness, because, after week three, there is no answer key to all but a few of the ungraded exercises. Different people do try working them out online, but there is no way to tell if their answers are correct, unless a mentor weighs in. The instructor assumes that people will form study groups and work out answers together, but this isn't an option for some people.
Was this review helpful to you? Yes
Matthew P
5.0 2 years ago
Matthew completed this course, spending 8 hours a week on it and found the course difficulty to be medium.
This was a great course. The instructor Dr. Devlin was able to make an otherwise difficult topic easy to understand. His explanations were crystal clear. There is a fair amount of assignments to do. This can be challenging, both qualitatively and quantitatively. In the end, I learned to write mathematical proofs.
Was this review helpful to you? Yes
Anonymous
5.0 a year ago
Anonymous is taking this course right now.
I took the course for personal enrichment and to fuel my (clueless, crazy and way too unreachable, for the most who claim to know me best) willing to learn more Maths and sciences! I started attending another MOOC about the Fibonacci numbers

Was this review helpful to you? Yes
Maboroshi M
3.0 4 years ago
by Maboroshi completed this course, spending 2 hours a week on it and found the course difficulty to be medium.
I can feel that the professor devoted a lot into this MOOC, and the evaluation rubric is somewhat interesting. Nevertheless, mathematics is indeed a bit dull, and it is not easy to hold on to the last...
0 person found
this review helpful
Was this review helpful to you? Yes
Anonymous
4.0 2 years ago
Anonymous completed this course.
Easy except towards to end. Real analysis is a tough subject and we only did a basic introduction. Learned a lot over again from a discrete math course I took years ago. Good introduction to proofs.
Was this review helpful to you? Yes
Shawn R
5.0 a year ago
by Shawn completed this course, spending 4 hours a week on it and found the course difficulty to be medium.
The professor was terrific. Every lecture video was clear and had quizzes within the videos that reinforced everything we were learning.
Was this review helpful to you? Yes
Anonymous
3.0 2 years ago
Anonymous is taking this course right now.
I am not able to access your course right now although I enrolled for the same in Sep 2016. How can i get access?
Was this review helpful to you? Yes
Anonymous
5.0 5 years ago
Anonymous completed this course.
Tough, fun and rewarding. Prof Devlin is an excellent and enthusiastic teacher.
Was this review helpful to you? Yes
Aswitala A
2.0 3 years ago
Aswitala is taking this course right now.
0 person found
this review helpful
Was this review helpful to you? Yes
  • 1

Class Central

Get personalized course recommendations, track subjects and courses with reminders, and more.

Sign up for free

Never stop learning Never Stop Learning!

Get personalized course recommendations, track subjects and courses with reminders, and more.