Back to Introduction to Mathematical Thinking

4.8

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1,955 ratings

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458 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....

AM

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.

NR

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

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By Nickolas F

•Aug 31, 2017

A truly amazing course that gives the student an excellent taste of mathematical thinking and makes even those who hate mathematics understand its depth. A special thank you to Dr. Keith Devlin for teaching this course and giving me a true glimpse into university level mathematics, but also to Coursera for giving me the ability to be an active student in such amazing courses. I hope that more courses like this are to follow in the future.

By James H

•Jul 18, 2020

This is an excellent preparation for higher pure maths study. It's essentially an introduction to proofs - building them and assessing them.

It's worth looking at, even if you think you know this stuff. If it's 10 years since you graduated, it's still worth working through, to get your mind in order; if you think you are comfortable with the material, watch the videos at high speed to save time, until you start failing the quizzes :)

By Christopher C

•Mar 31, 2018

What anyone could ask for in a basic proofs course: logic, proofs, induction, some application of what they learned to higher mathematics. I like the idea of teaching a bit of abstract algebra right away, but this course goes with some basic results of analysis (probably for the low-hanging surprising results in analysis). Nice job!

Grading proofs was subjective, but keep in mind the threshold to pass a quiz is very low.

By Marcus K

•Mar 17, 2018

I work in the digital visual effects industry as a developer and wanted to understand scientific papers better. Searching the the for solutions, I came across this course. It is very well structured and offers tons of materials to work with. You can test yourself with quizzes, assignments and problem sets throughout the course.

I can only highly recommend it .

By Phumlani D

•Jun 30, 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.

By Ali M

•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.

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 Wakash

•Aug 30, 2019

Good Course, A must take for college math majors. While the course covers most of the contents, Professor should have given more attention to Proofs and Real Analysis which are assigned just two weeks in this course.

By Wesley T

•Dec 06, 2017

I really want to learn this material. I believe the module may be more improved if the videos were subdivided into smaller chunks. Passionate speaker though, theres a lot of promise here.

By CA G N

•Jun 26, 2018

think differently....

By Mohammed A S

•Sep 26, 2017

This Course is only good if one has a group to study with. Online , whtatsapp, or social networking groups are not that effective. If you want to do this course make sure that you have friend or two planning to enroll with you.

By maria

•Sep 09, 2017

The detailed explanation of proving certain claims in the course are very ambiguous, which is the reason I discontinued the course.

By 徐致远

•Feb 14, 2020

First of all, thank you very much for this masterpiece. This is the most challenging course I've ever had on the Coursera.

One more comment on the final peer review assignment: the question about whether 0 is a natural number.

Only after taking this course and doing some research on the Internet do I realise that there's a lot of argument on this question. I am a college student from China, and I major in physics, rather than mathematics. For me, the statement "0 is the least natural number" is a fact that was written in my primary school's textbook. So I was quite surprised when I was told that 0 is not a natural number. After searching on the Internet, I finally got more knowledge on this.

Fortunately I was not supposed to lose too much on that. However, I do recommend that you make this clear in the course content so that everyone can discuss under a common assumption, regardless of their background education.

Above all, this course experience is a lot of fun. There's no standard answers here, only remarkable thinking and a space of infinity to explore. Thank you for all of it! I'm giving 23 out of 24 marks for this course, taking away 1 point for clarity about whether 0 is a natural number.

By Mudita S

•Jul 07, 2020

I work in publishing and have absolutely no day-to-day brush with Mathematics but since I had a high school background in the subject, I wanted to make contact again. This course served my purpose perfectly. The instructor, Dr. Devlin, has provided very detailed lectures and he never makes the subject boring. The in-lecture quizzes are a big help to keep your attention in check.

I was a bit apprehensive of the course content as I'm not from the United States and wondered if it would make sense to me, given my limited knowledge. But I stand corrected; it was easy to follow.

From structure to progression, this is indeed value for money. I'd highly recommend it!

By Avanish M

•Jul 03, 2020

It really was a different perspective to mathematics, and I enjoyed working with proofs and entering the world of mathematicians where even simple problems may have rigorous proofs. It was novel to view how these fundamental proofs have shaped the current state of mathematics today. Dr Keith Devlin was very efficient at teaching and I understood everything in the course and trusted his method even when the beginning weeks were very simple because he felt really knowledgeable and reliable. I would recommend this course to anyone who is interested in mathematics or wants to explore another side of mathematics that we wouldn't ever see in school.

By Ken L

•Jul 24, 2020

This was a return to mathematics for me after many years (I am in my late 60s). I completed modules in mathematics during my psychology degree and throughout my career had to use statistics for research purposes. The course has reawakened my interest and revealed something that I have overlooked, that deep down I have a love for mathematics!

The course tutor is outstanding, both in clarity, sense of humour and in having a kindly approach that inspires confidence. It is not an easy course and it certainly requires effort, but the reward for the effort is that what seems initially obscure gets quite a bit clearer and appreciation grows.

By Dr. A S M

•Aug 17, 2017

This is a very well designed course which is essential for mathematicians as well as for those who want to use mathematical way of thinking (which is needed in most of the subjects ) in their life. It prepares a sound base for the ones who have mathematical aptitude but could not study mathematics in their life . In fact thinking mathematically is the modern and most effective way of dealing with the situations at hand and this course is most suited for this purpose. Thanks to the entire team of professors and others who have developed this course.

By Shubham V S

•Jun 30, 2020

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.

Good to learn this course as it really helps me to open up my mind to opt for different approaches of an answer rather then getting the actual answer....

You should take this course. It’s a new way of thinking about things.

This is by far the best course of mathematics on Coursera!

Thank you Profesor Keith Devlin, you are a great teacher !

By Gilbert Y

•Aug 21, 2020

What a humbling course. I learned I'm not nearly as intelligent as I thought I was. Most of the content was doable with some effort. The most problematic was the content near the end about real analysis.

The course is all about mathematical proofs: expressing thoughts precisely, how to write proofs, how to reason, and grading proofs written by others. I didn't think that's what I'd be doing when I enrolled.

My one suggestion for the course is chop up the videos (averaging 30m each) into a bunch of shorter videos.

By Dana W C

•Aug 25, 2017

The one thing that was a problem for me was the last week, the scoring of peers was presented to me PRIOR to the videos working through solutions and "training" me to score those particular questions. Therefore, I did those tasks out of order. I believe for the second and third peers, their scores were fine, but the initial peer was rooked. Reflecting, they should have earned an overall score closer to 46 than the 33 attributed. If there was someway to remedy that...

Thank you.

By GBVN K

•May 17, 2017

Extremely interesting with nice and lucid explanation. This 9 weeks' learning journey is thoroughly knowledgeable and mathematics has become my favorite subject after completion of this course. Advise my fellow students to make best use of this course and come out of fear in order to learn mathematics. Extremely grateful for helping me earning first online course from the reputed Stanford University.

Thanks and Regards,

G. SAI YASHWANTH,

INDIA

By Harold M

•Aug 23, 2019

This is a great course on mathematical thinking. It covers important topics such as: the mathematical language, logic, number theory, real analysis.

These topics are presented in a clean and concise way by Dr. Devlin, and I highly recommend this course to any person interested in mathematical thinking, how to read and understand mathematical proofs, and for those interested in pursuing a mathematical career.

Thank you professor Devlin.

By Justin L

•Feb 19, 2017

With consistent effort, I have found this course to re-ignite my passion for mathematics. Keith Devlin, the instructor, does an excellent job of helping us to develop our ability to think in mathematical and logical ways. In short, I have found a new joy and excitement for doing mathematics, even stuff I consider hard. I have a new-found passion and new "eyes" for maths that I didn't have before. Excellent course!

By George P

•Mar 19, 2017

It is very good course that teaches simple at first glance concepts that later evolve to something more complex. Mr. Keith Devlin is very charismatic professor who knows his material very well and passes his energy and enthusiasm to students. One minor notice about the real numbers material, in my opinion it is too brief and needs slightly more time to be understood by many students.

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