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....

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

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.

筛选依据：

创建者 Eray C

•Feb 2, 2021

This is one of the best and most useful courses I made so far.

But the content also quite sophisticated! So be ready for struggles. Actually there is a problematic fact, that should be considered by the course provider:

Not everything is covered in the video lessons that is asked in the problem sets. And in the final test you have to work on some tasks for which you most probably will need to consult the internet for getting the required skills.

Nonetheless, by working on this course one really improves the way of thinking and understanding. Be ready for logic, number theory, mathematical proofs and some hard times ;)

The professor is very very likable and really wants you to improve your way of solving problems. And you instantly know that he really loves math and wants to share his enthusiasm. That's just so nice!

So really fantastic course!

创建者 Felipe B R

•Apr 16, 2022

Being Ingeneer and at my age , finding this course was a great discovery. It shows the beauty, creativity and effectiveness of reasonable thinking , which in my opinion, after a long career in businesses, is a key to well formulate problems and find solutions in all fields of human interest. It is excepcionally well structured and no detail is left unthought . Apart from the vast recognized top level of Dr Kevlin on the topic, his charisma helps to be motivated to go through all along his lectures, quizzes , assignments and Tests. Many thanks to Dr Kevlin and Coursera for this opportunity. For sure I will continue looking for new courses related with Maths

创建者 Avanish M

•Jul 3, 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.

创建者 Rohit D

•Oct 8, 2021

Being precise about language becomes very important in our lives, and this course starts by guiding one to improve one's usage of language. The professor challenges our thinking every now and then, thereby developing our reasoning. Introduction to mathematical proofs has certainly improved my approach to testing the truth or falsity of a claim. Emphasis on understanding is a key feature of this course. A key aspect of this course is Keith's humor, which is engaging. In summary, I have benefitted immensely from this course, and I recommend it to anyone who wishes to improve their thinking. After all, education is a preparation for life.

创建者 Cedric V L

•Oct 14, 2020

I used this course prior to enrolling at university for a software engineering degree. I always was bad at mathematics and was extremely worried I would never manage to get through the foundational courses which are very much focused on discrete mathematics. This course literally made me think different. It showed me that math is nothing to be afraid of, and literally reset my thinking about mathematical thinking. In fact, when I had to write my first proofs, I noticed it was very similar to what is taught here. I passed the courses with confidence and am now finishing my Master's thesis. Thank you!

创建者 Dr. A S M

•Aug 16, 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.

创建者 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 !

创建者 Charles K

•Aug 2, 2021

I thought the course delivered everything it promised and then some. It was well paced, well taught and the emphasis was correctly placed on learning to think mathematically as opposed to chasing grades or regurgitating formulas. Setting the pass mark at 30% allowed us to take chances and fully explore the material. I took a similar class 50 years ag and this time I decided to accompany my sister who had never takin this kind of course. We both had a great time discussing the concepts and examples. I highly recommend it.

创建者 Gilbert Y

•Aug 20, 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.

创建者 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.

创建者 shafiya

•Sep 11, 2021

Even though, I am a math graduate the course was completely novel to me. It helped me to think a new way of approaching theorems and problem solving. In my college I was given a particlular proof for each theorem and lemma and I was in a an impression that, that is the only way to prove that theorem. Now I had a feeling that I myself became a mathematician. Dr. Keith Devlin's lectures were so harmonious and knowledgeable. Thank you very much sir!

创建者 Yashwanth G

•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

创建者 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.

创建者 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!

创建者 Carlos C

•Jul 31, 2021

This course is extremely good!!!. I was looking for some inspiration to move forward my studies and i have found it. It helps you to open you mind, challenge and think different. I strongly recommend to complete the course and do not get frustrated, is not an easy one, but is also not pure mathematics mechanics, this is not about solve numerical exercises and learn recipes to answer problems. Enjoy it!!!.

创建者 Krzysztof H

•Dec 13, 2020

Great course, lot of fun and interesting concepts that open many doors. Lots of potential for real-world use. Thanks to this course I can now read mathematical texts more advanced than high school textbooks. The course has helped me in learning to learn the correct approach. Highly recommended to anyone wishing to learn to think in a new way. Also, Dr Keith Devlin is a BEST TEACHER EVER.

创建者 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.

创建者 El A F

•Nov 26, 2017

Thank you for the course, it really helped me understand more about thinking skills. Another benefit of the course for me , was understading mathematical symbols used in some foreign countries, since the ones unsed in this course were not the ones i have using during my scholarity(in France and Morroco) [for the negation of a statement for example]. Thank you again :)

创建者 Patricia M G I S S

•Jul 27, 2019

I'm in my last week of this course. I like this course very much, and the assessment of how many hours I needed to study gave me a reference point. I enjoyed the lectures online, the tutorials helped me to understand the professor Devlin. I definitely recommend this course, I'm thinking about taking another course relative to Introduction to Mathematical Thinking.

创建者 Jakob V

•Jan 28, 2017

5/5

Although I am really familiar with all the course materials and etc., I could still learn a thing or two from this course. Or in another words, the "Mathematical Thinking".

The quiz itself is not that challenging or hard, but there are a lot to ponder on with the assignments! Try to complete the course with a friend or two, and you will even get out of this.

创建者 Mia D

•Aug 29, 2019

This well-designed course casts light on some essentials of mathematics as well as fills some gaps between high-school-level and university-level mathematics (esp. in how to read a proof and how to catch the "big idea"). Plus, Prof. Keith is both passionate and encouraging.

Highly recommend to learners who are taking first year's mathematics in university.

创建者 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!

创建者 Fatima B

•Jul 16, 2022

This was a great course which helped me immensely in gaining new concepts and learning much more than I had expected. The teachers and the assigments were all a great help and I would really recommend this course to others as well. Moreover, It gave me an epic opportunity to interact with students all over te world and establish team work.

创建者 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/

创建者 Paolo I

•Jun 8, 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