Retour à Introduction à la pensée mathématique

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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

23 nov. 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.

PD

29 juin 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.

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par Mohammed A S

•26 sept. 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.

par zarghona H

•30 août 2020

all the videos and quiz are lock

par Yonatan G

•3 juil. 2017

Tengo Problemas con la traducción al Español, me notificaron que este curso tenia subtitulo en español me voy a dar baja.

par S M R R

•8 oct. 2020

This course has a great introduction to why you should take this course. Professor Keith Devlin introduced us to why high school mathematics is different from university mathematics. High school mathematics deals with math which invented kind of before the 18^{th} century. But what happens to the mathematics that was invented in the 19^{th} century. Because of your kind information many modern mathematics techniques invented in the 19^{th} century. How to deal with those problems?

In varsity level mathematics you just don’t use or apply formula that was predetermined but you think about the problem. You brainstorm and make the reasoning behind the problem. A mathematical proof needs to be dealt with great care. Because you have to deal with its uniqueness universality. Of course, you have some certain predefined tools that you learned in high school, but you need to think before applying, not as it was done as a template set in high school.

So, Coursera offers this course to introduce you to a glimpse of how mathematical thinking procedure works. This course introduces us to Logic and Logic Combinators, Logic Implication, and Equivalence, Quantifiers, several proof techniques such as proof by contradiction and proof by Induction, proofs involving Quantifiers, introductory Number Theory, and some proves associated with it. The hardest part of this course is Real Analysis. Each proof associated with Real Analysis involves so much thinking and reasoning. At the very last week, i.e. at the 10th week, you need to submit some assignments involving proof techniques that will be peer-reviewed before you get your certificate.

par 徐致远

•14 févr. 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.

par Steven S

•8 janv. 2023

I do completely agree that this course is the most basic skill to learn mathematics, and not just mathematics it is useful in everyday life, it helps you think clearly, out of the box and think systematically, basically to have a critical mindset/thinking. I seldom writing a review for a course, but because of how valuable the skills that are being taught in this course and also after the lesson that I've learned while taking the Assignment 4 - Week 2 of the course, I cannot help myself to put up a good review. And exactly what Dr. Keith says about taking/tackle the assignment slowly, I can tell you that it is true, you need to master this course even if it take much time longer that you plan to do.

For this reason I decided to purchase the course, and also I see that it has a book with the same title in Amazon. I'll buy the book once I finish with the course, dunno when, but hey at least I purchase the course to show my gratitude.

par Eray C

•2 févr. 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!

par Felipe B R

•16 avr. 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

par Avanish M

•3 juil. 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.

par Rohit D

•8 oct. 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.

par Cedric V L

•14 oct. 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!

par Dr. A S M

•16 août 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.

par Shubham V S

•30 juin 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 !

par Charles K

•2 août 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.

par Gilbert Y

•20 août 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.

par Dana W C

•25 août 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.

par Danai M P

•19 nov. 2022

The course was so good that I am seriously considering starting again from the beginning. Keith Devlin has the gift of explaining simply and clearly concepts that can be daunting in themselves. Challenging enough to keep me on my toes rewinding and listening to lectures again and again but not so much that I felt like giving up. We were encouraged to make use of the forums and connect with other students but I confess I did not do so. An excellent course.

par shafiya

•11 sept. 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!

par Yashwanth G

•17 mai 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

par Harold M

•23 août 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.

par Justin L

•19 févr. 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!

par Carlos C

•31 juil. 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!!!.

par Krzysztof H

•13 déc. 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.

par George P

•19 mars 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.

par Faïz E A

•26 nov. 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 :)

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