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Back to Introduction to Mathematical Thinking

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2,497 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.

AM

Nov 23, 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.

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By Victor O

•Sep 3, 2018

Keith did really great course for those who missed formal proofs method at school or at university. I wish I had this course in high school or in my first college year. Math, unlike to other STEM disciplines, is based not on experimental confirmations, but on the chain of logical steps (aka proofs). Keith explains and teaches you how it all works. I strongly reccommend to everybody who wants to establish truly solid background in maths and then be able to study it further in his required directions. Really enjoyed. Universe is very beautiful and math is such an astonishing side of it. Keith is amazing.

By Edwin C v E

•Nov 3, 2018

Excellent course. Many important mathematical concepts are covered during the course, such as proof techniques, quantifier handling, logical and mathematical thinking and objectively assessing other people’s work. The pace of the lectures as well as the variety of topics is good. The final chapter might be a little out of some students’ comfort zone, especially since the prof takes a deep dive quite quickly, but remains interesting nevertheless. Highly recommended.

By Alexis H

•Feb 12, 2019

Touches the foundamental parts of mathematics. Really helped with my mathematical thinking.

By Wesley T

•Dec 5, 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 Juan A

•Aug 20, 2021

last test is unnecesary and annoying

By Mudita S

•Jul 7, 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 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 Edmar O

•Aug 27, 2022

It was a mind wrecking course. Of all the courses I have taken in coursera, this is the most challenging one but has provided an eligntening experience. While doing the course, I realised that I need to go back to the basics of Algebra, Calculus and other Maths taken in high school.

What I like most with the course is that, the professor is patient enough to provide examples and explains everything in detail. The answers are almost provided but it leaves enough room for self-reflection and slef-learning. I would like to take this course again in case I want to refresh myself with Mathematical thinking.

By Bruce S

•Jun 30, 2020

The course was interesting and challenging. Professor Devlin did a very good job of explaining the material and, while I appreciated that he did not want to lead us by the hand, it would have been helpful to have all the assignment and problem set answers available somewhere. I went into the class knowing nothing of higher level mathematics or proofs and am interested in learning more. I would be interested in a followup course focusing on proofs.

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 30, 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 THOMAS

•Oct 2, 2022

I'll give a 5 star rank. Even though the videos where in low resolution and that I prefered to have solutions for all the excersices, you learn mathematical thinking. I wish I had learned this in high school. Highly recommend this course to people learning programming too !

By zeyad e

•Jan 17, 2017

i just had taken this course in the college and i don't understand a lot of things but after i started in the course a lot of thinking going to be more clear , thank you for this course .

By Yuliya A 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 Emilia “ A

•Sep 14, 2022

The course was amazing! It made me realize how I love mathematics, and Dr. Devlin, made everything so easy to understand, 10/10 would recummend it

By N A K

•May 22, 2022

Its been a wonderful experiance throughout, Keith has been fabulous, and the concepts have really done magic .

By Robert G

•Jan 31, 2021

Great but ditch the test flight as it seems really arbitrary on who is marking as the people marking including myself have no experience marking others work. Some of the assignments could have been more thoroughly reviewed as opposed to the "i will go through a few questions and leave the rest for you and your classmates to work out". When you are learning how to do proofs it is really dangerous to leave your learning up to other people who are learning how to do proofs.

By Rahul A K

•Jul 5, 2022

I wish to give this course 5 out of 5 stars for the content and for the way it illustrates the link between logic and mathematics. However, I am withholding one star because - my submissions for my final tests were evaluated after a very long delay and after many requests for evaluation. Please speed up your evaluation process. Apart from this, I love this course and its contents and the teacher's method of explaining.

By Zirou-matikz D

•Jun 25, 2021

El curso es bueno a secas. En mi opinión, se podrían usar materiales audiovisuales para hacerlo un poco más atractivo e interactivo, pero considerando que está basado en la lógica y el desarrollo del pensamiento individual, cumple con los objetivos del mismo.

By Wakash K

•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 Almaz M

•Dec 29, 2017

completely disagree with evaluation exercises as it allows to get >= 12 points for completely wrong solution. It's better to use [0,7] based system as used in IMO. it makes more sense and checks problem solving, not ability to bullshit

By Zhenqin L

•Dec 19, 2017

老师很幽默。讲的很细致，可是没人最后改我的作业，以后不交钱了。

By CA G N

•Jun 26, 2018

think differently....

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