Back to Introduction to Mathematical Thinking

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2,231 ratings

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540 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 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.

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.

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By 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.

By 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.

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 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!

By 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

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 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!!!.

By 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.

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.

By 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 :)

By 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.

By Voo T 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.

By 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.

By 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!

By 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/

By 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

By KRISHNA P

•Nov 15, 2020

I enjoyed the course immensely. I am 53-years old now and had finished my Bachelors in Math at the age of 21. Subsequently, I moved on to Engineering and did have to use Abstract Math. This course is an ideal introduction to future Math students. Prof. Delvin's empathy for first-timers will certainly encourage many future students.

By Jordi A

•Nov 29, 2018

This is a fantastic introduction to the world of college-level math. Recommended to HS students, social science majors who are quite analytical, and maybe even some STEM freshmen. While it takes considerable effort to follow the course and assignments, it's quite a learning experience, and I with I had taken it earlier in my life.

By bj d

•May 13, 2017

Excellent course! Started off slowly and methodically laying the foundations for successive lessons. Prof. Devlin explains, demonstrates and allows one to "hear" him think through solutions. My math skills got stronger, but more importantly, my approach to the logic of mathematical thinking can be transferred to other disciplines.

By Abhay G

•Jun 17, 2019

I get a new thinking in Mathematics. Now, i get a new approach to tackle mathematical problems.

I learnt some new different methods to prove the theorems and get a paradox(in which we have proved 1 = 2) that give me a new sight to see a problem.

I realise "Mathematics does not depend upon solution, it depends upon a process".

By Mikhail Z

•Sep 18, 2017

This course is a fun, thorough and thoughtful introduction to the basics of mathematical thinking. I've used it as a supplementary course for series of seminars for philosophy of mathematics. The peer-review assignment is a brilliant way to grasp the difference between solving a problem and thinking about solving a problem.

By Dimitrios G K

•Mar 5, 2021

Needless to say, how good Dr. Keith Devlin is, but I would like to mention the satisfaction anyone gets after finding a path to prove something on his own. Gradually, with a lot of humor, he introduces some key facts you can use in order to acquire the skills to analyze a problem and step by step to be led to its solution.

By Thong D L B

•Mar 25, 2019

I just want to say thanks to Prof. Keith Devlin. I have never been quite comprehend the proof techniques and usually have to prove statements arithmetically directly. Thanks to this course, I finally see how I can approach the problems more systematically, thus being able to find the answers faster and more consistently

By Adam M

•Mar 25, 2020

A great assignment-based introduction to discrete math with an emphasis on communication and thinking. This is a course to improve how you approach problems, and although it provides highly useful skills for university math courses, the disciplined thought process outlined in the course is applicable to the real-world.

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