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.

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!

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

The "Introduction to Mathematical Thinking" course is exceptional. It provides a comprehensive foundation in mathematical concepts and promotes critical thinking and problem-solving skills. The course is well-structured, engaging, and accessible, making it an invaluable resource for anyone looking to deepen their understanding of mathematics. Highly recommended for both beginners and those seeking to refine their mathematical abilities.

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.

The course was very helpful and fruitful. The topics are very interesting and engaging. The overall explanation was great and understandable. The course helps you to inquire a lot of skills like analysis, evaluation, critical thinking, and some other skills. The course was very interesting and fascinating through all the nine modules, and I feel a great feeling after finishing the course and getting my certificate.

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!

Exquisite, marvellous, brilliant, and all the complementary words one can think of. Professor Devlin is the benchmark of mathematical teaching. He lays out the building blocks of mathematical thinking so elegantly, beautifully and comprehensively, it surpasses the conventionalities of ordinary teaching, and verges on the borders of art. If you want to begin this journey, I cannot think of a better place to begin.

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!!!.

This course is great. Very well done. 100% recommended. Always good to work on foundational things. For me, it was a nice way to get back to math many years after finishing my engineering grad. Still feel that I learned a ton, especially because of the change of focus: understanding and proving results instead of just applying them. Thanks, Prof. Keith Devlin, Stanford and Coursera!

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.

Hello! I was fascinated by this course, I'm a Senior High School student learning from this course, with the use of Coursera. I actually like the learning methods wherein it has various video lessons to watch and gain knowledge as well as modules. Having an exercise materials such as quizzes and assignment really does helped me to understand furthermore the lessons. I LOVE THIS COURSE!

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.

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 :)

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.

I started my Physics degree course in 1976 and we had to look at mathematical analysis as a preliminary. As a raw undergrad it went over my head and the heads of many other people, something we preferred not to think about. This course should have been around then, things would have been much clearer.

All in all a challenging and worthwhile learning experience.

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.

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.

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/

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

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.

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.

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".

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.

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.