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.

An excellent course from an outstanding educator. The first few lectures should be of interest to anyone who wishes to think and communicate in a logical manner —including anyone alienated by high-school mathematics. The remainder of the course is a solid preparatory foundation for anyone considering a university mathematics degree but is also valuable more widely for the sciences, engineering and emerging technology-based subjects like data science. I took a physics degree (and later a PhD) nearly forty years ago, and while I had a good high-school mathematics background, I wish I'd had something like this in addition.

This was a great course. I've studied Mathematics independently for most of my career (I am a Software Engineer) but I always struggled with the less formulaic aspects of the field. I could memorize the quadratic formula, but I couldn't derive it. I could remember properties of real numbers, but couldn't provide an original proof to save my life. After taking this course, I'm now confident enough to reason about numbers, write effective proofs, and generally think more critically and abstractly about Mathematics. I'm looking forward to continuing to study the field, now with more confidence and practice!

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.

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.

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 !

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.

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.

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.

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

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.

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.

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!

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.

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.

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 .

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.

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!

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".