Great course ! Provided new skills on how to think about maths and improved my overall confidence with the subject. I feel like I can go further in the study of mathematics thanks to this.

The content of this course is very helpful. It explains the fundamentals of college mathematics, and the possible confusions about symbols. I'm not sure if it can clear all my confusions about symbols, but the light weight of the content has captured the gist of college mathematics. Even after I have graduated from college for 7 years and have rarely used something like partial differential equations, this course brings all the math I learnt back to life in a few hours. I also recommend following Prof. Keith Devlin's twitter. Although there's a bunch of political content in his tweets, reading them can help you get closer to the mind of the author, and get the sense of reality besides this MOOC.

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.

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.

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

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.

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。

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!

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.

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.

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.

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 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 :)

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.

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!

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.

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 !

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 .

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.

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

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

It's mind blowing.

Course is well structured, pace is doable and dr. Keith is pleasure to listen to.

Best math teaching I ever enjoyed. If I could I would take up stuying the subject with Dr. Devlin.