My love for Mathematics in the past few years is like the electrocardiogram (Điện tâm đồ) of a near-death patient, which is peaceful as the surface of a calm lake. This does not annoy me at all, despite for the fact that I used to be called the smartest one in class, in this specific topic particularly. Then, how did I end up like this? Fortunately, Professor Keith Devlin points out that this is not exceptional. It is not true that people are born to be good or bad at math by default, and keep up the trend till they die. In fact, there is always a transformation in mathematical thinking from high school to university level, that almost no one was told when they were students. Moving from being taught a fixed set of techniques to solve a problem, now you are asked to be able to abstract things and reason about it, which naturally confuse learners. To prepare for such transformation, this is the exact course you need. My personal opinion: I wish that I have taken this course 5 years ago, so I can learn a bit more about Algebra. First year undergraduate students, mark my words: take it!. Course review: In the first half of the course, Professor teaches the importance of understanding the primitive mathematical notations, how careful you should be when formulate a problem, and do not rush when attack it. The quizzes successfully demonstrate the second and third points. In the second half, it's amazing to see how one can derive mathematical reasoning solely from the truth tables, and apply it to produce appropriate techniques to solve problems. Only now that I know it's not black magic when somebody choose an arbitrary value that I have no idea where it comes from in a proof. In the last 2 weeks, he gives us a few touch on set theory and real analysis, the two subjects that I suddenly feel attracted to, not to mention his sense of humour when introducing them ;) Notably, throughout the whole course, Professor shows us how to evaluate a proof, and I do learn a thing or two about it. As he always says, the point of a proof is 1) establising the truth and 2) explaining it for the readers, math will be interesting once you learn its way of thinking. I now feel more ready than ever to read a mathematical problem; specifically, where to look for in the beginning of a proof, and the abstract idea of how the authors come up with their chain of deduction. Thank you so much Professor.

this course is given by a rock star in math (prof at Stanford and behind the interesting BrainQuake). Also some interesting concepts are shared. And finally: I love math! So why such a low rate? Because this is a very badly done MOOC from the pedagogical angle: you can't do 27-minutes video when we know that the average focus of a student is lower than that. Also don't ask for a lecture to read separately if you can't at least share the url where we can safely read it online. Finally locking the next weeks is ridiculous: let the student advancing at their pace. So very good in terms of pure math (not a surprise since Keith Devlin is pretty famous in the math world), but very frustrating in terms of pedagogy.

I found this course to be incomprehensible. The professor was rude and dismissive, when I asked for help.

I love this course.

I cried of the emotion when Dr. Keith explained the meaning of the Implication. I'm 35 and I did not know that. After week 2, all things that I have learned before of this course became make sense.

You should take this course. It’s a new way of thinking about things.

This course is like one of the greatest pieces of classical music if you like the classical music.

If you want to take the course, I recommend that you take it in advance. I recommend seeing the material slowly. Some parts require some effort. Please do the exercises and review the forum group.

This course is great because it teaches you the foundations of mathematical thinking, namely how to write rigorous and concise proofs. I really enjoyed the course and would recommend it to a friend.

An awesome course. Very easy to follow at the start, becomes more challenging at the end. I have a PhD in economics yet I struggled with the real analysis at the end. And that's just intro level! :-D

This is by far the best course of mathematics on Coursera!

The content was spread evenly, it includes everything that is required for a student to read and understand mathematical theorems. Concepts such as implications, equivalence, quantifiers are clearly and concisely explained, I am sure even for people who are learning university mathematics for the first time, the lectures are very easy to understand.

That being said though, as in any university math courses, solely listening and taking notes in the lecture could not make you a decent grade. The most important material provided by this course is the assignment, which is provided at the ‘download’ tab at the bottom of the video. The assignment deliberately included confusing examples and counterintuitive facts to trick people who have misunderstandings in their concepts, and detailed explanations for harder questions were provided as well. I love how professor Devlin reason as well: he proceeds very carefully, writing down what he speaks in every argument, and then translate it to symbols in mathematics.

I found that technique very efficient as I tackle the assignment problem. If you want to get out most from the course, remember to complete all the assignment and check your answer by asking your friends / in the forum!

The test flight peer-assessment is also a very enjoyable experience, looking at other MOOC-mates attempting to prove the same questions enables me to learn more on how to improve presentation style when writing as a mathematician.

Overall, this is a very interesting course for people who loves mathematics, it serves as a transition from high school mathematics to university mathematics as well. Highly recommended to people who wants to know more about what university mathematics looks like!

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.

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.

Good overall, but Dr. Devlin tends to ramble in lectures rather than getting to the point. He also seems somewhat inconsistent in how he evaluates proofs. Since proofs and their evaluating are the core of the course I found it frustrating that there isn't more care given to clarifying what constitutes a good proof.

Really great course. It's aimed at high school students, but I found it valuable even as a college graduate who has taken several math classes but never had a formal introduction to how to think about proofs. I wish I was able to take this class when I was an undergrad.

In the last lecture, based on what he previous taught, the professor give us the definition of limitation which is the beginning of the Calculus. I wish I taken this course before university.

The detailed explanation of proving certain claims in the course are very ambiguous, which is the reason I discontinued the course.

I was interested in mathematics till high school. But after that in engineering we have to learn Applied Mathematics(AM) and which is quiet boring for me. Due to these type of mathematics , I decided not to learn math anymore. But this course was very intuitive and focuses more on thinking and logical steps rather than computational parts. Now I love math more than I used to love before Engineering. I will definitely learn more mathematics because of enormous interest in this field. THANK YOU Prof. Keith Devlin for this course. Since, you're the reason why I love Mathematics. Sorry for English because it is not my native language. Sir please reply to my review if you have time :) .

Great course, it's really shows the way how to think in mathematical rigor. It gave me an intuition about what Mathematics is itself.

Thank you Profesor Keith Devlin, you are a great teacher !

Overall I thought it was pretty good. Explanations are straight forward, and easy to follow. Small little quizzes are given throughout videos to ensure that people are paying attention during the lessons.

The only negative part is that it's clearly a class that's designed around you working with multiple people. If you don't, you won't be able to study as well. Fortunately, there are forums, but with the nature of forums, responses can range from "immediate" to "never."

I am really not sure if you need 20-30 minutes videos to explain the material - I think maybe 7-10 minutes clear with some good examples would be more helpful, I fell sleep during some of the lectures, boring, long and not sure if necessary - on the other hand I guess 20-30 minutes is good because you learn to put up with arguments and clear them up yourself - also maybe this course was directed towards high school students thus the long explanations -Overall, as I said on the beginning, it would work better with clear definitions and some examples and discussion board -

Очень сложно сказать, что курс был полезен для меня в карьере или учебе (или как-то крайне интересен), однако благодаря курсу я стал лучше понимать язык математиков и освежил память по некоторым математическим законам. Огромное спасибо создателю курса за отдельные turorial-видео после assignments!

This is an excellent course, which provides insights into how mathematicians think about proofs. The exercises are not hard, but they do require careful thought. This is a well constructed course.

I am not familiar with the material and consider this course as a baby step into a completely new language, a journey in a world of thinking that shows our education system fails to inform and develop logic and rational thinking at the basic levels. At 67, I should have the basic knowledge to complete this course with ease. It reflects on the substance, or lack thereof, of the education system and the quality of teachers. Given the time, the effort and the patience of good teachers, every reasonable thinking person ought to be able to manage these basic skills. Thank you, Professor, for sharing your knowledge, it has been a great discovery for which I am immensely grateful.