Introduction to Mathematical Thinking

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!

I have just finished this course. I treated it just like a real course and did all the assignments, watched the videos, and took the final assessment.

In the beginning, this class is billed as a great class for anyone including those not good at or not interested in mathematics. This is probably true for the first three or four weeks. However, Number Theory and Real Analysis are introduced and nine of the ten questions on the final assessment require you to have at least a rudimentary understanding of the concepts Devlin introduces in the lectures of Weeks 7 and 8. I'm sure these are very basic ideas for Number Theory and Real Analysis, but as someone who was not familiar with them, I had to read and re-read the proofs in Devlin's book.

I will say I loved the concepts! The Division Theorem, in particular, was eye opening. It took me a while to understand what it was saying. The final assessment helped me to fully appreciate the Theorem. Now, I want to teach it to my 11 year old! I've previously taken Calculus, and been introduced to the limit theorem, but I had never really understood it before. Devlin did a great job at explaining it!!!

Devlin's explanation of his proof evaluation flummoxed me. I'm not sure who is to blame. I know this is the main point of the course, so I may continue my studies with Velleman's How to Prove It.

My biggest complaint is with the Coursera software and the poor communication regarding the final assessment. Latex was available in all the discussion forums, but not available in the final assessment. I spent about a week and half understanding and answering the questions. Then I spent a day and half learning Latex and creating a pdf so that fellow graders could easily read my work. Then, I went to the (timed) final assessment and had to fill in text boxes without the use of Latex. It made for some messy work after I had put a lot of effort in to not be messy.

There was also no warning of how the final assessment worked. After you plug your answers into the text boxes, you take 3 quizzes and watch 3 videos totaling about an hour and a half. These are also due on the same day your final assessment is due. The quizzes consist of Devlin's curation of other people's answers to the same final assessment. I was so tired after just completing the assessment. I really didn't feel one week was enough time to finish the assessment.

If you intend to complete the course, I highly recommend buying Devlin's inexpensive book Introduction to Mathematical Thinking. It was very helpful. I find Devlin to be a much better writer than lecturer. I would consider reading another text by him, but I'm not sure I'd consider another MOOC.

An excellent introductory course to mathematical thinking or a companion course to follow while shuffling through your first book about mathematical proofs. Professor Devlin's way of putting out lots of exercises and going through them meticulously afterwards is as challenging as it is rewarding.

If you really want to learn the subject material, active engagement in problem solving is required and all the exercises should be considered as obligatory. While you might learn something by just watching the videos and working with obligatory quizzes, the real beef is in working with optional practice problems. Coming up with even a simple proof on your own, making mistakes on the way, seems to be only way to learn proofs.

In my opinion the practice problems were the best part of the course. Being a fellow with humanities background and thus very little mathematical education, I advanced tremendously when struggling with optional problems and proofs.

I really enjoyed the online course. I thought it was well planned and layed out, easy for me to follow. The work load(h.w. & test)was just enough, so i could finish everything with enough time, learn about the topics and not feel over loaded and rushed.



Overall I really like this class because all lectures, assignments, and tests are straight forward. A couple things I dislike about the class are that there should be more opportunities for extra credit and it would be awesome if the final was an objective essay about what we have learned in this class or what we like about the class. I believe that I have more knowledge about ocean, weather, and marine lives and hopefully, I can use them in real life.



The course was everything you said it would be, fun but a lot of work. And it was! I enjoyed the web-labs because they were a lot of fun and easy to understand. And the answers were usually somewhere in the text. I also liked the assignments that required us to get online. Sometimes articles aside from the reading book gave me a better idea and understanding of the subject for that week. What I disliked was the short essay question because I found it difficult to explain certain concepts without introducing in some way, Ideas from the course notes or book (keeping in mind plagiarism). I never expected to learn so much from an online class; I now see the ocean life in a whole new way. I know I could have done better, but in the end I learned that an online class could be as much work or more than a regular class. However, I still enjoyed it very much.

As a mathematics teacher and a major in mathematics I found this course mostly a waste of time (from the point of view of a student intending to study mathematics) and a far cry from the description given in Mr. Devlin's introduction.
Mr. Devlin seems to have an obsession with formal logic (also known as "sentential logic" )and he dedicates most of the course to this rather negligible (mathematically speaking) subject as if mathematics and "mathematical thinking" depend on it (which they most certainly do not!) . As a result, students of the course expend enormous amounts time and energy in translating sentences into formal logic and vice versa instead of studying actual mathematical content and actual examples of mathematical thinking.

I absolutely love First in Math. I haven’t come across another website or app that is as engaging as First in Math. Students love logging on and trying to earn as many stars as possible. I like how it is aligned to the Common Core standards. Students are learning their basic math facts interactively and building on their critical thinking and problem-solving skills. Each student starts out on the same level and can work at their own pace through the program. It has video lessons and previews to grab the attention of the students. Having access to First in Math at home is a huge plus for me as a teacher, but parents as well. When a student reaches a certain number of math problems, First in Math will generate an additional Family User Name. Most importantly, First in Math allows teachers more time to teach the curriculum and reduces time having to actually teach those basic math facts.