Great but ditch the test flight as it seems really arbitrary on who is marking as the people marking including myself have no experience marking others work. Some of the assignments could have been more thoroughly reviewed as opposed to the "i will go through a few questions and leave the rest for you and your classmates to work out". When you are learning how to do proofs it is really dangerous to leave your learning up to other people who are learning how to do proofs.

I wish to give this course 5 out of 5 stars for the content and for the way it illustrates the link between logic and mathematics. However, I am withholding one star because - my submissions for my final tests were evaluated after a very long delay and after many requests for evaluation. Please speed up your evaluation process. Apart from this, I love this course and its contents and the teacher's method of explaining.

El curso es bueno a secas. En mi opinión, se podrían usar materiales audiovisuales para hacerlo un poco más atractivo e interactivo, pero considerando que está basado en la lógica y el desarrollo del pensamiento individual, cumple con los objetivos del mismo.

Good Course, A must take for college math majors. While the course covers most of the contents, Professor should have given more attention to Proofs and Real Analysis which are assigned just two weeks in this course.

completely disagree with evaluation exercises as it allows to get >= 12 points for completely wrong solution. It's better to use [0,7] based system as used in IMO. it makes more sense and checks problem solving, not ability to bullshit

think differently....

This Course is only good if one has a group to study with. Online , whtatsapp, or social networking groups are not that effective. If you want to do this course make sure that you have friend or two planning to enroll with you.

all the videos and quiz are lock

Tengo Problemas con la traducción al Español, me notificaron que este curso tenia subtitulo en español me voy a dar baja.

The "Introduction to Mathematical Thinking" course offered by Stanford University provides a refreshing and transformative approach to mathematics education. Unlike traditional math courses that focus on rote memorization and formulaic problem-solving, this course encourages students to develop mathematical thinking skills that can be applied to real-world scenarios.

One of the standout features of this course is its emphasis on thinking outside-the-box. Students are challenged to approach problems from different angles, develop creative solutions, and engage in critical reasoning. This approach not only enhances problem-solving abilities but also cultivates a deeper understanding and appreciation for the beauty and intricacy of mathematics.

The course is well-structured and incorporates a variety of instructional methods to cater to different learning styles. Through video lectures, interactive exercises, and problem-solving assignments, students are actively engaged in the learning process. The course also encourages collaborative learning and provides opportunities for discussion and peer feedback, fostering a supportive and interactive learning community.

The instructors are highly knowledgeable and passionate about the subject, and their enthusiasm is contagious. They guide students through the course material with clarity and provide valuable insights into the mindset and techniques used by professional mathematicians.

Another notable aspect of the course is its relevance beyond the confines of mathematics. The skills developed through mathematical thinking, such as logical reasoning, critical analysis, and creative problem-solving, have applications in various disciplines and in everyday life. This course equips students with transferable skills that can benefit them in their academic pursuits and future careers.

Overall, the "Introduction to Mathematical Thinking" course offers a refreshing departure from traditional math education. It challenges students to think differently, explore the depths of mathematics, and develop valuable cognitive skills. Whether you are a math enthusiast or someone seeking to enhance your problem-solving abilities, this course is a worthwhile and enriching learning experience.

This course has a great introduction to why you should take this course. Professor Keith Devlin introduced us to why high school mathematics is different from university mathematics. High school mathematics deals with math which invented kind of before the 18^th century. But what happens to the mathematics that was invented in the 19^th century. Because of your kind information many modern mathematics techniques invented in the 19^th century. How to deal with those problems?

In varsity level mathematics you just don’t use or apply formula that was predetermined but you think about the problem. You brainstorm and make the reasoning behind the problem. A mathematical proof needs to be dealt with great care. Because you have to deal with its uniqueness universality. Of course, you have some certain predefined tools that you learned in high school, but you need to think before applying, not as it was done as a template set in high school.

So, Coursera offers this course to introduce you to a glimpse of how mathematical thinking procedure works. This course introduces us to Logic and Logic Combinators, Logic Implication, and Equivalence, Quantifiers, several proof techniques such as proof by contradiction and proof by Induction, proofs involving Quantifiers, introductory Number Theory, and some proves associated with it. The hardest part of this course is Real Analysis. Each proof associated with Real Analysis involves so much thinking and reasoning. At the very last week, i.e. at the 10th week, you need to submit some assignments involving proof techniques that will be peer-reviewed before you get your certificate.

First of all, thank you very much for this masterpiece. This is the most challenging course I've ever had on the Coursera.

One more comment on the final peer review assignment: the question about whether 0 is a natural number.

Only after taking this course and doing some research on the Internet do I realise that there's a lot of argument on this question. I am a college student from China, and I major in physics, rather than mathematics. For me, the statement "0 is the least natural number" is a fact that was written in my primary school's textbook. So I was quite surprised when I was told that 0 is not a natural number. After searching on the Internet, I finally got more knowledge on this.

Fortunately I was not supposed to lose too much on that. However, I do recommend that you make this clear in the course content so that everyone can discuss under a common assumption, regardless of their background education.

Above all, this course experience is a lot of fun. There's no standard answers here, only remarkable thinking and a space of infinity to explore. Thank you for all of it! I'm giving 23 out of 24 marks for this course, taking away 1 point for clarity about whether 0 is a natural number.

Wonderful Class! As taking the class, I truly was grasping everything he was teaching and I loved his book which was short much compared to the oversized book most other students get assigned. Reading the book went straight to the point and there was never a need to decrypt his words for it was easy to follow through. The book also made it easy to know where to refer back to and taking this class as with the upmost respect that it deserves flourished a changed mindset that endows into not only a mathematical mindset, but also a logistical mindset that better helps my sense of speech and my perspective on life when doing about anything! I've taken it to my own to recommend this to my classmates and even shown my book with the notes I've written in it to my classmates in hopes to inspire them to try this course because i do feel as though this is a class of better help to digest information I can and do learn from other classes too!

I do completely agree that this course is the most basic skill to learn mathematics, and not just mathematics it is useful in everyday life, it helps you think clearly, out of the box and think systematically, basically to have a critical mindset/thinking. I seldom writing a review for a course, but because of how valuable the skills that are being taught in this course and also after the lesson that I've learned while taking the Assignment 4 - Week 2 of the course, I cannot help myself to put up a good review. And exactly what Dr. Keith says about taking/tackle the assignment slowly, I can tell you that it is true, you need to master this course even if it take much time longer that you plan to do.

For this reason I decided to purchase the course, and also I see that it has a book with the same title in Amazon. I'll buy the book once I finish with the course, dunno when, but hey at least I purchase the course to show my gratitude.

This is one of the best and most useful courses I made so far.

But the content also quite sophisticated! So be ready for struggles. Actually there is a problematic fact, that should be considered by the course provider:

Not everything is covered in the video lessons that is asked in the problem sets. And in the final test you have to work on some tasks for which you most probably will need to consult the internet for getting the required skills.

Nonetheless, by working on this course one really improves the way of thinking and understanding. Be ready for logic, number theory, mathematical proofs and some hard times ;)

The professor is very very likable and really wants you to improve your way of solving problems. And you instantly know that he really loves math and wants to share his enthusiasm. That's just so nice!

So really fantastic course!

Being Ingeneer and at my age , finding this course was a great discovery. It shows the beauty, creativity and effectiveness of reasonable thinking , which in my opinion, after a long career in businesses, is a key to well formulate problems and find solutions in all fields of human interest. It is excepcionally well structured and no detail is left unthought . Apart from the vast recognized top level of Dr Kevlin on the topic, his charisma helps to be motivated to go through all along his lectures, quizzes , assignments and Tests. Many thanks to Dr Kevlin and Coursera for this opportunity. For sure I will continue looking for new courses related with Maths

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.

Being precise about language becomes very important in our lives, and this course starts by guiding one to improve one's usage of language. The professor challenges our thinking every now and then, thereby developing our reasoning. Introduction to mathematical proofs has certainly improved my approach to testing the truth or falsity of a claim. Emphasis on understanding is a key feature of this course. A key aspect of this course is Keith's humor, which is engaging. In summary, I have benefitted immensely from this course, and I recommend it to anyone who wishes to improve their thinking. After all, education is a preparation for life.

I used this course prior to enrolling at university for a software engineering degree. I always was bad at mathematics and was extremely worried I would never manage to get through the foundational courses which are very much focused on discrete mathematics. This course literally made me think different. It showed me that math is nothing to be afraid of, and literally reset my thinking about mathematical thinking. In fact, when I had to write my first proofs, I noticed it was very similar to what is taught here. I passed the courses with confidence and am now finishing my Master's thesis. Thank you!

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 !

I thought the course delivered everything it promised and then some. It was well paced, well taught and the emphasis was correctly placed on learning to think mathematically as opposed to chasing grades or regurgitating formulas. Setting the pass mark at 30% allowed us to take chances and fully explore the material. I took a similar class 50 years ag and this time I decided to accompany my sister who had never takin this kind of course. We both had a great time discussing the concepts and examples. I highly recommend it.

What a humbling course. I learned I'm not nearly as intelligent as I thought I was. Most of the content was doable with some effort. The most problematic was the content near the end about real analysis.

The course is all about mathematical proofs: expressing thoughts precisely, how to write proofs, how to reason, and grading proofs written by others. I didn't think that's what I'd be doing when I enrolled.

My one suggestion for the course is chop up the videos (averaging 30m each) into a bunch of shorter videos.

This course was amazing for learning fundamental concepts of university mathematics like formal logic and proof writing. Devlin is a fantastic teacher. I was able to complete the course without any formal mathematical training, but it was definitely challenging. For someone thinking about studying mathematics in college, this is a great course to see if you enjoy the material. This course has inspired me to study mathematics for my undergrad, and I hope you find it as useful as I did!

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.