Learn how to think the way mathematicians do – a powerful cognitive process developed over thousands of years.
Mathematical thinking is not the same as doing mathematics – at least not as mathematics is typically presented in our school system. School math typically focuses on learning procedures to solve highly stereotyped problems. Professional mathematicians think a certain way to solve real problems, problems that can arise from the everyday world, or from science, or from within mathematics itself. The key to success in school math is to learn to think inside-the-box. In contrast, a key feature of mathematical thinking is thinking outside-the-box – a valuable ability in today’s world. This course helps to develop that crucial way of thinking....

PD

2020年6月29日

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.

NR

2018年3月4日

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

篩選依據：

創建者 Ali M

•2019年11月24日

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.

創建者 Bruce S

•2020年6月30日

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.

創建者 Nickolas F

•2017年8月31日

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.

創建者 James H

•2020年7月18日

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 :)

創建者 Christopher C

•2018年3月30日

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.

創建者 Marcus K

•2018年3月17日

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 .

創建者 Phumlani D

•2020年6月30日

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.

創建者 Yuliya S

•2017年6月12日

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.

創建者 Alexis H

•2019年2月12日

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

創建者 Wakash

•2019年8月30日

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.

創建者 Wesley T

•2017年12月5日

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.

創建者 CA G N

•2018年6月26日

think differently....

創建者 Mohammed A S

•2017年9月26日

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.

創建者 S M R R

•2020年10月8日

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.

創建者 徐致远

•2020年2月14日

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.

創建者 Mudita S

•2020年7月7日

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!

創建者 Avanish M

•2020年7月3日

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.

創建者 Ken L

•2020年7月24日

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.

創建者 Cedric V L

•2020年10月14日

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!

創建者 Dr. A S M

•2017年8月16日

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.

創建者 Shubham V S

•2020年6月30日

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 !

創建者 Gilbert Y

•2020年8月20日

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.

創建者 Dana W C

•2017年8月25日

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.

創建者 GBVN K

•2017年5月17日

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

創建者 Harold M

•2019年8月23日

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.

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