Introduction to Mathematical Thinking

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9/10 stars
based on  39 reviews
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FREE

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Coursera online courses
Coursera's online classes are designed to help students achieve mastery over course material. Some of the best professors in the world - like neurobiology professor and author Peggy Mason from the University of Chicago, and computer science professor and Folding@Home director Vijay Pande - will supplement your knowledge through video lectures. They will also provide challenging assessments, interactive exercises during each lesson, and the opportunity to use a mobile app to keep up with yo...
Coursera's online classes are designed to help students achieve mastery over course material. Some of the best professors in the world - like neurobiology professor and author Peggy Mason from the University of Chicago, and computer science professor and Folding@Home director Vijay Pande - will supplement your knowledge through video lectures. They will also provide challenging assessments, interactive exercises during each lesson, and the opportunity to use a mobile app to keep up with your coursework. Coursera also partners with the US State Department to create “learning hubs” around the world. Students can get internet access, take courses, and participate in weekly in-person study groups to make learning even more collaborative. Begin your journey into the mysteries of the human brain by taking courses in neuroscience. Learn how to navigate the data infrastructures that multinational corporations use when you discover the world of data analysis. Follow one of Coursera’s “Skill Tracks”. Or try any one of its more than 560 available courses to help you achieve your academic and professional goals.

Provider Subject Specialization
Humanities
Sciences & Technology
4433 reviews

Course Description

Learn how to think the way mathematicians do - a powerful cognitive process developed over thousands of years.
Reviews 9/10 stars
39 Reviews for Introduction to Mathematical Thinking

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Henry profile image
Henry profile image
10/10 starsCompleted
  • 2 reviews
  • 2 completed
4 years, 9 months ago
I graduated from 2 of the most prestigious universities in the US and over the years I've watched a few dozens online classes and I have to say Intro to Math Thinking is one of the best classes anywhere, online or off. Devlin is imaginative as a teacher. The way he approaches math is so creative that it's a joy to watch his lectures. This class is more than about math, it's about proper thinking and reasoning. In addition, Devlin cares about teaching (and your learning) and it shows throughout his lectures, and especially when he explains the solutions to the exercises.
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Randy Burgess profile image
Randy Burgess profile image
8/10 starsTaking Now
  • 1 review
  • 0 completed
6 months, 3 weeks ago
IN A NUTSHELL: This MOOC has excellent content, but the weaknesses of the Coursera platform undermine it. DETAILS: I was able to complete fairly enjoyable 7 weeks out of the scheduled 10 weeks of this course before health reasons forced me to opt out of weeks 8, 9, and 10. Some specific points: 1) The blurb for the course says it's meant not just for math majors, but for anyone interested in logic; however I'm not so sure about this, given that the focus is entirely on applying logic in a mathematical context, i.e. to proofs. 2) You'll want a good background in high school algebra, especially factoring, to do well in the final weeks, which are somewhat more math-intensive. 3) The instructor, Keith Devlin, has said he will no longer be involved; this may or may not pose a problem in getting good mentors in future. Mentors are very important to this content! 4) The revised Coursera platform lacks features, especially with the forum ... IN A NUTSHELL: This MOOC has excellent content, but the weaknesses of the Coursera platform undermine it. DETAILS: I was able to complete fairly enjoyable 7 weeks out of the scheduled 10 weeks of this course before health reasons forced me to opt out of weeks 8, 9, and 10. Some specific points: 1) The blurb for the course says it's meant not just for math majors, but for anyone interested in logic; however I'm not so sure about this, given that the focus is entirely on applying logic in a mathematical context, i.e. to proofs. 2) You'll want a good background in high school algebra, especially factoring, to do well in the final weeks, which are somewhat more math-intensive. 3) The instructor, Keith Devlin, has said he will no longer be involved; this may or may not pose a problem in getting good mentors in future. Mentors are very important to this content! 4) The revised Coursera platform lacks features, especially with the forum - no preview, no in-forum alerts, etc. 5) A big problem with Coursera is that students can race ahead as they please; this makes forum participation more erratic since not everyone is in the same week of content anymore. ecommendation: To get the most out of the strong video & homework content, you might want to have arrange for your own outside study group or mentor.​
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Charles King profile image
Charles King profile image
2/10 starsDropped
  • 6 reviews
  • 4 completed
6 months, 3 weeks ago
I suppose even Stanford needs some EZ-PASS courses for the athletes. This course is long on grandiose claims, but short on any real meat, and the pacing is glacial. It certainly is *not* a course for anyone with any prior experience of maths or science at even an advanced high school level, and is better suited for those needing remedial help with the basic concepts of propositional logic. Devlin's approach may be useful for those who need a lot of hand-holding, but his waffling method of presentation and failure to present formal definitions with the clarity they require just became irritating. Towards the end I would just let the lecture run in the background while I was doing something else and check in every couple of minutes to see if he'd got to something interesting. For those hoping for a course that covers elements of real analysis (as he advertises at the start), look elsewhere. He doesn't get beyond the basic definit... I suppose even Stanford needs some EZ-PASS courses for the athletes. This course is long on grandiose claims, but short on any real meat, and the pacing is glacial. It certainly is *not* a course for anyone with any prior experience of maths or science at even an advanced high school level, and is better suited for those needing remedial help with the basic concepts of propositional logic. Devlin's approach may be useful for those who need a lot of hand-holding, but his waffling method of presentation and failure to present formal definitions with the clarity they require just became irritating. Towards the end I would just let the lecture run in the background while I was doing something else and check in every couple of minutes to see if he'd got to something interesting. For those hoping for a course that covers elements of real analysis (as he advertises at the start), look elsewhere. He doesn't get beyond the basic definition of a series.
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 profile image

10/10 starsCompleted
  • 26 reviews
  • 24 completed
1 year, 6 months ago
This course has been valuable to my understanding of mathematics and my mathematical thinking skills . After completing this course , i found myself more capable of tackling other mathematical problems . But apart from that , this course provides a first insight into number and set theory as well as proof writing . It is suitable for students who do not need much external discipline as it relies on students forming study groups and the students own interest .
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Mirza Ibrahimovic profile image
Mirza Ibrahimovic profile image
10/10 starsCompleted
  • 12 reviews
  • 11 completed
1 year, 9 months ago
I crown Keith the king of MOOCs. This is how an online course should be done. It is exceptionally well made and ran. His enthusiasm is contagious. If you want to improve your math beyond high school level, highly recommend this course.
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Student

10/10 starsCompleted
1 year, 9 months ago
Instructor is very engaging and thorough, does a very good job of helping to ensure that difficult concepts are understood. Assignments (both graded and practice) are very helpful, instructive, and quite fun, though often challenging. Since the course is essentially pass/fail based on completing the assignments, the challenge is definitely worth it. Overall, a very interesting course taught by a very good professor that would be highly worthwhile for anyone in STEM fields, not to mention the general public.
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Ervin Lang profile image
Ervin Lang profile image
10/10 starsCompleted
  • 5 reviews
  • 5 completed
1 year, 10 months ago
This was the first MOOC I took roughly 2 years ago. K. Devlin is a fantastic instructor. The course helps to build the fundaments for critical thinking. Would recommend it to everyone.
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Student

6/10 stars
1 year, 11 months ago
The content is mathematical thinking (...or how to think logically). The last section of the class is for math majors, but the first and middle parts are almost pure logic with a math slant and is appropriate for anyone. The style is inquiry based learning (IBL), so it isn't typical of most online classes. IBL is great if you are used to asking a lot of questions and doing a lot of self learning (which I am), but I don't think IBL is well suited for a MOOC since it requires the students to seek a lot of feedback and there are very few TA to give quality feedback and the study groups can be hit or miss depending on whether you are in a group where someone(s) understands the material or not. I found the instructor annoying more because the many times he repeated things and the superfluous chitchat on the lectures than his teaching. The video time could have been cut by half if he cut out all that stuff, and quite frankly, it made ... The content is mathematical thinking (...or how to think logically). The last section of the class is for math majors, but the first and middle parts are almost pure logic with a math slant and is appropriate for anyone. The style is inquiry based learning (IBL), so it isn't typical of most online classes. IBL is great if you are used to asking a lot of questions and doing a lot of self learning (which I am), but I don't think IBL is well suited for a MOOC since it requires the students to seek a lot of feedback and there are very few TA to give quality feedback and the study groups can be hit or miss depending on whether you are in a group where someone(s) understands the material or not. I found the instructor annoying more because the many times he repeated things and the superfluous chitchat on the lectures than his teaching. The video time could have been cut by half if he cut out all that stuff, and quite frankly, it made it a pain to go back and watch lectures for content. To be honest, I learned more from his (very concise) book than I did from the videos. He is not a natural teacher, so the concepts could be more clearly presented. (My high school logic class was IBL and the teacher was much better at it than Devlin, so I know what good IBL teaching/facilitating is.) Overall, there is probably a better mathemathical thinking/logic class out there than this one, but it is a Stanford class, so there is a prestige factor. It's run by Coursera, so the provider is a pro at this.
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Alexander Cheboub profile image
Alexander Cheboub profile image
10/10 starsCompleted
  • 1 review
  • 1 completed
2 years, 1 month ago
The course is illuminating and has changed the way I view the world and problems in general. Prof Devlin style of teaching is to be commended - he describes abstract methods of reasoning with an almost crystal clarity.
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Khadija Niazi profile image
Khadija Niazi profile image
10/10 starsCompleted
  • 1 review
  • 1 completed
3 years, 5 months ago
This course has been an amazing journey for me. This course first caught my eye in September 2012. I enrolled in this course out of curiosity but to my amazement, I found this course very challenging but at the same time very interesting as well. I remember being very confused at the sight of the lectures. So I decided to unenroll and take the next iteration, when I had better knowledge. So I decided to take the next iteration, that came in September 2013, at my own pace because I wanted to take this course pressure- free. So that the material could really sink in better before I take this course for real. I watched all the lectures and attempted all the quizzes. The only things I didn't do were the assignments and the test-flight because that required a live course with active forums. I was really surprised at the intricacy of this course. So finally the day came, February 3rd 2014, the day when I was going to start this course for ... This course has been an amazing journey for me. This course first caught my eye in September 2012. I enrolled in this course out of curiosity but to my amazement, I found this course very challenging but at the same time very interesting as well. I remember being very confused at the sight of the lectures. So I decided to unenroll and take the next iteration, when I had better knowledge. So I decided to take the next iteration, that came in September 2013, at my own pace because I wanted to take this course pressure- free. So that the material could really sink in better before I take this course for real. I watched all the lectures and attempted all the quizzes. The only things I didn't do were the assignments and the test-flight because that required a live course with active forums. I was really surprised at the intricacy of this course. So finally the day came, February 3rd 2014, the day when I was going to start this course for real. After watching the lectures and attempting the quizzes, I realized that my understanding had already begun to improve. The real turning point came when I started attempting my assignments and posting them on the forum. Each week, there was a set of problems given to us. We were recommended and encouraged to attempt these questions and discuss it with your peers. When I looked at the solutions of other people, I realized how to make my solution better. The main goal of the course is to make the student see mathematics in a different way. Not only as a tool for calculation but as a universal language which polishes your understanding. After mastering this language, the student is able to solve problems efficiently and formulate thinking process which helps them in this course. Moreover with the help of mathematics we can understand the problems better by visualizing an image of the problem and translating the problem into a mathematical statement. This is the first and most important step to gain success in this course. In my opinion there were many plus points in this course, which made it unique and one of the best: For me, this course needs your active participation in the forums if you are a beginner. Healthy debate is encouraged by the professor and the exchange of ideas is essential. This course may be hard at first but taking it twice and discussing your problems on the forums will make you sail through this course. The other important and striking factor of this course was the non-stop, passionate interaction of the professor in the forums. He made sure to comment on as many threads and posts as possible, encouraging his students and discussing problems. He encouraged group activities but at the same time he also encouraged good working ethics. He discouraged unnecessary competitiveness and told the students to focus only on the point of this course, learning. For him, learning is the crux of this course. He once wrote: "The course is in no way set up as putting anyone in competition with anyone else. I think this is a big plus of free, open MOOCs." In my point of view, this thinking brings out the best in every student. In his course every student was actively helping their fellow peers. This course really lays the foundation of mathematical thinking. I have one suggestion though: Please make a sequel for this course because this course deserves one. There are still many things we have yet to explore. For the people who want to take this course, you may find this course hard at first but with the help of your peers and the wonderful lectures, you will be able to sail through. This course is for the people who are not afraid to try. "It's just like riding a bicycle, at first you will keep falling but then one day you will find out that you can ride and you will wonder why it seemed so hard at first." --Keith Devlin.
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Greg Hamel profile image
Greg Hamel profile image
10/10 starsCompleted
  • 116 reviews
  • 107 completed
3 years, 5 months ago
Introduction to Mathematical Thinking is a great course that covers several topics that are often not covered in high school math including proofs, logic, quantifiers and beginning real analysis. The professor does a good job engaging students with material that is quite dense, with a lot face time, encouragement and walkthroughs of solutions and proofs. I didn't anticipate actually completing the entire course when I signed up; I did mainly because the professor is so good. The course also includes some interesting supplementary material about the pros and cons of MOOCs.
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Miguel Vargas profile image
Miguel Vargas profile image
9/10 starsCompleted
  • 4 reviews
  • 4 completed
3 years, 4 months ago
In general, I really liked this course. You need to take some time to complete assignments and problem sets. I would like to have a little help or perhaps some extra material, but it is no a problem at all. I learnt some aspects and concepts that I didn't understand when I take a similar class at the university. By the way, Keith Devlin is extremely organize.
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David Towles profile image
David Towles profile image
10/10 starsCompleted
  • 1 review
  • 1 completed
3 years, 5 months ago
This class renewed my passion for math. It is an excellent introduction to college level mathematical thinking, with an emphasis on reading, writing and working through proofs. I wish I would have taken this class years ago before I struggled through real analysis. Including all of the classes I took in college, this is one of my top 5 favorites.
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Margie Christensen profile image
Margie Christensen profile image
10/10 starsCompleted
  • 1 review
  • 1 completed
3 years, 10 months ago
This course has been one of the greatest learning experiences of my life. It had been over 40 years since I had taken a math class, and although I earned a teaching certificate with a math minor, I didn't learn to think mathematically. I wanted to learn how to think and write proofs. A great learning experience comes with a price, however, and that price included frustration as I wrestled with topics I hadn't learned previously, and problem set scores that got lower every week. The lectures are stimulating and clear, and Dr. Devlin has a unique teaching style and ability to connect with students through video. When I sat down to write the final exam, I was surprised and excited to find that somewhere among the frustration and discouragement I had actually gained the ability to write a mathematical proof! As Dr. Devlin says, it's like learning to ride a bike. It seems like you aren't making much progress, and then, suddenly, you can d... This course has been one of the greatest learning experiences of my life. It had been over 40 years since I had taken a math class, and although I earned a teaching certificate with a math minor, I didn't learn to think mathematically. I wanted to learn how to think and write proofs. A great learning experience comes with a price, however, and that price included frustration as I wrestled with topics I hadn't learned previously, and problem set scores that got lower every week. The lectures are stimulating and clear, and Dr. Devlin has a unique teaching style and ability to connect with students through video. When I sat down to write the final exam, I was surprised and excited to find that somewhere among the frustration and discouragement I had actually gained the ability to write a mathematical proof! As Dr. Devlin says, it's like learning to ride a bike. It seems like you aren't making much progress, and then, suddenly, you can do it! Thank you, Dr. Devlin for a great course!
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Student profile image

Student

10/10 starsCompleted
3 years, 10 months ago
The course requires High School maths skill and commitment. The journey starts with Logical Statements and ends with Real analysis. In a way it traces the key developments in Mathematics in the last few centuries and reads like the "Modern History of Mathematics". Along the way you are encouraged to ponder over maths problems and learn to think like a Mathematician. Just felt the last part of the course can be better spaced as the concepts are a bit arcane.
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Amy Wilson profile image
Amy Wilson profile image
8/10 starsCompleted
  • 7 reviews
  • 4 completed
3 years, 10 months ago
I'm a software developer who studied discrete maths and semantics at university so I am not within the stated demographic of this course. I signed up because the reviews were great and I admired Professor Devlin's commitment to the pedagogical side of it, and also because the course's promotional material indicated that this course would address the huge difference in mindset between high school maths and university maths, and I was curious what that was since I didn't remember it (In retrospect I think this may be a US/UK concept and some other countries like New Zealand where I'm from must be doing better with a gradual transition on this front). I almost quit in the first couple of weeks as it became clear I was familiar with the material already, but then I read one of Professor Devlin's blog posts where he says that if the first week or so seems easy, it's only because you are not connecting with the material on the right level,... I'm a software developer who studied discrete maths and semantics at university so I am not within the stated demographic of this course. I signed up because the reviews were great and I admired Professor Devlin's commitment to the pedagogical side of it, and also because the course's promotional material indicated that this course would address the huge difference in mindset between high school maths and university maths, and I was curious what that was since I didn't remember it (In retrospect I think this may be a US/UK concept and some other countries like New Zealand where I'm from must be doing better with a gradual transition on this front). I almost quit in the first couple of weeks as it became clear I was familiar with the material already, but then I read one of Professor Devlin's blog posts where he says that if the first week or so seems easy, it's only because you are not connecting with the material on the right level, and you will find yourself lost by the middle of the course. Well that sounded like a challenge! So I stuck with it. In the last week or so with real analysis, there was some material that was new to me. Proof grading against a course rubric was the major component of this course (more so than in previous iterations), and I have to say that I found this a very frustrating experience (and not in the good way which is ultimately rewarding). The professor's grading often seemed fickle, docking points from a very clear proof for lack of clarity and reasons one moment and giving full marks to something very terse the next. I'm sure there were (mostly) good reasons for his choices, but they were not communicated in a way that allowed me to calibrate effectively. I ended up bombing on the practice exam gradings, even though my own exam got a good grade. This course is obviously very rewarding to many people so I gave it a good grade despite my own mixed experience. But for my money, for people with a solid maths background, I would recommend Calculus: Single Variable by Robert Ghrist over this course. It was more difficult and more fun.
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Student

10/10 starsCompleted
3 years, 10 months ago
I was used to applying given formulas to solve problems . Now I learnt to think of the various ways to solve a problem . Also I learnt to be more specific about statements, I did the Jo Boelers course and was motivated to do this one. The beginning was really interesting but towards the end , the topics were new and I had to struggle to grasp the ideas.. The best part was learning to grade proofs. Finally I got the hang of it , otrI think I have, only during the peer assessment period, Thanks Prof Devlin
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Student

10/10 starsCompleted
3 years, 10 months ago
The course was extremely engaging and compelling. I managed to follow it with almost no math literacy at all, and although (because?) it was challenging, it was fascinating! Prof. Devlin's lectures were fantastic.
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Lindsay Dunseith profile image
Lindsay Dunseith profile image
10/10 starsCompleted
  • 1 review
  • 1 completed
3 years, 10 months ago
This is a great course, accessible to students who have only school Mathematics but invaluable for teachers of Mathematics to improve their teaching. Keith Devlin is a wonderful teacher. Being taught by Dr. Devlin is a real joy. He is inspiring and challenging, he has a great sense of humour and at all times he is directly communicating to the learner. In the course videos one very soon forgets that this is a MOOC and it feels like being in a small class or workshop. His style is engaging and informal, while at the same time presenting rigorous mathematical material. His focus is on the learning process and he takes students through the material with an emphasis on learning itself, as much as learning new material. He, and the community TA’s are actively involved in the forums while at the same time encouraging students to participate in the forums and learn from each other. The problem sets are well paced, with exercises prior to th... This is a great course, accessible to students who have only school Mathematics but invaluable for teachers of Mathematics to improve their teaching. Keith Devlin is a wonderful teacher. Being taught by Dr. Devlin is a real joy. He is inspiring and challenging, he has a great sense of humour and at all times he is directly communicating to the learner. In the course videos one very soon forgets that this is a MOOC and it feels like being in a small class or workshop. His style is engaging and informal, while at the same time presenting rigorous mathematical material. His focus is on the learning process and he takes students through the material with an emphasis on learning itself, as much as learning new material. He, and the community TA’s are actively involved in the forums while at the same time encouraging students to participate in the forums and learn from each other. The problem sets are well paced, with exercises prior to the problem sets that allow students to discuss issues before working on the submitted problem sets. I really enjoyed doing this course and although the material was not too much of a problem for me (I am a teacher) I have learned a lot about teaching in this course and have now integrated some of Dr. Devlin’s style into my own teaching.
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Jim Humelsine profile image
Jim Humelsine profile image
10/10 starsCompleted
  • 7 reviews
  • 7 completed
3 years, 10 months ago
Most MOOCs focus upon learning. This MOOC focuses upon thinking. The learning MOOCs are great. I’ve learned a lot in them, but the mathematical thinking stretches one’s brain to the point of almost hurting. I was not a math major in college, but I had a lot a math related courses being a computer science major. I thought most of the course would be review for me. Most of the material was review; however, a large chunk of the course, especially the second half, is about proofs. I thought I knew what a proof was. Dr. Devlin shook my core beliefs. I’m still a bit shaky - and I was a student/TA for the course as well! This course will frustrate you. It will enlighten you. If you complete it, you will have a great feeling of accomplishment as well as a very solid foundation for additional mathematics … and thinking in general. This course offers behind-the-scene videos which I’ve not seen in other MOOCs. The first three-quarter of the vid... Most MOOCs focus upon learning. This MOOC focuses upon thinking. The learning MOOCs are great. I’ve learned a lot in them, but the mathematical thinking stretches one’s brain to the point of almost hurting. I was not a math major in college, but I had a lot a math related courses being a computer science major. I thought most of the course would be review for me. Most of the material was review; however, a large chunk of the course, especially the second half, is about proofs. I thought I knew what a proof was. Dr. Devlin shook my core beliefs. I’m still a bit shaky - and I was a student/TA for the course as well! This course will frustrate you. It will enlighten you. If you complete it, you will have a great feeling of accomplishment as well as a very solid foundation for additional mathematics … and thinking in general. This course offers behind-the-scene videos which I’ve not seen in other MOOCs. The first three-quarter of the videos consisted of a round table discussion with Dr. Devlin, a staff TA and a moderator. These short videos talked about MOOCs in general and how they are constructed. The final videos were presentations Dr. Devlin has made at Stanford, including lectures on the origins of numbers. We even get to see him shoot a cactus in the final video - it makes sense in the context of the video.
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Student

9/10 starsCompleted
3 years, 10 months ago
High school equivalent. The course gives lots to think about and encourages self formed study groups. It isn't as slick looking as so e others (but far better than yet others), but does give a "cosy" feel. The material is challenging. There is lots of good background information. I liked the challenge and Professor Devlin's style. I disliked the feeling of having to rush so e of the material as real life happened.
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Student

10/10 starsTaking Now
3 years, 10 months ago
I left high school almost 40 years ago with good grades for math but with a lot of unanswered questions and a feeling of uneasiness about it; Now in a ten-week course a lot of these questions have been answered! It was an elating experience, given by charismatic people who care deeply about their subject but also -funny to feel that in an online course- about students! It was my first online course and it has wetted my appetite.
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Karen Carlson profile image
Karen Carlson profile image
10/10 starsCompleted
  • 2 reviews
  • 1 completed
3 years, 10 months ago
I'm not a math person; this course was very difficult for me; and I got terrible scores in the second half; but in spite of that, I made progress, and, best of all, I'm looking forward to giving it another shot in the next cycle, something that's encouraged - and I'm inspired enough to do prep work in between so I can do better than I did this time. Terrific atmosphere on the message boards, great teacher communication, lots of support. Also lots of side talk on the method behind the madness, which I appreciate, just because it's interesting to me. It takes a lot to get me through a math class, and it was all here.
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Anna Fazendeiro profile image
Anna Fazendeiro profile image
9/10 starsTaking Now
  • 1 review
  • 0 completed
3 years, 10 months ago
The subject matter dictates that this course is rather small and cozy compared with other MOOCs. Prof. Devlin's cheerful countenance and his active participation in the discussion forums makes this course worthwhile for anyone who always wanted to brush up on logical skills and mathematical thinking. But be prepared to struggle if your high school maths is rusty - the course starts smoothly with some language analysis and then dives deeper and deeper into a forest of scary, abstract symbols. I loved this course and will probably take it again to work on the concepts I didn't really grasp well yet.
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Student

10/10 starsTaking Now
3 years, 10 months ago
This is a wonderful course and it will challenge and trouble you as you progress, but it is worth it! I recommend it for anyone interested in a chance to think outside the box and look at mathematics from a logical thought process instead of following the equations/rules. Prof Devlin has a terrific attitude and approach to students and mathematics. Note, it gets very tough near the end, but stick with it! It's very worth the effort.
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No one of consequence profile image
No one of consequence profile image
6/10 starsTaking Now
  • 30 reviews
  • 18 completed
3 years, 11 months ago
A reasonably solid introduction to advanced mathematical ideas. The instructor goes on and on about how it's not about getting answers but about how you think. Nevertheless the assignments do in fact require you to get answers, and at times not enough practice problems are covered in lecture to solidify the ideas. Nevertheless this could be a decent supplement to other courses in, say, discrete mathematics.
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Stephanie profile image
Stephanie profile image
10/10 starsCompleted
  • 1 review
  • 1 completed
3 years, 12 months ago
The first MOOC I finished was Prof. Keith Devlin's Introduction to Mathematical Thinking. I liked the idea of a course about thinking. I didn't want to absorb and then regurgitate information. I wanted to improve the way my brain performs. The first couple of lectures were reassuring. I was able to complete the homework (which was voluntary but is the real key to learning in this class). I understood the concepts explained in the lecture, and I did well on the multiple-choice quizzes. Everything was fantastic. The next few lectures were a bit of a jungle. I felt like I understood the lectures, except I had to play the video twice in some spots, and when I tackled the homework I'd initially complete maybe half of the answers. Then I'd watch the videos again, or use an answer from one question to help me figure out how to answer another question. When I ultimately finished the homework assignments, I felt triumph. I could feel myself l... The first MOOC I finished was Prof. Keith Devlin's Introduction to Mathematical Thinking. I liked the idea of a course about thinking. I didn't want to absorb and then regurgitate information. I wanted to improve the way my brain performs. The first couple of lectures were reassuring. I was able to complete the homework (which was voluntary but is the real key to learning in this class). I understood the concepts explained in the lecture, and I did well on the multiple-choice quizzes. Everything was fantastic. The next few lectures were a bit of a jungle. I felt like I understood the lectures, except I had to play the video twice in some spots, and when I tackled the homework I'd initially complete maybe half of the answers. Then I'd watch the videos again, or use an answer from one question to help me figure out how to answer another question. When I ultimately finished the homework assignments, I felt triumph. I could feel myself learning. This was why I was taking MOOCs! The next few lectures were a struggle. The course was getting harder, and people were dropping out. I started to see forum posts like, "Thank you for the class, see you next time." But I'd put in too much time and effort. We were getting deep into proof mechanics, which had bedeviled me since high school, and I wanted to learn this. I struggled through the homework and couldn't answer all of the questions, but I was able to succeed in the class from a scoring perspective, primarily because of the multiple-choice nature of the quizzes. I understood which proofs were and weren't valid -- a victory in itself. My brain was twisting itself in new ways, uncomfortably, like a traveling salesman who mistakenly joined Cirque du Soleil. Then came the final exam. It was peer graded and entirely focused on doing proofs from scratch. It was also a quantum leap from the multiple-choice quizzes I'd been completing, and from the homework I'd been struggling through and sort-of completing. I was in trouble. I considered trying to bs some answers. I decided that this would be pointless and would serve no one. No one was judging me here, except myself. It would take me at least 40 to 60 hours to struggle through this exam, and I did not have 40 to 60 hours available. I didn't turn in the exam. I decided that I could take the class again later, and get to the next layer of proof mastery then. I had already transformed the way my brain worked, and that was my goal all along. I mentally said farewell to my certificate of completion. Then I received one. With distinction. It seems my performance on the quizzes outweighed my non-performance on the exam. I was surprised and extremely happy, but I also felt that I wanted to return and try harder, certificate or no. It's almost like there should be two levels of this class: Level 1, the fundamentals, which I completed, and Level 2, the proof mastery, which in all fairness I did not (although I did learn how to analyze proofs). Regardless, I think this is one of the most useful, real-world applicable courses on Coursera or the entire Internet, and I would recommend it to anyone. I'm no longer afraid of a jumble of math symbols when I see them on a page. I can dive in, sort out the meaning, and understand the point the author is trying to make. Which is amazing. (An even more complete review is at http://changenexus.org)
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AJT P profile image
AJT P profile image
5/10 starsCompleted
  • 7 reviews
  • 7 completed
4 years, 1 month ago
I found this course quite dull. Professor Devlin wanted to make the experience "like he was sitting next to you looking at a proof together". It doesn't really work very well on Coursera. Some lecturers leave long pauses in their lectures........... and Professor Devlin is one of them. Long pauses make lots of sense in a physical lecture as it leaves time for thinking. Here's the thing though: Coursera has a pause button. If I have a "Woah!" moment, I'll hit pause or rewind. Of course, I could watch these lectures on high speed, but I don't want the words to be faster - I just want less ......... - not more............. - less................ redundancy .................... and verbal................ whitespace.................. OK.................... what's.................... next.............? It's not just the pauses either. Professor Devlin doesn't seem relaxed in front of a camera. There's a fixed smile that never seems to make... I found this course quite dull. Professor Devlin wanted to make the experience "like he was sitting next to you looking at a proof together". It doesn't really work very well on Coursera. Some lecturers leave long pauses in their lectures........... and Professor Devlin is one of them. Long pauses make lots of sense in a physical lecture as it leaves time for thinking. Here's the thing though: Coursera has a pause button. If I have a "Woah!" moment, I'll hit pause or rewind. Of course, I could watch these lectures on high speed, but I don't want the words to be faster - I just want less ......... - not more............. - less................ redundancy .................... and verbal................ whitespace.................. OK.................... what's.................... next.............? It's not just the pauses either. Professor Devlin doesn't seem relaxed in front of a camera. There's a fixed smile that never seems to make it to the eyes making me feel that he's finding it all a bit dull too - like he's having to make small-talk at a party his missus has dragged him to. The assignments aren't terribly interesting either. In the last couple of weeks you're asked to submit proofs for given propositions which are peer reviewed. At least that's something different. Professor Devlin does talk about the challenges of working with MOOCs in supplementary videos. I just don't think his team found the right solution to these challenges. Perhaps they should look at how others have tackled this problem? It's not a bad course though. It's useful stuff and the delivery probably works really well in the physical world - it just feels pretty clunky for Coursera.
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Michael (Mickey) Hegarty profile image
Michael (Mickey) Hegarty profile image
10/10 starsCompleted
  • 4 reviews
  • 4 completed
3 years, 12 months ago
Took the first session of this course in Fall 2012. Bottom line, this Stanford course is fast paced and packed with information. However, Professor Devlin is a great choice to take you through it. Take the Man's course and you may well discover a new way of thinking, Alternatively, if your previous mathematics education was lacking or left you with a sincere dislike of mathematics, take this course and be amazed!.
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deicidereigns profile image
deicidereigns profile image
7/10 starsCompleted
  • 16 reviews
  • 16 completed
4 years, 4 months ago
As much as the professor tried to emphasise being clear about thoughts and ideas, I found many of his ideas unclear. In other words, he wasn't consistent with his usage. He tries to gives examples, be clear, and break things down, but then at other times he doesn't (or if he is, he isn't doing it very well). This inconsistency lost me more than a few times. I had to rewind several videos to try and untangle what he was trying to say, what assumptions he was making, etc. The most difficult sections I found to be the middle lectures about proofs. For example, at one time he said that there aren't exact 'proof' formulas you can use, but then later will say "and since I am using so-and-so type of proof, I need to do this." Things like this just compound. He could do a much better job at first outlining the various proof types, moving more in depth into the structure(s) of each, then finally broadening each type of proof. Another annoying... As much as the professor tried to emphasise being clear about thoughts and ideas, I found many of his ideas unclear. In other words, he wasn't consistent with his usage. He tries to gives examples, be clear, and break things down, but then at other times he doesn't (or if he is, he isn't doing it very well). This inconsistency lost me more than a few times. I had to rewind several videos to try and untangle what he was trying to say, what assumptions he was making, etc. The most difficult sections I found to be the middle lectures about proofs. For example, at one time he said that there aren't exact 'proof' formulas you can use, but then later will say "and since I am using so-and-so type of proof, I need to do this." Things like this just compound. He could do a much better job at first outlining the various proof types, moving more in depth into the structure(s) of each, then finally broadening each type of proof. Another annoying part is that the week's lectures are only released half-way through the week with the assignment due less than a week later. It gives a shortened time to study and can be a problem for the many different schedules that people have. He should release all the material at the beginning of the week or extend the assignment due dates. Also, people can make their own decisions about how to study once the material is out, the professor shouldn't be making these decisions for them. The course is admirable in scope, but there are still a lot of problems. It's like a snake eating its own tail with all the pedagogy ideas their trying to implement. Because of this, the course could have been a medium difficulty, but turns unnecessarily into a hard one. However, the course did have one of the best Certificate of Completions, describing in great detail what we studied in the course. I'd like to contrast this to other courses, which often give a vague description on the Certificate of Completion and usually not useful if you want to present it to other people so they can see what you did in the course.
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