Introduction to Mathematical Thinking
Provided by:
Provided by:
Course Details
Cost
FREE
Upcoming Schedule
- On demand
Course Provider
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
Course Description
Learn how to think the way mathematicians do - a powerful cognitive process developed over thousands of years.
Sort By
- 2 reviews
- 2 completed
5 years, 6 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.
- 1 review
- 0 completed
1 year, 3 months 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.
- 6 reviews
- 4 completed
1 year, 3 months 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.
- 26 reviews
- 24 completed
2 years, 3 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 .
- 12 reviews
- 11 completed
2 years, 6 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.
Student
10/10 starsCompleted
2 years, 6 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.
- 5 reviews
- 5 completed
2 years, 7 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.
Student
6/10 stars
2 years, 8 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.
- 1 review
- 1 completed
2 years, 10 months 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.
- 1 review
- 1 completed
4 years, 2 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.
- 116 reviews
- 107 completed
4 years, 2 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.
- 4 reviews
- 4 completed
4 years, 1 month 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.
- 1 review
- 1 completed
4 years, 2 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.
- 1 review
- 1 completed
4 years, 7 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!
Student
10/10 starsCompleted
4 years, 7 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.
- 7 reviews
- 4 completed
4 years, 7 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.
Student
10/10 starsCompleted
4 years, 7 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
- 1 review
- 1 completed
4 years, 7 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.
- 7 reviews
- 7 completed
4 years, 7 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.
Student
9/10 starsCompleted
4 years, 7 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.
Student
10/10 starsTaking Now
4 years, 7 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.
- 2 reviews
- 1 completed
4 years, 7 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.
- 1 review
- 0 completed
4 years, 7 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.
Student
10/10 starsTaking Now
4 years, 7 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.
- 30 reviews
- 18 completed
4 years, 8 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.
- 1 review
- 1 completed
4 years, 9 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)
- 7 reviews
- 7 completed
4 years, 10 months 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.
- 4 reviews
- 4 completed
4 years, 9 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!.
- 16 reviews
- 16 completed
5 years, 1 month 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.