Introduction to Mathematical Thinking @ FIX University Cultural Campus

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Introduction to Mathematical Thinking

Keith Devlin

Learn how to think the way mathematicians do - a powerful cognitive process developed over thousands of years.

Announcements

Tutorial Sessions

The next set of Tutorial Session videos will be released at 10:00AM PDT on Wednesday October10. Note that the tutorial sessions are more than mere presentations of solutions to the previous week's assignments and problem session. They are really lectures based on problems that you have (I hope) already attempted. You can expect to expand your knowledge of the course material beyond the Monday and Friday lectures. Not all questions on the assignments sheets and problem set are considered in the tutorial session. Whereas the lectures were all recorded before the course started, I record the tutorials the day before they are posted, so they can reflect issues raised in the forums.

-- KD

Tue 9 Oct 2012 9:00:00 PM PDT

Problem Set 3

I added an explanatory clause to Question 5. If you already submitted your solution, you might want to go back and check what you did before the deadline. See this forum thread for details.

Sun 7 Oct 2012 10:23:00 AM PDT

Kindle edition of textbook re-released

The initial problem with Kindle edition of the course companion book has now been resolved, and the bookhas been re-released by Amazon. I just viewed it online on Amazon's Kindle Fire emulator, and it looks great, as does a copy I have running on my Mac Kindle app. Anyone who already purchased a copy of the mangled file that was available for a few hours at the end of last week should find their copy automatically replaced by the correct file within a few days. (I have a direct contact at Kindle to approach if there are further problems; they are taking steps to resolve this.)

-- KD

Sat 6 Oct 2012 6:00:00 PM PDT

Lecture 6 - first in-lecture quiz

I just noticed that in my explanation of the last part of the first in-lecture quiz, at one point I say "true" when I meant "false". By now you may be sufficiently comfortable with this material that you did not even notice. (I did not spot it when I went through the video during editing! I heard what I was expecting to hear, not what I actually heard.) I actually repeat the point, and the second time I use the right word. But when I get chance, I'll fix that video.

-- KD

Fri 5 Oct 2012 11:24:00 AM PDT

Kindle edition of textbook - System glitch at Amazon

If you are thinking of buying the Kindle version of the companion book but have not done so, please hold off for a while. The version of the Kindle edition I have (which was manually created by Kindle engineers) looks as good as any e-book I've seen. But apparently something got screwed up in the Kindle system when the file was uploaded for sale. The folks at Kindle are working on correcting it as a matter of urgency. If you already bought a copy, I am sure you will be able to get the new version at no extra charge when they have resolved the issue. Sorry about that.

-- KD

Fri 5 Oct 2012 9:38:00 AM PDT

Kindle edition of the textbook

The engineers at Kindle have just competed the digital version of the companion book. I have a copy and it looks great! It is now officially available, though it may take a few hours to appear on the various Amazon websites around the world. Sorry this was not available sooner.

Thu 4 Oct 2012 12:37:00 PM PDT

Looper

Clearly, Looper would have benefitted from taking this course!

Thu 4 Oct 2012 11:30:00 AM PDT

Course philosophy

From some of the forum discussions, it’s clear that some of you are putting way too much emphasis on the lectures. They are not lessons in the traditional sense of an instructional session that has been lesson-planned. They simply provide an example of a professional engaged in mathematical thinking. Other than editing out pauses while I think, and speeding up some of the handwriting, what you see is what happened when I sat down at my desk. There are errors and slips. Some I noticed during video editing, others are being discovered by some of you. That’s how mathematics gets done. It's a messy, error-prone, human endeavor. (Admittedly, since I’ve given this course many times before, and wrote the companion book just a few months ago, it might look like I’m just reading from the book, but that’s not the case.)

So please don’t pore over the videos repeatedly looking for rules or for answers. They are to set the agenda, provide some key ideas, give an example of one individual thinking mathematically (in real time), and (arguably more importantly) to provoke reflection and discussion.

In other words, the onus is on the student to figure things out. In putting together this course, I set out to try to create over the Internet the kind of experience you’d get if you were sitting next to me in my office at Stanford, or next to any other professional mathematician. (To be sure, not everyone likes this approach, but it’s pretty common in university education.)

The core learning mechanisms in the course are working on the assignments and the associated discussions, both on the forums and in the various groups people have created.

There’s pedagogic research to support this “be less helpful” approach, even at high school level, let alone university. If you are curious about the course philosophy, check out my recent MOOCtalk blog, where I reference some of that research.

Maybe it helps to know this, maybe not. Either way, I hope you stick with the course.

-- KD

Mon 1 Oct 2012 5:30:00 PM PDT

Welcome to Week Three

We are now a 60K MOOC. Some late registrations last week pushed the total enrollment to 61,086. While many students simply watch the videos (in many cases because busy schedules don't leave them enough time to really get involved), to date there have been 260,466 completions of the live, in-lecture quizzes. That's a lot of learning!

This week we complete our analysis of language. To get a sense of how far we've come, the last question in Assignment 6 (Friday) deals with one of the most significant applications of linguistic precision in the entire history of mathematics. It took mathematicians over two thousand years to make that journey the first time.

-- KD

Mon 1 Oct 2012 6:00:00 AM PDT

Grading Update

Hi Everyone,

The grading problems for late assignments have been fixed! Let us know if you still have problems with your Problem Set 1 grades, but I believe there should not be any more issues.

Problem Set 2 has now been up for a couple of days, and many of you have already completed it. Do not be alarmed if you do not get a score right away. A Coursera-wide update caused Problem Set 1 answers and scores to be available right away, but that was not how we set things up originally. Making the scores and answers available right away certainly can lead to good forum conversations (as our many discussions of Alice demonstrate), but it also means that students have a very high chance of coming across "spoilers" before they do the Problem Set. Thus for Problem Set 2, and all future Problem Sets, you won't get your score or the answers until after the deadline.

Hope you're having a good weekend, and keep up the good work!

- Paul

Sat 29 Sep 2012 8:11:00 PM PDT

Puzzled about Alice?

If you had trouble with the two questions about Alice in Problem Set 1, make sure to "attend" the tutorial session just released, where I explain some of the problems in Assignments 1 and 2 and in Problem Set 1.

If you are not following the forums closely, do make sure to check out this thread, which is a superb example of how MOOC learning should occur.

-- KD

Wed 26 Sep 2012 10:01:00 AM PDT

Late Submission Bug

Currently the system is deducting 20% for late submissions instead of 10%. We're working on fixing that, and once we do we'll regrade the quizzes so that everyone gets their appropriate grade.

UPDATE: It seems that the bug has been resolved. Let us know in the forums if you have any further late submission issues.

Wed 26 Sep 2012 8:47:00 AM PDT

Assignment 3

Assignment 3 is now available.

Mon 24 Sep 2012 1:05:00 PM PDT

First Problem Set released

Look top right. This is the first graded assignment. At the end of Lecture 2, I say that Problem Sets are due in by noon the following Wednesday. After I recorded that, we had to change the schedule to require submission by the Tuesday at noon. Sorry about that.
-- KD

Fri 21 Sep 2012 1:48:00 PM PDT

Assignments: #2 just released

Assignment 2 (from Lecture 2) can now be found on the "Course assignments" page. (See the left-hand navigation column.) Every lecture has an associated assignment, released at noon that day. Please look at the "Course assignments" page after each lecture, to find its assignment.

Remember, although the assignments are not graded, working on them (coupled with the forum discussions they generate) forms the central part of this course. The lectures play a minor role. No one ever learned to think mathematically by sitting in a lecture, even less by watching one on a screen. The lectures merely set the agenda, give a bit of context and motivation, and provide some examples of mathematical thinking. Recognizing this fact is a key to success (or even survival) at university-level mathematics.
-- KD

Fri 21 Sep 2012 12:00:00 PM PDT

Community TAs total tops 900

Thanks to over 900 of you who have signed up as Community TAs. That's far more than I hoped for, and should go a long way to ensure the course is a success for many of you. Back in early May when I began planning this MOOC, I realized that I had to find a way to ensure that a student with a problem could get it speedily -- and correctly -- answered. In a campus class of 25 students, they can come to me. But with over 56,000 students (the latest count), that's not possible! So I put out a plea for help on the blogosphere. My hope was that we could build up a Wikipedia-like online community of volunteers. With over 900 volunteering already, it looks like there will be one TA for every 50 students. As a result, if you post a question on the forum, the chances are good that you'll get a knowledgable response. Learning math is hard. Thank you all of you who have volunteered to help others turn that into "hard-but-possible".
-- KD

Thu 20 Sep 2012 6:17:00 AM PDT

Kindle edition of the textbook

The good folks at Kindle have confirmed that they can take the manuscript of the (optional) textbook and produce a genuine Kindle edition that will play on all Kindle platforms. (The version generated by their automatic conversion algorithm, which I tried originally, could not handle the embedded mathematics.) This will require some technical expertise, and will take some time, so the Kindle edition likely won't be available in time to be of help for this iteration of the course, unfortunately. However, I think it helped persuade them to offer to do this that many of you had asked for a Kindle edition. We are all of us pioneers in this new medium, and we clearly need one another. Thanks for making your views known.
-- KD

Wed 19 Sep 2012 6:21:00 PM PDT

First course assignment

The assignment from Lecture 1 can be found on the "Course assignments" page. (See the left-hand navigation column.) Unfortunately, the Coursera platform cannot currently display the assignments in the Upcoming Items box on the Home Page, so you should look at the "Course assignments" page after each lecture, to find the associated assignment.
-- KD

Wed 19 Sep 2012 10:15:00 AM PDT

Set Theory supplement

In response to comments on the forum, I've updated the Set Theory supplement to correct a couple of typos and to add a longer preamble clarifying when you need this material and how you might best use the supplement. As several students commented, the supplement assumes familiarity with material that is covered in the first part of the course, and hence can appear daunting if you have not previously seen this stuff (or have long forgotten it). We won't really use much set theory until the final week of lectures, so there is plenty of time to become familiar with it. Thanks for all those students who helped others with the exercises. Collaborative group work is what this course is all about, and it was great for me, as instructor, to observe it in action!
-- KD

Tue 18 Sep 2012 6:21:00 AM PDT

Community TA identification

Thanks to all who volunteered to be Community Teaching Assistants. Having Community TAs is a new feature that Coursera is implementing for the first time for our course. At this stage, there is some manual work required to take the volunteers' enrollment names from the Course Survey and tag them so that their status as Community TAs is indicated when they post to the forum discussions. It will thus be some days before those identifications will appear. In the meantime, if you have not yet completed the survey, please do so. It is not a course requirement, but the more feedback we get, the better our chances of making improvements to the course in future years, and, more generally, increasing our understanding of how people learn math.

Mon 17 Sep 2012 9:30:00 PM PDT

Course survey

MOOCs are very new. I think this is the first time anyone has given a mathematics transition course in MOOC format. Because the focus is on the difficult transition from high school math to university-level mathematics, which is very different, I am working with two researchers from Stanford's School of Education, who want to find out what and how people learn in this kind of environment, and in particular how their attitudes to mathematics affect their performance and how those attitudes change as a result of taking a course such as this. This is very non-invasive research. All we ask you to do is fill out an online survey now, at the start of the course, and then again at the end. It should not take more than a few minutes. One benefit to me, as instructor, is that the results we get can help me improve the course when I give it again next year. You will find the survey here. (Please ignore the stated due date; that's a Coursera system default that they have not had chance to fix. We'd like you to complete the questionnaire right away.) One of the questions asks you if you are willing to serve as a "Community TA". Please check out what this entails in the appropriate section of the course website. Many thanks.
-- KD (for me, Molly, and Paul)

Sat 15 Sep 2012 10:30:00 PM PDT

What is a mathematics transition course?

This course is an example of what is generally called a "mathematics transition course," designed to assist students make the transition -- which most of us find difficult -- from high school math to university-level mathematics. Many colleges and universities offer such a course to the incoming class. There is an informative recent blog about such courses here.
Several of the comments are from instructors who have given such courses (as did the blogger - at Harvard). Those comments make it particularly interesting. Definitely worth a read. For one thing, when you reach the stage of thinking you are totally lost (a very common reaction), you will know that you are not at all alone -- it's part of making the transition!
Incidentally, if you are wondering what "mathematical thinking" is, check out this article.
-- KD

Sat 15 Sep 2012 10:15:00 PM PDT

Meet the Team (two short videos)

Three weeks before the course launch date, I went into the campus TV studio with my two course assistants to record a short video to introduce you to the two people who will be working hard to keep the course running smoothly. (You'll see a lot of me, but Paul and Molly will be working behind the scenes, though you are likely to see Paul's contributions to the forum discussions.) You'll find the seven minute video we recorded in the Videos section of the course website (which is where you will also find the lectures and solutions to some of the assignments, when they are released).
During the course of recording that introduction, the three of us got into a discussion about our backgrounds, our motives in giving this MOOC, and our views on mathematics, science, education, and our expectations for the MOOC format. The camera was rolling all the time, so we were able to select a few parts of that discussion. This video is not a planned part of the course, but we felt it might interest you to know more about our thinking as we designed this course. (You can also find out about my own experiences in putting this MOOC together from my blog MOOCtalk.org.)
You can find out more about Molly, Paul, and myself in the About Us section of the course website.
--KD

Sat 15 Sep 2012 10:00:00 PM PDT

Welcome!

Welcome to the course on Mathematical Thinking. This page is where you will find notifications of upcoming assignments, submission deadlines, course updates, and messages from me and my TAs, Paul and Molly.
-- KD

Sat 15 Sep 2012 9:45:00 PM PDT