Using the wiki

[James Crook]

If you haven't yet, please add your name to the list on:

http://onlinemathcircle.com/wiki/index.php?title=L2_Study_Group

We're going to start using the wiki more as it is better for equations.

--James.

[Shri Ganeshram]

Hi James,

I'm actually interested in learning Differential Equations; there are a few motivations for this:

 

1. Diff Eq is really useful in physics and optimization and will open me up to possibilities there, given my decent linear algebra background (a university course in it).
2. I can test out of Diff Eq at the end of the summer for MIT, and the testing situation is more leniant when you do it prior to obtaining 2nd year status (which I will hopefully obtain at the end of my first semester).
3. I'm going to MIT to study math, and I would like to be one of the top students--studying early is a great way to do this.

 

I think OCW and the book that I would use at MIT is the best route for this.

I also have a set of problems that I will need to turn in if I want to get credit, and the set is extremely large, containing a couple of problems from each section of the book.

 

-Shri

[James Crook]

Shri,

I'd be glad to help you achieve this.

I'd like you to start a page on the wiki about pre-requisites for the DE course.  As you progress through the course, make a note on the wiki page when pre-requisite techniques/knowledge are used.  

The idea is that the wiki page will allow someone else who also wanted to learn DEs to check out if they are ready.  They could check their knowledge, and practice examples of those topics.  Then when they came to the actual course content they could focus just on what was new.  

For example, before starting on the DE course someone should:

Know how to use l'Hopital's rule.

Know how to sum standard infinite sums like 1+x+x^2+x^3+x^4+....  and the range of x for which the sum is valid.

Be fluent with partial fractions.

Be fluent with the chain rule.

... quite a lot more.

Ideally for each of these topics that you add as you go along, I'd like two simple diagnostic questions too - how you'd check that someone really does know these topics.  I'm not asking for contest questions.  I'm asking for diagnostic questions - so it should be easy to make up some questions like that.  It will be mainly about the LaTeX - which you need to have anyway.

Taking on the DE course looks a very good challenge to me, and will be tremendously helpful in your first year at MIT.

--James.

[Shri Ganeshram]

How is this so far James, http://onlinemathcircle.com/wiki/index.php?title=Differential_equations#Prerequisites ?

And I really want to thank you for all the help you've been giving me and OMC; I've become so much better at LaTeX, helping others, and independently studying because of it.

[James Crook]

Shri, that's perfect.  Exactly what I hoped for.

You will add more pre-requisites like the ones there when you spot them being needed in the course.

Much later we can convert these to a diagnostic test where we do not say what principle is used and list the questions in no particular order.  A student can work through, note the items that they find trickier or can't do, and then look up the rule or principle they need to learn or practice.

--James.

[Shri Ganeshram]

That sounds great James!
I should be getting the book shortly. For the time being, I will use Youtube/Online Materials/OCW to start nailing the basics in.

-Shri

[James Crook]

I'd like a few more people from this group starting to get up to speed on using LaTeX to write mathematical formulas on the wiki.

I've created a page for the mathematical facts we've had so far as part of 'Task 1'.

http://onlinemathcircle.com/wiki/index.php?title=L2_Task_1

I'd like to see some of those mathematical facts that we've had in e-mails now appearing on the wiki too.

You are very welcome to write up a mathematical fact someone else provided.  It's a wiki and wikis are collaborative, so other people may edit and improve something you wrote.

If someone does a good write up of Abe's fact about triangles and circles, I'll create the diagram to go with it.

I'm giving 4 days for seeing some progress on this task - not just about the triangles and circles - but for all the facts we had for task 1.

--James.

[James Crook]

2 days left on this task.

I've seen almost no progress on this.  Abe's fact is now on the wiki, but without a proof.  That's not encouraging me to put the time in to make a nice diagram to go with it.  What you get out of this program is related to what you put into it.

I've put the http://onlinemathcircle.com/wiki/index.php?title=Square_wave_from_sines on the wiki.  I'd like to see more of our facts on the wiki and more LaTeX.  

http://onlinemathcircle.com/wiki/index.php?title=L2_Task_1

--James

[Shri Ganeshram]

Guys, I really need one of you all to step in for this. I'm actually in a tight situation at the moment (I'm TA'ing 2 3-hour classes a day, holding office hours for these classes, and RA'ing a group of 8th/9th graders, on top of running OMCIP, mentoring for OMCIP, writing lecture notes, and working on an MIT diff eq course). It should be a little easier once I'm relieved of my temporary RA duties on Friday.
-Shri

[Jonathan Joo]

Is it okay that I am not familiar with LaTeX, or is that something that I should learn as soon as possible?

-Jonathan

[James Crook]

Yes it's OK to post things on wiki already, even without knowing LaTeX.

You will need to learn LaTeX, but you can do that by looking at similar equations in the wiki.  For example when you see

\cdots

in the LaTeX, you'll see a row of dots in the equation.

For now, other people (probably me) will fix up equations that you put in the wiki.  You can and should then take a look later and see what the right LaTeX was.

--James.