Monday, July 21, 2014

I found this useful: What Is Complex Analysis?

Course Guidance, Johns Hopkins University Math Department - click for "What is Linear Algebra" etc
Because seeing the forest sometimes helps you see the trees.
I spent a couple of hours on such summaries and also on several related wikipedia entries (the field, its applications, its origins) as well as mathworld/mathematica entries.

Getting a panoramic scope of the math helps.  In this case, the histories and human stories - Euler, Gauss, Riemann, ...; the connections to the future via modern physics research and prominent math research prizes, or to popularly-used industry and engineering solutions (the present), or merely as artifacts (the past) - all of these add colour and motivate the learner to slog through the textbook exposition and exercises if necessary, or to skip and simply enjoy the knowledge of the forest without a visit to the trees. 

I feel good about my short investment in getting these varied overviews on Complex Analysis.
May it help me turn the corner on this little subject, for which it's strangely true that although I've worked several examples and taken a couple of courses in it, I just don't (didn't?) "really" understand it beyond the Cauchy-Riemann equations.  This is not the same as saying that I haven't solved questions correctly; it's just that I then forget how, which proves that I never really believed the solution paradigm maybe?
Complex Variables and related webpages - This was breakfast

And as for the strategy of grazing material about a topic in a general-interest fashion, I will reuse that and see how it helps me tackle Tensors, and Multivariable Calculus, and theories of PDEs, where I still have sizeable gaps in understanding, largest of all with Tensors I think.   

Friday, June 13, 2014

Mathematics being this romantic thing


Perelman, who I find adorable by the way, is described in this documentary - in Russian, with English subtitles - as a national hero.
I find the movie deeply poetic; so musical in fact that I want to learn mathematics or - who knows - do mathematics.  I'm just not sure how to proceed.

A butterfly flutter from afar reaches the ear to whisper and stir the belly like a song wake up drive yo! 

Tuesday, March 25, 2014

Nice Little Mathematics Movie

In this series of factorization diagrams, prime numbers usually make a single circle, while other numbers are grouped by their factors into colourful patterns.
Enjoy
http://www.datapointed.net/visualizations/math/factorization/animated-diagrams/
which I found through StudyGeek (web, twitter, facebook, and a really cool tumblr feed of math-related images
UPDATE : or was it @PlusMathsOrg ?  Or @MAAnow ?  

Sunday, February 9, 2014

Garry Kasparov was here

Along with Bill (Clinton) and Rafa (Nadal), Kasparov is one of the top five "famous" people I'll love to share a long lunch with sometime.  It looks like I just missed a fabulous chance to do so as he was in my country, my city, and in fact my alma-mater - the great Queen's College - last week.
Dang, Queen's College, why didn't you invite me? 
What I love most about Kasparov is how he turned from
supreme mastery of one extremely well-defined field (chess)
to
an application in a much murkier but more consequential problem (liberty and liberalization.)

Like him, I also think that life imitates math, life imitates sport, life imitates chess, life imitates art, and that it is good for the world's best minds to have the balls courage to attempt the world's biggest fixes (how to achieve happiness, eternal life, food/water, health, peace, class, etc)

I think the big lessons from the Kasparov switch are: 1. you have to know when to retire, that is, when to shift focus 2. sometimes try applying the best math to the biggest problems.

Sunday, November 24, 2013

You can teach Calculus without really needing to teach

And you can learn Calculus in about ten hours a week. 

Check out these online courses: Precalculus, Calculus One, and Single-Variable Calculus.  Each is about three months (one semester) long, available on Coursera for FREE, and includes weekly video lessons, peer-interactions, testing and evaluation, and a certificate of completion.  I'll tell you when I evaluate other sources of online course materials: udemy, edX, and so on. 

If I was assigned to teach a large Calculus class, I would probably just reuse these resources as it would be hard to do better than some of the online courses I've tried.  Even for a small class, I might embed this material, as in modularity, as in a course within a course
http://xinvogue.blogspot.com/2013/10/course-within-course.html
From Calculus Single Variable on Coursera
 When using these online courses or MOOCs as they are now called, the teacher is still useful.  The teacher needs to study several and select which resources to use, and also to monitor and enhance the experience where possible. 

For more elementary mathematics, like primary and secondary school (but also up to Calculus and hobby math), I like the quizzes at Khan Academy for math drill.  Khan also has extremely, extremely good video lessons. 

Monday, November 18, 2013