Giving math a shot (again).

[Dafe]

Hi,

I am a working mechanical engineer (Bachelor), and am trying to learn math (again).
My grades from virtually every math class I've taken are great, but I now know that's the case because my school was rubbish.

The last two months I've done a bit of math daily. I'm currently going through the linear algebra course using the video lectures, notes and book from mit ocw.
The course is far more demanding than the one I took several years ago.

My question is, how long do you guys spend going through such a course?
Do you re-read the book several times to make all the theory stick?

Up till now, I've read all the material, done all the problems that have solutions and done the first Quiz. I scored about 60% so there's still work to be done...
Before I give another Quiz a chance, I am re-reading some theory and might do a problem or two.

Is this a good way to go about it, or do you guys have some better suggestions?

Thanks.

 

[mrb]

Up till now, I've read all the material, done all the problems that have solutions and done the first Quiz. I scored about 60% so there's still work to be done...
Before I give another Quiz a chance, I am re-reading some theory and might do a problem or two.

Is this a good way to go about it, or do you guys have some better suggestions?

Do more than a problem or two.

 

[206PiruBlood]

Most of your math study time should probably be devoted to solving problems. How much time do you dedicate to this as apposed to video lectures, notes and books from MIT's OCW? It is easy to read notes or watch a lecture and think you understand, but until you can more or less solve problems without much effort, you haven't fully grasped the material.

 

[Dafe]

Hi,
thanks for the reply.

I spend most of my time doing problems as you suggest.
After I have done quite a few problems from the book, I do one exam from the MIT site.
I only watch the lectures once, after I have gone through the material on my own.

So it's basically; do problems until you puke, and then do some more :)

 

[vortmax]

i would disagree with that. Doing problems until you puke teaches you how to do those problems but doesn't do much to teach you the math. When you do a set of problems, you need to be able to look back over it and ask yourself, "Do I really know why I just did that".

One technique that helps me is to be overly verbose on a few problems. Write the solution out as if you were explaining it in a textbook or to a group of students. Draw graphs, figures, etc...anything it takes to visualize what is going on. If you apply a theorem, or identity, write it down and WHY you can and want to use it. At each step, ask yourself the question "Why did I actually do this?". If you cannot give yourself a solid explanation, then go look it up and figure out why/how you are using it.

 

[Dafe]

Hi vortmax,

I think you make some good points.
Sometimes it feels like I'm not really thinking while doing problems.
I'm trying to, as you say, step back and try to elaborate on the solution.
It does take a lot of time, but I hope it'll be worth it.

Anyone else with a different approach?

 

[Sankaku]

I'm currently going through the linear algebra course using the video lectures, notes and book from mit ocw.

Just a personal opinion, but I found the Strang videos really inconsistent. Some of the lectures were pure inspiration, but others were just random and frustrating. He jumped all over the place and stuttered when he lost track of where he was going.

I haven't had a chance to watch them, but there are several Linear Algebra video courses here:
http://www.uccs.edu/~math/vidarchive.html
Use
archive.php?type=valid
on the url when it asks for your registration.

They may provide a different approach...

Edit: I did notice that the ones marked "mathonline" use an annoying digital overhead, so I preferred the look of the older lectures.

 

[Dafe]

Thank you very much for that wonderful link Sankaku!
Yeah, Strang does look a bit confused from time to time, but I really like the way he teaches. His book is also very nice.

 

[lurflurf]

The Axler linear algebra book (which is better than Strang have a look) is one of the few books that suggest a reading speed. The rate suggested by Axler is one page per hour. That rate is also reasonable for other books, though more wordy books could be read a littele fast and more terse books a little slower. You should also solve about one problem per page read (not counting filling in arguments in reading, and simple exercises) at an approximate rate of one hour per problem. Thus to learn say two hundred pages of material should take about 600 hours. Another rule of thumb is to study a hundred hours per hourof exam. You could then study 600 hours on the assumption that what you are learning should be examined over six hours.
something like
200 hours reading primary source
100 hours reading secondary source
100 hours solving problems
50 hours outlining
35 hours of lecture
20 hourse of asking and answering questions
95 hours as needed

or just spend the amount of time that seems right

 

[Dafe]

Great post lurflurf!
I will get a copy of that book, thanks!

 

[Sankaku]

Another rule of thumb is to study a hundred hours per hourof exam.

Wow. I don't consider myself a particularly fast study - but that seems huge.

Taking the North American system:
If the usual "3 credit" course has a 3 hour exam and most people take 5 courses per 15 week term, that would be 100 hours of study time per week - over 14 hours per day. Seems a little overkill to me!

However, I don't think all exams are created equal so maybe you are thinking of the European system...