## Sunday, January 15, 2012

### Useful Websites for School

I've often said that I don't think I could do well in school in an age without the internet.  The bulk of my time spent learning is spent on various websites increasing my understanding of concepts.  While random sites found via googling are often useful, I've compiled a list of websites I go to time and time again.  I've mentioned some of these before, and some are quite well known, so you may have already visited them.

I've mentioned Wolfram Alpha a few times here, but it really deserves its own post.  If you've never used it before, it is a "computational engine".  Similar to a search engine, but aiming to answer questions directly rather than simply via links.  While it can be used for any subject, I pretty much only use it for math.
http://www.wolframalpha.com/input/?i=integral+of+sin+x+2x^3
http://www.wolframalpha.com/input/?i=sum+of+1%2F2^n+from+1+to+infinity
http://www.wolframalpha.com/input/?i=area+between+y%3D|x|+and+y%3Dx^2-6
http://www.wolframalpha.com/input/?i={{45%2C+-34%2C+120%2C+1}%2C+{-14%2C+25%2C+-67%2C+0}%2C+{12%2C+75%2C+-72%2C+1}%2C+{1%2C+42%2C+83%2C+82}}

While there are other systems that can solve math like this, Wolfram Alpha stands out two ways.  First is that it does a very good job of interpreting input correctly.  If you've ever tried to use a program like Maple or a graphing calculator to solve things, you know it gets pretty annoying to input what you actually want.  Even if you think you have the input right you don't know for sure.  Wolfram Alpha shows what it thinks you've inputted so you know for sure if it is correct.  The second thing is the show steps button.  With a simple click Wolfram Alpha will show you how it solved the problem.  This doesn't always help, as sometimes it uses a very labor intensive brute force method, but helps quite often.  Note the random and examples buttons near the search box if you want to see examples of what kinds of things it can do.

I've written about Khan Academy before, but it is really an amazing site.  It consists of 10 minute videos on a wide range of science and math subjects, including: arithmetic, differential equations, calculus, bio, chem, physics, and economics.  The videos are made by Sal Khan, an electrical engineer who went to MIT and worked as a hedge fund analyst.  He is amazing at explaining things in an intuitive way.  I highly recomend you just go and watch a few videos.

MIT OCW
MIT Open Courseware is a site where MIT posts videos of their lectures.  The site has been around for over a decade now, and they probably have nearly the entire course catalog on there, usually with several different lecturers.  They also have the HW, tests, and answer keys.  In other words you can get an entire MIT education minus the piece of paper at the end for free.  While I don't like these videos as much as Khan's, you can't ignore the extra rigor and breadth in the MIT videos.  If you are looking for some to sample, here is the first in an excellent 5 part series on an overview of calculus.  Here's a great Physics I video.

Ptable.com
A dynamic periodic table.  I know if you're not currently in a chemistry class you will probably want to skip over this, but I recommend you check it out.  It is a very well done site, and presents a huge range of data in a amazingly simple way.  Most the fun stuff is in the properties tab, so click over to that one.  Then click the various properties (like melting point, or date of discovery) and examine how various properties vary with location in the periodic table.

Physics Forums
The Physics Forums are a great site to waste hours at reading through posts.  They are centered mainly around physics, but have forums for math, and other sciences as well.  Even if you are not interested in physics there are often some very interesting threads on there.  They also have homework help forums where you can post problems and they will attempt to guide you through it.

Cramster
Cramster is very useful site, that I probably would have put higher in this list if not for the fact that it's pretty exclusively useful for people actually taking classes.  It has worked out solutions for the odd problems for most textbooks.  The answers are generally a lot better than the ones in solutions manuals.  The have even number solutions if you are willing to pay something absurd like \$100 a year.

Paper Rater
I've written about Paper Rater in greater detail before, so I'll be brief here.  Essentially, Paper Rater is an enhanced grammar checker.  You enter text and it goes through and gives you stats and possible issues with it.

Graphing Calculator