Thursday, February 27, 2014
Well Ordering Principle
The well ordering principle states that every non empty subset of positive numbers contains a least element. So a subset of all positive natural numbers has a least element. Here is a link explaining more:
Big Data
Big data sets are becoming increasingly more prevelant in today's world. We are constantly looking for new and better ways to analyze these data sets. New tactics and technology is being made to help improve this. By identifying patterns you can speed the process up. Here is a link to an article relating to this topic: http://www.sciencedaily.com/releases/2014/02/140218185128.htm
Sequences
Sequences are great but they can be very challenging at times. There are several formulas to learn and different types of sequences. There are geometric and arithmetic. There can also be infinite solutions. But, if you stick to the formulas and plug in the right numbers you can't go wrong. For arithmetic sequences. Here are the formulas:
Wednesday, February 19, 2014
Factorials
Today in Mathland we learned about sequences and factorial a. My favorite was the factorials! They are so neat. You take a number and multiply it with all the numbers that come before it. So if you have 4! you multiply 4x3x2x1. And you get 24. You can also divide and multiply factorials together. That's when it gets really fun. I can't wait for a quiz on factorials!
Here is an example of dividing and multiplying factorials.
Sum Formula
Today in Mathland we learned about the Sum Formula for arithmetic sequences. Now sequences can get very complicated pretty quick. But as long as you stick to the basics you should be fine. Make sure you keep track of your variable "n" and don't mix up Sn and An. So, stick to the basics, and they will work wonders for you!
Here is the formula:
Saturday, February 15, 2014
Educreations
We had to split our video up, but here are out examples.
Video 1
http://itunes.apple.com/us/app/educreations-interactive-whiteboard/id478617061?ls=1&mt=8Video 2
Video 3
Friday, February 7, 2014
Cryptography!
What a wonder Cryptography. Today in Mathland we learned the Art of Cryptography. It is a simple idea, but an elaborate process. First you take a word or message, for example Cheese. Then you pick numbers that will symbolize each letter. Then, you create an encryption matrix, which just has to be a matrix that has an inverse. Next, you make 1x3 matrices out of your word or phrase. So, if we are using cheese, let's let 3 represent c, 8 represent h, 5 represent the e's, and 19 represent s. So you would take the matrix (3 8 5) and multiply it by the encryption matrix you chose, and your message is encrypted. To decode the message simply take the 1x3 matrices and multiply them by the inverse matrix of your encryption matrix.
Inverse Matrices
Today in Mathland, we took a stroll down to Inverse Lane and learned how to find the inverse of a matrix. The key in this lesson is that not every Matrix has an inverse. We call those such Matrices singular. But, here is how you find the inverse.
You set a matrix with just 1's on the main diagonal next to your original matrix. Then you use Gauss Jordan to make your original matrix all ones on the main diagonal, but all the changes you do apply to both soft your matrices. And once your original matrix is solved, your inverse is the second matrix. Here is am example.
This lesson wasn't to challenging. I hope my explanation was helpful, and will be a great guide for anyone who wishes to visit Inverse Lane.
Thursday, February 6, 2014
No Solution or Infinite Solutions
When given a system of equalities, there are 3 possibilities for the solution. No solution, infinite solutions, or exactly one solution. The key is knowing which of the 3 is correct for the system you're working with. 
For further detail, here is the link to the website.
You know your system has infinite solutions when you get a row of zeroes in your augmented matrix. For example in the picture the 3rd row is all zeroes.
You know you have a system with no solutions, when you get an impossible equation such as all zeroes in a row except for the last number is not a zero. For example in the picture the second row has all zeroes besides the last number.
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