19th century math tactic gets a makeover—and yields answers up to 200 times faster

http://phys.org/news/2014-06-19th-century-math-tactic-makeoverand.html

Now, let's get it implemented on a micrologix!

I love it when someone from outside a specific discipline comes up with a solution the experts never envisioned!

Can it beat the common core math we are teaching our third graders?

72-12 = ?

12 + 3 = 15.
15 + 5 = 20.
20 + 10 = 30
30 + 20 = 50
50 + 20 = 70
70 + 2 = 72
3 + 5 + 10 + 20 + 20 + 2 = 60

72-12 = 60.

That method of subtraction is valid though not the only way. I hope multiple ways are taught.

It is very similar to the method used to count back change to a customer in retail, starting with the price of the item(s) adding enough change to get to an even dollar, adding dollars to get to a $5 or $10 mark then adding larger bills until you reach the tendered amount.

bernie_carlton said:

It is very similar to the method used to count back change to a customer in retail, starting with the price of the item(s) adding enough change to get to an even dollar, adding dollars to get to a $5 or $10 mark then adding larger bills until you reach the tendered amount.

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Have you been to a retail location recently when the POS computer/cash register was out of commission? I don't think anyone under 50 knows how to count change anymore!

Tom Jenkins said:

Have you been to a retail location recently when the POS computer/cash register was out of commission? I don't think anyone under 50 knows how to count change anymore!

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I had a cashier type in $10.00 instead of $20.00 for the amount I gave them a few years ago. They had to get a manager to count the change back.

TConnolly said:

Can it beat the common core math we are teaching our third graders?

72-12 = ?

12 + 3 = 15.
15 + 5 = 20.
20 + 10 = 30
30 + 20 = 50
50 + 20 = 70
70 + 2 = 72
3 + 5 + 10 + 20 + 20 + 2 = 60

72-12 = 60.

Click to expand...

I can see the value in this. The goal is to put things in terms that are easier to understand. It's easier to count by fives and tens so putting it in those terms makes things easier.

Now, this method probably isn't the best to solve 72-12 in the real world, but one thing I've found with math classes is that they show you the method with problems that may not be best suited for that method, but they do it that way to get you used to the method itself which is more useful with more complicated problems. When I took College Algebra quite often I'd think something like "why are we using the quadratic equation on this problem? Completing the square is easier!" But completing the square isn't always possible when the equations get more complicated.

I use the gauss-seidel method to solve system of equations. I think there is a relaxation term in my method but it is pretty crude. I can see where a few tweaks would make a huge speed up in having the solution converge. I wish they would have shown more in the video. It looks like it is using a weight average of four terms to calculate a better estimate.

I HATE MODERN MATH ( that is what they called it over 50 years ago ).

If you haven't figured it out I have a general contempt for most teachers. There are a few good one but most shouldn't be teaching.

I learned to add and subtract watching my mother balance the check book. This is a very practical application. The way she showed me was to the simple borrow and carry method. I could do this before second grade. Between second grade and third grade we hired a painter. During a lunch break I showed him my base ball cards. I asked him how to calculate base ball averages. He taught me. I learned math the old fashioned way. I learned because I could find a use for it. I think making math relevant is more important.

Originally posted by Peter Nachtwey:

The way she showed me was to the simple borrow and carry method.

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My biggest issue with most of the elementary teaching is students are shown the method but not the basis behind the method. Students can borrow and carry because they have been shown how but have no feel for orders of magnitude.

One of my sons had the hardest time with multiplication and long division until I got on him about making sure all his numeric columns lined up. When I tried to explain to him why this was important to make the solution work his eyes glassed over. If you don't understand WHY a method works how can you be expected to extend that method to the solution of more complicated problems?

Keith

This is what I used. It is Gauss-Seidel with over relaxation. The idea is to play around with the w in this example to get the best results. If there was a way to estimate w more accurately or have it change on-the-fly that would be a huge improvement.
http://www.mathworks.com/matlabcentral/fileexchange/28226-successive-over-relaxation/content/sor.m
The method in the link works better than the normal Gauss-Seidel when w is set to the optimal value. When w=1 it is the same as Gauss-Seidel.
In the video it looked like they used u instead of w.

For more information, the article from the John Hopkins University is available at:

http://engineering.jhu.edu/fsag/wp-content/uploads/sites/23/2013/10/JCP_revised_WebPost.pdf

danatomega said:

For more information, the article from the John Hopkins University is available at:

http://engineering.jhu.edu/fsag/wp-content/uploads/sites/23/2013/10/JCP_revised_WebPost.pdf

Click to expand...

I was lost at the first sentence.

While young Yang may have speeded up the Jacobi methods for intense simulations, the method has never been without advocates. I use Jacobi/Newton iterative calculations regularly for more plebeian applications. I don't however, try to implement them on a PLC. That would be foolhardy...

For smaller examples like the 3x3 example in the pdf file one could easily implement the algorithm in a PLC if using structured text but it wouldn't happen in one scan.

I used the SOR technique to compute the second and fourth derivatives at each point when implementing a fifth order spline. I tend not to work with arrays in this application because most of the entries would be zero. I like to find symbolic solutions because they execute faster

Thanks danatomega for the link. I do understand it an I am going to work through it today. I will start with the simple example in the pdf.