# How to use math software

Higeo

"I will show you how to use math software"

Pyon

"It sounds a little difficult."

Penta

"Using it will be hard."

Higeo

"First, you can use the math software Mathematica as a high efficient calculator. Perhaps most of you can use calculators If you can find someone who is good at using computers in your research group, she or he will help you to use the more advanced tools of the software. As for the case of our research group, Dr. Miyadera who is the advisor of the group found it difficult to make a program for Mathematica when he and his students began to do research. At that time, his students made most of the program. Now he can make Mathematica program after more than 20 years of experience."

In our method, we change some parts of the original problem to make a new one, and we study the new one by the mathematical software.

We use a math software "Mathematica", and one License of Mathematica costs 300 dollars in most of Asian countries.

If you want to use it for free, you can use "WOLFRAM PROGRAMMING LAB" on the web.

https://www.wolfram.com/programming-lab/The website looks like this.

Please Click the button "Start the programming! (You don't have to sign in.)" Then, you will see the screen like this.

And choose "Try It Yourself" or

choose "Elementary Introduction to the Wolfram Language" to learn how to use Mathematica.

If you choose "Try It Yourself", please click "File" in the screen like this,

and click "New Notebook" in "File".

You will see the screen like this.

Please put in the following numerical expressions.

{Binomial[28, 2] + Binomial[24, 2], 28*24}/Binomial[52, 2] // N

And push "shift" and "return(enter)" at the same time.

Or, please click "Evaluation" in same page's menu and click "Evaluate Cells" in it. Then,you will see the numbers like this.

{0.493213, 0.506787}

This example comes from the variant of a game that uses cards instead of dice.

We will explain about it.

When both two cards are even numbers or odd numbers, the the sum of two cars' numbers is even.
_{24}C_{2} + _{28}C_{2} = 654

When one card is even and other is odd, the sum is odd. The number of combinations is 24 X 28 = 672

The number of combination of two cards is _{52}C_{2} , and divide them by _{52}C_{2}.

As for our research by using "Mathematica", see the following article.

Reference

Chocolate Games

How High School Students Discovered New Formulas Using Mathematica

Ryohei Miyadera, Shunsuke Nakamura, Yu Okada, Ryo Hanafusa

https://www.mathematica-journal.com/volume/v15/