Update

I wrote about the Common Core State Standards for Mathematics in the “CA CCSSM” section of MathwithJoy. I am currently working on “roadmaps” for each class that I may teach in the future.

I will also fix the “Card Dealer” and “Bouncing Ball” applications during spring break. I am looking for my RSA cryptosystem application; if I can’t find it, I might have to rewrite it when I have time. I am currently working on my first GeoGebra/Javascript application inspired by the CCSSM Workshop that I attended at CSUN this past weekend. The presenter at the workshop was Heather Dallas, Executive Director, UCLA Philip C. Curtis Jr. Center for Mathematics and Teaching.

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Bouncing Ball

There is a tutorial (link) online on creating a clone of the arcade game “Breakout.” I decided to modify it; I was hoping that  - in the process – I would learn more about using Javascript and the <canvas> element as well as creating a web application that could help Algebra 1 students explore the concept of slope.

Here’s the link: http://mathwithjoy.com/apps/bouncingball/bouncingball.html.

Please note that I developed this application for fun and that it is not meant for commercial, business, or professional use.

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Card Dealer

I developed a web application that deals cards. I think this application may be useful in mathematics classrooms for activities requiring a deck of cards. I still have to work out a couple of bugs and clean up the code.

Here’s the link: http://mathwithjoy.com/apps/carddealer/carddealer.html.

Credit for the card images and some of the Javascript code (for constructing and shuffling a deck of cards) goes to Michael Moncor who wrote “Sams Teach Yourself Javascript in 24 Hours.” This is an excellent book. Click on this link to the book’s webpage on the publisher’s website for more information.

I looked at algorithms (available all over the internet) for shuffling a deck of cards and they all seem to do the following: pick two random cards in the deck, switch their order, and repeat many times.

Please note that I developed this application for fun and that it is not meant for commercial, business, or professional use.

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RSA cryptosystem

I developed a web application that will encrypt a message given the enciphering modulus n and the public key e. n must be a positive integer that is a product of two very large and distinct primes (p and q) and e must be a positive integer such that \left(e, \phi(n)\right))=1.

The web application will calculate the private key d by solving the congruence de \equiv 1 \left(mod \phi(n) \right).

The web application can also decrypt a message given the private key d and the enciphering modulus n.

Here’s the link:

Please note that I developed this application for fun and that it is not meant for commercial, business, or professional use.

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Solving cubic equations

I developed a web application that calculates the real root of a cubic equation for one of the classes I’m taking at CSUN.

Here’s the link: http://mathwithjoy.com/apps/cubic/cubic.htm.

Given a cubic equation of the form ax^{3}+bx^{2}+cx+d=0, the web application calculates the coefficient p of the first-degree term and the constant q of the depressed cubic equation that is the result of substituting in y-\dfrac{b}{3a} for x.

p=\dfrac{3ac-b^{2}}{3a^{2}}

q=-\dfrac{2b^{3}-9abc+27a^{2}d}{27a^{3}}

The web application then calculates u and v (y=u+v).

u=\sqrt[3]{\dfrac{q+\sqrt[2]{q^{2}+\dfrac{4p^{3}}{27}}}{2}}

v=\sqrt[3]{\dfrac{q-\sqrt[2]{q^{2}+\dfrac{4p^{3}}{27}}}{2}}

The web application then calculates the real root x of the cubic equation.

x=u+v-\dfrac{b}{3a}

There are fields below the value of x on the web application. These are for the other two roots of the cubic equation. I have not finished writing the code for this yet. I also have to figure out how to non-real numbers in the calculations.

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My math notes

I just finished developing the structure for a web application I call “My Math Notes” that will contain basic mathematical concepts and definitions for classes I’ve taken at CSUN. This web application is optimized for mobile operating systems like iOS and Android.

The link is http://www.mathwithjoy.com/apps/mymathnotes/.

Whenever I add an entry related to a math class I’m taking or have taken, I will add a link to that entry in the web application.

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Wheel

I developed a web application (“Wheel”) that calculates pro rate and short rate factors. The web application is optimized for mobile operating systems like iOS and Android.

Here’s the link: http://www.mathwithjoy.com/apps/wheel/wheel.htm.

Please note that I cannot guarantee the accuracy of the results of this application. I just developed it for fun, not for actual business use.

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Notepad for math proofs

I developed a web application that might help you type math proofs for posting on websites and inserting into documents. I call the tool “Mathpad.”

Here is the link: http://mathwithjoy.com/apps/mathpad/mathpad.htm.

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Calculating the traditional short rate unearned factor

The traditional short rate unearned factor is not 90% of the pro rate unearned factor. The traditional short rate unearned factor can be greater or less than 90% of the pro rate unearned factor depending on the policy term and number of days the policy stayed in force.  You can calculate the traditional short rate unearned factor using the following method:

d = the number of days the policy stayed in force

u = the unearned factor we are calculating

\left[x\right] symbolizes “round x down to the nearest integer”

12-Month Terms

  • If d < 23 then u = \dfrac{\left[(90-\dfrac{d}{3.65})+5.55-\dfrac{d}{4}\right]}{100}
  • If 23 \leq d \leq 186 then u = \dfrac{\left[90-\dfrac{d}{3.65}\right]}{100}
  • If 186 < d then u = \dfrac{\left[(90-\dfrac{d}{3.65})+(\dfrac{d}{18.29})-9.98\right]}{100}

6-Month Terms

  • If d\cdot2 < 23 then u = \dfrac{\left[(90-\dfrac{d\cdot2}{3.65})+5.55-(\dfrac{d\cdot2}{4})\right]}{100}
  • If 23\leq d\cdot2 \leq 186 then u = \dfrac{\left[90-\dfrac{d\cdot2}{3.65}\right]}{100}
  • If 186 < d\cdot2 then u = \dfrac{\left[(90-\dfrac{d\cdot2}{3.65})+(\dfrac{d\cdot2}{18.29})-9.98\right]}{100}
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